Related papers: Static large deviations for a reaction-diffusion m…
We present analytical expressions for the time-dependent and stationary probability distributions corresponding to a stochastically perturbed one-dimensional flow with critical points, in two physically relevant situations: delayed…
A calculational approach in fluid turbulence is presented. Use is made of the attracting nature of the fluid-dynamic dynamical system. An approach is offered that effectively propagates the statistics in time. Loss of sensitivity to an…
We consider a system of reaction-diffusion equations in a bounded interval of the real line, with emphasis on the metastable dynamics, whereby the time-dependent solution approaches the steady state in an asymptotically exponentially long…
We study the hydrodynamic limit for a model of symmetric exclusion processes with heavy-tailed long jumps and in contact with infinitely extended reservoirs. We show how the corresponding hydrodynamic equations are affected by the…
This work deals with two problems arising in mathematical ecology. The first problem is concerned with diploid branching particle models and its behavior when rapid stirring is added to the interaction. The particle models involve two types…
We investigate the convergence, in the small mass limit, of the stationary solutions of a class of stochastic damped wave equations, where the friction coefficient depends on the state and the noisy perturbation if of multiplicative type.…
Despite its conceptual and practical importance, the rigorous derivation of the steady incompressible Navier-Stokes-Fourier system from the Boltzmann theory has been {an} outstanding {open problem} for general domains in 3D. We settle this…
We consider a class of generalized long-range exclusion processes evolving either on $\mathbb Z$ or on a finite lattice with an open boundary. The jump rates are given in terms of a general kernel depending on both the departure and…
We consider the one-dimensional totally asymmetric simple exclusion process (TASEP) with position-dependent hopping rates. The problem is solved,in a mean field/adiabatic approximation, for a general (smooth) form of spatial rate variation.…
Diffusion with stochastic resetting, instantaneous returns of a diffusing particle to a reference point, creates a stationary probability distribution. The paradigm is extended here to a doubly stochastic protocol in which the resetting…
We analyze the stability of stationary solutions of a singular Vlasov type hydrodynamic equation (HE). This equation was derived (under suitable assumptions) as the hydrodynamical scaling limit of the Hamiltonian evolution of a system…
We study a class of random processes on $N$ particles which can be interpreted as stochastic model of luminescence. Each particle can stay in one of two states: Excited state or ground state. Any particle at ground state is excited with a…
The selection of an equilibrium state by maximising the entropy of a system, subject to certain constraints, is often powerfully motivated as an exercise in logical inference, a procedure where conclusions are reached on the basis of…
Physically motivated stochastic dynamics are often used to sample from high-dimensional distributions. However such dynamics often get stuck in specific regions of their state space and mix very slowly to the desired stationary state. This…
The linear hydrodynamic stability of a model for confined quasi-two-dimensional granular gases is analyzed. The system exhibits homogeneous hydrodynamics, i.e. there are macroscopic evolution equations for homogeneous states. The stability…
We study the asymptotic behaviour of scaling solutions with a dissipative fluid and we show that, contrary to recent claims, the existence of stable accelerating attractor solution which solves the `energy' coincidence problem depends…
We analyse a dynamic control problem for scalar reaction-diffusion equations, focusing on the emulation of pattern formation through the selection of appropriate active controls. While boundary controls alone prove inadequate for…
We study two problems. First, we consider the large deviation behavior of empirical measures of certain diffusion processes as, simultaneously, the time horizon becomes large and noise becomes vanishingly small. The law of large numbers…
A driven diffusive model of three types of particles that exhibits phase separation on a ring is introduced. The dynamics is local and comprises nearest neighbor exchanges that conserve each of the three species. For the case in which the…
A reaction--diffusion replicator equation is studied. A novel method to apply the principle of global regulation is used to write down the model with explicit spatial structure. Properties of stationary solutions together with their…