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Aerospace Engineering

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Aerospace Engineering is a branch of engineering that focuses on the design, development, testing, and production of aircraft and spacecraft. It encompasses various disciplines, including aerodynamics, materials science, structural analysis, propulsion, and avionics, to ensure the safe and efficient operation of vehicles in the atmosphere and outer space.
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Geophysical Fluid Dynamics
by shantanu ghosal

1981, Journal of Applied Mechanics-transactions of The Asme

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Numerical Solution of the Euler Equations by Finite Volume Methods Using Runge-Kutta Time-Stepping Schemes
by eli turkel
A new combination of a finite volume discretization in conjunction with carefully designed dissipative terms of third order, and a Runge Kutta time stepping scheme, is shown to yield an effective method for solving the Euler equations in... more
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Numerical solution of the Navier-Stokes equations
by LUCAS WANGWE

1968, Math. Comp

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Computational fluid mechanics and heat transfer
by raghu neel

1984

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Classification of hyperspectral remote-sensing data with primal SVM for small-sized training dataset problem
by Stéphane Girard

2008, Advances in Space Research

An algorithm of hyperspectral remote sensing images classification is proposed based on the frequency spectrum of spectral signature. The spectral signature of each pixel in the hyperspectral image is taken as a discrete signal, and the... more
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Numerical solutions of the Euler equations by finite volume methods using Runge-Kutta time-stepping …
by Eli Turkel

1981, AIAA paper

Numerical Solution of the Euler Equations by Finite Volume Methods Using Runge-Kutta Time-Stepping Schemes ... 1. What is the most efficient time stepping scheme? ...
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Distributed Consensus in Multi-vehicle Cooperative Control: Theory and Applications
by Wei Ren

2008

Single UAV Experiment
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The exergy method of thermal plant analysis By T.J. Kotas; published by Butterworths, London, Boston, Durban, Singapore, Sydney, Toronto, Wellington, 1985; price £45.00; ISBN 408-01350-8
by Pedro Pires

1987, Chemical Engineering and Processing

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Surrogate-based analysis and optimization
by Tushar Goel

2005, Progress in Aerospace Sciences

A major challenge to the successful full-scale development of modern aerospace systems is to address competing objectives such as improved performance, reduced costs, and enhanced safety. Accurate, high-fidelity models are typically time... more
Fig. 1. Key stages of the surrogate-based modeling approach.
Fig. 2. Anatomy of surrogate modeling: model estimation + - model appraisal. The former provides an estimate of function f while the latter forecasts the associated error.
Fig. 3. Multiple surrogates may be consistent with the data. For a given problem we may have preference for one or the other (e.g., additional information about the function f is available), but often which is the best surrogate is not clear a priori.
Fig. 4. A surrogate modeling scheme provides the expected value of the prediction E(f,) (solid line) and the uncertainty associated with that prediction illustrated here using a probability density function 0.
Fig. 5. Alternative loss functions for the construction of surrogate models. The quadratic loss function (i.e., Ly1 norm) is the most commonly used in part because it typically allows easy
Fig. 6. A Latin Hypercube Design with NV, = 6, Nay = 2 for X uniformly distributed on the unit square. In practice, the number of points in the data set is severely limited (e.g., due to computational expense) and often during the construction of the surrogate model a balance between bias and variance errors is sought. This balance can be achieved, for example, by reducing the bias error while imposing penalties on the model complexity (e.g., Tikhonov regularization).
Fig. 7. LHS designs with significant differences in terms of uniformity [36]. While LHS represents an improvement over unrest- ricted stratified sampling [37] it can provide sampling plans with very different performance in terms of uniformity (issue b) measured by, for example, max- imum minimum-distance among design points, or by correlation among the sample data. Fig. 7 illustrates this
where, h is a column vector with the radial basis functions evaluations, On the other hand, the prediction variance is the variance of the estimated model f(x) plus the error f(x) =h'w,
Fig. 8. The basic SMF algorithm.
Fig. 9. Schematic of Hybrid Boeing Element (US Patent 6253539).
Fig. 10. Design variables and objectives of the single element rocket injector: (a) design variables; (b) objective functions.
Fig. 11. Simulation domain and boundary conditions of the injector flow model.
Fig. 12. Comparing the unrefined (336 x 81) (thicker lines) and refined (430 x 81) (thinner lines) grids.
Fig. 13. Main factor (S;,) influence on objective variability: (a) TFinax, (b) TWa, (c) TTinax and (d) Xec. While it is well established that variations in injector geometry can have a significant impact on performance and environmental objectives such as combustion chamber wall and injector face temperatures and heat fluxes [107], these sensitivities are seldom quantified. As shown in Vaidyanathan et al. [10], once surrogates become available, these sensitivities can be computed using Sobol’s method (Section 6). The sensitivity information cited above can be used for screening purposes and therefore, ease the search for optimum designs. In fact, surrogate models that included only essential variables (with the non essential
Fig. 14. Pareto optimal solution set and nine (9) representative solutions from the same set. The circles identify the representa- tive of a specific cluster. For cluster | it is seen that the value of « is fixed at 0 (shear coaxial injector) (Fig. 15a) and AHA is fixed at 1 (Fig. 15b). This suggests that in this cluster, the designs are sensitive to « and AHA, both of which reach their extreme values. The remaining two design variables
Fig. 15. Box plots for the design variables in cluster 1, 3, 6 and 9, (a) « (b) AHA (c) AOA and (d) OPTT. The horizontal line shows the mean value for all the variables on POF.
Fig. 16. Box plots for the objectives in cluster 1, 3, 6 and 9, (a) TFmax (b) X¢- and (c) TT max. The horizontal line shows the mean value of the objectives on POF.
Fig. 17. Pareto optimal front: (a) TFmax vs. Xec (b) TFimax VS. TTmax- The fundamental issues that arise in the SBAO of computationally expensive models such as those found in aerospace systems were discussed. The issues included the selection of the loss function and regularization criterion to identify the surrogates, design of experi- ments, surrogate selection and identification, sensitivity analysis, and how to incorporate surrogates in optimiza- tion efforts when constraints are present. Some of these issues were demonstrated through the multi-objective optimal design of a liquid rocket injector.
Examples of kernel functions and related estimation schemes
Different techniques in sensitivity analysis, and application examples, can be found in the works of Iman and Helton [68], Kleijnen [69] and Frey and Patil [70], and references therein “Independent from assumptions about the model being linear, etc. >There are exceptions e.g., the Spearman rank-order correlation coefficient.
Range of design variables (« is an acute angle in degrees and X is the thickness of OPTT in inches)
Independent variables and objectives for Cases X and Y from CFD computations (normalized values shown) Table 4
Minimizing individual objectives. Value in parenthesis (1) indicates which objective function is minimized (normalized values shown) Table 5
Objective function and design variables of nine (9) representa- tive designs from the Pareto optimal solution
Partial correlation coefficients (Reorr) of design variables vs. objectives for different clusters along the POF Table 7
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Computational methods for fluid flow
by Michael Leschziner

1984, Computer Physics Communications

Computational Methods for Fluid Flow" is a welcome addition to the computational physics literature. It has that essential feature lacking in many books on the subject in that it takes a practical approach to a practical subject. The book... more
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Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids
by Eiyad Abu-Nada

2008, International Journal of Heat and Fluid Flow

Heat transfer and fluid flow due to buoyancy forces in a partially heated enclosure using nanofluids is carried out using different types of nanoparticles. The flush mounted heater is located to the left vertical wall with a finite... more
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The ozone monitoring instrument
by Piet Stammes

2006, IEEE Transactions on Geoscience and Remote Sensing

The Ozone Monitoring Instrument (OMI) flies on the National Aeronautics and Space Adminsitration's Earth Observing System Aura satellite launched in July 2004. OMI is a ultraviolet/visible (UV/VIS) nadir solar backscatter spectrometer,... more
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Sun earth connection coronal and heliospheric investigation (SECCHI)
by E. Mazy

2002, Advances in Space Research

The Sun Earth Connection Coronal and Heliospheric Investigation (SECCHI) is a five telescope package, which has been developed for the Solar Terrestrial Relation Observatory (STEREO) mission by the Naval Research Laboratory (USA), the... more
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Development and Validation of a Three-Dimensional Finite Element Model of the Face
by Mahmood Jabareen

2009, Journal of Biomechanical Engineering-transactions of The Asme

Due to both its shape and its structural architecture, the mechanics of the pelvic bone are complex. In Finite Element (FE) models, these aspects have often been (over)simplified, sometimes leading to conclusions which did not bear out in... more
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Distributed piezoelectric-polymer active vibration control of a cantilever beam
by Abdelmajid Hm

1985, Journal of Guidance Control and Dynamics

An active vibration damper for a cantilever beam was designed using a distributed-parameter actuator and distributed-parameter control theory. The distributed-parameter actuator was a piezoelectric polymer, poly (vinylidene fluoride).... more
Notice that the control voltage appears in only one of the boundary conditions. Equations (8) and (9) describe a linear distributed-parameter system that has only boundary control. Since the actuator is spatially distributed, it was easily in- cluded in the equations of motion without nonlinear terms (e.g., spatial delta functions). This allows one to keep a linear distributed-parameter model throughout the analysis, avoiding any problems that may be caused by ‘‘truncating’’ the model.
The input voltage V(t) appears in only one term. Therefore, to minimize dF/dt, the feedback voltage should be chosen so that the term it appears in is always as negative as possible, or
SE TR OCTAPANEN a eee lee” MENTE ACR A NEE ee The test procedure was to hold ‘the tip of the beam at 2 cm displacement, release it, and observe the vibrations. By holding the tip of the beam and then releasing it, very little of the second and higher modes were introduced in the initial conditions. For the constant-gain controller, the gain was set so that the maximum voltage amplitude would not exceed the voltage limit V,,,,. The maximum gain, allowed was easily determined experimentally since the maximum voltage occur- red’ when the beam was’ first released. For the constant- amplitude controller, the initial gain was determined in the same manner, but the gain was increased after the beam was released to keep the amplitude of the feedback voltage con- stant. This was done by. adjusting the gain on thé audio Fig. 7 Apparatus used for preliminary testing of the active damper. plied to the PVF,. The phase shift is necessary because the first mode of the cantilever beam is near 6 Hz, much below the linear region of an audio amplifier. Fhe logarithmic plotter was used to determine the damping via the log decrement method. The plotter allowed a determination of how the damping changed with amplitude of vibration, especially with the nonlinear feedback of the constant- -amplitude controller.
b) Logarithmic plot of tip displacement decay envelope. a) Feedback voltage and tip displacement for the uncontrolled beam. Fig. 8 First-mode test results for the uncontrolled beam.
b) Logarithmic plot of tip displacement decay envelope. Fig. 8 First-mode test results for the uncontrolled beam.
Fig. 9 First-mode test results for the constant-gain controller, Vmax = 100 V rms.
a) Feedback voltage and tip displacement for the constant-amplitude controller. Fig. 11 First-mode test results for the constant-amplitude controller, Vinax = 100 V rms.
B) LOSATRIMNe Prot OF UP displacement decay envelope. Fig. 12 First-mode test results for the constant-amplitude controller. Vinax = 200 V rms.
a) Feedback voltage and tip displacement for the constant-amplitude controller.
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Underestimating Costs in Public Works Projects: Error or Lie?
by Bent Flyvbjerg

2002, Journal of the American Planning Association, vol. 68, no. 3, pp. 279-295

This article presents results from the first statistically significant study of cost escalation in transportation infrastructure projects. Based on a sample of 258 transportation infrastructure projects worth US$90 billion and... more
Figure 3. Inaccuracy of cost estimates in transportation projects over time, 1910-1998 (fixec
lable 1. Inaccuracy of transportation project cost estimates by type of project (fixed prices)
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A hybrid RANS-LES approach with delayed-DES and wall-modelled LES capabilities
by Michael Shur

