$d$维指数飞行的碰撞密度和平均停留时间
Collision densities and mean residence times for $d$-dimensional exponential flights
摘要：
在本文中，我们分析了{ \em指数航班}，随机过程，管理许多随机输运现象，如中子传播，化学/生物物种迁移，或电子运动的演变的一些方面。我们介绍了一个一般的框架$d$维设置，并强调指数航班代表一个欺骗性的简单系统，在大多数情况下，封闭形式的公式很难得到。我们推导出一些新的精确（在可能的情况下）或渐近的结果，其中的2D系统，一个长期存在的问题，在物理学中的稳态概率密度，并在一个给定的体积的平均停留时间。有界或无界，以及散射或吸收域进行检查，并进行蒙特卡罗模拟，以支持我们的研究结果。
英文摘要：
In this paper we analyze some aspects of {\em exponential flights}, a stochastic process that governs the evolution of many random transport phenomena, such as neutron propagation, chemical/biological species migration, or electron motion. We introduce a general framework for $d$-dimensional setups, and emphasize that exponential flights represent a deceivingly simple system, where in most cases closed-form formulas can hardly be obtained. We derive a number of novel exact (where possible) or asymptotic results, among which the stationary probability density for 2d systems, a long-standing issue in Physics, and the mean residence time in a given volume. Bounded or unbounded, as well as scattering or absorbing domains are examined, and Monte Carlo simulations are performed so as to support our findings.
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