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It is shown that the characteristics of the mesoscopic fluctuations in the conventional quantum-diffusion model and the model of the non-coherent (`classical') diffusion in media with long-range correlated disorder are quite similar in the…
Biochemical reactions can happen on different time scales and also the abundance of species in these reactions can be very different from each other. Classical approaches, such as deterministic or stochastic approach, fail to account for or…
Metastability is a common obstacle to performing long molecular dynamics simulations. Many numerical methods have been proposed to overcome it. One method is parallel replica dynamics, which relies on the rapid convergence of the underlying…
Extensive simulations are performed of the diffusion-limited reaction A$+$B$\to 0$ in one dimension, with initially separated reagents. The reaction rate profile, and the probability distributions of the separation and midpoint of the…
Developments in dynamical systems theory provides new support for the macroscale modelling of pdes and other microscale systems such as Lattice Boltzmann, Monte Carlo or Molecular Dynamics simulators. By systematically resolving subgrid…
Hybrid particle-field methods are computationally efficient approaches for modelling soft matter systems. So far applications of these methodologies have been limited to constant volume conditions. Here, we reformulate particle-field…
One aim of the equal load sharing fiber bundle model is to describe the critical behavior of failure events. One way of accomplishing this, is through a discrete recursive dynamics. We introduce a continuous mesoscopic equation catching the…
Coupling between chemical fuel consumption and phase separation can lead to condensation at a nonequilibrium steady state, resulting in phase behaviors that are not described by equilibrium thermodynamics. Theoretical models of such…
This article presents a multi-physics methodology for the numerical simulation of physical systems that involve the non-linear interaction of multi-phase reactive fluids and elastoplastic solids, inducing high strain-rates and high…
A variety of simulation methodologies have been used for modeling reaction-diffusion dynamics -- including approaches based on Differential Equations (DE), the Stochastic Simulation Algorithm (SSA), Brownian Dynamics (BD), Green's Function…
We develop and present a unified multi-scale model (involving three scales of spatial organisation) to study the dynamics of rigid aggregating particles suspended in a viscous fluid medium and subject to a steady poiseuille flow. At…
The separation between molecular and mesoscopic length and time scales poses a severe limit to molecular simulations of mesoscale phenomena. We describe a hybrid multiscale computational technique which address this problem by keeping the…
Chemical reactions involve the movement of charges, and this work presents a mathematical model for describing chemical reactions in electrolytes. The model is developed using an energy variational method that aligns with classical…
Smoothed dissipative particle dynamics (SDPD) is a widely used particle-based method for modelling soft matter systems at mesoscopic and macroscopic scales, offering thermodynamic consistency and direct control over the fluid's transport…
We consider viscous, heat conducting mixtures of molecularly miscible chemical species forming a fluid in which the constituents can undergo chemical reactions. Assuming a common temperature for all components, we derive a closed system of…
Stochastic reaction-diffusion models are employed to represent many complex physical, biological, societal, and ecological systems. The macroscopic reaction rates describing the large-scale kinetics in such systems are effective,…
We introduce an infinite particle system dynamics, which includes stochastic chemical kinetics models, the classical Kac model and free space movement. We study energy redistribution between two energy types (kinetic and chemical) in…
Hydrodynamic interactions in a suspension of spherical particles confined between two parallel planar walls are studied under creeping-flow conditions. The many-particle friction matrix in this system is evaluated using our novel numerical…
We formulate and compute a class of mean-field information dynamics for reaction-diffusion equations. Given a class of nonlinear reaction-diffusion equations and entropy type Lyapunov functionals, we study their gradient flows formulations…
The simulation of stochastic reaction-diffusion systems using fine-grained representations can become computationally prohibitive when particle numbers become large. If particle numbers are sufficiently high then it may be possible to…