2008, International Journal of Heat and Fluid Flow

A CFD strategy is proposed that combines delayed detached-eddy simulation (DDES) with an improved RANS-LES hybrid model aimed at wall modelling in LES (WMLES). The system ensures a different response depending on whether the simulation... more
Fig. 19. Comparison of mean velocity profiles in recovery region of BFS flow predicted by RANS, DDES, and IDDES based on SA model with experiment.
Fig. 18. Comparison of mean friction coefficient distributions in BFS flow predicted by RANS, DDES, and IDDES based on SA model with experiment.
Fig. 1. Two types of variation of the subgrid length-scale (4) across plane channel compared to variation of the scale based on cube root of cell volume (dotted line).
Fig. 2. Profiles of functions fg and f., in plane channel.
where the quantities rg and rg, are the “turbulent” and “laminar” analogues of rg (6) defined by the relations and c; and c,; are additional model constants which depend on the background RANS turbulence model and should be adjusted so that the function feo is virtually zero when either rgt or rg is close to 1.0.
Fig. 3. Comparison of mean velocity profile from Smagorinsky LES of developed channel flow at Re, = 400 with A defined by (4) and as cube root of cell volume with DNS of Moser et al. (1999). The second example illustrating the advantage of the length- scale (4) is a WMLES of the high Reynolds number (Re, = 18,000) channel flow. The simulation uses a DES-like WMLES method, which couples the Prandtl-van Driest RANS and the Smagorinsky SGS models:
Fig. 4. Mean velocity profiles in developed channel flow computed with the use of DES model (19) and subgrid length-scale defined by (4) at Re, = 1100 and 18,000.
Fig. 6. Profiles of the function f. and ratio of length-scales of MSST-based IDDES and MSST RANS models in developed channel flow at different Re,.
Fig. 5. Profiles of the functions fy and (1—fa:) in developed channel flow at different Re, from simulations with MSST version of IDDES and presence of initial turbulence content.
Fig. 7. Profiles of IDDES eddy viscosity normalized by molecular viscosity in developed channel flow at different Re,.
Fig. 8. Comparison of XZ-cuts of instantaneous vorticity magnitude from simulation of channel flow with MSST-based IDDES and MSST-based DDES at Re, = 2400 The advantages of IDDES are clearly seen in a direct comparison of the flow visualizations from the simulations with the use of this model and MSST-based DDES presented in Fig. 8. The figure shows that IDDES does capture the major known features of the turbu- lence in the channel reasonably well. In particular, it does not al- low the formation of smooth nearly one-dimensional eddies and excessive damping of turbulence at the RANS-LES interface, the way DES97 (Piomelli and Balaras, 2002) and DDES do. DDES fails, specifically, near the wall, whereas the two models behave very similarly near the center of the channel. To conclude the discussion of simulations of channel flow with the use of IDDES operating in WMLES mode, recall that all the re- sults presented above were obtained on grids with the streamwise
Fig. 9. Profiles of mean velocity (a) and resolved and modelled shear stresses (b) from MSST-based IDDES of channel flow at different Re,
Fig. 10. Comparison of predictions of developed channel flow at Re; = 2400 with MSST-based IDDES and MSST-based DDES.
Fig. 11. Effect of streamwise grid step on prediction of developed channel flow at Re, = 2400 with MSST-based IDDES. step, Ax, twice as large as the spanwise step, Az. Although this is common LES practice motivated by the knowledge of the turbu- lence structure in the channel and the flow direction, this is not practical for more complex flows, and so it is of interest to evaluate the reaction of the model to an alteration of the Ax/Az value. It is illustrated by Fig. 11, where the results of the simulation with Ax/ Az = 2 are compared with those with Ax/Az = 1.0 and 4.0, Az being kept constant. The value 1.0 is much more likely in engineering practice, since the direction of the flow, especially very near the wall, is not known at the grid-design stage. One can see that, as ex- pected, an increase of Ax results in a growth of the modelled and decrease of the resolved parts of the shear stresses. Nonetheless, in the considered range of Ax/Az this does not cause a significant alteration of the total shear stress and the mean velocity profile. Therefore, the dependence chosen on Ax and Az individually ap- pears quite successful. Let us now consider the performance of IDDES in the same flow but with no initial turbulent content. This situation is implemented by starting the simulations from a steady MSST RANS solution. In this case, independently of the Reynolds number, the solution re- turned by IDDES is identical to the initial RANS solution, which is exactly the behaviour that should be observed in accordance with the design of IDDES. The results do not depend on the wall-parallel grid spacing at all. This is seen in Fig. 12, where the velocity profiles are plotted from the simulations with the use of MSST-based IDDES and RANS. The figure also shows profiles of the functions f; and f;, which help to understand the reason for this performance. One can see that at any y* one of the functions (either f; or f;) is equal to 1.0, which results in the zeroing of fez (see (12)) and, therefore, of f. as well (see (10)). Thus, in the situation considered (no turbu- lent content) IDDES actually reduces to a DDES-like model (15) and behaves exactly as DDES does in this situation, i.e., returns the
Fig. 12. Profiles of the functions f; and f; (13) and mean velocity in plane channel computed with MSST-based IDDES initialised by MSST-RANS solution.
Fig. 13. Schematic of the hydrofoil and mean flow streamlines from IDDES. Letters denote positions of sections, where experimental data of Blake, 1975 and full-LES of Wang and Moin (2002) are available (B: x/h=—4.5; C: -3.125; D: —2.125; E: —1.625; F: —1.125; G: —0.625). Inflow turbulent content was generated as follows. Parallel to the simulation of the hydrofoil, a similar simulation of flat plate boundary layer was running (in this simulation the triggering of turbulence is performed with the use of the recycling procedure omployed by Spalart et al. (2006) for DNS), and the results of this simulation are fed into the inflow boundary of the hydrofoil simulation.
Fig. 15. Comparison of streamwise velocity and rms of its fluctuations in hydrofoil boundary layer predicted by different simulation approaches. (a) Mean velocity magnitude from IDDES, LES, and hybrid RANS-LES at different cross-sections and from SA and MSST RANS at section G; (b) rms from IDDES, LES, and hybrid RANS-LES at different cross- sections.
Fig. 16. XY-cuts of instantaneous fields of eddy viscosity and function f, from MSST-based IDDES of BFS flow.
Fig. 17. Snapshot of vorticity magnitude on the step wall from MSST-based IDDES and DDES of BFS flow.
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The Infrared Space Observatory (ISO) mission.
by Sajjad Nia

1996, Astronomy and …

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Tomographic particle image velocimetry
by Bernhard Wieneke

2006, Experiments in Fluids

This paper describes the principles of a novel 3D PIV system based on the illumination, recording and reconstruction of tracer particles within a 3D measurement volume. The technique makes use of several simultaneous views of the... more
Fig. 1 Principle of tomographic-PIV The working principle of tomographic-PIV is sche- matically represented in Fig. 1. Tracer particles im- mersed in the flow are illuminated by a pulsed light source within a 3D region of space. The scattered light pattern is recorded simultaneously from several view- ing directions using CCD cameras similar to stereo- PIV, applying the Scheimpflug condition between the image plane, lens plane and the mid-object-plane. The particles within the entire volume need to be imaged in ocus, which is obtained by setting a proper f/#. The 3D particle distribution (the object) is reconstructed as a 3D light intensity distribution from its projections on the CCD arrays. The reconstruction is an inverse problem and its solution is not straightforward since it is in general underdetermined: a single set of projections can result from many different 3D objects. Determining he most likely 3D distribution is the topic of tomog- raphy (Herman and Lent 1976), which is addressed in
where 4 is a scalar relaxation parameter, which for ART is between 0 and 2 and for MART must be <1. In ART the magnitude of the correction depends on the residual I(x, yi) — )Vjen, Wij E(Xj, Yj, Z;) multiplied by a scaling factor and the weighting coefficient, so tha only the elements in E(X, Y, Z) affecting the ith pixe are updated. Alternatively in MART the magnitude o the update is determined by the ratio of the measured pixel intensity J with the projection of the current objec Vien, Wij E(X;, Yj, Z)) The exponent again ensures tha only the elements in E(X, Y, Z) affecting the ith pixe are updated. Furthermore, the multiplicative MART scheme requires that EF and J are definite positive.
To quantify the accuracy of the reconstruction pro- cess, the reconstructed object E,(X, Z) is compared with the exact distribution of light intensity Ey(X, Z)
Fig. 4 Detail of the MART reconstruction (Fig. 3) showing individual particles
Stereo-PIV (Scarano et al. 2005; Wieneke 2005), which can reduce calibration errors to less than 0.1 pixel.
0.75. The reconstruction accuracy can be further assessed by counting the number of intensity peaks or particles. Each reconstructed object contains 24,400 actual particles (peaks within 1.5 voxel radius in the correct position) and 91,600 ghost particles considering only peaks values above 10 in arbitrary units. Even though the number of ghost particles exceeds signifi- cantly the number of actual tracer particles, their peak intensity J, is lower as shown by the probability density function of peak intensity (Fig. 8). The expected peak intensity for an actual particle is 70 against 23 for a ghost. Therefore, the contribution of the ghost particles to the cross-correlation map, hence velocity measure- ment, is limited. particles. Each reconstructed object contains 24,400
Fig. 8 PDF of particle peak intensity for actual and ghost particles in the reconstructed objects The displacement field is obtained from the recon- structed object using a 3D extension of the WIDIM algorithm (Scarano and Riethmuler 2000) with 41° voxels interrogation volumes at 75% overlap. Therefore, each interrogation volume contains on average 25 particle tracers. The measured vector field contains 66 x 66x10 vectors shown in Fig. 9-left where the overall motion pattern is well captured. The surface corresponding to a vorticity magnitude of 0.13 voxels/voxel returns the expected torus. Figure 9-right presents the vectors in the cross section at x = 0.25 mm with the corresponding vorticity in x-direction (con- tours), where the flow symmetry and the two vortex
A four-camera system (Fig. 11) is used to record 12-bit images of the tracer particles at 1,280 x 1,024 pixels resolution from different directions. The cameras are equipped with Nikon objectives set at //8. Scheimpflug adapters are used to align the mid-plane of the illuminated area with the focal plane. The effective field of view common to all cameras is 50 x 50 mm’. Table 1 lists the properties specific to each camera, such as the magnification M, the focal length f and the viewing angle in x and y-direction 0, and 6,, respectively.
In real experimental conditions an assessment of the reconstruction quality is not straightforward, since the actual particle distribution is unknown. It is possible, however, to estimate the number and intensity distri- bution of the ghost particles by comparing the light intensity reconstructed outside and inside the illumi- nated region (representing reconstruction noise and signal plus noise, respectively). Note that the light sheet position can be clearly identified within the reconstructed volume (Fig. 12) due to the application of a slit in the light path. The results confirm that the expected peak intensity for the ghost particles is lower than for the actual tracer particles (as in Fig. 8). Moreover, the ratio of actual particles over ghost particles is 2 considering only the range of peak intensities corresponding to the actual particles. For further detail on the assessment of reconstruction volumes in real experiments the reader is referred to Elsinga et al. (2006). The imaging system is calibrated by scanning a plate with 15 x 12 marks (crosses) through the volume in depth direction in steps of 4 mm over a total range of 8mm. In each of the three calibration planes the relation between the physical coordinates (X, Y, Z) and image coordinates is described by a third order polynomial fit. The calibration accuracy is approxi- mately 0.2 pixels. Linear interpolation is used to find the corresponding image coordinates at intermediate z-locations.
The secondary vortex structures are also clearly visible in Fig. 14 (blue and red depending on the ori- entation of vorticity in stream wise direction) and ap- pear to be organized in counter rotating pairs. Figure 15 shows in detail how the secondary vortices curl in between the primary Karman vortices. Their effect is to first distort the primary rollers, as observed in the upper two snapshots of Fig. 14 at x/D = 4.5, and finally they cause the breakup of the primary vortices. The two snapshots of Fig. 14-bottom show a more regular span wise organization of the secondary vorti- ces yielding a quasi periodic behavior. From a visual inspection the normalized spatial wave length 4,/D is
To improve the visualization of the structural orga- nization of the flow the span wise and the combination of stream wise and z component of vorticity are color- coded in Fig. 14. The four uncorrelated snapshots show different phases of the vortex shedding cycle. The top- left snapshot (corresponding to Fig. 13) contains parts of four Karman vortices; two from the lower cylinder surface (green) at x/D = 2.8 and 6, and two from the upper surface (cyan) at x/D = 2.5 and 4.5. The nor- malized vorticity level in these vortices w,D/u., = 2.2 agrees fairly well with the recent planar PIV mea- surements in the Reynolds number range 2,000 to 10,000 from Huang et al. (2006), who report an average normalized peak vorticity of 2.1 at x/D = 3.
noise or reconstruction artifacts, when present, are in fact expected to propagate particle (displacement) information along viewing lines ultimately resulting in a quasi-uniform particle displacement along that line. Clearly such effects do not play a dominant role in the current experiment. Further confidence in the measurement technique is given by recent quantitative comparisons between tomographic- and stereo-PIV, which showed a good agreement of the returned flow statistics (mean and RMS) along profiles in the cylinder wake (Elsinga et al. 2006) and velocity distribution in a vortex ring (Wie- neke and Taylor 2006).
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Micro-doppler effect in radar: phenomenon, model, and simulation study
by Shen-shyang Ho

2006, IEEE Transactions on Aerospace and Electronic Systems

When, in addition to the constant Doppler frequency shift induced by the bulk motion of a radar target, the target or any structure on the target undergoes micro-motion dynamics, such as mechanical vibrations or rotations, the... more
As shown in Fig. 2, the radar is stationary and located at the origin Q of the radar coordinate system (U,V,W). The target is described in a local coordinate system (x,y,z) attached to it and has translations and rotations with respect to the radar coordinates. To observe the target’s rotations, a reference coordinate system (X,Y,Z) is introduced, which shares the same origin with the target local coordinates and, thus, has the same translation as the target but no rotation with respect to the radar coordinates. The origin O of the reference coordinates is assumed to be at a distance Ro from the radar.
Fig. 3. Geometry for radar and vibrating scatterer.
Fig. 5. Rotations by Euler angles (¢,6,w).
Fig. 6. Geometry of radar platform vibration. micro-Doppler frequency becomes
Fig. 7. Frequency representation of signal reflected from vibrating scatterer.
Fig. 8. Block diagram of simulation.
Fig. 9. Micro-Doppler modulation induced by vibration.
Fig. 11. (a) Geometry of radar and tumbling target. (b) Trajectory of scatterer in tumbling target. the simulated micro-Doppler modulation signature is shown in the Fig. 10(c), which is identical to the theoretical analysis. The rotation period can be obtained from the rotation angular velocity as T = 27/||@|| = 0.8165 s and is verified by both the theoretical result and the simulated result.
Fig. 12. Micro-Doppler modulations induced by target’s tumbling.
ig. 13. (a) Geometry of radar and target with coning motion. (b) Calculated. (c) Simulated signatures of micro-Doppler modulation induced by coning motion. where the skew symmetric matrix is defined by z=-—1.0 m),t modulation ca The micro-Do hen the theoretical micro-Doppler culated by (56) is shown in Fig. 13(b). ppler of the point A, is zero frequency, and the micro-Doppler modulations from points P, and P, are t he two sinusoidal curves about the zero frequency. For computer simulation, assuming the PRF is 2,000 pulse/s, i.e., 2,000 pulses can be transmitted wi hin | s of dwell time, the simulated micro-Doppler modulation signature in the joint time-frequency domain is shown in Fig. 13(c), which is identical to the rotation pe he theoretical result and verifies that riod is T = 27/||@|| = 0.5 s.
Fig. 14. Micro-Doppler signatures of vibrating cornel reflectors.
Fig. 15. Micro-Doppler signature of walking person with swinging arms.
Bilinear Time-Frequency Transforms To analyze the time-varying frequency characteristics of the micro-Doppler modulation and visualize the localized joint time and frequency information, the signal must be analyzed by using a high-resolution time-frequency transform, which characterizes the temporal and spectral behavior of the analyzed signal. For example, by examining the time information and the sign of the micro-Doppler shift caused by a movement, the direction of the movement at the specific time could be found.
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Numerical Simulation of Mixed-Mode Progressive Delamination in Composite Materials
by Carlos Davila

