Uniform grid

For example, the pruned (75,302) grid, denoted (75,302)p contains about 7,500 integration points per atom. In general, pruning reduces the size of a uniform grid by about 66%. 

Two lines of research in subsequent considerations of such equations are evident in available publications in this area over recent years. No much is known in the case of an arbitrary complex domain. The first one is connected with nonequidistant grids, while the second one deals with some modifications of available methods. Even a constant step in each direction does not allow to overcome the difficulties in the near-boundary zones as a result of emerging non-uniform grids. 

Here the coefficients and f(x) are so chosen as to provide on a uniform grid a local approximation of order 2. By analogy with Chapter 4, Section 3 it is plain to justify the uniform convergence of scheme (81) with the rate... 

Note that, for a uniform grid, both Vp(.v) and A7P scale as Nv/M. Using these definitions, the empirical PDF is defined as... 

Last not least, there is a great variety of proprietary lO-design software that has been developed at research facilities and university institutes. E.g., at the TU Delft the S-matrix oriented software Photonic CAD was established several years ago, an innovative 10 design framework based on Hewlett Packard s Microwave Design System. Actual academic work e.g. addresses modes of bent waveguides, BMS-3D" ° is a quite new bend mode solver of the IRE, Prague, or FDTD-schemes with non-uniform grids, a topic of special importance to improve computational efficiency when multi-scale feature sizes are requested, to name a few of recent tasks, only. 

For monitoring to clc substances, such as dioxin cleanup, assume we have calculated an x and s for each unit area or rectangular panel potentially needing cleanup and have been given an action level of 1 ppb. The action level Is a constant and has no variance. The x and s are computed from a field triplicate of a composite of subsamples equally spaced from a uniform grid covering the panel. The null hypothesis says "no difference," and represents the status quo. Hopefully, nonpolluted or less than 1 ppb Is the status quo, and polluted or equal to or larger than 1 ppb Is the exception. 

Similar to the two previous cases (see Sections 9.5.2 and 9.5.3), the problem is solved numerically, whereas the liquid film region is discretized in a spatially uniform grid. The process is considered as an isothermal operation, assuming plug flow of both phases and constant flow rate values of both gas and liquid phases due to low solute concentrations [70]. In the bulk liquid, reaction equilibrium condition is used as a boundary condition for the film region. In order to describe film diffusion, the simple Fick s law is applied. 

The Poisson distribution has been used several times in this text in connection with problems involving small independent probabilities. For example, suppose we desire to find the distribution of v random particles on an 7V-square uniform grid, N being large and each square equally accessible the distribution will then be given by the expression... 

In order to express the above set of equations in finite difference form, the grid lines are labeled as shown in Fig. 3.19, i lines running in the Y-direction normal to the surface and j lines running in the X-direction parallel to the surface. Although not necessary, a uniform grid spacing, AY in the Y-direction, will be used here for simplicity. 

Instead of using the method of separation of variables, a numerical solution to Eq. (4.144) can be easily obtained. Here, a numerical finite-difference solution will be discussed. A series of grid lines in the Z and R directions are introduced as shown in Fig. 4.16, a uniform grid spacing, ARt being used in the radial coordinate direction. 

An explicit finite-difference procedure will be used here in dealing with the momentum and energy equations. Consider the nodal points shown in Fig. 4.27. It will be seen that a uniform grid spacing is used in the -direction. 

A uniform grid spacing in the T-direction will be used here. Consider, as was done in Chapter 3, the nodal points shown in Fig. 10.16. 

Because uniform grid spacing has been used, the mean Nusselt numbers are given by ... 

Fig. i 2D example of a uniform grid applied to the unit cell. The ions are on grid points 02 41 23... 

The above equations are solved in a domain —1 < rr < 25 and 0 core size of the convecting vortex that is in this case identified with the diameter of the convecting cylinder. A uniform grid spacing of Ax = 0.04, is used in the streamwise... 

The best configuration of ensembles of microelectrodes is a collection of micro discs of equal size, arranged on a uniform grid, at equal distances from each other. Sometimes this is not feasible, and ensembles containing electrodes of nonuniform size and/or distance have been considered. Ensembles of strip microelectrodes have also been constructed, and the variation of current with time for such configurations has been evaluated. 

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