快速变化表面上扩散的多尺度分析
A multiscale analysis of diffusions on rapidly varying surfaces
摘要：
分子在表面上的侧向扩散在各种生物过程中起着非常重要的作用，包括脂质跨膜运输、突触传递和其他现象，例如胞吞和胞吞、信号转导、趋化性和细胞生长。在许多情况下，表面可以具有空间不均匀性和/或快速变化的形状。使用热激发Helfrich弹性膜的模型的概括，我们考虑准平面表面上的横向扩散的问题，具有空间和时间的波动。利用均匀化理论的结果，我们表明，在膜波动的特征长度和时间尺度和扩散粒子的特征尺度之间的尺度分离的假设下，横向扩散过程可以很好地近似由布朗运动的平面上具有恒定的扩散张量$D$，这取决于在一个高度非线性的方式上的表面的详细属性。有效的扩散张量将取决于相对尺度的空间和时间的波动，对于不同的标度制度，我们证明了在每种情况下的宏观极限的存在。
英文摘要：
Lateral diffusion of molecules on surfaces plays a very important role in various biological processes, including lipid transport across the cell membrane, synaptic transmission and other phenomena such as exo- and endocytosis, signal transduction, chemotaxis and cell growth. In many cases, the surfaces can possess spatial inhomogeneities and/or be rapidly changing shape. Using a generalisation of the model for a thermally excited Helfrich elastic membrane, we consider the problem of lateral diffusion on quasi-planar surfaces, possessing both spatial and temporal fluctuations. Using results from homogenisation theory, we show that, under the assumption of scale separation between the characteristic length and time scales of the membrane fluctuations and the characteristic scale of the diffusing particle, the lateral diffusion process can be well approximated by a Brownian motion on the plane with constant diffusion tensor $D$ which depends in a highly nonlinear way on the detailed properties of the surface. The effective diffusion tensor will depend on the relative scales of the spatial and temporal fluctuations and, for different scaling regimes, we prove the existence of a macroscopic limit in each case.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