2003, Journal of Composite Materials

A new decohesion element with the capability of dealing with crack propagation under mixed-mode loading is proposed and demonstrated. The element is used at the interface between solid finite elements to model the initiation and... more
Table 5. Ratio between middle and end loads.
Figure 2. Pure mode constitutive equations: (a) Mode II or Mode III; (b) Mode 1.
In order to avoid interpenetration of the crack faces, the following condition is introduced: Using 5™** in the constitutive equation, the irreversibility of damage is taken into account. This is shown in Figure 2: if the relative displacement decreases, the point unloads elastically towards the origin with a reduced, secant, stiffness (point 3 in Figure 2). The irreversible, bi-linear, softening constitutive behaviour for single-mode loading shown in Figure 2 can be defined as [23,39,44]:
Figure 3. Mixed-mode fracture toughness. tone = fae Bf Ta ea a ae Sewer ee Le By using three parameters, Gjc, Gyjc and ny, the B—K criterion represents the mixed- mode fracture toughness over the range of mode mixities, whereas the two-parameter power law criterion that is usually implemented in decohesion elements can lead to inaccurate results over a large range of mode ratios. Furthermore, using the power law criterion with a =2 in epoxy based composites, values of mixed-mode fracture toughness higher than Gyc occur in the interval 0.9 < Gyj/Gy < 1.0. Experimental evidence (Figure 3) shows that the highest mixed-mode fracture toughness of epoxy composites occurs for Gy/Gr=1, ie., G6 = Gc. Therefore, using of the power law criterion with a=2 in
Figure 4. Mixed-mode softening law. The mixed-mode softening law presented above is a single-variable response similar to the bi-linear single-mode law illustrated in Figure 2, defined by a damage evolution law (48), maximum mixed-mode relative displacement, (49), and loading function (50). Only one variable, the maximum relative displacement variable 6"**, is used to track the damage at the interface. By recording the highest value attained by 64,,, the unloading response is as shown in Figure 2. The relative displacements for initiation and ultimate failure are functions of the mode mixity £, the material properties, and the penalty stiffness. The mixed-mode softening law can be illustrated in a single three-dimensional map by representina Mode I on the 0—rT—Sé: nlane. and shear mode on the 0—rT—6..... plane. as
where 4,, is the Kronecker delta. It is worth noticing that Equation (47) provides the stiffness to control interpenetration of the crack faces of the decohesion element. In order to define the loading and unloading conditions, the variable maximum mixed-mode relative displacement, 5”**, and the loading function, F, are defined as:
Table 1. Properties for AS4/PEEK [55,58]. The experimental tests were performed by Reeder and Crews [55] at different Gy/G ‘atios (0.0, 0.2, 0.5, 0.8 and 1.0), ranging from pure Mode I loading to pure Mode | oading*. The specimens are 102 mm-long, 25.4mm-wide, with two 1.56mm-thick arm [he material properties are shown in Table 1, and a penalty stiffness K= 10° N/mm? ised. The initial delamination length of the specimens (ao) and the mixed-mode fractur oughness obtained experimentally [55] are shown in Table 2. It is worth noticing that th nitial delamination length for the ENF test specimen, ag =39.3mm, leads to stab ropagation of the delamination. For the material and geometry used here, it was show xy Reeder and Crews [55] that for initial delamination lengths smaller than 35m instable propagation occurs, because G exceeds Gc as the delamination grows. Models using 150 decohesion elements along the length of the specimens, and
The Modes I and II loads for each case are shown in Table 6.
Figure 7. Prediction of the mixed-mode fracture toughness using the B-K criterion over the entire range of mode ratio.
?The load—displacement relations experimentally determined for the different mode ratios are not reported in [55]. This information was provided by the author of the experiments [58].
Table 3. Experimental [55,58] and numerical maximum loads.
Table 4. Lengths of the lever.
Table 6. Mode I and Mode II load components. APPENDIX B: DETERMINATION OF THE LOAD-POINT DISPLACEMENT The information available from the MMB test relates the load to the displacement of the load-point (Figure 5). Since the lever is not simulated in the numerical models, it is necessary to calculate the load-point displacement using the information available from the numerical models of the MMB test specimens. The load-point displacement, Arp, is obtained from the pure mode displacement components, A; and Ay, as [60]:
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Lower-upper symmetric-Gauss-Seidel method for the Euler and Navier-Stokes equations
by Uğur Yenice

2012, AIAA journal

A NEW multigrid relaxation scheme is developed for the steady-state solution of the Euler and Navier-Stokes equations. The lower-upper Symmetric-Gauss-Seidel method (LU-SGS) does not require flux splitting for approximate Newton... more
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Scanning Tunneling Microscopy Observations of Mercury Droplets on Graphite
by Maki Kawai

1996, Langmuir

Solid-phase epitaxy (SPE) of Ge on a clean, 7 X 7-reconstructed Si( 111) surface is investigated by scanning tunneling microscopy. Although Ge layers of four monolayers (ML) thick crystallize in the registry of the 7 X 7 reconstruction... more
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Viscous-inviscid analysis of transonic and low Reynolds number airfoils
by Mark Drela

1987, AIAA Journal

A method of accurately calculating transonic and low Reynolds number airfoil flows, implemented in the viscous-inviscid design/analysis code ISES, is presented. The Euler equations are discretized on a conservative streamline grid and are... more
Fig. 1 Isolated airfoil boundary conditions. Fig. 2. Jumps at bubble reattachment.
An expression for the density thickness shape parameter H** has been derived by Whitfield'* for turbulent flows. Here it is used for laminar flows as well. This is justified on the grounds that H** has a fairly small effect in transonic flows and is neglibile at low subsonic speeds.
Fig. 3 Orr-Sommerfeld spatial amplification curves. The present method employs a spatial-amplification theory based on the Orr-Sommerfeld equation, which is essentially the e? method pioneered by Smith and Gamberoni!? and ngen.”° The e? method assumes that transition occurs when the most unstable Tollmien-Schlichting wave in the boundary ayer has grown by some factor, usually taken to be e? ~ 8100. To calculate this amplification factor, the distur- bance growth rates must be related to the local boundary- ayer parameters. Using the Falkner-Skan profile family, the Orr-Sommerfeld equation has been solved for the spatial amplification rates of a range of shape parameters and unstable frequencies. As done by Gleyzes et al.,? the envelopes of the integrated rates are approximated by straight lines as follows:
Fig. 4 Boundary-layer variable locations. By applying the discrete amplification equation to the laminar subinterval, the transition onset location &, can be implicitly defined in terms of the neighboring primary variables. The boundary-layer variables at ~,, can thus be in- terpolated from the ith and i—Ith stations. The actual discrete equations governing the transition interval are weighted averages of the laminar and turbulent subintervals. Although this formulation precisely defines the transition onset location in a continuous manner, it is still necessary to define how the turbulence develops afterward. To date, no useful empirical laws describing transitional Reynolds stresses have been formulated and most likely won’t be for- mulated for some time, given the complexity of the problem. The approach adopted here is to set the initial value of C? at &,, to 0.7 times its equilibrium value, as indicated in Fig. 5. The key to the success of such a simple model is that the momentum integral equation (4), which governs the all-
Because the grids used in the present scheme are regular, the linearized Newton system (38) is highly structured and has a large, very sparse block-tridiagonal coefficient matrix. The vector of unknowns 6Q is grouped into J subvectors of length 27+ 5 (where J=number of streamwise stations, and J=number of streamlines). Each subvector contains the
Fig. 7 Calculated (heavy line) and experimental (symbols) drag polars for LNV109A airfoil.
Fig. 9 LNV109A calculated and experimental pressiire distribu- tions. Fig. 8 LNV109A calculated and experimental pressure distribu- tions.
Fig. 11 LA203A calculated and experimental pressure distribu- tions. Fig. 10 Calculated (heavy line) and experimental (symbols) drag polars for LA203A airfoil.
Fig. 12 LA203A calculated suction surface 6* and 6 distributions.
Fig. 13 RAE 2822 calculated and experimental pressure distri- butions.
Fig. 14 RAE 2822 calculated and measured H distributions.
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Survey of Nonlinear Attitude Estimation Methods
by John Crassidis

2007, Journal of Guidance, Control, and Dynamics

This paper provides a survey of modern nonlinear filtering methods for attitude estimation. Early applications relied mostly on the extended Kalman filter for attitude estimation. Since these applications, several new approaches have been... more
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Transport phenomena
by Ricardo Slp

2002, Applied Mechanics Reviews

where € =b/a<1. Thus for tubes of the same cross-sectional area, the ratio W,, /W. decreases from unity (both tubes circular) to values less than unity as € becomes smaller.
For the square cross section (see Problem 3B.3), the ratios corresponding to Eqs. 5 and 8 may be found to be
c. The maximum velocity is then
Let us verify that the average velocities in the two regions are given by Eqs. 2.5-20 and 21. In region I, the average velocity is given bv
When r = R, all of the normal stresses are zero, in agreement with Example 3.1-1.
Alternatively, one can write i in polar form and use the fact that has a unit length:
The first term is zero, because of the assumption of incompressibility (see statement just above Eq. 4.2-1). Then we get finally
Then the kinetic contribution to the force on the sphere is given by
We start by converting the various derivatives from y (x, y) tc erivatives of f (7):
Combining the results in Eqs. 12 and 13 gives
The mass rate of flow can then be obtained by using Eq. 2.3-21 after doing an integration by parts. The dashed underlined terms are zero.
When tT, > 0 and Ll, > LU, the Newtonian result is recoverec
Then the derivative with respect to x is replaced by a derivative with respect to 7):
The adjoint matrix is the transpose of the matrix of cofactors (a cofactor is a "signed minor"):
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International Reference Ionosphere 2007: Improvements and new parameters
by Bodo Reinisch

2008, Advances in Space Research

The International Reference Ionosphere (IRI), a joint project of URSI and COSPAR, is the de facto international standard for the climatological specification of ionospheric parameters and as such it is currently undergoing registration as... more
Fig. 1. Global distribution of IRI members including the newest members (red/gray) and the Steering Committee members (underlined). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this paper.)
Fig. 2. Average ratio between the Alouette/ISIS sounder data and the IRI model at noon for different modified dip latitude ranges using the current IRI topside model (IRI-2001, top) and the corrected model (IRI-2007a, bottom). The model and data are normalized to the respective F-peak densities and heights (Bilitza, 2004).
“ig. 4. Vary-Chap interpolation (dotted line) between the RPI plasmasphere model (Huang et al., 2004) and the IRI peak at a magnetic latitude (Mlat) of 35°N on Jun 25, 2003. Also shown is the «-Chapman profile with constant scale height that provides a good fit near the peak but is much too small higher ip. The right panel shows the derived scale height function with the transition height h; = 1002 km, a scale height Hy = 250 km at hy, and a shape facto 3} = 1.4. (Reinisch et al., 2007). The IRI generally describes the E-region electron den- sity well, but it does not yet include the ionization enhance- ment at auroral latitudes caused by precipitating particles. One of the new features in IRI-2007 is a Neural Network a large volume of EISCAT incoherent scat ~700,000 data points) and also with 115 profiles from rocket borne wave propagation experiments nell et al., 2004; McKinnel and Friedrich, 2006). T ime, riometer absorption, local magnetic index zenith angle, and atmospheric pressure, the later NN) model for this auroral region that was trained with er data obtained (McKin- he model describes the density variations in terms of local magnetic K, solar accounts for variations with height and season. The riometer absorp- ion and K index track storm-related changes in the E- region. This modeling approach uses ground-based radio wave absorption measurements as the proxy to represent
Fig. 5. IMAZ model profiles for auroral E-region density for different levels of riometer absorption Ly (McKinnel and Friedrich, 2006)
Fig. 6. Electron temperature from satellite database versus dip latitude for high (red) and low (blue) solar activity and for summer solstice (upper panel) and equinox (lower panel); the special invdip latitude is used here which is close to the dip latitude at middle and low latitudes and close to invariant latitude at higher latitudes; the solar index is the solar radio flux at 10.7 cm wavelength. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this paper.) the Akebono data to better understand plasmaspheric pro- cesses (see Kutiev et al. (2002) for references).
Fig. 7. Daytime and nighttime latitudinal profiles of O*, H*, and He* densities during equinox as measured by ISS-b (e) at 1000 km (top panel) and as predicted by the new IRI model (solid line) and by the earlier IRI standard (dashed line) and Danilov-Yaichnikov option (dash-dot line). The bottom panel shows a similar comparison for ISIS-2 at 1400 km also at equinox.
Fig. 8. Diurnal variation of the Upper Ion Transition Height as given by several models illustrating the large uncertainties in modelling thi: important parameter: (a) IRI standard model (see pp. 71-76 in Bilitza 1990), (b) Danilov and Yaichnikov (1985), (c) Miyazaki (1979) mode based on Taiyo in-situ measurements, (d) Kutiev et al. (1984) based on in- situ measurements from OGO-6, IC-2, Alouette-1, and ISS-b, (e Intercosmos 13 model (Kutiev et al., 1994), and (f) the most recent mode of Truhlik et al. (2004) (TTS) that includes variations with solar activity
Fig. 9. Probability of spread F as a function of Local Time (x-axis: LT = 25 is same as LT = 1 AM) and month at the Brazilian ionosonde stations Fortaleza (upper row) and Cachoeira Paulista (lower row) and an intermediate latitude (middle row) for different levels of solar activity (below F10.7 = 100 — left column, above F10.7 = 180 — right column, and in-between — middle column (Abdu et al., 2003). Illustrating the fact that spread F is primarily a winter night phenomenon and probabilities increase with solar activity.
IRI, IRI-2001; cor, IRI-2007a; NeQ, IRI-2007b; TTS, Triskova et al. (2006) model. Mean and standard deviation (std) of the data-model differences [(data-model)/data] for the different Alouette and ISIS data sets (n = number of profiles) Table 1
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Wind turbine wake aerodynamics
by Antonio Crespo and 
1 more
Nord-Jan Vermeer

2003, Progress in aerospace sciences

The aerodynamics of horizontal axis wind turbine wakes is studied. The contents is directed towards the physics of power extraction by wind turbines and reviews both the near and the far wake region. For the near wake, the survey is... more
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A Correlation-Based Transition Model Using Local Variables—Part I: Model Formulation
by Florian Menter

2006, Journal of Turbomachinery-transactions of The Asme

A new correlation-based transition model has been developed, which is based strictly on local variables. As a result, the transition model is compatible with modern computational fluid dynamics (CFD) approaches, such as unstructured grids... more
Fig. 1 Scaled vorticity Reynolds number (Re,) profile in a Bla- sius boundary layer
Fig. 2 Relative error between vorticity Reynolds number (Re,) and the momentum thickness Reynolds number (Re,) as a function of boundary layer shape factor (H)
Reg, in Eq. (7) is the critical Reynolds number where the inter- mittency first starts to increase in the boundary layer. This occurs upstream of the transition Reynolds number Reg,. The connection between the two can be obtained from an empirical correlation, where The main difference to other intermittency models lies in the formulation of the function Foye, which is used to trigger the intermittency production. It is formulated as a function of the vorticity (in this case strain rate) Reynolds number
where f is a time scale that is present for dimensional reasons. The blending function Fy, is used to turn off the source term in the boundary layer and allow the transported scalar Re o to diffuse in from the freestream. F'g, is equal to zero in the freestream and one in the boundary layer. It is defined as follows: The boundary condition for Re g at a wall is zero flux. The bound- ary condition for Reg, at an inlet should be calculated from the
>mpirical correlation based on the inlet turbulence intensity. The model constants for the transport equation are as follows, where cy, controls the magnitude of the source term and og con- trols the diffusion coefficient:
where P; and D, are the production and destruction terms from the turbulent kinetic energy equation in the original SST turbu- lence model and Yer is the effective intermittency obtained from Eqs. (24)-(26). 3.4 Coupling With the Turbulence Model. The new transi- tion model has been calibrated for use with the SST turbulence model Menter [12]. The transition model is coupled with the tur- bulence model as follows:
Fig. 7 Skin friction (Cf) for the T3A test case (FSTI=3.5%) their main variable, the turbulence intensity is already based on the local freestream velocity and therefore does violate Galilean invariance. This is not problematic, as the correlations are defined with respect to a wall boundary layer and all velocities are there- fore relative to the wall. However, multiple moving walls in one domain will require additional information. It should also be stressed that the empirical correlation is used only in the source term (Eq. (18)) of the transport equation for transition onset mo- mentum thickness Reynolds number. Finally, because the momen- tum thickness (6,) is present in the pressure gradient parameter (Ag), Eqs. (41)-(43) must be solved iteratively. In the present work, an initial guess for the local value of 6, was obtained based on the zero pressure gradient solution of Eq. (41) and the local value of U, p, and yw. With this initial guess, Eqs. (41)-(43) were solved by iterating on the value of 6, and convergence was ob- tained in less then ten iterations.
Fig. 8 Skin friction (Cf) for the T3B test case (FSTI=6.5%) Test cases presented in this paper include the ERCOFTAC [1,2] T3 series of flat plate experiments and the well-known Schubauer and Klebanof [18] flat plate experiment, all of which are com- monly used as benchmarks for transition models. The first three cases (T3A-, T3A, and T3B) have zero pressure gradient with free-stream turbulence levels of 1%, 3% and 6% that correspond to transition in the bypass regime. The Schubauer and Klebanof [18] test case has a low free-stream turbulence intensity and cor- responds to natural transition. The T3C4 test case consists of a flat plate with a favorable and adverse pressure gradient imposed by
Fig. 10 Skin friction (Cf) for the Schubauer and Klebanof [18] test case (FSTI=0.18%)
Fig. 11 Predicted skin friction (Cf) for the T3C4 test case with and without the modification for separated flow transition
Fig. 9 Skin friction (Cf) for the T3A-test case (FSTI=0.87%)
Fig. 12 Intermittency (y, top), effective intermittency (7.4, middle), and turbulence intensity (Tu, bottom) for the T3C4 test cass
Fig. 13 Normalized wall friction velocity distributions (u,/U, on the suction side of the Genoa cascade Ubaldi [19] The authors would like to acknowledge the support and techni- cal contributions from Dr. William Solomon at GE Aircraft En- gines. The model development and validation at ANSYS CFX
Table 1 Summary of all test case inlet conditions low turbulence intensities, the new correlation has been designed to predict a large increase in Reg, whenever a favorable pressure gradient is present. This is based on Drela’s [14] e" model, which indicates that small favorable pressure gradients will cause a large increase in Re». Based on the Fashifar and Johnson [15] data, the effect appears to be reduced as the freestream turbulence intensity increases and the new correlation is designed to reflect this. The new empirical correlation is defined as follows:
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Direct numerical simulation of turbulent flow over wavy surfaces
by Bojan Niceno

univ-ubs.fr

The present study adresses the turbulent flow over a wavy surface by direct numerical simulation (DNS). Compared to classical channel flow the wavy surface structure adds a degree of complexity to the flow by inducing streamline... more
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Maximum Likelihood Estimation of the Parameters of Multiple Sinusoids From Noisy Measurements
by Randolph Moses

