Two-dimensional simulations

Chang, S. L., Lyezkowski, R. W., and Berry, G. R, Spectral dynamics of computer simulated two-dimensional fewtube fluidized beds. AIChE. Symp. Ser. 2b9, 2b7 (1989). 

Plasma reactor simulations range from zero-dimensional (well-mixed) to three-dimensional. Well mixed [104-106] and one-dimensional models (including plug flow models [107, 108]) are best for sorting out the complicated gas and surface chemistry to arrive at a reduced reaction set for use in multidimensional simulations. Two-dimensional simulations can address the important aspect of reaction uniformity across the wafer radius. Three-dimensional simulations are useful for studying azimuthal asymmetries in the reactor due to non-axisymmetric power deposition, or non-axisymmetric gas inlets and pumping ports [109, 110]. 

Nauman and He [1994] simulated two dimensional spinodal decomposition for ternary polymer mixtures. Variations in volume fraction and interaction parameters of the constituents yielded a multiplicity of different morphologies, some of which were verified in the film experiments. A phase classification was presented for the morphologies obtainable with ternary polymer blends. 

Applications of the EOF have been presented by Gebhart et al. (1990), Ashbaugh et al. (1984), Wolff et al. (1985), and Henry et al. (1991). Henry et al. (1991) compared simulated two-dimensional data generated by a simple dispersion model and the above version of the EOF using simple wind fields. One of the comparisons is shown in Table 24.9. For... 

Fig. 2 A set of five integral projections of a simulated two-dimensional spectrum containing seven responses. Note the situation upper right) where two responses are eclipsed, giving a projected response with an increased integral in that particular direction...

Here we consider simulated two-dimensional random data for four different classes with 50 objects in each class. At first. 

The reservoir simulator developed for this study simulates two-dimensional areal flow of a single-phase, slightly compressible fluid in a closed square reservoir. It is based on the equations developed in previous studies (11,12). The reservoir rock is assumed to be deformable, heterogeneous and anisotropic. The momentum transport equation is... 

Several commercially available simulation packages can be used to simulate two-dimensional or three-dimensional UME and SECM problems, from relatively simple and... 

Figure 1.3 A plot of a computer-simulated two-dimensional random walk of n = 18.050 steps. The walk starts at the upper left-hand comer of the track and works its way to the right-hand edge. (Some regions are completely black this is due to repeated traversals.) The straight-line distance, as the crow flies , is only 196 step lengths. This is in agreement with the expected root-mean-square displacement which is (2n) = 190 step lengths. (Diagram from H.C. Berg, Ref. [13].)...

FIDAP is a general purpose finite element code for simulating two-dimensional, axisymmetric, or full three dimensional equations of viscous incompressible Newtonian or non-Newtonian fluid flow, including the effects of heat transfer. 

FIGURE 4 Classic (black dashed lines) and robust (red solid lines) PCs for a simulated two-dimensional data set containing 151 samples. 

FIGURE 5 Projection of a simulated two-dimensional data set containing 13 samples onto a sphere of unit radius when the centre is at LI-median (red bullets are the samples projected). 

Figure 5-3. Simulated two-dimensional powder patterns obtained with non-zero values for the biaxiality parameter (dotted lines). The experimental spectrum is superimposed on each of the simulated ones (solid lines). Figure reprinted with permission from J. R. Hughes, G. Kothe, G. R. Luckhurst, J. Malthete, M. E. Neubert, I. Shenouda, B. A. Timimi, and M. Tittelbach, J. Chem. Phys., 107, 9252 (1997). Copyright 1997, American Institute of Physics...

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