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首页> 外文期刊>Journal of Scientific Computing >The Narrow Escape Problem—A Short Review of Recent Results
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The Narrow Escape Problem—A Short Review of Recent Results

机译：逃生问题-近期研究成果简短回顾

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The narrow escape problem in diffusion theory, which goes back to Lord Rayleigh, is to calculate the mean first passage time, also called the narrow escape time (NET), of a Brownian particle to a small absorbing window on the otherwise reflecting boundary of a bounded domain. The renewed interest in the NET problem is due to its relevance in molecular biology and biophysics. The small window often represents a small target on a cellular membrane, such as a protein channel, which is a target for ions, a receptor for neurotransmitter molecules in a neuronal synapse, a narrow neck in the neuronal spine, which is a target for calcium ions, and so on. The leading order singularity of the Neumann function for a regular domain strongly depends on the geometric properties of the boundary. It can give a smaller contribution than the regular part to the absorption flux through the small window when it is located near a boundary cusp. We review here recent results on the dependence of the absorption flux on the geometric properties of the domain and thus reveal geometrical features that can modulate the flux. This indicates a possible way to code information physiologically.
机译：扩散理论中的狭义逸出问题可以追溯到瑞利勋爵（Lord Rayleigh），它的目的是计算布朗粒子到其他反射边界上的小吸收窗的平均第一次通过时间，也称为狭义逸出时间（NET）。有界域。对NET问题的重新关注是由于它与分子生物学和生物物理学有关。小窗口通常代表细胞膜上的小目标，例如蛋白质通道（是离子的目标），神经元突触中神经递质分子的受体，神经元脊柱的狭窄脖子（是钙的目标）离子等。规则域的Neumann函数的前导奇异性很大程度上取决于边界的几何特性。当它位于边界尖点附近时，它对通过小窗口的吸收通量的贡献比常规部分要小。我们在这里回顾了吸收通量对畴的几何特性的依赖性的最新结果，从而揭示了可以调节通量的几何特征。这指示了生理上编码信息的可能方式。

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