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We investigate the dynamics of dissipative systems with stochastic forcing and focus in particular on mean-square stability. First we show, under a natural condition on the drift and diffusion, that the stochastic system is mean-square…
Many growth processes lead to intriguing stochastic patterns and complex fractal structures which exhibit local scale invariance properties. Such structures can often be described effectively by space-time trajectories of interacting…
Spontaneous stochasticity is a modern paradigm for turbulent transport at infinite Reynolds numbers. It suggests that tracer particles advected by rough turbulent flows and subject to additional thermal noise, remain non-deterministic in…
We present a phenomenological treatment of diffusion-driven martensitic phase transformations in multi-component crystalline solids that arise from non-convex free energies in mechanical and chemical variables. The treatment describes…
It was discovered recently that frictional granular materials can exhibit an important mechanism for instabilities, i.e the appearance of pairs of complex eigenvalues in their stability matrix. The consequence is an oscillatory exponential…
We show that the structure of the fluctuations close to spinodals and mean-field critical points is qualitatively different than the structure close to non-mean-field critical points. This difference has important implications for many…
The diabatic approach to collective nuclear motion is reformulated in the local-density approximation in order to treat the normal modes of a spherical nuclear droplet analytically. In a first application the adiabatic isoscalar modes are…
This article studies typical dynamics and fluctuations for a slow-fast dynamical system perturbed by a small fractional Brownian noise. Based on an ergodic theorem with explicit rates of convergence, which may be of independent interest, we…
The cloud of cold atoms obtained from a magneto-optical trap is known to exhibit two types of instabilities in the regime of high atomic densities: stochastic instabilities and deterministic instabilities. In the present paper, the…
We develop a general theory dealing with stochastic models for dynamical systems that are governed by various nonlinear, ordinary or partial differential, equations. In particular, we address the problem how flows in the random medium…
In the framework of the time-dependent mean field theory, we solve the Vlasov-Nordheim equation and study the sensitive dependence of this highly non-linear equation on the initial conditions. We find that, when nuclear matter is inside the…
A system of partial differential equations representing stochastic neural fields was recently proposed with the aim of modelling the activity of noisy grid cells when a mammal travels through physical space. The system was rigorously…
The understanding of the statistical properties and of the dynamics of multistable systems is gaining more and more importance in a vast variety of scientific fields. This is especially relevant for the investigation of the tipping points…
We review here the development of the general formalism for the study of fermion propagation in the presence of stochastic media. This formalism allows the systematic derivation of evolution equations for averaged quantities as survival…
The usual Langevin approach to describe systems driven by noise fails to describe the long time behavior of systems with multiple attractors. The solution of the associated linear Fokker-Planck equation is always unique, even though it…
Metastability is an ubiquitous phenomenon in nature, which interests several fields of natural sciences. Its description in the framework of thermodynamics and statistical mechanics has been a taboo for long time since it is a genuine…
We develop mean-field kinetic equations for a lattice gas model of a binary alloy with vacancies (ABv model) in which diffusion takes place by a vacancy mechanism. These equations are applied to the study of phase separation of finite…
This article is concerned with stochastic control problems for backward doubly stochastic differential equations of mean-field type, where the coefficient functions depend on the joint distribution of the state process and the control…
Double-diffusive instabilities are often invoked to explain enhanced transport in stably-stratified fluids. The most-studied natural manifestation of this process, fingering convection, commonly occurs in the ocean's thermocline and…
On the basis of the previously formulated mathematical model of a statistical system with a scalar interaction of fermions and the theory of gravitational-scalar instability of a cosmological model based on a two-component statistical…