变阶分数主方程与粒子的聚集：非均匀溶酶体分布
Variable-order fractional master equation and clustering of particles: non-uniform lysosome distribution
摘要：
在本文中，我们制定了空间依赖的变阶分数主方程模型集群的粒子，细胞器，活细胞内。我们发现它的解决方案，在长时间限制描述非均匀分布，由于空间依赖的分数指数。在连续空间极限下，该分数阶主方程的解与空间相关的变阶分数阶扩散方程的解完全相同。此外，我们发现，群集的溶酶体，哺乳动物细胞的健康功能的一个重要的细胞器，表现出空间依赖性的分数指数。此外，我们证明了溶酶体在活细胞中的非均匀分布是准确地描述了空间依赖的变阶分数主方程的渐近解。最后，分数阶主方程的Monte Carlo模拟验证了我们的解析解。
英文摘要：
In this paper, we formulate the space-dependent variable-order fractional master equation to model clustering of particles, organelles, inside living cells. We find its solution in the long time limit describing non-uniform distribution due to a space dependent fractional exponent. In the continuous space limit, the solution of this fractional master equation is found to be exactly the same as the space-dependent variable-order fractional diffusion equation. In addition, we show that the clustering of lysosomes, an essential organelle for healthy functioning of mammalian cells, exhibit space-dependent fractional exponents. Furthermore, we demonstrate that the non-uniform distribution of lysosomes in living cells is accurately described by the asymptotic solution of the space-dependent variable-order fractional master equation. Finally, Monte Carlo simulations of the fractional master equation validate our analytical solution.
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。
