复杂几何条件下扩散粒子最大寿命的快速计算
Rapid calculation of maximum particle lifetime for diffusion in complex geometries
摘要：
分子在生物细胞和组织内的扩散受到拥挤的强烈影响。表征扩散的关键量是粒子寿命，其是扩散粒子通过撞击吸收边界而离开所花费的时间。计算粒子寿命提供了有价值的信息，例如，通过允许我们比较扩散的时间尺度和反应的时间尺度，从而帮助我们开发适当的数学模型。以前的方法来量化粒子寿命集中在平均粒子寿命。在这里，我们采取不同的方法，并提出了一个简单的方法来计算最大粒子寿命。这是一个时间之后，只有一个小的特定比例的粒子在系综留在系统中。我们的方法产生的最大粒子寿命的准确估计，而平均粒子寿命总是低估这个值与随机模拟的数据相比。此外，我们发现，平均和最大粒子寿命之间的差异变得越来越重要，当考虑扩散阻碍障碍物。
英文摘要：
Diffusion of molecules within biological cells and tissues is strongly influenced by crowding. A key quantity to characterize diffusion is the particle lifetime, which is the time taken for a diffusing particle to exit by hitting an absorbing boundary. Calculating the particle lifetime provides valuable information, for example, by allowing us to compare the timescale of diffusion and the timescale of reaction, thereby helping us to develop appropriate mathematical models. Previous methods to quantify particle lifetimes focus on the mean particle lifetime. Here, we take a different approach and present a simple method for calculating the maximum particle lifetime. This is the time after which only a small specified proportion of particles in an ensemble remain in the system. Our approach produces accurate estimates of the maximum particle lifetime, whereas the mean particle lifetime always underestimates this value compared with data from stochastic simulations. Furthermore, we find that differences between the mean and maximum particle lifetimes become increasingly important when considering diffusion hindered by obstacles.
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