An improved particle-based method with applications to multiscale biophysical problems
An improved particle-based method for continuum mechanics with both stochastic and deterministic reaction-diffusion of chemical species in moving boundaries is presented. The method enables the simulation of a class of biophysical problems that could not be resolved by using classical mesh-based approaches.This dissertation is divided in three parts: in Chapter 1, we present an introduction of particle-based methods, with an overview of its advantages and limitations, along with recent improvements and applications. In Chapters 2 and 3, we propose solutions to two crucial factors that limit the applicability of particle-based methods to biophysical problems, respectively: (a) the lack of a discrete spatial stochastic formulation for reaction-diffusion systems, and (b) the onset of numerical instabilities that cause particles to penetrate moving wall boundaries. In Chapter 4, we summarize our results and conclude that the usage of our method provide a robust particle-based multiphysics framework that extends the reach of particle-based methods to new types of problems including those of biological relevance.