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In this case the marginal distributions of the interparticle distances are also identical, but they are clearly not independent, since they are constrained to obey triangle inequalities (for example). The simplest form of the independent pairs approximation consists in assuming that the interparticle distances are also independent, except that when reaction occurs all the distances involving the reacting particles are removed along with the particles. Thus, given that there are N unreacted particles at time t, there are N(N — l)/2 interparticle distances, each of which is equally likely to be the next pair to encounter, and each of which will make a reactive encounter in the interval [t,t + dt} with probability X ( t } d t .

S. Carslaw and J. C. Jaeger. Conduction of Heat in Solids. Oxford University Press. 1959. T. J. Chuang. G. \V. Hoffman, and K. B. Eiscnthal. Picosecond studies of the cage effect and collision induced predissociation of iodine in liquids. Chem. Phys. Lett.. 25 (1974). pp. 201 205. P. Clifford and N. J. B. Green. On the simulation of the Smoluchowski boundary condition and the interpolation of browman paths. Molec. Phys.. 57 (1986). pp. 123 128. P. Clifford. N. J. B. Green, and M. J. Pilling. Stochastic model based on pair distribution functions for reaction in radiation-induced, spurs containing one type of radical J.

62] A. Mozumder, S. M. Pimblott, P. Clifford, and N. J. B. Green, Electron-ion geminate escape probability in anisotropic media, Chem. Phys. , 142 (1987). pp. 385-388. [63] R. M. Noyes, Effects of diffusion rates on chemical kinetics, Prog. React. , 1 (1961), pp. 129-160. [64] E. Pardoux and D. Talay, Discretization and simulation of stochastic differential equations, Acta Applic. , 3 (1985), pp. 23-47. [65] J. B. Pedersen, The reactivity dependence of the recombination probability. J. Chem. , 72 (1980), pp.

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