Related papers: A multi-species model with interconversion, chippi…
We study a minimal lattice model which describes bidirectional transport of "particles" driven along a one dimensional track, as is observed in microtubule based, motor protein driven bidirectional transport of cargo vesicles, lipid bodies…
We consider the diffusion-advection problem in two simple cellular flow models (often invoked as examples for subdiffusive tracer's motion) and concentrate on the intermediate time range, in which the tracer's motion indeed may show…
We study a class of evolution models, where the breeding process involves an arbitrary exchangeable process, allowing for mutations to appear. The population size $n$ is fixed, hence after breeding, selection is applied. Individuals are…
We review recent progress on the zero-range process, a model of interacting particles which hop between the sites of a lattice with rates that depend on the occupancy of the departure site. We discuss several applications which have…
An asymmetric exclusion model on an open chain with random rates for hopping particles, where overtaking is also possible, is studied numerically and by computer simulation. The phase structure of the model and the density profiles near the…
Self-organized pattern formation is vital for many biological processes. Reaction-diffusion models have advanced our understanding of how biological systems develop spatial structures, starting from homogeneity. However, biological…
We revisit a classical continuum model for the diffusion of multiple species with size-exclusion constraint, which leads to a degenerate nonlinear cross-diffusion system. The purpose of this article is twofold: first, it aims at a…
We consider a cross-diffusion system for which the diffusion of each species is governed solely by the aggregate density through a pressure law of logarithmic or fast diffusion type. The model is set over a one dimensional bounded interval,…
Numerous experimental studies have demonstrated that the microenvironment is a key regulator influencing the proliferative and migrative potentials of species. Spatial and temporal disturbances lead to adverse and hazardous…
The aim of this paper is to study a PDE model for two diffusing species interacting by local size exclusion and global attraction. This leads to a nonlinear degenerate cross-diffusion system, for which we provide a global existence result.…
We present a general framework for incorporating non-reciprocal interactions into the Ising model with Glauber dynamics, without requiring multiple species. We then focus on a model with vision-cone type interactions. We solve it in a fully…
The impact of environmental fluctuation on species diversity is studied with a model of the evolutionary ecology of microorganisms. We show that environmental fluctuation induces evolutionary branching and assures the consequential…
Cellular differentiation in a developping organism is studied via a discrete bistable reaction-diffusion model. A system of undifferentiated cells is allowed to receive an inductive signal emenating from its environment. Depending on the…
We propose a novel approach to modeling cell migration in an anisotropic environment with biochemical heterogeneity and interspecies interactions, using as a paradigm glioma invasion in brain tissue under the influence of hypoxia-triggered…
Exchange of biochemical substances is essential way in establishing communication between bacterial cells. It is noticeable that all phases of the process are heavily influenced by perturbations of either internal or external parameters.…
It has been well established that particulate systems show the jamming transition and critical scaling behaviors associated with it. However, our knowledge is limited to (nearly) monodisperse systems. Recently, a binary mixture of jammed…
Motivated by recent findings, we discuss the existence of a direct and robust mechanism providing discontinuous absorbing transitions in short range systems with single species, with no extra symmetries or conservation laws. We consider…
A new model ecosystem consisting of many interacting species is introduced. The species are connected through a random matrix with a given connectivity. It is shown that the system is organized close to a boundary of marginal stability in…
Generalizing the well-known lilypond model we introduce a growth-maximal hard-core model based on a space-time point process of convex particles. Using a purely deterministic algorithm we prove under fairly general assumptions that the…
This paper concerns the long term behaviour of a growth model describing a random sequential allocation of particles on a finite cycle graph. The model can be regarded as a reinforced urn model with graph-based interactions. It is motivated…