Related papers: A particle system approach to aggregation phenomen…
Reaction-diffusion processes are the foundational model for a diverse range of complex systems, ranging from biochemical reactions to social agent-based phenomena. The underlying dynamics of these systems occur at the individual…
An algorithm for measurement of entropy in multiparticle systems, based on recently published proposal of the present authors, is given. Dependence on discretization of the system and effects of multiparticle correlations are discussed in…
The microscopic approach to the description of the phase behaviour and critical phenomena in binary fluid mixtures is proposed. It is based on the method of collective variables with a reference system. The physical nature of the order…
In this article we propose and investigate a hierarchy of mathematical models based on partial differential equations (PDE) and ordinary differential equations (ODE) for the simulation of the biophysical phenomena occurring in the…
The qualitative solvent- and temperature-dependent conformational behavior of a peptide in the proximity of solid substrates with different adsorption properties is investigated by means of a simple lattice model. The resulting pseudophase…
We consider the utilization of a computational model to guide the optimal acquisition of experimental data to inform the stochastic description of model input parameters. Our formulation is based on the recently developed consistent…
A method for computing the thermopower in interacting systems is proposed. This approach, which relies on Monte Carlo simulations, is illustrated first for a diatomic chain of hard-point elastically colliding particles and then in the case…
Flocking refers to collective behavior of a large number of interacting entities, where the interactions between discrete individuals produce collective motion on the large scale. We employ an agent-based model to describe the microscopic…
We are interested in exploring interacting particle systems that can be seen as microscopic models for a particular structure of coupled transport flux arising when different populations are jointly evolving. The scenarios we have in mind…
We investigate an interacting particle model to simulate a foraging colony of ants, where each ant is represented as an active Brownian particle. The interactions among ants are mediated through chemotaxis, aligning their orientations with…
We draw an analogy between droplet formation in dilute particle and polymer systems. Our arguments are based on finite-size scaling results from studies of a two-dimensional lattice gas to three-dimensional bead-spring polymers. To set the…
We prove the existence of weak solutions of a class of multi-species cross-diffusion systems as well as the propagation of chaos result by means of nonlocal approximation of the nonlinear diffusion terms, coupling methods and compactness…
In a system of noisy self-propelled particles with interactions that favor directional alignment, collective motion will appear if the density of particles increases beyond a certain threshold. In this paper, we argue that such a threshold…
Years ago Edwards proposed a thermodynamic description of dense granular matter, in which the grains (the `atoms' of the system) interact with inelastic forces. The approach is intriguing but is not justified from first principles, and…
Based on a class of moderately interacting particle systems, we establish a quantitative approximation for density-dependent McKean-Vlasov SDEs and the corresponding nonlinear, nonlocal PDEs. The SDE is driven by both Brownian motion and…
In this article an upscaled model is presented, for complex networks with highly clustered regions exchanging some abstract quantities in both, microscale and macroscale level. Such an intricate system is approximated by a partitioned open…
In this paper we consider an interacting particle system in $\mathbb{R}^d$ modelled as a system of $N$ stochastic differential equations driven by L\'evy processes. The limiting behaviour as the size $N$ grows to infinity is achieved as a…
We study the existence and the exponential ergodicity of a general interacting particle system, whose components are driven by independent diffusion processes with values in an open subset of $\mathds{R}^d$, $d\geq 1$. The interaction…
Nanoparticles introduced in living cells are capable of strongly promoting the aggregation of peptides and proteins. We use here molecular dynamics simulations to characterise in detail the process by which nanoparticle surfaces catalyse…
Convenient variational formula for collective diffusion of many particles adsorbed at lattices of arbitrary geometry is formulated. The approach allows to find the expressions for the diffusion coefficient for any value of the system's…