论文标题
与一个小目标相遇的扩散相遇的统计数据：三种互补方法
Statistics of diffusive encounters with a small target: Three complementary approaches
论文作者
论文摘要
在统计物理学中，对静态靶标的扩散搜索是一个常见的问题，这些问题在化学和生物学中有许多应用。我们从不同的角度看一下这个问题，并研究了扩散粒子和目标之间的相遇统计数据。尽管最近以光谱膨胀的形式得出了该问题的精确解决方案，但在dirichlet to-neumann运算符的本本basis上，后者通常很难访问任意目标。在本文中，我们提出了三种互补方法，以近似在有限的限制域中重新定位的与目标相遇小的相遇数量的概率密度。特别是，我们得出一个简单的完全显式近似，这仅取决于一些几何特征，例如表面积和目标的谐波容量以及限制域的体积。我们讨论了三种方法的优点和局限性，并检查它们的准确性。我们还推断出一个明确的近似值，以分配第一次跨时间的分布，在该时间上，相遇数量超过了规定的阈值。讨论了它与常见的第一学期时间问题的关系。
Diffusive search for a static target is a common problem in statistical physics with numerous applications in chemistry and biology. We look at this problem from a different perspective and investigate the statistics of encounters between the diffusing particle and the target. While an exact solution of this problem was recently derived in the form of a spectral expansion over the eigenbasis of the Dirichlet-to-Neumann operator, the latter is generally difficult to access for an arbitrary target. In this paper, we present three complementary approaches to approximate the probability density of the rescaled number of encounters with a small target in a bounded confining domain. In particular, we derive a simple fully explicit approximation, which depends only on a few geometric characteristics such as the surface area and the harmonic capacity of the target, and the volume of the confining domain. We discuss the advantages and limitations of three approaches and check their accuracy. We also deduce an explicit approximation for the distribution of the first-crossing time, at which the number of encounters exceeds a prescribed threshold. Its relations to common first-passage time problems are discussed.
