Regularly distributed array

In the same maimer as for the regularly distributed array, we can use the diffusion domain approximation to transform each Voronoi cell into a cyhndrical cell of the same base area, A , and of radius rd , as illustrated in Figure 10.6(b), thus reducing the problem of simulating each cell from... 

Fig. 10.9. (a) Schematic diagram of a regularly distributed array of microband elec-... 

An infinitely extended, linear, and regular system of points is called a row, and it is completely described by its repeat distance a. A planar regular array of points is called a net, which can be specified by two repeat distances a and b and the angle y between them. The analogous system of regularly distributed points in three dimensions constitute a lattice (or space lattice), which is described by a set of three non-coplanar vectors (a, b, c) or six parameters the repeat intervals a, b, c and the angles a, p,y between the vectors. As far as possible, the angles are chosen to be obtuse, particularly 90° or 120°, and lattices in one, two, and three dimensions are illustrated in Fig. 9.2.1. 

A number of methods exist for fabricating microelectrode arrays [6] and a variety of array geometries are encountered with the most common being arrays of microdiscs and arrays of microbands. Microdiscs are most frequently arranged as a regularly distributed (i.e., a square or... 

In Chapter 9, we studied the problem of a single electroactive microdisc on an infinite supporting surface. Here we consider the situation where an array of such microdiscs are embedded in a surface in a regular distribution as illustrated in Figure 10.1. It is assumed that electroactivity only occurs at the microdisc electrodes, not on the supporting surface. 

We now turn our attention to randomly distributed arrays of microdisc electrodes as illustrated in Figure 10.5 though they are not as commonly encountered as regularly distributed microdisc arrays, techniques do exist for their fabrication [22] and so here we consider the simulation of such arrays. Though the specific example of a randomly distributed microdisc array is of limited utility, the techniques for generating a random distribution of particles are applicable to a range of electrochemical problems. 

Using this approach it would take approximately N times longer to simulate a single randomly distributed array than it would to simulate a regular array, which is clearly impractical, as N is likely to be very large. 

E. Kyriakis-Bitzaros and C. Goutis. An efficient decomposition technique for mapping nested loops with constant dependencies onto regular processor array processors. Journal of Parallel and Distributed Computing, 16, pages 258-264, 1992. 

Zeolites constitute a group of hydrated crystalline aluminosilicates containing regularly shaped pores with sizes from 1 nm to several nanometers. This provides them with the ability to reversibly adsorb and desorb specific molecules. Chemical synthesis of semiconductors inside such pores permits the fabrication of regularly distributed, highly size-monodispersed nanocrystal arrays. This has been applied to CdS, Pbl2, and Ge. 

The formation of a hierarchical order in the final crack distribution was first investigated by Basant [8] and Nernat-Nasser [9]. They assumed that a regular array of growing cracks showed a special type of instability where every second crack is left behind while the others advance. With this assumption they were able to calculate the instants of instability or bifurcation of the solution. We adopted that view in our earlier papers [5]. Our latest numerical results, however, shov/ that this is not necessarily so Regular crack arrays evolve in a more complex way [10], and the bifurcation mode proposed by [8,7] is definitely ruled out in some cases. It has been shown that bifurcation modes with every third or fourth crack propagating will be present then. It is not yet clear whether there... 

In addition to lipid movement proteins are also usually able to migrate laterally at rapid rates. This was originally shown following cell fusion where antibody labelling revealed that the proteins from one cell were rapidly found distributed evenly across the entire surface of the fused cell. However, not all membrane proteins exhibit such freedom of movement. For example, the purple patches in the membrane of the photosynthetic bacterium Halobacterium halobium have proteins arranged in a regular geometric array where rotational freedom is severely restricted. 

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