Anomalous and nonergodic multiscale modeling, analyses and algorithms
Deng Weihua
Abstract
Anomalous and nonergodic phenomena are ubiquitous in nature. With the development of experimental technology, various new experimental phenomena are still emerging. To explain the phenomena/reveal the mechanism, we establish the microscopic models (random processes) and conduct the stochastic analysis and statistical analysis on the microscopic model. At the same time, we derive the macroscopic equation that the probability distribution of some macroscopic statistical observables (such as particle position, functional of the particle's trajectory, escape probability, and first passage time) satisfies, and then study the regularity of the 解 of the equations and the numerical computational method of the equations. Anomalous and nonergodic multiscale dynamics in non-static media will be a research topic with important theoretical value and application prospects in mathematics and natural science. Anomalous and nonergodic dynamics on manifolds are also worth studying. Cross-scale anomalous and nonergodic dynamics in all cases are important research topics too.