1989, IEEE Transactions on …

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Heat transfer enhancement by using nanofluids in forced convection flows
by Cong Nguyen

2005, International Journal of Heat and Fluid Flow

In the present paper, the problem of laminar forced convection flow of nanofluids has been thoroughly investigated for two particular geometrical configurations, namely a uniformly heated tube and a system of parallel, coaxial and heated... more
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Dielectric Barrier Discharge Plasma Actuators for In-Flight Transition Delay
by Cameron Tropea

2014, AIAA Journal

scholarships were essential for the realization of this project. To Prof. Dr. Fernando Martini Catalano, for the friendship, support, knowledge and experience shared with me throughout all these years, either as teacher when I was an... more
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Large Eddy Simulation of turbulent combustion for gas turbines with reduced chemistry
by Ghislain Lartigue

2002

We model flameless combustion with complex chemistry and LES. A comprehensive sensitivity analysis of the results is presented. Large scale rotational and helical modes are identified. The reaction layer structure is presented including... more
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Viscous flow computations with the method of lattice Boltzmann equation
by Li-Shi Luo

2003, Progress in Aerospace Sciences

The method of lattice Boltzmann equation (LBE) is a kinetic-based approach for fluid flow computations. This method has been successfully applied to the multi-phase and multi-component flows. To extend the application of LBE to high... more
In the discretized velocity space, the density and momentum fluxes can be evaluated as Fig. 1. A 2-D 9-velocity lattice (D2Q9) model.
Fig. 2. Layout of the regularly spaced lattices and curved wall boundary.
Fig. 3. Distribution of the pressure coefficient CP on the surface of a 2-D circular cylinder of radius r = 6.6, and center- to-center distance H/r = 20. The stagnation point is located at 0 = 180°. The LBE result denoted by symbol x is obtained with t = 0.6 and Re = 40. The solid line is the result obtained by using a 3-D multi-block, body-fitted grid, and pressure- based NS solver with a much finer resolution [96].
Fig. 5. Schematic for uniform flow over a sphere. where @ accounts for the non-Stokesian effect of the drag. For two types of the boundary conditions at (vy = +H/2,2= +H/2), byym is used to denote the non- Stokesian correction for the case where the symmetry conditions are imposed at (vy = +H/2,z = +H/2) and Punb 18 used to denote the results for the case where the extrapolation for f,’s is used at (vy = +H/2,z = +H/2) in order to simulate the unbounded flow. The D3Q19 model was used. Fig. 4. Drag coefficient for a uniform flow over a column of cylinders over a range of radius r (a) Re = 100 and (b) Re = 10 [96]. For Re = 100, Benchmark solution was given by Fornberg [100].
gives more scattered result than the method of momentum exchange. For smaller radius, i.e., insuffi- cient lattice resolution, while both methods give poor results, the stress integration yields much larger errors.
Fig. 6. Variation of the non-Stokesian correction factor with sphere radius at Re = 10 [96]. (a) Flow over a single sphere in an unbounded field [96]. (b) Flow over a planer array of spheres. Data are from the LBE simulations.
Fig. 7. Unsteady flow around a cylinder at Re = 100: instantaneous isobars computed by Filippova and Hanel [83] using local grid refinement technique. The typical interface structure is shown in Fig. 9. The line MN is the fine grid block boundary, while the line AB is the coarse grid block boundary. The coarse block boundary is in the interior of the fine block, and the fine block boundary is in the interior of the coarse block. This arrangement of the interface is convenient for the information exchange between two neighboring blocks. For example, grid Q is an interior lattice node of the coarse block. After the collision step, the values of incoming distribution functions fo(t"*!, Xp), f3(t"*!, Xz) and f4(t’*!, Xz) from boundary nodes D, E, and F, respectively, are needed in order to _ obtain filt™!, XQ), At! XQ) and fa(e"t!, Xq) at the end of A flow over an asymmetrically placed cylinder in the channel [103] was calculated with the grid refinement
Fig. 8. Unsteady flow around a cylinder at Re = 100 computed by Filippova and Hanel [83]. Coefficients of drag Cp and lift C, and pressure difference Ap between the front and end points of cylinder vs. the number of time steps in coarse grid: solid lines—boundary- fitting conditions; dashed lines—bouncing-back conditions; straight dotted lines—bounds of reference values Cp max; CL max} Ap/(to + T/2) [103]. Reprinted from Journal of Computational Physics, Vol. 147, Filippova and Hanel, Grid refinement for lattice-BGK models, 219-228 (1998), with permission from Elsevier Science.
Fig. 9. Interface structure between two blocks of different lattice spacing [84].
Fig. 11. Streamlines in the cavity flow at Re = 100 [84]. Fig. 10. Block layout for a 2-D cavity. Lattice spacing i: reduced by a factor of 8 for graphical clarity [84].
Fig. 12. Comparison of velocity between results of single- block, multi-block [84] and result of Ghia et al. [105]. (a) Comparison of w-velocity along the vertical line through geometric center and (b) comparison of v-velocity along the horizontal line through geometric center. The computations were carried out using (i) a single- block with uniform lattice (129 x 129) with the walls placed halfway between lattices, and (ii) a multi-block whose layout is shown in Fig. 10. For the multi-block case, in the two upper corner regions, the grid resolution is increased by a factor of 4 comparing with the single- block case. For Re = 100, the streamlines shown in Fig. 11 were obtained from the single-block solution and the pattern is not discernable from those of the
Fig. 13. Pressure contours in the cavity flow from the single- block LBE simulation [84].
Fig. 15. Enlarged view of pressure contour in the circled region in Fig. 14 near the intersection of three blocks. The figure demonstrates that the block interface and corner are well handled [84]. To validate the above arguments, pressure and shear stress near the block interfaces were examined. Fig. 15 shows a local, enlarged view of the pressure contour
Fig. 14. Pressure contours in the cavity from multi-block LBE solution [84] (for the circled region, see Fig. 15).
Fig. 18. Comparison of Cp between the multi-block simulation and Xfoil [106] calculation as a function of Re for flow over NACAO0012 airfoil. The straight line is the slope according to the laminar boundary layer theory [84]. It is worth pointing out that there is a significant saving in the computational cost using the multi-block method in LBE simulations. There were three different sizes of grids used for the NACA0012 airfoil simulation. There were 1025 x 129=132225 fine grids, 93200 intermediate grids with m = 4, and 139 628 coarse grids (with m= 8 in reference to the finest grids) with a total of about 3.6 x 10° grids in the entire domain. If the fine grid system were used in the entire domain, the number of the grids would be Nyx N= 5698 x 1153~6.57 x 10° which is 18 times more than
Fig. 16. Shear stress contour. Solid and dash lines represent positive and negative values, respectively [84]. It is also noted that at Re = 500, the value of Cp = 0.1761 compared well with the results reported by
Fig. 17. Block and lattice layout for flow over NACA 0012. The lattice spacing is reduced by a factor of 32 for graphical clarity [84].
Fig. 20. Regions of stability and instability in the LBE computation for fully developed 2-D channel flow using the boundary condition of Mei et al. [87], for 4 <i The above three boundary condition treatments all have second-order accuracy for curved boundary. The difference is that the first two need to construct a fictitious fluid point inside the solid wall, and perform a collision step at that node, while the scheme of Bouzidi et al. only requires the known values of f, on the fluid side and no additional collision is required. It is
Fig. 31. Configuration of distribution functions which are used to construct inlet boundary condition. (a) Schematic for determining the equilibrium distribution at the inlet and (b) schematic for determining the non-equilibrium distribution at the inlet.
Fig. 30. (a) Drag coefficient Cp for flow over oscillating zero- thickness flat plate using three different boundary conditions: Filippova and Hanel [83], Bouzidi et al. linear [88], and linear scheme of Yu et al. [89]. (b) Enlarged view of Cp in the circled region in Fig. 30a when A changes from less than 0.5 to larger than 0.5. The figure demonstrates the discontinuity in the temporal variation caused by the Filippova and Hianel [83] and Bouzidi et al.’s boundary treatment [88].
Comparison of drag coefficient using three boundary treat- ments
Fig. 21. Convergence of the factor Q computed by LBE with Bouzidi et al.’s quadratic ( ) and linear interpolation (x ) vs. computational domain size. In the simulation, the fraction of volume occupied by cylinders is kept constant [88]. Courtesy of P. Lallemand.
Bouzidi et al. [88] presented a simpler boundary condition based on the bounce-back for the wall located at arbitrary position. In their work, both linear scheme and the quadratic schemes were given to obtain fg(x¢, t + dt) which is equivalent to fz(xp,f). The linear version was as follows: Fig. 19. Regions of stability and instability in the LBE computation for fully developed 2-D channel flow using Filippova and Hiinel’s boundary condition [83], for 4 <t [87].
Fig. 23. Quadratic convergence of the wall-slip velocity using the boundary conditions of Yu et al. [89] in constant pressure- driven channel flow. A Poiseuille flow (see Fig. 22) was used to illustrate the accuracy of the scheme by Yu et al. [89]. This flow is driven by a body force acting as a constant pressure gradient Vp along the x—direction [115]. To assess the computational error of the LBE solution of the velocity, uLpe(y), the following relative L2-norm error is defined:
Fig. 22. Lattice distribution in channel flow simulations with arbitrary A. where p,, is the fluid density at the wall which can be obtained by using suitable extrapolation from the nearby fluid nodes. To avoid computational instability, we simply set p = p(xr) since we are dealing with nearly incompressible flows.
Fig. 24. Dependence of relative L-norm error for the boundary conditions of Yu et al. [89] on the lattice resolution H in steady-state pressure-driven channel flow simulations.
Fig. 25. Variation of (A’ — A) as a function of 1/H for A = 0.01, 0.5, and 0.99 using the linear scheme of Yu et al. [89].
Fig. 26. Dependence of relative Lj-norm error, defined in Eq. (40), on the lattice resolution H using the linear scheme of Yu et al. [89] in the steady-state pressure-driven channel flow. Fig. 26 shows E% as a function of H for A = 0.01, 0.5, and 0.99. Basically, E has reached the machine error.
Fig. 27. Slip wall velocity as a function of A using the linear scheme of Yu et al. [89] and Bouzidi et al.’s [88] linear scheme for t=0.502, 0.51, 0.6 and 0.8. The value of (1/v)(dp/dx) is fixed.
Fig. 28. Slip wall velocity as a function of A using the quadratic scheme of Yu et al. and Bouzidi et al. [88] for t= 0.502, 0.51, 0.6 and 0.8. The value of (1/v)(dp/dx) is fixed. It is further noticed that the largest magnitude of the slip velocity occurs mainly near 4 = 1. This can be attributed to the fact that the interpolation formula given by Eq. (35) has the largest error at A = 1. Thus to reduce the wall-slip velocity, the second-order interpola- tion formula may be used [89]. Fig. 28 shows the wall- slip velocity as a function of A using both quadratic forms of Yu et al.’s scheme and Bouzidi et al.’s scheme for t = 0.502, 0.51 and 0.6. Note that for the quadratic scheme of Yu et al., the slip velocity is amplified by a factor of 100 for t = 0.502 and by a factor of 10 for t = 0.51 in order to show all curves on the same scale. For the low viscosity (t = 0.502) case, the slip velocity using Bouzidi et al.’s quadratic scheme is over 100 times of that using the quadratic formula of Yu et al.
Fig. 33. Pressure variation (9 —1)/3 at point M at the beginning stage of computation by using the bounce-back inlet condition. Uniform velocity is given as initial condition [116]. Grunau [117] placed the inlet at the lattice node xa (xj = xq and A = 1) as opposed to the lattice halfway link between the grids in which 4 = 0.5 as shown in
Fig. 32. Computational domain and boundary conditions. It is seen in Fig. 33 that indeed that first impulse of the pressure wave at point M occurs near t~189. This confirms the forgoing analysis on the nature of the pressure wave propagation. And such transient varia- tion for t<t, is completely independent of the choice of the inlet boundary conditions.
Fig. 34. Schematics of distribution function at inlet for Zou and He’s method [114] at an inlet, wherefo, fs, fs, fs, fo. f7 are known and f\, fo, fg are to be determined. Zou and He [114] proposed a method to specify the inlet boundary condition based on the idea of bounce- back of the non-equilibrium distribution. In this treatment, the inlet is at nodes (xj = xa in Fig. 31a).
Fig. 35. Pressure variation (p — 1)/3 at point M at the early stage of computation. Uniform velocity is given as initial condition [116].
Fig. 38. Comparison of the drag coefficient (a) and lift coefficient (b) [116] with the benchmark results given in Schafer and Turek [103].
Fig. 37. Shear stress profile along y-direction at nodes which are 0.5 lattice unit downstream from the inlet [116]. Fig. 36. Velocity profile along y-direction at nodes which are 0.5 lattice unit downstream from the inlet [116].
solution while the bounce-back inlet treatment is incapable of producing sensible solution at this Rey- nolds number.
where M is the 9 x 9 matrix transforming F to R. In the vector R, p is the fluid material density, e is the energy, ¢ is related to the square of the energy, j, and j, are the momentum density (or mass flux), g, and q, correspond to the energy flux, and py, and px, correspond to the diagonal and off-diagonal components of the viscous stress tensor. An inherent disadvantage of the SRT d’Humieres [93] presented a 2-D MRT lattice Boltzmann model for the 2-D lattice structure shown in Fig. 1. In this model, a new set of variables R = (p, e, ide Cid Wy Deaenl is introduced and R is related to the set of F = (fo. fis fos fa» fas fs» fo» fr» fay as follows:
Fig. 42. Comparison of the density profiles at x/L = 0.5125 between the SRT model and MRT model at Re = 1000 [95]. To further develop, a quantitative understanding of the performance of the two models for flow over a flat plate, the streamwise variation of various macroscopic quantities near the plate y/L = 0.0125, which is half-grid
Fig. 40. Comparison of the relative error in the evolution of the wall shear stress for Stokes first problem between the SRT and MRT models [95]. The flow over a flat plate has a singularity in pressure and stresses at the leading edge of the plate. A schematic of the flow is shown in the insert of Fig. 41. Reynolds number based on the length is Re = UL/v = 1000. Fig. 41 compares the density deviation, p — 1, from the far field value (9 = 1) as a function of y at x/L = 0.0125, which is half grid away from the leading edge, based on the MRT and SRT models under otherwise identical conditions. When there is insufficient numerical resolu- tion for high Reynolds number flows, a non-physical
Fig. 43. Comparison of the viscous normal stress profiles at x/L = 0.5125 between the SRT model and MRT model at Re = 1000 [95].
Fig. 41. Comparison of the density profiles near the leading edge (x/L = 0.0125) between the SRT model and MRT model at Re = 1000 [95].
Fig. 44. Comparison of pressure coefficient as a function of x at y/L = 0.0125 between the SRT model and MRT model [95]. at y/L = 0.0125 as a function of x for solutions based on these two models where p,, is the pressure at the centerline of the inlet. It is noted that the singularity at x =0 resulted in oscillation in C, for about 4-5 grid points after the leading edge in the MRT model.
Fig. 45. Diagonally driven cavity flow.
Fig. 46. Cavity flow Re = 500 computed by d’Humieres et al. [120], pressure contours at z = 0.5: (a) MRT and (b) LBGK There has been an ongoing effort in construction of stable LBE models and schemes to simulate fully compressible and thermal flows [121-142]. The existing thermal lattice Boltzmann equation (TLBE) models can be classified into three categories. The first category, which is also the simplest approach, is that of passive scalar [121,122,123]. In this approach, the temperature is treated as a passive scalar which is advected by the flow velocity but does not affect the flow fields (density and velocity). The flow fields and the passive-scalar tem- perature are represented by two sets of distribution functions: one simulates the NS equation, and the other simulates the advection-diffusion equation satisfied by
Keywords. Lattice Boltzmann equation; Force evaluation; Grid refinement; Multi-block; Boundary condition; Single-relaxation-time; Multi-relaxation-time The method of lattice Boltzmann equation (LBE) is a kinetic-based approach for fluid flow computations. This method has been successfully applied to the multi-phase and multi-component flows. To extend the application of LBE to high Reynolds number incompressible flows, some critical issues need to be addressed, noticeably flexible spatial resolution, boundary treatments for curved solid wall, dispersion and mode of relaxation, and turbulence model. Recent developments in these aspects are highlighted in this paper. These efforts include the study of force evaluation methods, the development of multi-block methods which provide a means to satisfy different resolution requirement in the near wall region and the far field and reduce the memory requirement and computational time, the progress in constructing the second-order boundary condition for curved solid wall, and the analyses of the single-relaxation-time and multiple-relaxation-time models in LBE. These efforts have lead to successful applications of the LBE method to the simulation of incompressible laminar flows and demonstrated the potential of applying the LBE method to higher Reynolds flows. The progress in developing thermal and compressible LBE models and the applications of LBE method in multi-phase flows, multi-component flows, particulate suspensions, turbulent flow, and micro-flows are reviewed. © 2003 Published by Elsevier Science Ltd.
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Stability of Steady Frictional Slipping
by Andy Ruina

