Related papers: Bosonic reaction-diffusion processes on scale-free…
Mathematical modeling is now used commonly in the analysis of signaling networks. With advances in high resolution microscopy, the spatial location of different signaling molecules and the spatio-temporal dynamics of signaling microdomains…
A hybrid mesoscopic multi-particle collision model is used to study diffusion-influenced reaction kinetics. The mesoscopic particle dynamics conserves mass, momentum and energy so that hydrodynamic effects are fully taken into account.…
The study of reaction-diffusion systems on networks is of paramount relevance for the understanding of nonlinear processes in systems where the topology is intrinsically discrete, such as the brain. Until now reaction-diffusion systems have…
To mimic the complex transport-like collective phenomena in a man-made or natural system, we study an open network junction model of totally asymmetric simple exclusion process with bulk particle attachment and detachment. The stationary…
Stochastic chemical systems with diffusion are modeled with a reaction-diffusion master equation. On a macroscopic level, the governing equation is a reaction-diffusion equation for the averages of the chemical species. On a mesoscopic…
We study a simple reaction-diffusion population model [proposed by A. Windus and H. J. Jensen, J. Phys. A: Math. Theor. 40, 2287 (2007)] on scale-free networks. In the case of fully random diffusion, the network topology cannot affect the…
The dynamic behaviour of stochastic spreading processes on a network model based on k-regular graphs is investigated. The contact process and the susceptible-infected-susceptible model for the spread of epidemics are considered as prototype…
Reaction-diffusion processes on networked systems have received mounting attention in the past two decades, and the corresponding theory of network dynamics has been continuously enriched with the advancement of network science. Recently,…
We study reaction-diffusion processes with multi-species of particles and hard-core interaction. We add boundary driving to the system by means of external reservoirs which inject and remove particles, thus creating stationary currents. We…
Consider a graph where the sites are distributed in space according to a Poisson point process on $\mathbb R^n$. We study a population evolving on this network, with individuals jumping between sites with a rate which decreases…
We study the decay process for the reaction-diffusion process of three species on the small-world network. The decay process is manipulated from the deterministic rate equation of three species in the reaction-diffusion system. The particle…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
A molecule traveling in a realistic propagation environment can experience stochastic interactions with other molecules and the environment boundary. The statistical behavior of some isolated phenomena, such as dilute unbounded molecular…
We investigate the BCS-BEC crossover in a bilayer system of fermionic dipoles at zero temperature using the fixed-node diffusion Monte Carlo technique. The dipoles are confined on two parallel planes separated by a distance $\lambda$ and…
The propagation of signalling molecules within cellular networks is affected by network topology, but also by the spatial arrangement of cells in the networks. Understanding the collective reaction--diffusion behaviour in space of signals…
The spread of viruses in biological networks, computer networks, and human contact networks can have devastating effects; developing and analyzing mathematical models of these systems can be insightful and lead to societal benefits. Prior…
We present a mathematical study for the development of Multiple Sclerosis in which a spatio-temporal kinetic { theory} model describes, at the mesoscopic level, the dynamics of a high number of interacting agents. We consider both…
A reaction network is a chemical system involving multiple reactions and chemical species. Stochastic models of such networks treat the system as a continuous time Markov chain on the number of molecules of each species with reactions as…
A simple model to study cooperation is the two-species symbiotic contact process (2SCP), in which two different species spread on a graph and interact by a reduced death rate if both occupy the same vertex, representing a symbiotic…
Reaction-diffusion systems where transition rates exhibit quenched disorder are common in physical and chemical systems. We study pair reactions on a periodic two-dimensional lattice, including continuous deposition and spontaneous…