Grey boundary condition

The effect of grey boundary condition (partial reflection caused by particle contact) in the A+A -A 0 ld-lattice reaction was simulated in [106] whereas more refined problem for the combined reaction... 

FIG. 19 Scheme of a simple fluid confined by a chemically heterogeneous model pore. Fluid modecules (grey spheres) are spherically symmetric. Each substrate consists of a sequence of crystallographic planes separated by a distance 8 along the z axis. The surface planes of the two opposite substrates are separated by a distance s,. Periodic boundary conditions are imposed in the x and y directions (see text) (from Ref. 77). 

Therefore, making use of this simple model one can solve and qualitatively analyze different peculiarities of the monomolecular recombination. Partially reflecting boundary conditions (grey recombination sphere) are studied in [50, 68], For the effects of reaction sphere anisotropy, see Chapter 5. 

The boundary condition (4.2.8) is also called the grey sphere - in contrast to the earlier-considered black sphere, equation (3.2.16), which is its limiting... 

Figure 4.11 A percolation fractal embedded on a 2-dimensional square lattice of size 50 x 50. Cyclic boundary conditions were used. We observe, especially on the boundaries, that there are some small isolated clusters, but these are not isolated since they are actually part of the largest cluster because of the cyclic boundary conditions. Exits (release sites) are marked in dark gray, while all lighter grey areas are blocked areas. Reprinted from [87] with permission from American Institute of Physics.

Fig. 15.13. Spontaneous formation of quasi-regular concentric waves in a heterogenous medium. Plotted are the simulation results in a 2-dimensional lattice (15.11) of 150x150 predator-prey oscillators (15.6) with periodic boundary conditions at 6 consecutive time instances (from a to f) starting from homogeneous initial conditions. Plotted is the density of the prey as grey level. Parameters K = 3, k = 3.5, x = b = 1, 5 = 1, e = 0.1, C = diag(l, 1). Growth rates o are taken from a uniform distribution in the range 5 0.4.

Figure 7.10 Illustration of Stick Boundary Condition. Solute biological macromolecule shown as single grey sphere moves with an average velocity through water (shown as light blue spheres). Water molecules in immediate hydration layer move at the same average velocity due to tight hydration interactions. Under Slip Boundary Conditions, water molecules do not possess hydration interactions and therefore do not move with the biological macromolecule at all.

Fig. 1 Schematic two-dimensional drawing of the curved boundary condition in the LBM the numerical grid is divided into fluid cells (white grid cells) and solid cells (grey grid cells). The effective contour of the curved obstacle (bold solid line) is discretised by the distribution functions (black arrows). The relative distance between the fluid node and the curved particle surface is weighted through the parameter qai (dashed lines). Please note that grid nodes (small open squares) are always located at the front left bottom vertex within the cubic grid cells...

There exist however even more ways of looking at ion-specific effects. Interfaces contain hazy or grey areas, with physical properties often quite different (and not always intermediate ) from those of the two phases that they connect. One could thus treat the interface as an inter-phase , i.e. as a different phase, in which the ions can distribute, and regard the ion-surface interaction as a partitioning phenomenon (Fig. 1, middle). Mathematically, this picture stands between the other two, although it is really a more complicated way of handling the boundary condition. 

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