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We investigate the long term behavior in terms of global attractors, as time goes to infinity, of solutions to a continuum model for biological aggregations in which individuals experience long-range social attraction and short range…
Spatial and temporal pattern formation in reaction-diffusion systems is typically studied with two or more equations, as scalar reaction-diffusion equations confined to convex domains do not admit stable inhomogeneous states in time or…
We introduce a simple spherical model whose structural properties are similar to the ones generated by models with directional interactions, by employing a binary mixture of large and small hard spheres, with a square-well attraction acting…
We investigate the emergent interactions between two active Brownian particles coupled by an attractive harmonic potential and in contact with a thermal reservoir. By analyzing the stationary distribution of their separation, we demonstrate…
In the current work we consider the numerical solutions of equations of stationary states for a general class of the spatial segregation of reaction-diffusion systems with $m\geq 2$ population densities. We introduce a discrete multi-phase…
We obtain a Liouville property for stationary diffusions in random environment which are small, isotropic perturbations of Brownian motion in spacial dimension greater than two. Precisely, we prove that, on a subset of full probability, the…
We consider a system of q diffusing particle species A_1,A_2,...,A_q that are all equivalent under a symmetry operation. Pairs of particles may annihilate according to A_i + A_j -> 0 with reaction rates k_{ij} that respect the symmetry, and…
We consider an aggregation model for two interacting species. The coupling between the species is via their velocities, that incorporate self- and cross-interactions. Our main interest is categorizing the possible steady states of the…
We investigate the behavior of identical dipolar fermions with aligned dipole moments in two-dimensional multilayers at zero temperature. We consider density instabilities that are driven by the attractive part of the dipolar interaction…
We consider particle systems that are perturbations of the voter model and show that when space and time are rescaled the system converges to a solution of a reaction diffusion equation in dimensions $d \ge 3$. Combining this result with…
We propose a model for demixing of two species by assuming a density-dependent effective diffusion coefficient of the particles. Both sorts of microswimmers diffuse as active overdamped Brownian particles with a noise intensity that is…
We consider an interacting particle system with two species under strong competition dynamics between the two species. Then, through the hydrodynamic limit procedure for the microscopic model, we derive a one-phase Stefan type free boundary…
Various biological cells secrete diffusing chemical compounds into their environment for communication purposes. Secretion usually takes place over the cell membrane in a spatially heterogeneous manner. Mathematical models of these…
We are concerned with the persistence of both predator and prey in a diffusive predator-prey system with a climate change effect, which is modeled by a spatial-temporal heterogeneity depending on a moving variable. Moreover, we consider…
We consider fluids where the attractive interaction at distances slightly larger than the particle size is dominated at larger distances by a repulsive contribution. A previous investigation of the effects of the competition between…
The microscopic structure and movement of reaction fronts in reaction diffusion systems far from equilibrium are investigated. We show that some three-site interaction models exhibit exact diffusive shock measures, i.e. domains of different…
The persistence of biodiversity of species is a challenging proposition in ecological communities in the face of Darwinian selection. The present article investigates beyond the pairwise competitive interactions and provides a novel…
Hydrodynamic systems arising in swarming modelling include nonlocal forces in the form of attractive-repulsive potentials as well as pressure terms modelling strong local repulsion. We focus on the case where there is a balance between…
The main objective of this article is to study the order-disorder phase transition and pattern formation for systems with long-range repulsive interactions. The main focus is on the Cahn-Hilliard model with a nonlocal term in the…
We analyze free energy functionals for macroscopic models of multi-agent systems interacting via pairwise attractive forces and localized repulsion. The repulsion at the level of the continuous description is modeled by pressure-related…