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This paper investigates the principal spectral theory and the asymptotic behavior of the principal spectrum point for a class of time-periodic cooperative systems with nonlocal dispersal operators, incorporating both coupled and uncoupled…
Elliptic flow of the hot, dense system which has been created in nucleus-nucleus collisions develops as a response to the initial azimuthal asymmetry of the reaction region. Here it is suggested that the magnitude of this response shows a…
The diffusion behavior of particles moving in complex heterogeneous environment is a very topical issue. We characterize particle's trajectory via an underdamped Langevin system driven by a Gaussian white noise with a time dependent…
We study the large time behavior of the sublinear viscosity solution to a singular Hamilton-Jacobi equation that appears in a critical Coagulation-Fragmentation model with multiplicative coagulation and constant fragmentation kernels. Our…
We introduce a model of interacting Random Walk, whose hopping amplitude depends on the number of walkers/particles on the link. The mesoscopic counterpart of such a microscopic dynamics is a diffusing system whose diffusivity depends on…
We study the qualitative homogenization of second order viscous Hamilton-Jacobi equations in space-time stationary ergodic random environments. Assuming that the Hamiltonian is convex and superquadratic in the momentum variable (gradient)…
We study the planar front solution for a class of reaction diffusion equations in multidimensional space in the case when the essential spectrum of the linearization in the direction of the front touches the imaginary axis. At the linear…
Nonreciprocity, a hallmark of nonequilibrium systems, can generate dynamics not possible near thermodynamic equilibrium, including oscillatory and rotating patterns. The onset of temporal oscillations is often evident in linearized…
We study the dynamics of periodic wave trains in reaction-diffusion systems on the real line under large, fully nonlocalized modulations. We prove that solutions with nearby initial data converge, at an enhanced diffusive rate, to a…
We develop an efficient method to calculate probabilities of large deviations from the typical behavior (rare events) in reaction--diffusion systems. The method is based on a semiclassical treatment of underlying "quantum" Hamiltonian,…
We study the spatio-temporal dynamics of a model of polar active fluid in two dimensions. The system exhibits a transition from an isotropic to a polarized state as a function of density. The uniform polarized state is, however, unstable…
In the framework of irreversible thermodynamics, we study autonomous systems of reaction-diffusion equations to show how the entropy and free energy of an open and irreversible reactor depend on concentrations. To do this, we find a…
We studied the self-diffusion of colloidal ellipsoids in a monolayer near a flat wall by video microscopy. The image processing algorithm can track the positions and orientations of ellipsoids with sub-pixel resolution. The translational…
The behavior of the self diffusion constant of Langevin particles interacting via a pairwise interaction is considered. The diffusion constant is calculated approximately within a perturbation theory in the potential strength about the bare…
We study the discrete nonlinear Schr\"oinger equation with weak disorder, focusing on the regime when the nonlinearity is, on the one hand, weak enough for the normal modes of the linear problem to remain well resolved, but on the other,…
While the energy-dependent neutron diffusion equation is widely employed in nuclear engineering, its status as an approximation to the transport equation is not yet completely understood, and several different approximations are in use to…
Asymptotic concentration behaviors of linear combinations of weight distributions on the random linear code ensemble are presented. Many important properties of a binary linear code can be expressed as the form of a linear combination of…
A reaction-kinetic model for a two-species gas mixture undergoing pair generation and recombination reactions is considered on a flat torus. For dominant scattering with a non-moving constant-temperature background the macroscopic limit to…
A class of parabolic-parabolic Keller-Segel systems with degenerate diffusion and volume filling is studied in a bounded domain subject to no-flux boundary conditions. The equations are derived from a multiphase fluid model. The interplay…
Inspired by one--dimensional light--particle systems, the dynamics of a non-Hamiltonian system with long--range forces is investigated. While the molecular dynamics does not reach an equilibrium state, it may be approximated in the…