Download or read book Hybrid Continuous-Discrete Dynamics Methods for Reaction-diffusion Processes written by Saranah Selmi and published by . This book was released on 2018 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this thesis is to develop a hybrid continuous-discrete multiscale method for reaction diffusion methodologies. The approach has been implemented in two different application areas: (1) heterogeneous nanocatalysis and (2) disease spreading dynamics. In the first part of this thesis, we present how the approach can be used to advance our understanding regarding chemically powered nanomachines. To describe the motion of a catalytic nanoswimmer, we simultaneously couple a fluctuating hydrodynamics (FHD) method that models the continuum domain of our system (i.e., the fluidic environment around the nanoswimmer) with a chemical master equation (CME) that describes the catalytic activity powering the nanoswimmer. We validate this approach by demonstrating that numerical results are in excellent agreement with analytical predictions of a simple one-dimensional linear model. Then, we analyze the impact of thermal fluctuations in the continuum domain coupled with the inherent stochastic nature of the chemical reaction at the catalytic interface. The proposed method is also capable of handling more sophisticated chemical reactions and different geometries. Therefore, this model can be used as a practical mathematical tool to determine how the interplay among nonlinear reactivity, structural complexity, and nonequilibrium fluctuation affects the mobility of chemically powered nanomachines. In the second part of this thesis, the proposed hybrid methodology is slightly modified to study epidemics dynamics. Scholars are aware that in some cases, local dynamics of diseases may affect the overall spreading in the entire population. The presented method couples agent-based models that are capable of describing local dynamics in detail with metapopulation structured models and continuum reaction-diffusion equation-based approaches that are capable of modeling the overall dynamics of the outbreak. First, we present the mathematical formulation of this novel multiscale approach. Then, we apply the method to a simple model that describes the effects of the epidemics dynamics within an airport (discrete model) and the effects of the disease's spread within a city (continuum model).