不可逆反应和扩散逃逸：定态性质
Irreversible Reactions and Diffusive Escape: Stationary Properties
摘要：
我们研究了三个基本的扩散控制反应过程--湮灭、聚结和聚集。我们研究的演变开始与最自然的不均匀的初始配置，其中半线是均匀填充的粒子，而互补的半线是空的。我们表明，渗透到最初空的半线的粒子的总数是有限的，并有一个固定的分布。我们确定平均密度的演变，从中我们得出初始空半行中粒子的平均总数N;例如，对于湮灭，\langle N \rangle = 3/16+1/（4π）。对于聚结过程，我们设计了一个程序，原则上允许计算P（N），在最初的空半行中找到正好N个粒子的概率;我们在第一个非平凡的情况下完成计算（N=1）。作为一个副产品，我们得到两个领先粒子之间的距离分布。
英文摘要：
We study three basic diffusion-controlled reaction processes -- annihilation, coalescence, and aggregation. We examine the evolution starting with the most natural inhomogeneous initial configuration where a half-line is uniformly filled by particles, while the complementary half-line is empty. We show that the total number of particles that infiltrate the initially empty half-line is finite and has a stationary distribution. We determine the evolution of the average density from which we derive the average total number N of particles in the initially empty half-line; e.g., for annihilation \langle N\rangle = 3/16+1/(4π). For the coalescence process, we devise a procedure that in principle allows one to compute P(N), the probability to find exactly N particles in the initially empty half-line; we complete the calculations in the first non-trivial case (N=1). As a by-product we derive the distance distribution between the two leading particles.
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