1983, Journal of Applied Mechanics

The shear resistance of slipping surfaces at fixed normal stress is given by τ = τ(V, state). Here V = slip velocity, dependence on “state” is equivalent to functional dependence with fading memory on prior V(t), and ∂τ(V, state)/∂V&gt;0.... more
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THEORY AND ANALYSIS OF ELASTIC PLATES AND SHELLS Second Edition
by Tareq Dahb
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Unscented Filtering for Spacecraft Attitude Estimation
by John Crassidis

2003, Journal of Guidance, Control, and Dynamics

A new spacecraft attitude estimation approach based on the Unscented Filter is derived. For nonlinear systems the Unscented Filter uses a carefully selected set of sample points to more accurately map the probability distribution than the... more
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Analysis of the flax fibres tensile behaviour and analysis of the tensile stiffness increase
by christophe baley

2002, Composites Part A: Applied Science and Manufacturing

The knowledge of the behaviour of flax fibres is of crucial importance for their use as a reinforcement for composites materials. Flax fibres were tested under tensile loading and in repeated loading -unloading experiments. We have shown... more
Fig. 2. Section of a bundle of fibres. The morphological structure of multicellular fibres makes them analogous to the modern reinforced rigid matrix composites. The properties of fibres are also determined by the physical, mechanical and chemica properties of the morphological constituents and_ their interfaces. The polymers involved in the composition of fibres are cellulose, hemicellulose, lignin and pectin. Lignin and pectin act mainly as bonding agents [6]. Typica composition of flax fibres reported by several authors are given in Table | [7—9]. Various parameters can account for the varying accounts of one constituent given by one author to another. These include the species and the variety of the plant, agricultural variables such as soil quality, the weathering conditions, the level of plant maturity, the quality of the retting process [10] and measurement
Fig. 4. The structure of a flax fibre cell [12-15]. The microstructure of natural fibres is extremely complex due to the hierarchical organisation at different length scale and the different materials present in variable proportions. One has mesoscopic scale, fibre consisting of two cell walls arranged as concentric cylinders with a small channel in the middle called the lumen, which contributes to the water uptake as shown in Figs. 4 and 5 [12-15]. The outer cell wall designed as the primary cell wall is only 0.2 wm thick [16]. The bulk of the fibre is essentially constituted by the layer S2 of the secondary wall cell (Fig. 4). The flax fibre consists of highly crystalline cellulose fibrils spirally wound in a matrix of amorphous hemicellulose and lignin (Fig. 6). They are oriented with a tilt angle of 10° [1,7,16] with the axis of the fibre and hence display a unidirectional structure. A new technique for the
Fig. 3. Example of polygonal section in flax fibres.
Fig. 5. Section of a sample of composite flax fibres/epoxy matrix (break in the liquid nitrogen). Fibres, close diameters, present a hollow part (lumen) which can be significant.
Fig. 6. Principle of the flax fibre structure. Helical arrangement of fibrils in natural cellulose fibre [3].
Fig. 8. Break area of a flax fibre after a tensile test. The secondary wall shows a structure of unidirectional composite, microfibrils are directed according to the axis of the fibre. Max flores was measured using the Standard method for single material (NFT 25-704, ASTM D 3379-75), by taking into account the compliance of the system. The load cell allows measurements in the range of 0O-2N with an accuracy of 0.01%. The accuracy of the displacement measurement is +m. A load—displacement curve for a flax fibre loaded to the point of breaking is shown in Fig. 10. The stress—strain curve is strongly influenced by any of the following conditions such as the rate of loading, sample moisture content, specimen length (where structural imper- fections in the fibre come into effect), and the extent of mechanical preconditioning. Thus, a large spread in the characteristic values is observed from one fibre to another, as it will be seen from now on. For the sake of clarity, just a typical curve will be presented each time from now on. Fora load larger than a threshold the extension is proportional to the load in agreement with Hookean behaviour. From the slope of the linear part of the curve we can calculate the Young’s modulus taking into account the dimensions (length, average diameter) of the fibre. Before tensile test,
Fig. 7. Break area of a flax fibre after a tensile test. The secondary wall shown a structure of unidirectional composite, microfibrils are directed according to the axis of the fibre.
Fig. 10. Typical load—displacement curve for flax fibre (length free of fibre LO: 10 mm, speed test 1 mm/mn, speed elongation: 0.1 mm7').
Fig. 9. Flax fibres. Examples of defects.
Fig. 12. Load—displacement curve for flax fibre. After the second unloading, a very small increasing plastic deformation can be observed.
Fig. 11. Definition of fatigue tensile test: successive loading—unloading cycles.
Fig. 14. Successive loading—unloading cycles with load increasing in every cycle.
Fig. 13. Tensile fatigue test of one flax fibre. Evolution of the Young’s modulus (linear part of the load—displacement curve) according to the number of cycles.
Fig. 15. Evolution of the Young’s modulus (linear part of the load— displacement curve) according to the number of cycles.
Fig. 16. Scattering of Young’s modulus of flax fibres.
Fig. 17. Young’s modulus plotted as a function of fibre diameter. Finally, it is important to underline that the elastic properties discussed so far relate to low strain rates. For rapid rates, we obtain a dynamic modulus whose order of magnitude is very different [24].
Fig. 18. A flax fibre is likened to a unidirectional ply with discontinues fibres, where X is the direction of test and (L,T) are the local axes. Among other factors, to be considered are the mechanical properties of the fibre and the matrix, the degree of fibre— matrix interfacial adhesion, the fibre cross-section and the fibre orientation within the matrix all of which influence the mechanical characteristics of the composite. In order to derive an analytical equation, realistic approximations have to be made. We have considered that fibres are discontinuous
The knowledge of the behaviour of flax fibres is necessary for use as a reinforcement of composite materials. We noticed two striking phenomena on the elastic behaviour of flax fibres. First of all, the Young’s modulus decreases with the fibre diameter. Secondly, the Young’s modulus increases in the longitudinal direction during a tensile test. We suggest that the dependence of the Young’s modulus on the fibre diameter is related to the approximation of ignoring Fig. 20. Tensile test with loading—unloading cycles. Relative Young’s modulus measured and calculated (Vg: volume fraction of fibrils; Vv; = 64% continuous line, V; = 74% dotted line).
Fig. 19. Young’s modulus plotted as a function of displacement, experimental results and calculated (Ve volume fraction of fibrils; Vp = 64% continuous line; V; >= 74% dotted line).
Examples of composition of flax fibres [7-9] Table 1
Mechanical properties of flax fibre. Values collected from many different publications [4,7,18,21]
Elastic properties estimated of a flax fibre
Data: elastic properties of main flax fibre components [5,34—39] estimation of the Young’s modulus of the flax fibre is calculated for these two values. Considering that the cellulose density is very close to that of the flax fibres (cellulose density 1.58 g/cm? [18]; flax density 1.541 g/cm?) the mass fraction will be considered equal to the volume fraction. We further assume that the fibre has neither lumen nor defects. The Young’s modulus is estimated for orientation of the cellulose fibrils of 10° (for the initial orientation) and 0° (just before the break).
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Gas-assisted focused electron beam and ion beam processing and fabrication
by Patrik Hoffmann

