Many real-world complex systems — from biochemical networks and ecological dynamics to epidemics and socioeconomic models — share a common mathematical structure: agents or particles that move, interact, and change in number. Stochastic reaction-diffusion processes provide a natural and unifying framework to model this broad class of systems, yet their standard probabilistic formulations...
All-atom and coarse-grained molecular dynamics~\cite{ref1}, Langevin dynamics~\cite{ref2}, Brownian dynamics~\cite{ref3,ref4}, and compartment-based stochastic reaction–diffusion models~\cite{ref4,ref5} are computational methodologies that have been applied to the spatio-temporal modelling of numerous intracellular processes. They differ in the level of biological detail they can capture and...
Particle-based stochastic reaction-diffusion processes are widely used in modeling biological processes. There is now a well-developed set of results detailing their basic properties, how they rigorously relate to macroscopic reaction-diffusion PDE models, and a variety of numerical simulation methods for their accurate and efficient approximation. In contrast, adding drift to these models...
Particle-based models with pairwise interactions provide a natural framework to describe clustering phenomena in biological systems, but their simulation and analysis become computationally demanding at large scales. In this talk, I will present two complementary approaches for efficient coarse-grained modeling of particle clustering dynamics. First, I will show that stochastic partial...
Stochastic reaction–diffusion systems provide a fundamental framework for modeling spatially structured biochemical processes such as gene regulation, neurotransmission, and protein clustering. This minisymposium focuses on efficient modeling and simulation approaches that bridge interacting particle-based descriptions and coarse-grained models, including compartment-based reaction–diffusion...
