Related papers: Anomalous diffusion for a class of systems with tw…
We consider the hydrodynamic behavior of some conservative particle systems with degenerate jump rates without exclusive constraints. More precisely, we study the particle systems without restrictions on the total number of particles per…
We consider stationary stochastic dynamical systems evolving on a compact metric space, by perturbing a deterministic dynamics with a random noise, added according to an arbitrary probabilistic distribution. We prove the maximal and…
This article proposes a highly accurate and conservative method for hyperbolic systems using the finite volume approach. This innovative scheme constructs the intermediate states at the interfaces of the control volumes using the method of…
Hydrodynamic noise is the Gaussian process that emerges at larges scales of space and time in many-body systems. It is justified by the central limit theorem, and represents degrees of freedom forgotten when projecting coarse-grained…
We consider relativistic hydrodynamics in the limit where the number of spatial dimensions is very large. We show that under certain restrictions, the resulting equations of motion simplify significantly. Holographic theories in a large…
We analyze a diffuse interface model for multi-phase flows of $N$ incompressible, viscous Newtonian fluids with different densities. In the case of a bounded and sufficiently smooth domain existence of weak solutions in two and three space…
We study dynamics of a locally conserved energy in ergodic, local many-body quantum systems on a lattice with no additional symmetry. The resulting dynamics is well approximated by a coarse grained, classical linear functional diffusion…
In this work we study a degenerate pseudo-parabolic system with cross diffusion describing the evolution of the densities of an unsaturated two-phase flow mixture with dynamic capillary pressure in porous medium with saturation-dependent…
Although one-dimensional systems that exhibit translational symmetry are generally believed to exhibit anomalous heat transport, previous work has shown that the model of coupled rotators on a one-dimensional lattice constitute a possible…
We show that the one-dimensional (1D) two-fluid model (TFM) for stratified flow in channels and pipes (in its incompressible, isothermal form) satisfies an energy conservation equation, which arises naturally from the mass and momentum…
Anomalous diffusion is predicted for Brownian particles in inhomogeneous viscosity landscapes by means of scaling arguments, which are substantiated through numerical simulations. Analytical solutions of the related Fokker-Planck equation…
We introduce a schematic non-linear diffusion model where density fluctuations induce a rich out of equilibrium dynamics. The properties of the model are studied by numerical simulations and analytically in a mean field approximation. At…
We consider solutions of two-dimensional $m \times m$ systems hyperbolic conservation laws that are constant in time and along rays starting at the origin. The solutions are assumed to be small $L^\infty$ perturbations of a constant state…
We present counter-intuitive examples of a viscous regularizations of a two-dimensional strictly hyperbolic system of conservation laws. The regularizations are obtained using two different viscosity matrices. While for both of the…
In finite-dimensional dynamical systems, stochastic stability provides the selection of physical relevant measures from the myriad invariant measures of conservative systems. That this might also apply to infinite-dimensional systems is the…
The effect of a change of noise amplitudes in overdamped diffusive systems is linked to their unperturbed behavior by means of a nonequilibrium fluctuation-response relation. This formula holds also for systems with state-independent…
Two-dimensional turbulent flows, and to some extent, geophysical flows, are systems with a large number of degrees of freedom, which, albeit fluctuating, exhibit some degree of organization: coherent structures emerge spontaneously at large…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
The evolution equations of anomalous magnetohydrodynamics are derived in the extreme relativistic regime and contrasted with the treatment of hydromagnetic nonlinearities pioneered by Lichnerowicz in the absence of anomalous currents. In…
We consider an unpinned chain of harmonic oscillators with periodic boundary conditions, whose dynamics is perturbed by a random flip of the sign of the velocities. The dynamics conserves the total volume (or elongation) and the total…