Related papers: Field theories and quantum methods for stochastic …
Understanding realistic complex systems requires confronting significant conceptual, theoretical and experimental limitations rooted in the persistence of views that originated in the mechanics of simple moving bodies. We define the…
This article addresses reaction networks in which spatial and stochastic effects are of crucial importance. For such systems, particle-based models allow us to describe all microscopic details with high accuracy. However, they suffer from…
A mesoscopic multi-particle collision model for fluid dynamics is generalized to incorporate the chemical reactions among species that may diffuse at different rates. This generalization provides a means to simulate reaction-diffusion…
The primary goal of this paper is to characterize solutions to coupled reaction-diffusion systems. Indeed, we use operators theory to show that under suitable assumptions, then the solutions to the reaction-diffusion equations exist. As…
Open biochemical systems of interacting molecules are ubiquitous in life-related processes. However, established computational methodologies, like molecular dynamics, are still mostly constrained to closed systems and timescales too small…
Since the quantum field theory treats a system of particles, there must be a distribution which is associated with the system of particles. It means that a meaningful quantity is adjoined in the system of particles. It seems that these…
Subdiffusion has been proposed as an explanation of various kinetic phenomena inside living cells. In order to fascilitate large-scale computational studies of subdiffusive chemical processes, we extend a recently suggested mesoscopic model…
The dynamics of phase transitions plays a crucial r\^ole in the so-called interface between high energy particle physics and cosmology. Many of the interesting results generated during the last fifteen years or so rely on simplified…
Quantum stochastic differential equations have been used to describe the dynamics of an atom interacting with the electromagnetic field via absorption/emission processes. Here, by using the full quantum stochastic Schroedinger equation…
Chemical reactions inside cells are generally considered to happen within fixed-size compartments. Needless to say, cells and their compartments are highly dynamic. Thus, such stringent assumptions may not reflect biochemical reality, and…
Reaction networks are widely used models to describe biochemical processes. Stochastic fluctuations in the counts of biological macromolecules have amplified consequences due to their small population sizes. This makes it necessary to favor…
For reaction-diffusion processes with at most bimolecular reactants, we derive well-behaved, numerically tractable, exact Langevin equations that govern a stochastic variable related to the response field in field theory. Using duality…
Surfaces serve as highly efficient catalysts for a vast variety of chemical reactions. Typically, such surface reactions involve billions of molecules which diffuse and react over macroscopic areas. Therefore, stochastic fluctuations are…
The dynamics of ecological as well as chemical systems may depend on heterogeneous configurations. Heterogeneity in reaction-diffusion systems often increase modelling and simulating difficulties when non-linear effects are present. One…
The modeling and simulation of stochastic reaction-diffusion processes is a topic of steady interest that is approached with a wide range of methods. \rev{At the level of particle-resolved descriptions, where chemical reactions are coupled…
Diffusion processes have been widely used for approximations in the queueing theory. There are different types of diffusion approximations. Among them, we are interested in those obtained through limits of a sequence of models which…
Reaction-diffusion processes can be adopted to model a large number of dynamics on complex networks, such as transport processes or epidemic outbreaks. In most cases, however, they have been studied from a fermionic perspective, in which…
Large complexes of classical particles play central roles in biology, in polymer physics, and in other disciplines. However, physics currently lacks mathematical methods for describing such complexes in terms of component particles,…
Several different methods exist for efficient approximation of paths in multiscale stochastic chemical systems. Another approach is to use bursts of stochastic simulation to estimate the parameters of a stochastic differential equation…
Stochasticity plays important roles in reaction systems. Vector fields of probability flux and velocity characterize time-varying and steady-state properties of these systems, including high probability paths, barriers, checkpoints among…