2008, Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures

Beams of electrons and ions are now fairly routinely focused to dimensions in the nanometer range. Since the beams can be used to locally alter material at the point where they are incident on a surface, they represent direct... more
Fic. 51. FEB and FIB fabricated photonic crystals. (a) FEB deposited band gap filter (Ref. 468). (b) FIB (Ga*) iodine-enhanced etching of InP. The central hole was FIB etched into a photonic crystal structure (Y splitter) (from Ref. 410). (c) A FIB milled plasmonic resonance structure in a 300 nm thick silver membrane; the groove periodicity is 500 nm, groove depth is 60 nm, and hole diameter is 250 nm (Ref. 469).
Fic. 22. Comparison of simulations from Ref. 210 with analytical estima- tion AT=const X L*. The SiO, pillar with 100 nm diameter was irradiated with a 20 keV, 500 pA beam of electrons. Insets show 30 electron trajecto- ries at pillar lengths of 20, 100, and 300 nm and illustrate the shift of the interaction volume from the substrate into the pillar. (The conical apex shape is omitted.)
Fic. 1. Schematics of FIB and FEB nanofabrication systems. Gas injection systems (GIS) with external and internal precursor reservoirs are shown. Beam control is achieved by lithography software addressing pixels within the field of view for a defined dwell time.
Fic. 2. Distribution of focused electron and ion beams. (a) Measured FEB distribution (20 keV): the solid line is a Gaussian with FWHM=4.4 nm. Courtesy of S. Babin, Abeam Technologies. (b) Simulated Holtsmark distribution for 30 keV Ga* ions at 1 pA. The FIB has a FWHM=7 nm but extends to 70 nm. Based on Ref. 52, courtesy V. Callegari, Empa. According to Fig. 2, for an astigmatism and aberration- where f(r) is in electrons or ions per unit area and time, a is the standard deviation, 7p is the beam current, and éo is the elementary charge. Jp can be measured in a Faraday cage. The standard deviation can be derived from knife edge measurements, *“4 resolution measurements of Au spheres on C,” or from the frequency spectrum of specifically de- fined patterns.“°*7 The latter method and the knife edge method have the advantage of being an operator independent measurement. The frequency spectrum of images with non- specific patterns is also used but the relation of such deter- mined beam size to the standard deviation depends on the (individual) signal to noise cutoff.’® Different definitions of beam size are in use. For any incident peak function, one can define the widths at 1/e, 1/e? (e=Euler’s constant), the full width at half maximum (FWHM), and full widths (FW) comprising 50% or 90% of all electrons or ions. For the
Fic. 3. Beam size of the FEI Novalab Dual Beam with a Schottky field emission gun (FEG) and a liquid Ga metal ion source (Ref. 54) and a Hitachi $3600 with a thermionic W filament. WD stands for working distance. (a) Maximum beam current vs beam FWHM. Symbols represent measured values (from frequency spectrum) extrapolated with a I,=d* 3 dependence. (b) Corresponding average incident particle flux.
Fic. 4. Precursor depletion and replenishment in FEB induced processing: Molecules adsorb, desorb, and diffuse at the surface and are dissociated undet electron impact. (a) FEB induced deposition: the nonvolatile dissociation products form the deposit growing coaxially into the beam. Volatile fragments are pumped away. (b) FEB induced etching: the surface adsorbed molecules dissociate under electron impact into reactive species and react to volatile compounds with the substrate material.
Fic. 5. Principle of FIB milling (or sputtering). Note the amorphized surface region containing implanted ions. This physical sputter contribution is also present during gas-assisted FIB etching and deposition, which was omitted here for clarity. For electrons physical sputtering is orders of magnitudes lower at the same charged particle energy due to the different masses of electrons and ions. where Yy¢ is the net deposition or etch yield, Y., is the chemical deposition or etch yield due to dissociation of the molecule, and Y, is the physical sputter yield. The plus sign applies for gas-assisted FIB etching, whereas the minus sign holds for gas-assisted FIB deposition. The dependence on energy and radius is not explicitly noted anymore since the yields are given in units of dissociated or sputtered atoms per incident ions. The conversion of the sputter yield into a sput-
The adsorption term in Eq. (2.2) describes a nondissociative Langmuir adsorption, where np is the maximum monolayer The next conceptual point is a differential adsorption rate equation describing the behavior and surface density of mol- ecules. Four key processes as shown in Fig. 4 are generally considered to determine the surface density n(r,t) of ad- sorbed molecules: (a) adsorption from the gas phase gov- erned by the precursor flux J, the sticking probability s, and coverage n/ng; (b) surface diffusion from the surrounding area to the irradiated area governed by the diffusion coeffi- cient D and the concentration gradient; (c) spontaneous ther- mal desorption of physisorbed molecules after a residence time 7; and (d) molecule dissociation governed by the prod- uct of(r). For the molecule adsorption rate, dn/dt follows
Fic. 7. Secondary electron (SE) energy spectrum per primary electron (PE). Comparison of experimental data of Ni (Ref. 70) with the quantum mechanical electron reflection model of Schaefer and Hoelzl (Ref. 70) and the model of Chung and Everhart (Ref. 71). The surface below the experimental curve was set to the secondary electron yield=1.1 of Ni at Ey=400 eV. (b) Energy spectrum of excited surface atoms (ESA) per primary ion (PI). Monte Carlo simulation [sRIM (Ref. 73)] of the energy normal to the surface. The nonsputtered dislocated Si atoms constitute the excited surface atoms responsible for dissociation (surface below the curve, E<4.7 eV). At 30 keV, the ESA yield is Ypg,=5.5 Si/Ga ion and the sputter yield is Y;=2.6 Si/Ga ion. Besides the direct interaction with the beam, the dissocia- tion of surface adsorbed molecules involves substrate medi- Incident primary ions also incur inelastic and elastic col- lisions, which are often referred to as electronic and nuclear collisions in the FIB community. Heavier ions such as gal- lium lose a significant fraction of their energy in nuclear collisions. As a consequence they have a very short range compared to electrons (see Appendix A) and dislocate many substrate atoms along their trajectory. The dislocated atoms themselves further collide with neighboring substrate atoms in nuclear collisions and initiate collision cascades giving rise to sputtering and a distribution of excited surface atoms around the incident primary ion beam [see Fig. 6(b)]. Sec- ondary electrons are generated during inelastic collisions of primary ions. For Ga ions impinging with 1—30 keV onto
Fic. 6. (a) Scheme of interactions of primary electrons generating an emit- ted flux of secondary electrons and backscattered electrons. All electrons can dissociate surface adsorbed molecules via electronic excitation. (b) Scheme of interactions of primary ions generating secondary electrons and a colli- sion cascade of substrate atoms. The nonsputtered target atoms remain as excited surface atoms contributing to molecule dissociation (modified from Ref, ‘57);
Fic. 8. MC-simulated radial distributions of emitted secondary electrons (SEs) and backscattered electrons (BSEs) per primary electron (PE): Zero diameter electron beam impinging normal with 25 and 3 keV at r=0 on planar bulk silicon. The SE exit depth was taken as 5.2 nm and the mean exit energy as 70 eV. (a) Double-log plot showing the SE distribution tails extending to the range of backscattered electrons Rgsg. (b) Log plot of the secondary electron flux. Comparison of the FWHM and FW50 (full width containing 50% secondary electrons). For both electron beam and ion beam induced processes, the minimum dimensions of the structures that can be pro- duced are larger than the incident beam diameters. The radial flux distributions of the emitted secondary and backscattered electrons and of the excited surface atoms determine the minimum dimensions of the structures that can be fabricated. Calculations of these radial distributions rely on Monte Carlo simulations. Figure 8(a) shows the radial flux distributions for electron bombardment of bulk silicon with a zero diam- eter beam. The emitted secondary electron distribution com- prises all electrons with an exit energy <50 eV and the back- scattered distribution all electrons with energies 250 eV until the incident electron energy. The MC program MOCASIM (Ref. 81) was used and works with small-angle and large-angle Mott cross sections for inelastic energy losses and with Gryzinski and Moller cross sections (inner shell excitation)®’ * for inelastic collisions. It applies a straight line approximation with exponential decrease for secondary electron generation and parametrized escape depths and exit energies.*°*’ The radial density of secondary electrons is one to two orders of magnitude larger than backscattered elec- Analogous MC simulations for excited surface atoms gen- erated by incident primary ions could be performed but we would like to mention an experimental approach to estimate the extent of this distribution proposed by Ref. 67: from measured chemical FIB deposition yields Yp [deposited metal atoms/ion], the diameter of the excited surface atom distribution is obtained by calculating how much surface the number of decomposed molecules initially covered, namely,
Fic. 9. Electron impact total cross sections for gas phase CF, (reproduced from Ref. 92).
Fic. 11. (a) Electron impact deposition cross section of benzene [reproduced from Kunze (Ref. 110)]. For comparison the generic ionization cross sections according to Alman (Ref. 97) and the BEB theory (Ref. 96) are shown. (b) Electron impact deposition cross section for W(CO), and secondary electron (SE) yield of pure W [reproduced from Hoyle (Ref. 64)].
Fic. 12. Plot of o(E)/a9 vs energy of excited surface atom according to the kinetic energy transfer model. The excited surface atom is gold and the precursor molecule Me,Au(hfa). The dissociation energy of this molecule was assumed to be 1 eV (adapted from Ref. 57).
Fic. 15. Relative milling yield as a function of angle from normal for silicot dioxide and for silicon. Note that both experiment and simulation show « decrease in yield as the angle approaches 90° (from Ref. 136).
Fic. 13. Milling yield as a function of angle of incidence of 30 keV Ar ions on a (111) surface of Si, rotated about the (112) axis. The milling yield is seen to drop when the ions are incident along a crystal symmetry direction. For an amorphized target the curve is smooth (from Ref. 135).
Fic. 16. (a) Milling with a stationary FIB. Self-focus effect due to reflection of ions at the steep sidewalls. The reflected ions mill at the periphery of the pit bottom and temporarily form a nonplanar bottom (from Ref. 35). (b) Redeposition during FIB milling of silicon with Ga ions. The milling was performed by a series of single scans from left to right. The increasing depth is due to the angular dependence of the sputter yield (adapted from Ref. 28).
Fic. 17. (a) Tube-based precursor supply. The flux distribution impinging on the substrate depends on the supply angle a, the distance d, the height H, and the inner diameter D of the tube. The access region for FIB/FEB is indicated. (b) Measurement and simulation of impinging precursor distribution. Tube inclination of 60° and inner tube diameter 0.5 mm. The precursor flux peak is covered by the tube geometry (from Ref. 179).
Fic. 18. MC-simulated molecule flux impinging on the substrate for differ- ent tube geometries. (a) Cross section of tube geometries along the tube axis. (b) Molecule flux distribution taken along the tube axis. The x-axis is in units of the inner tube radius. (c) Molecule flux distribution from top view. White dashed lines represent the tube periphery. The color code is red (highest flux) to blue (lowest flux=0) (from Ref. 181).
Fic. 19. Lines deposited with (hfa)Cu-VTMS precursor and varying scan direction with respect to the gas flux. Note that the variation of gas pressure ove! the scanned field is negligible. Lines 1-7 are scanned with the same speed. Line | is scanned away from the gas feed tube and line 7 is scanned toward the gas feed tube. (a) Schematics of the experimental setup and example of writing sequence. (b) SEM micrographs, tilted views (70°) of the resulting structures at three different scan speeds. Left: front views; right: side views (from Ref. 182).
Fic. 20. (a) Gas phase effects. Typically the incident beam traverses about 5—10 mm gas phase at background pressure and roughly 0.5—1 mm at locall: increased pressure before impinging on the substrate. (b) MC-simulated trajectories (SRIM) of incident ions traversing 1 mm water vapor at 1.4 mbar.
Fic. 21. (a) Example of fractal branch electron contamination deposition from background pressure hydrocarbons in the presence of large electro- static fields. Scale bar, 250 nm (from Ref. 197). (b) Local electric field around amorphous carbon filaments due to irradiation, imaged by defocus of the objective lens in the TEM. Colors represent image brightness: red: high field (bright); blue: low field (dark). Local field highest at the tips: hydro- carbon molecules aggregate there (from Ref. 198).
Fic. 23. Compositional and morphological changes along a horizontal freestanding rod deposit due to a temperature gradient generated while depositing a vertical tip. The precursor was (hfa)Cu-VTMS and contains the elements Cu, C, F, O, and Si, which are detected by EDXS at the cold base part (To =room temperature) as a result of pure irradiative dissociation. Hydrogen is also present but cannot be detected. At the rod end Cu is predominantly detected by EDXS (at same scale with base part EDXS) while the other elements did mostly disappear due to thermal dissociation of the molecule. The metal nanocrystal size also increases from a few nanometers to several 100 nm with increasing temperature. The resolution, however, is ‘now determined by the tem- perature distribution, being apparently less confined than the is a good estimate that can be readily applied to pillars and freestanding rods. Equation (2.16b) can be rewritten as AT yittar=Const AsL gop. For coaxial alignment of pillar and in- cident beam, the average trajectory path can be taken as the observable apex cone length. If the pillar is smaller than the cone length, part of the trajectories still penetrates into the bulk substrate; the average pillar trajectory path becomes As~Lgep and thus AT) jiar~ const Eiken. The square depen- dence shows good agreement with a combined Monte Carlo/
Fic. 24. Reference system and processes involved in FEB induced deposi- tion. Inside the irradiated area precursor molecules are depleted by dissocia- tion. Replenishment occurs by gas phase transport and by diffusion. The symbols J, s, 7, D, and o denote the molecule flux, the sticking probability, the residence time, diffusion coefficient, and the dissociation cross section. V is the volume of the decomposed molecule. (b) Schematics of incident beam size, size of generated secondary distributions, and deposit size in terms of the full width at half maximum (FWHM). Additionally, the effec- tive residence times 7 and the diffusion paths p inside and outside the irra- diated area are indicated.
Fic. 25. Calculated deposit shapes according to Eq. (3.2) for differing mol- ecule depletion 7 (no diffusion, p=0). The incident Gaussian beam has a FWHM of 24 nm. The FWHM of the deposit (FWHM,) is increasing with increasing depletion.
Fic. 26. Molecule density n(r) in different FEB and FIB process regimes (red line). The beam size (FWHM,) and beam flux intensity (fo) is high- lighted in yellow (for simplicity the beam flux distribution is flat top and the FWHM, thus corresponds to the cylinder diameter). The density 7, is established outside the irradiated area and nj, (blue dashed line) represents the density inside the irradiated area without diffusion. The degree of deple- tion depends on the ratio of the effective residence times 7;, and 7,,, defined in the context of Eq. (3.2). The replenishment by diffusion in the center is given by nC. It increases with increasing diffusion path inside the irra- diated area p,, and decreasing size of the irradiated area. (a) Diffusion- enhanced regime. The diffusive replenishment recovers part of the irradia- tive depletion. (b) Precursor-limited regime. The diffusion contribution is negligible since the diffusion path is small compared to the size of the irradiated area (beam diameter). (c) Electron- or ion-limited regime. The diffusive replenishment fully compensates irradiative depletion due to the large ratio of diffusion path vs size of irradiated area. (d) Electron- or ion- limited regime at low irradiative depletion.
Fic. 28. (a) f/R vs f plot for electron beam induced deposition using me- thylphenylpolysiloxane (pump oil DC 704) and a 225 eV beam (from Ref. 8). (b) Product of the electron impact cross section with the residence time of the oil molecule on the deposit vs reciprocal absolute temperature. The slope gives the desorption enthalpy of 0.43 eV (from Ref. 8).
Fic. 27. (a) Normalized steady state deposition rate at indicated depletion representing the deposit shape. Note the shape transition from flat top, p =0, indented, p=0.17, round, p=1.3, to Gaussian, p=, and the related decrease of the deposit FWHM (FWHM) with increasing diffusive replen- ishment p. (b) Normalized deposit size vs normalized diffusion path for varying depletion (indicated). At p=2 the diffusion path equals the beam size. Circles represent the scaling law in Eq. (3.8). The inset shows the FWHMp definition of indented deposits (from Ref. 218).
Fic. 29. Shape fitting with continuum model. AFM image and line scans of FEB deposits from Cu(hfa), precursor. Exposure times are indicated. Fits (dashed lines) were obtained with o=0.6 nm? (=molecule size), r=107? s (typical value), and D=4x10-’ cm?s~!. Other deposition parameters: Gaussian beam with FWHM=110 nm (5 keV) and fo=9 X 10¢ nm? s7!. Precursor supply with sJ/ng=10 ML/s (from Ref. 218).
Fic. 31. Comparison of FEB (10 keV) and FIB (30 keV Gat) deposition rates with Si(OCH;),4 precursor (TMOS). Solid lines represent the analytical solution of Eq. (3.13) fitted to the experimental data. (a) The dwell time variation was performed at t,=10 ms. (b) The refresh time variation was performed at t;=200 ns. Experimental data and FIB fits were reproduced from Ref. 231.
Fic. 30. (a) Normalized molecule density n(t)/n,,, for one on/off cycle and a continuous exposure. Typical dwell times are in the microsecond range whereas the refresh time range is around several milliseconds. Here we have chosen t7=1 X 107+-t, and an irradiative depletion T= 1000. Note that deple- tion can be effectively reduced due to small dwell times and long replenish- ment (refresh) cycles. (b) Comparison of the total process time for gas- assisted FEB and FIB etching of a 100 nm deep box into SiO,. For large boxes the total process time becomes electron and ion limited. At small box sizes the process (and the throughput) becomes molecule limited (courtesy of K. Edinger, NaWoTec GmbH).
Fic. 32. Digital serpentine raster scan scheme with overlap. The (Gaussian) beam dwells for a time fy at (x,y) and is then moved by Ax and Ay to the next exposure spot. The scan is repeated after a refresh time f,.
Fic. 33. (a) FEB deposition events on the surface of the deposit or substrate, which can be traced by MC trajectory simulation. (b) Simulated variation in secondary electron energy spectra (normalized) as a function of radical dis- tance from the center of a zero diameter 20 keV incident electron beam for a 80 nm thick planar Cu membrane (from Ref. 20).
Fic. 34. (a) Sequence of simulated profiles of a contamination pillar grown by a 200 keV, zero diameter PE beam on a 10 nm carbon foil. (b) Evolution of pillar geometry: height (circles), base diameter (triangles), and diameter at half its height (squares) (from Ref. 238). Of note is that the apex diameter is constant and about 6 nm.
Fic. 36. Experimental relation of vertical deposition rate R vs pillar length L obtained from data of Ref. 240. Deposition with 25 keV and 500 pA elec- tron beam and two copper precursors. The data were fitted with a power law.
