论文标题
在任意维度中的粒子环境相互作用：一个统一的分析框架，以惰性空间异质性建模扩散
Particle-Environment Interactions In Arbitrary Dimensions: A Unifying Analytic Framework To Model Diffusion With Inert Spatial Heterogeneities
论文作者
论文摘要
删节的摘要：随机移动实体和空间疾病之间的惰性相互作用在量化系统的扩散特性方面起着至关重要的作用。这些相互作用仅影响实体的运动，例子范围从沿树突状刺发生的分子到由于植被稀疏而导致动物的抗促进剂位移。尽管这种系统的普遍性，但仍缺少在空间异质性的情况下明确模拟运动的一般框架。在这里，我们应对这一挑战并开发一种分析理论，以模拟任意形状和维度领域中的惰性粒子环境相互作用。我们使用一个离散的空间公式，使我们能够将代理和环境之间的相互作用建模为晶格位点之间的动力学。可以使用我们的框架对空间疾病的相互作用，例如不可渗透和可渗透的障碍物或增加或降低的扩散率以及许多其他区域的相互作用。我们为扩散粒子的职业概率和相关传输量（例如第一步，回报和退出概率及其各自的手段）提供精确表达式。我们发现了一个令人惊讶的特性，即在准1D系统中存在可渗透屏障的情况下，平均第一通道时间的疾病无动现象。我们通过考虑跨越规模和学科的三个例子来证明形式主义的广泛适用性。 （1）我们探讨了透皮药物输送的增强策略。 （2）我们将疾病与动物的决策过程联系起来，以研究thigmotaxis。 （3）我们说明了通过在基因转录过程中通过转录因子对启动子区域进行对启动子区域的搜索来对粒子之间的惰性相互作用进行建模的使用。
Abridged abstract: Inert interactions between randomly moving entities and spatial disorder play a crucial role in quantifying the diffusive properties of a system. These interactions affect only the movement of the entities, and examples range from molecules advancing along dendritic spines to anti-predator displacements of animals due to sparse vegetation. Despite the prevalence of such systems, a general framework to model the movement explicitly in the presence of spatial heterogeneities is missing. Here, we tackle this challenge and develop an analytic theory to model inert particle-environment interactions in domains of arbitrary shape and dimensions. We use a discrete space formulation which allows us to model the interactions between an agent and the environment as perturbed dynamics between lattice sites. Interactions from spatial disorder, such as impenetrable and permeable obstacles or regions of increased or decreased diffusivity, as well as many others, can be modelled using our framework. We provide exact expressions for the generating function of the occupation probability of the diffusing particle and related transport quantities such as first-passage, return and exit probabilities and their respective means. We uncover a surprising property, the disorder indifference phenomenon of the mean first-passage time in the presence of a permeable barrier in quasi-1D systems. We demonstrate the widespread applicability of our formalism by considering three examples that span across scales and disciplines. (1) We explore an enhancement strategy of transdermal drug delivery. (2) We associate the disorder with a decision-making process of an animal to study thigmotaxis. (3) We illustrate the use of spatial heterogeneities to model inert interactions between particles by modelling the search for a promoter region on the DNA by transcription factors during gene transcription.
