Related papers: Anomalous diffusion for a class of systems with tw…
We consider a hyperbolic system of three conservation laws in one space variable. The system is a model for fluid flow allowing phase transitions; in this case the state variables are the specific volume, the velocity and the mass density…
Given a first-order nonlinear hyperbolic system of conservation laws endowed with a convex entropy-entropy flux pair, we can consider the class of weak solutions containing shock waves depending upon some small scale parameters. In this…
Energy transport can be influenced by the presence of other conserved quantities. We consider here diffusive systems where energy and the other conserved quantities evolve macroscopically on the same diffusive space-time scale. In these…
We show analytically that there is anomalous diffusion when the diffusion constant depends on the concentration as a power law with a positive exponent or a negative exponent with absolute value less than one and the initial condition is a…
We introduce a class of interacting fermionic quantum models in $d$ dimensions with nodal interactions that exhibit superdiffusive transport. We establish non-perturbatively that the nodal structure of the interactions gives rise to…
In this paper, we consider a stochastic model of incompressible non-Newtonian fluids of second grade on a bounded domain of $\mathbb{R}^2$ with multiplicative noise. We first show that the solutions to the stochastic equations of second…
We study diffusion of colloids on a fluid-fluid interface using particle simulations and fluctuating hydrodynamics. Diffusion on a two-dimensional interface with three-dimensional hydrodynamics is known to be anomalous, with the collective…
We investigate a hydrodynamic system of Navier--Stokes/Cahn--Hilliard type, which describes the motion of a two-phase flow of two incompressible fluids with unmatched densities coupled with a soluble chemical species. Derived from Onsager's…
Diffusion in an evolving environment is studied by continuos-time Monte Carlo simulations. Diffusion is modelled by continuos-time random walkers on a lattice, in a dynamic environment provided by bubbles between two one-dimensional…
Non-interferometric experiments have been successfully employed to constrain models of spontaneous wave function collapse, which predict a violation of the quantum superposition principle for large systems. These experiments are grounded on…
We present the derivation of the hydrodynamic limit under Eulerian scaling for a general class of one-dimensional interacting particle systems with two or more conservation laws. Following Yau's relative entropy method it turns out that in…
Many approaches to modelling reaction-diffusion systems with anomalous transport rely on deterministic equations and ignore fluctuations arising due to finite particle numbers. Starting from an individual-based model we use a…
A stochastic version of an inviscid dyadic model of turbulence, with multiplicative noise, is proved to exhibit energy dissipation in spite of the formal energy conservation. As a consequence, global regular solutions cannot exist. After…
Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…
This paper presents an {\it ab initio} derivation of the expression given by irreversible thermodynamics for the rate of entropy production for different classes of diffusive processes. The first class are Lorentz gases, where…
Diffusion models do not recover semantic structure uniformly over time. Instead, samples transition from semantic ambiguity to class commitment within a narrow regime. Recent theoretical work attributes this transition to dynamical…
In studies of interfaces with dynamic chemical composition, bulk and interfacial quantities coupled via surface conservation laws of excess surface quantities. While this approach is for microscopically sharp interfaces, its applicability…
Flow networks can describe many natural and artificial systems. We present a model for a flow system that allows for volume accumulation, includes conduits with a non-linear relation between current and pressure difference, and can be…
A continuum model for self-organized dynamics is numerically investigated. The model describes systems of particles subject to alignment interaction and short-range repulsion. It consists of a non-conservative hyperbolic system for the…
We demonstrate that hyperuniformity, the suppression of density fluctuations at large length scales, emerges generically from the interplay between conservation laws and non-equilibrium driving. The underlying mechanism for this emergence…