Fic. 35. MC-simulated pillar shapes (12 nm tall) for differing deposition regimes including precursor kinetics (precursor: WF,) (adapted from Ref. 251). The secondary electron contribution to deposition for the electron- limited regime is highlighted (without secondary electrons the pillar would have the Gaussian shape of the beam). The molecule-limited regime leads to loss of deposit resolution due to depletion in the central irradiated area. The FWHM of the incident | keV Gaussian electron beam is 2.7 nm.
Fic. 37. SEM image of a FEB deposited pyramid connecting four predepos- ited Au electrodes. The precursor was Me,Au(tfa) and the electron beams 25 keV and 200 pA. (a) As-deposited composite Au-carbonaceous matrix. (b) After thermal annealing at 400 °C for 30 min in air. Note the formation of large visible Au grains due to removal of carbon by oxidation. The dis- tance of the electrodes is 1 wm.
Fic. 39. Endpoint detection by time-resolved sample current measurements. The sample current is the difference of incident ion current and emitted electro: (or ion) current. The emitted current is different for SiO, and Al causing a variation as a function of milling time or via depth. The pit is 3 X 3 pum’. The lowe part of the figure shows the display at three points (labeled on the curve) during milling. Note that because the pit being milled is becoming deeper, fewe secondary electrons escape at point 3 than at point 2. At point 3 the milled pit is about 2 4m deep. The Ga ion beam (68 keV) is stepped in 100 nm steps (fron Ref. 157). process. All of these methods depend on the fact that the secondary electron yield depend sont he material, and so as one mills into a multilayer film material the current or the image will change as the milling reaches the boundary be- tween films. This technique is imited to holes that do not have high-aspect ratio so that a significant fraction of the secondary electrons leave the sample current result of mil ing t surface. See Fig. 39 for a hrough an Al/SiOs;, End point detection during FIB milling can be carried out by monitoring the sample (stage) current or the secondary electron current or by imaging the milled area during the
Fic. 38. (a) Simplified drawing of the reflectometry setup. Abbreviations stand for m=mirror, 1=lens, OF=optical fiber, and P-D=photodiode (from Ref. 379). (b) Reflectometry curves as a function of time for FEBID with Si(OCH;),. Insets are optical microscope images of the deposits with corresponding deposition time and thickness (from Ref. 379).
Fic. 41. (a) Schematic diagram of the cantilever mass sensor for FIB/FEB induced process monitoring with local precursor supply from a microtube gas injection system. The mass added to or removed from the cantilever is detected as a negative or positive resonance frequency shift, respectively (from Ref. 90). (b) (Top) FIB induced deposition experiment from the pre- cursor (CH3);PtCpCH;: A=mass loading due to adsorption. C=mass loss due to desorption. B=FIB exposure of a 1X1 zm? rectangle. (Bottom) Evolution of the FIB (30 kV, 10 pA) deposited mass corresponding to part B. Inset: SEM tilt view (52°) of the FIB deposit (from Ref. 90).
Fic. 40. (a) Schematic drawing of the electron paths in the deposits. The respective contributions of electrons trajectories to the measured current are highlighted (from Ref. 424). SEs generated at entrance and exit points of electrons are not shown. (b) Jn situ sample current and SE detector signal monitoring during deposition and correlation of the current features to the deposit geometry (top: top view; bottom: tilt view) (from Ref. 424).
Fic. 42. (a) Four predeposited gold electrodes on SiO;/Si substrate (inset) connected by a rectangular FEB deposit from acrylic acid (from Ref. 269). The outer electrodes were used for a two point measurement. (b) Real-time two point resistance measurement corresponding to (a). Note that changes during interruptions, postirradiation, and air exposure can be monitored (from Ref. 269).
Fic. 44. TEM of an amorphous DLC pillar showing core Ga implantation (dark grains). Deposited with phenantrene and 30 keV Ga’ ions (taken from Ref. 27). 7 The composition and microstructure of copper’ ° (see Fig. 45) and gold**° films obtained by focused ion beam induced deposition using organometallic precursors have also been studied. In the case of gold the precursor was dimethylgold hexafluroacetylacetonate, and in the case of copper it was (hfa)CuVTMS — [copper(I)-hexafluroacetylacetonate _tri- methylvinylsilane]. The films consist of either metal particles 50—100 nm diameter in a carbon matrix, or columns of
Fic. 43. TEM of FEB deposit substructures from differing precursors. Typical electron beam conditions were 25 keV, 100 pA, and an electron flux of about 10!° electrons /cm*s. (a) Amorphous dielectric Si-O-C tip from tetraethoxysilane (TEOS). (b) Nanocomposite tip (dark field TEM) from Co,(CO),. The metal nanocrystals embedded in the carbonaceous matrix result in diffraction rings (inset). (c) Polycrystalline pure gold deposit from AuCIPF; (from Ref. 384).
Fic. 46. (a) Principle of resonance experiment. When the resonance frequency of the pillar is approached, the secondary electron detector (SED) measures the peak curve since the pillar vibration intersects the focused electron beam (FEB) from (Ref. 426). (b) Tilt view of FIB deposited carbon pillars from phenanthrene precursor. Excitation of the fundamental resonance mode (left) and the second order resonance mode (right) from (Ref. 431).
Fic. 45. Top view TEM micrographs of 50-100 nm thick copper containing films deposited at various temperatures using a 25 keV Ga* ion beam at ar average current density of 20 ~A/cm?. The local (hfa)CuVTMS gas pres: sure was 1.5 mTorr and the ion beam dwell time was 100 ns. The ion beam current was 60 pA into a scanned area of 10 X 30 wm? (Ref. 376). Chiang (Ref. 236) noted that thermal decomposition of the (hfa)CuVTMS molecule starts at 64 °C.
Fic. 47. High resolution FEB and FIB photomask repair. (a) SEM image of a FEB repaired mouse-bite-type clear mask failure using an organometallic Pt precursor and 1 keV electrons at 10—250 pA (from Ref. 18). (b) AFM image of gas assisted FIB etching. Boxes were etched into TiN using Br, gas and Ga* ions (20 keV, 22 pA) (from Ref. 435).
Fic. 49. (a) Cross section of a gas-assisted FEB processed via hole penetrat- ing through several dielectric layers to a metal layer. The aspect ratio is 10 (depth: 1 jm; diameter: 100 nm). After via hole etch the metal layer was connected by gas-assisted FEB metal deposition (courtesy of Nawotec/Carl Zeiss SMT). (b) FIB image of cross-sectioned FIB-Cu filled via holes using the precursor (hfa)Cu-VTMS. Left: 1 X 1 X 8.2 jum? via (may be incomplete cross section). Right: 1 X 1 x 9.2 wm? via (from Ref. 377).
Fic. 48. High resolution FEB and FIB functionalized sensors. (a) FEB de- posited MFM tip on commercial silicon AFM sensor. (b) A 40 nm diameter FIB milled hole into a magnetic coating of commercial silicon sensor (taken from Ref. 443).
Fic. 50. Schematic of the fabrication sequence for making a connection to an underlying metallic layer covered by another layer. (a) Cut through the upper metal layer, (b) deposition of silicon dioxide insulator, (c) cutting of new hole down to lower metal layer, and (d) deposition of metal connection (from Ref. 380). (e) Focused ion beam image of the completed structure fabricated as shown in (d) (from Ref. 380).
Fic. 52. FEB and FIB fabricated napoelectronic units. (a) FEB deposited gold lines (FEBID) to connect a single wall carbon nanotube (NT) to lift-of prefabricated gold electrodes (EBL) (from Ref. 349). (b) FIB (Ga*) XeF,-enhanced etching of Ti for interdigitated electrodes (from Ref. 232).
Fic. 54. Structures obtained after etching FEB and FIB masked substrates. (a) Si structure formed by CF, plasma etching using a FEB deposited mask from W(CO), (Ref. 65). (b) Ga doped Si structure obtained by Ga*-FIB implantation and successive KOH wet etch (Ref. 527).
Fic. 53. FEB and FIB fabricated emitters. (a) FEB deposited emitter in a plate anode arrangement (Ref. 503). (b) FIB deposited emitter-anode ar- rangement on glass fiber (from Ref. 504).
Fic. 55. FEB and FIB fabricated mechanical structures. (a) FEB deposited clamp to fix a nanowire to a AFM cantilever pyramid (Ref. 543). (b) Nanotweezers with 25 nm resolution (Ref. 548). (c) FIB deposited electrostatically actuated gripper (Ref. 549). (d) FIB deposited four wing rotor (Ref. 550).
Fic. 56. FEB and FIB fabricated biological structures. (a) Nanopore diam- eter tuning with FIB deposition from tetraethoxysilane (TEOS). Nanopores were FIB milled into membrane (Ref. 555). (b) Biocompatible FIB depos- ited diamondlike carbon microtube with an in vitro grown nerve (Ref. 556). (c) Hole of 3 nm diameter milled by FIB into a 20 nm thick SiC membrane (from Ref. 55).
Fic. Al. Electron range R; [Eq. (A1)] and projected ranges of ions in bulk silicon according to SRIM (Ref. 73).
Fic. B1. Energy loss for electrons according to Eq. (B1) and nuclear/ electronic losses of Ga and He ions according to sRIM (Ref. 570). There are different presentations of the energy deposited by focused incident electron or ion beams. Figure D1 shows APPENDIX D: DEPOSITED ENERGY where f,(7) is the (MC-simulated) distribution of scattered electrons (or ions) arriving on the planar substrate after hav- ing passed the gas phase. Figure C1 shows such an integrated radial skirt distribution for a 20 keV electron beam (with zero diameter), which scattered when passing through a 1 mm thick gas phase of Co,(CO)g molecules at its vapor pressure of 0.4 mbar. The scattered fraction amounts to 21% of the incident primary electrons. In comparison a Gaussian distribution having the same full width containing 50% of the scattered electrons is shown.
Fic. D2. MC simulation of dissipated energy H(z) for 3 keV electrons (Ref. 81) and 30 keV Ga and He ions [srim (Ref. 73)]. Note the differences in energy and depth for the two ion species.
Fic. Cl. Integrated radial distribution of scattered electrons incident on the substrate from a 20 keV zero diameter beam passing through | mm Co,(CO)g at P=0.4 mbar obtained from MC simulations (Ref. 81). The curve approaches 100% at larger distances. The scattered fraction is 21% of the PE. In comparison a Gaussian with the same FWS50 is shown.
Fic. D1. MC simulation (Ref. 81) of the deposited energy density distribution in units of eV/nm?/PE into a Si bulk substrate by a 20 keV electron beam with zero tilt and diameter. The electron beam incidence is at r=z=0. The left hand side of the figure represents a zoom into the vicinity of the incident electron beam. where K, and J, are modified Bessel functions and p =2p/FWHMsg represents the diffusion lengths normalized to the FWHM of f(r). The surface diffusion length of molecules outside the irradiated area is defined as pyy=(D Toy)? and at the beam center p,,=(Dz7,,)!*. The dimensionless depletion is defined as T=7,,,/ Tj, 1.€., aS the ratio of the effective residence times outside the irradiated area and in the irradia- with y=0.19Z7 and Rp defined as in Eq. (Al). Equation (D1) gives a 20% agreement with MC simulations at low
Fic. El. Plot of C, vs the inverse of irradiative depletion (7!) according to Eq. (E1). The legend shows values of the normalized diffusion path outside the irradiated area: 2p54,/ FWHMsg.
TABLE I. Properties of electron beam systems. The numbers quoted are very approximate. The minimum beam diameter in any system in practice depends als« on electronic noise and vibration. As the beam acceptance angle is increased, the beam current and the beam diameter increase but over much of the range the current density incident on the sample remains approximately constant. Also as the beam energy is lowered, the beam diameter increases.
“For a table of other alloys and references, see Ref. 32. TABLE II. Comparison of various ion sources. Unnormalized brightness is most often quoted in the literature. To get normalized (reduced) brightness divide by the extraction voltage typically about 10 kV. The total beam current and the beam diameter (usually taken as FWHM see below) depend on the acceptance angle, but the current density remains constant over much of the range.
“Calculated from sRIM simulations (Ref. 73). "From Ref. 60. “From Ref. 78. TABLE III. Comparison of yields for electron and ion irradiation of silicon with 5 and 30 keV incident energies. Yields are in units per primary ion or per primary electron. Ygs,=yield of excited surface atoms, Y, =physical sputter yield, Ys,=secondary electron yield, and Ygsg=backscattered electron yield.
TABLE V. Sputter yields for normal incidence, different ions, incident ener- gies, and materials.
“From density and molar mass [Eq. (2.8b)]. b . . Longest dimension of molecule. “Apparent diameters from Ref. 176. Note the different diameters for XeF, obtained from the different methods TABLE VI. Summary of vapor pressures (P,,,) and molecule diameters (6,,,) of selected precursors. The mean free path X was calculated at vapor pressure according to Eq. (2.8a). The monolayer density was calculated according to ny=1 15467. The Knudsen number (Kn=)/diameter) was calculated for a typical tube diameter of 0.6 mm.
TABLE VII. Skirt MC simulations [Mocasim (Ref. 81)] of incident electrons (zero diameter beam, 30 and 3 keV) traversing 1 mm water vapor at a pressure of 1.4 mbar (density: 1X 10-° g/cm?). Mean free electron paths (\,), the fraction of scattered incident primary beam electrons (Ng), and skirt full widths comprising 10% and 50% of all scattered electrons are given.
TABLE VIII. Parameters determined from focused electron, ion, and photon induced deposition and etching experiments using the continuum model. The diffusion coefficient and the residence time are given at room temperature.
TABLE IX. Calculated minimum diffusion coefficients D and minimum exposure dwell times t, for the electron- or ion-limited regime. Typical ranges o incident peak flux f) and beam size FWHM, are taken for a focused electron beam (5 keV, field emission filament) and an ion beam (30 kV, Ga). Ranges fo the cross section o were chosen from literature results discussed in Sec. III B.
“http://encyclopedia.airliquide.com
“http://encyclopedia/airliquide.com *http://metaloids.com/docs/diger_msds “References 283 and 284. TABLE XII. FEB and FIB induced deposition using hydride precursors. The precursors, vapor pressures P\,, deposition rates, and the deposition conditions are given. Other symbols are © (beam diameter), P,., (residua vacuum pressure), Py, (pressure during deposition or estimated local pressure on sample surface), and tg. (deposition time).
TABLE XIII. FEB and FIB induced deposition with halogen based precursors. Enthalpies of evaporation and sublimation AH)y,/syp;, deposition condition: deposit composition, and electrical resistivity are reported. Further symbols are © (beam diameter), P,., (residual vacuum pressure), Pg.p (pressure durin deposition or estimated local pressure on sample surface), and t4., (deposition time). “Reference 268.
TABLE XIV. FEB and FIB induced deposition using carbonyl and trifluorophosphine precursors. Vapor pressures P,,,, deposit composition, and electrica resistivity are given. Values for the evaporation and sublimation enthalpies AH, 5/.4,; were collected from Refs. 169, 267, 268, and 337. Other symbols are ¢ (beam diameter), P,., (residual vacuum pressure), Py.) (pressure during deposition or estimated local pressure on sample surface), and ty.) (deposition time)
sidual gas. The deposits contained 60 at. % metal in an amor- phous matrix that contained mainly P but also some C, O, and N.*°° type of bonding. Simple o-type bonds are involved in light main group metals and transition metals with alkyl groups, delocalized bonds involving double bonds, triple bonds, and aromatic systems are generally weaker ligand to metal bonds. As an example the bisbenzene chromium (C,H,),Cr is considered to be unstable at room temperature.» More complicated is the bond cleavage of Si—C in alkylsilanes or AIL-C in alkylalanes.
TABLE XV. FEB and FIB induced deposition using organometallic precursors. Vapor pressures P,,,,, deposition conditions, deposit composition, and electrica resistivity are given. Values for the evaporation and sublimation enthalpies AH yap/sup; Were collected from Refs. 268 and 360. Other symbols are © (bean diameter), P,., (residual vacuum pressure), Pye, (pressure during deposition or estimated local pressure on sample surface), and tg.) (deposition time). “Reference 361. Estimated from Ref. 362. ‘Reference 360.
TABLE XVI. FEB and FIB induced deposition using acetylacetonate precursors. Vapor pressures P,,,, deposition conditions, deposit composition, and electrical resistivity are given. Values for the evaporation and sublimation enthalpies AH, y/.44; Were collected from Refs. 266, 268, and 269. Other symbols are © (beam diameter), P,., (residual vacuum pressure), P4., (pressure during deposition or estimated local pressure on sample surface), and ty.) (deposition time). The abbreviations for acetylacetonate, trifluoroacetonate, hexafluoroacetylacetonate are acac, tfa, and hfa, respectively. VTMS=Vinyltrimethylsilane, MHY =2-methyl-1-hexen-3-yne, DMB=3,3-dimethyl-1-butene.
TABLE XVII. FEB and FIB induced deposition of oxides. Vapor pressures P,,,, deposition conditions, and the deposit compositions are given. Structure formulas are given for identification purposes. Other symbols are © (beam diameter), P,., (residual vacuum pressure), P,., (pressure during deposition o estimated local pressure on sample surface), and fg., (deposition time).
TABLE XVIII. FEB and FIB induced deposition of metals and metal oxides with additional reactive gases. Vapor pressures P,,,, deposition conditions, and the deposit compositions are given. ESEM stands for environmental scanning electron microscope and UHV-SEM for ultrahigh vacuum scanning electron microscope.
TABLE XIX. FEB induced deposition of pure oxides with additional reactive gases. Vapor pressures P,,,, deposition conditions, and the deposit compositions are given. Compositions marked with (no g.) were obtained without additional gas. Other symbols are © (beam diameter), P,., (residual vacuum pressure), P dep (pressure during deposition or estimated local pressure on sample surface), and fg.) (deposition time). UHV-SEM stands for ultrahigh vacuum scanning electron microscope. tron beam observation of (frozen) hydrated biological samples.*”° Etching of carbon in the form of synthetic dia- mond was carried out with oxygen, hydrogen, water, and air as precursor. Oxygen proves to be the most efficient etchant for diamond; the formation of amorphous carbon does not 384,396,397 take place. CrO, and Cr, but seems not to attack at all si0." The presence of oxygen and chlorine atoms in the dissociation products upon irradiation helps to form the volatile CrO,Cl, compound, whereas the presence of nitrogen helps to protect against SiO, etching by reacting locally with the Si to Si,Ny, a better etch resistant material. The high polarity of the pre- cursor results in a sufficiently long residence time for induc- ing the chemical reaction. Table XX summarizes the FEB induced etching results.
TABLE XX. Etch precursor gases, materials to be etched, etching conditions, and results for focused electron beam induced etching.
TABLE XXI. Gas-assisted FIB etching. The rate enhancement refers to milling without precursor gas. “The gas pressure values may be very uncertain. The measurement and/or estimation procedures are not specified in all cases. 'These enhancement factor values (as well as others in the table, no doubt) depend strongly on the milling rate with no gas present. The authors quote 1.: atoms/ion at both 5 and 20 keV but mention large variations from run to run. This value is low compared to what is quoted in Table V above. The discrepancy may be due to some of the reasons we discussed in Sec. II C 2 on milling yield. “The difference between the two results on silicon etching (Refs. 406 and 407) may be due to the fact that in reference g the current density in the Ga bean was five orders of magnitude lower (the beam was deliberately defocused) than the current density in Ref. 407. So the results in Ref. 407 of the etch rate ma have been influenced by a depletion of precursor molecules. “All three materials, Si, SiO,, and Si,N,, “etch” more slowly by about a factor of 3 than they mill with no gas present. Presumably this is due to the fact tha the material reoxidizes as it is being milled.
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Direct measurement of quasiparticle lifetimes in graphene using time-resolved photoemission
by Tomasz Durakiewicz

