chloride ion ingress in concrete is the main reason of concrete corrosion. in real world both uncertainty and stochasticity are main attributes of almost all measurements including testing and modeling of chloride content profile in concrete. regarding these facts new models should be able to represent at least some of the uncertainties in the predictions. in this paper after inspiration from c...

The Adaptive Two-Regime Method (ATRM) is developed for hybrid (multiscale) stochastic simulation of reaction-diffusion problems. It efficiently couples detailed Brownian dynamics simulations with coarser lattice-based models. The ATRM is a generalization of the previously developed Two-Regime Method [Flegg et al., J. R. Soc., Interface 9, 859 (2012)] to multiscale problems which require a dynam...

OF THE DISSERTATION Stochastic Modeling of Advection-Diffusion-Reaction Processes in Biological Systems

In this paper, we study the existence and uniqueness of solutions for several classes of stochastic evolution equations with non-Lipschitz coefficients, that is, backward stochastic evolution equations, stochastic Volterra type evolution equations and stochastic functional evolution equations. In particular, the results can be used to treat a large class of quasi-linear stochastic equations, wh...

We show how using Clifford algebras and their representations can greatly simplify the analysis of integrable systems. In particular, we apply this approach to the XX-model with non-diagonal boundaries which is among others related to growing and fluctuating interfaces and stochastic reaction-diffusion systems. Using this approach, we can not only diagonalize the system, but also find new hidde...

We develop numerical methods for reaction-diffusion systems based on the equations of fluctuating hydrodynamics (FHD). While the FHD formulation is formally described by stochastic partial differential equations (SPDEs), it becomes similar to the reaction-diffusion master equation (RDME) description when those SPDEs are spatially discretized and reactions are modeled as a source term having Poi...

A method is developed for incorporating diffusion of chemicals in complex geometries into stochastic chemical kinetics simulations. Systems are modeled using the reaction-diffusion master equation, with jump rates for diffusive motion between mesh cells calculated from the discretization weights of an embedded boundary method. Since diffusive jumps between cells are treated as first order react...

Reaction-Diffusion systems are important in the field of non-equilibrium phenomena with relevance to biological and synthetic pattern formation. While homogenous distribution of chemicals was always believed to be a stable state, the symmetry-breaking treatment by Turing on such systems in 1951 showed pattern formation could be more stable in certain cases. This paper reviews the treatment by T...

We study front propagation and diffusion in the reaction-diffusion system A ⇌ A + A on a lattice. On each lattice site at most one A particle is allowed at any time. In this paper, we analyze the problem in the full range of parameter space, keeping the discrete nature of the lattice and the particles intact. Our analysis of the stochastic dynamics of the foremost occupied lattice site yields s...