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41.
Horacio G. Rotstein Amy Novick-Cohen Rina Tannenbaum 《Journal of statistical physics》1998,90(1-2):119-143
Metallic cluster growth within a reactive polymer matrix is modeled by augmenting coagulation equations to include the influence of side reactions of metal atoms with the polymer matrix:
where > 0 and where c
k denotes the concentration of the kth cluster and p denotes the concentration of reactive sites available within the polymer matrix for reaction with metallic atoms. The initial conditions are required to be non-negative and satisfy
and p(0) = p
0. We assume that
for 01, which encompasses both bond linking kernels (R
jk
= j
k
) and surface reaction kernels (R
jk
= j
+ k
). Our analytical and numerical results indicate that the side reactions delay gelation in some cases and inhibit gelation in others. We provide numerical evidence that gelation occurs for the classical coagulation equations ( = 0) with the bond linking kernel (d ) for 1/2<1. We examine the relative fraction of metal atoms, which coagulate compared to those which interact with the polymer matrix, and demonstrate in particular a linear dependence on –1 in the limiting case R
= jk
, p
0=1. 相似文献
42.
43.
A tagged particle interacting with a finite but unbounded number of particles is considered. Some examples of asymptotic completeness are given which are uniform in the number of particles. 相似文献
44.
45.
In this paper we show that each factorization structure on a small category , satisfying certain conditions, yields a presheaf on and a morphism of presheaves . We then give connections, and set up one to one correspondences, between subclasses of the following classes: (a) closure operators on (b) subobjects of (c) morphisms from to (d) weak Lawvere–Tierney topologies (e) weak Grothendieck topologies (f) closure operators on . 相似文献