2012, Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures

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Analysis and interpretation of instantaneous turbulent velocity fields
by Kenneth Christensen

2000, Experiments in Fluids

Methods of analyzing and interpreting velocity-®eld data (both two-and three-dimensional) to under-
to obtain the filtered (large-scale) field, u (fis the filtering kernel and D is the domain of the velocity field). If the filtering kernel is shift-invariant (i.e., homogeneous) then f(x,x’) can be simplified to f(x — x’). The total field is the sum of the large-scale field and the remaining smaller- scale field
Fig. 2a-c. Visualization of an isolated turbulent eddy by Galilean | decomposition for three different convection velocities: a ] Ug = 0.65 Ucz3 b Ue = 0.78 Uc c Ug = 0.91 Uc... Ug = 0.78 n Uc, is the ‘correct’ convection velocity based upon the Kline anc Robinson (1989) definition
are intimately associated with the mean flow. Thus, comparing Fig. 3 to Fig. 4a, one sees the large region of relatively uniform momentum in the Galilean
composition. These regions provide important clues to the structure of the logarithmic layer (Meinhart and Adrian 1995). In Figs. 3b and 4a, the uniform mo-
As mentioned previously, vorticity analysis is generall; used to identify locations of vortices and to calculate
scale field found by SED appears qualitatively similar to the LES-decomposed small-scale field calculated using a Gaussian filtering kernel. It clearly isolates vortices A-I, the same vortices seen in the other velocity decompositions.
turbulent kinetic energy and a sink for the kinetic energy of the mean. Therefore, these stresses play a crucial role in understanding the underlying dynamics of turbulence.
Fig. 10a-d. Visualization of net fictitious force imposed by the velocity fluctuations near the wall in pipe flow for Reynolds and Galilean decompositions. a Reynolds decomposition; b Galilean, Ug. = 0.5 Ucr; ¢ Galilean, Uc, = 0.75 Ucr; d Galilean, Ug. = 0.81 Uc
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PIV measurements of a microchannel flow
by Juan Santiago

1999, Experiments in Fluids

A particle image velocimetry (PIV) system has been developed to measure velocity fields with order 1-m spatial resolution. The technique uses 200 nm diameter flow-tracing particles, a pulsed Nd : YAG laser, an inverted epi-fluorescent... more
Fig. 1. Schematic of a micro PIV system. A pulsed Nd: YAG laser is used to illuminate 200 nm diameter fluorescent flow-tracing particles through an epi-fluorescent inverted microscope. A cooled 1300 x 1030 pixel x 12 bit interline-transfer CCD camera is used to record the particle images
Fig. 2. Detail of the nominally 30 jim x 300 jim rectangular glass microchannel, which is glued to a circular capillary tube and a 170 um glass coverslip for support. Plastic tubing connects the capillary tube to the syringe pump
a velocity-vector spacing of 450 nm is achieved. The technique uses epi-fluorescent microscopy, a CCD camera, and two Nd: YAG lasers to image 200 nm diameter fluorescent polysty- rene particles. The spatial resolution and the accuracy of the measurements is limited primarily by the diffraction limit of the recording optics and the size of the sub-micron seed particles.
Fig. 4. Ensemble-averaged velocity profile measured in a nominally 30 um x 300 pm channel. The symbols represent ensemble-averaged and streamwise-averaged PIV data. The solid line is the analytical solution for Newtonian flow through a rectangular channel
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Phase change memory technology
by Geoffrey W Burr

2010, Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures

We survey the current state of phase change memory (PCM), a non-volatile solid-state memory technology built around the large electrical contrast between the highly-resistive amorphous and highly-conductive crystalline states in so-called... more
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Correlation between structural and optical properties of WO3 thin films sputter deposited by glancing angle deposition
by Nicolas Martin

2013, Thin Solid Films

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Shock Waves and High-Strain-Rate Phenomena in Metals
by Marc Meyers

1982, Journal of Applied Mechanics

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The International Laser Ranging Service
by Erricos C . Pavlis

2002, Advances in Space Research

The International Laser Ranging Service (ILRS) was established in September 1998 as a service within the IAG to support programs in geodetic, geophysical, and lunar research activities and to provide data products to the International... more
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Elastic-Plastic Contact Analysis of a Sphere and a Rigid Flat
by Izhak Etsion

2002, Journal of Applied Mechanics-transactions of The Asme

An elastic-plastic finite element model for the frictionless contact of a deformable sphere pressed by a rigid flat is presented. The evolution of the elastic-plastic contact with increasing interference is analyzed revealing three... more
Fig. 1 A deformable sphere pressed by a rigid flat
Finite Element Model (FEM)
first time. This occurs very close to the boundary of the contact area, at r/a=0.94. For 6<w/@,<56 the annular plastic subre- gion remains within the contact area. Its outer boundary, which first reaches the edge of the contact area at w/@,=6.2, coincides with that of the contact area while its inner boundary gradually moves towards the contact center as the elastic core shown in Fig. 4 shrinks. For w/w,>56 the outer boundary of the annular plastic subregion somewhat exceeds the boundary of the contact area while the inner elastic core continues to shrink and disappears completely at w/w,=68. From there on the entire contact zone is plastic and the rate of its radial expansion increases substantially.
From Fig. 7 it can be seen that the dimensionless mean contact pressure of the finite element analysis at w/w,=110 approaches the value p/Y =2.8. This is identical to the ratio between the hardness and yield strength found experimentally for many mate- rials as indicated by Tabor [18]. Hence, the value of p at this point is that of the material hardness, H, and, hence, w/w,=110 marks the inception of the fully plastic regime where the mean contact pressure assumes a constant value equals to the material hardness.
Fig.9 Dimensionless contact load, P/P,, as a function of the dimensionless interference, w/«,, in the elastic-plastic regime
Fig. 8 Dimensionless contact area, A/A,, as a function of the dimensionless interference, w/«,, in the elastic-plastic regime
The accuracy of the curve fitting for Eqs. (7) and (8) was better than 97% throughout the range of w/a,.
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Use of Kriging Models to Approximate Deterministic Computer Models
by Timothy Simpson

2005, AIAA Journal

The use of kriging models for approximation and global optimization has been steadily on the rise in the past decade. The standard approach used in the Design and Analysis of Computer Experiments (DACE) is to use an Ordinary kriging model... more
The one-dimension test problem calculates the output temperature of a chemical reaction. The ratio of oxidant to the fuel being burned is increased from no oxidant to an excess of oxidant. In this process the reaction increases temperature to a maximum and then decreases as excess oxidant is added as shown in Figure 1. There are flat portions in the output temperature as the reaction moves through regions of phase changes in the product of combustion. The sample points used to fit the kriging models are also included in Figure 1. They are evenly spaced at 0.1 increments from 0 to | for a total of 11 points. A set of 500 evenly spaced verification points is used to evaluate the RMSE for each kriging model.
See ee nnn dE ee nr enn le ne aT placed on a 30x30 grid is used to evaluate the RMSE for the metamodels. Figure 3: Two-Dimension LHS Points
Figure 4 shows the results of using the three kriging models to approximate the one-dimension test problem; a second-order response surface is also shown for comparison. On visual inspection, the Ordinary kriging method appears to perform the best at reproducing the output of the computer model. This is confirmed with the estimated RMSE values shown in Table Al in the Appendix, though the cross- validation errors do not yield the same conclusion. The relative errors for the different models are summarized in Figures 7 and 8. In these figures, the errors of the kriging models are normalized against the second-order response surface errors for cach example.
— A series of plots of the fitted metamodels for the two- dimension Test Function | are shown in Figure 5. Since it is difficult to plot the actual surface and the fitted surface on the same graph so a second series of plots are given in Figure 6 showing the resulting errors in predicting with the metamodels. t is easy to see that none of the higher-order features of Test Function | are reproduced by the second-order response surface model. The Ordinary kriging model begins to reproduce some of these features, but not as clearly as the Universal and Detrended models appear to perform. The Ordinary kriging model does not appear to be as linear in the x, direction as the Universal and Detrended kriging models. The error plots of the fitted metamodels for Test Function 1 are also shown in Figure 6. The scale of the error axis is different in each plot. By inspection of these plots, it appears that Universal kriging performs slightly better than Detrended kriging and is followed by Ordinary kriging and the second- order response surface model. This same type of visual comparison could be done for the remaining two-dimension examples, but the estimated assessments give a more objective comparison of the prediction errors of the metamodels.
The use of CV to find the optimal kriging model parameters always improves the cross-validation assessment over the use of MLE. The amount of improvement depends on the how close the distribution of the outputs is to being gaussian. Figure 9 shows the distribution of the data modeled by t he correlation functions for the 6-Hump Camelback Function. This is the part of the data modeled by the random process part of Eq. (1). Figures 9(a,c,e) show the sample distri bution that MLE uses to select the optimal parameters. The continuous line represents the process variance selected using MLE. All of the data is unbiased. The output from the actua computer model is shown in Figures 9(b,d,f). By using Universal or Detrended kriging, the process appears to be better described as being gaussian. MLE also does better at approximating the actual process than CV (see Table A5).
The most commonly used spatial correlation function shown in Table 1 is the gaussian function. It provides a very smooth and infinitely differentiable surface and is defined with only one parameter that is used to control the range of influence of nearby points. The gaussian function is a special case of the exponential function when p=2. The exponential function permits control of both the range of influence and the smoothness of the approximation function, though it is not infinitely differentiable like the gaussian function. The cubic function has only one parameter like the gaussian function and can control the range of influence but is only differentiable once. The Matern function, like the exponential function, has two parameters to control its properties. Stein [13] suggests this function is superior to the others due to its flexibility to control the selection of parameters to control its differentiability and the range of influence. In this work, the exponential spatial correlation function is used, requiring the selection of the optimal @ and p parameters.
Table A2: Model Parameters and Error Assessments for Test Function 1
Table A6: Model Parameters and Error Assessments for Five-Dimension Function Table A3: Model Parameters and Error Assessments for Mystery Function
Table A4: Model Parameters and Error Assessments for Branin Function
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Biodegradable polymers/bamboo fiber biocomposite with bio-based coupling agent
by Nanang Masruchin

2006, Composites Part A: Applied Science and …

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