Related papers: Accurate stochastic simulation of nonlinear reacti…
Diffusion of colloidal particles in a complex environment such as polymer networks or biological cells is a topic of high complexity with significant biological and medical relevance. In such situations, the interaction between the…
In particle-based stochastic reaction-diffusion models, reaction rate and placement kernels are used to decide the probability per time a reaction can occur between reactant particles, and to decide where product particles should be placed.…
We model the diffusive shock acceleration of particles in a system of two colliding shock waves and present a method to solve the time-dependent problem analytically in the test-particle approximation and high energy limit. In particular,…
Stochastic reaction-diffusion models have become an important tool in studying how both noise in the chemical reaction process and the spatial movement of molecules influences the behavior of biological systems. There are two primary…
A coupled system of nonlinear mixed-type equations modeling early stages of angiogenesis is analyzed in a bounded domain. The system consists of stochastic differential equations describing the movement of the positions of the tip and stalk…
In this paper, we study the diffusion approximation for singularly perturbed stochastic reaction-diffusion equation with a fast oscillating term. The asymptotic limit for the original system is obtained, where an extra Gaussian term…
Explicit simulations of fluid mixtures of highly size-dispersed particles are constrained by numerical challenges associated with identifying pair-interaction neighbors. Recent algorithmic developments have ameliorated these difficulties to…
We study analytically the dynamics and the micro-structural changes of a host medium caused by a driven tracer particle moving in a confined, quiescent molecular crowding environment. Imitating typical settings of active micro-rheology…
We combine conditional state density construction with an extension of the Scenario Approach for stochastic Model Predictive Control to nonlinear systems to yield a novel particle-based formulation of stochastic nonlinear output-feedback…
In many biological situations, a species arriving from a remote source diffuses in a domain confined between two parallel surfaces until it finds a binding partner. Since such a geometric shape falls in between two- and three-dimensional…
An autocatalytic reacting system with particles interacting at a finite distance is studied. We investigate the effects of the discrete-particle character of the model on properties like reaction rate, quenching phenomenon and front…
We prove the existence of a solution to an equation governing the number density within a compact domain of a discrete particle system for a prescribed class of particle interactions taking into account the effects of the diffusion and…
Diffusion-limited association reactions are ubiquitous in nature. They are particularly important for biological reactions, where the reaction rates are often determined by the diffusive transport of the molecules on two-dimensional…
System state estimation constitutes a key problem in several applications involving multi-agent system architectures. This rests upon the estimation of the state of each agent in the group, which is supposed to access only relative…
This paper proposes a novel reaction-diffusion system approximation tailored for singular diffusion problems, typified by the fast diffusion equation. While such approximation methods have been successfully applied to degenerate parabolic…
Compartmentalised biochemical reactions are a ubiquitous building block of biological systems. The interplay between chemical and compartmental dynamics can drive rich and complex dynamical behaviors that are difficult to analyse…
Several stochastic simulation algorithms (SSAs) have been recently proposed for modelling reaction-diffusion processes in cellular and molecular biology. In this paper, two commonly used SSAs are studied. The first SSA is an on-lattice…
In recent years, several particle-based stochastic simulation algorithms (PSSA) have been developed to study the spatially resolved dynamics of biochemical networks at a molecular scale. A challenge all these approaches have to address is…
Biochemical networks play a crucial role in biological systems, implementing a broad range of vital functions. They normally operate at low copy numbers and in spatial settings, but this is often ignored and well-stirred conditions are…
We consider one-dimensional diffusions, with polynomial drift and diffusion coefficients, so that in particular the motion can be space-inhomogeneous, interacting via one-sided reflections. The prototypical example is the well-known model…