Related papers: Linear Stochastic Dyadic model
Discrete multiplicative turbulent cascades are described using a formalism involving infinitely divisible random measures. This permits to consider the continuous limit of a cascade developed on a continuum of scales, and to provide the…
We survey the recent advance in the rigorous qualitative theory of the 2d stochastic Navier-Stokes system that are relevant to the description of turbulence in two-dimensional fluids. After discussing briefly the initial-boundary value…
Inertial particles in turbulent flows are characterised by preferential concentration and segregation and, at sufficient mass loading, dense particle clusters may spontaneously arise due to momentum coupling between the phases. These…
How stochastic, microscopic events generate deterministic, macroscopic properties is a fundamental question in physics. We address this question by developing a quantum master equation model for concentrated radical solutions, where random…
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…
We provide a numerical study of the macroscopic model of [3] derived from an agent-based model for a system of particles interacting through a dynamical network of links. Assuming that the network remodelling process is very fast, the…
We study three classes of continuous time Markov processes (inclusion process, exclusion process, independent walkers) and a family of interacting diffusions (Brownian energy process). For each model we define a boundary driven process…
Impulsive systems are a very flexible class of systems that can be used to represent switched and sampled-data systems. We propose to extend here the previously obtained results on deterministic impulsive systems to the stochastic setting.…
Exact generalized stochastic representation of deterministic interaction between two dynamical (quantum or classical) systems is derived which helps when considering one of them to replace another by equivalent commutative ($c$-number…
The local approach to construct master equation for a composite open system with a weak internal coupling is simple and seems reasonable. However, it is thermodynamic consistent only when the subsystems are resonantly coupled. Efforts are…
Understanding the structural evolution of granular systems is a long-standing problem. A recently proposed theory for such dynamics in two dimensions predicts that steady states of very dense systems satisfy detailed-balance. We analyse…
Synthetic turbulence is a relevant tool to study complex astrophysical and space plasma environments inaccessible by direct simulation. However, conventional models lack intermittent coherent structures, which are essential in realistic…
We investigate the large population dynamics of a family of stochastic particle systems with three-state cyclic individual behaviour and parameter-dependent transition rates. On short time scales, the dynamics turns out to be approximated…
This paper is concerned with the well-posedness and regularity of the distributional solutions for the stochastic acoustic and elastic scattering problems. We show that the regularity of the solutions depends on the regularity of both the…
We examine the existence and uniqueness of invariant measures of a class of stochastic partial differential equations with Gaussian and Poissonian noise and its exponential convergence. This class especially includes a case of stochastic…
A number of simplified dynamical problems is studied in an attempt to clarify some of the mechanisms leading to turbulence and the existing proposals to control this transition. A simplified set of boundary layer equations displays a…
We develop a theory for thermodynamic instabilities of complex fluids composed of many interacting chemical species organised in families. This model includes partially structured and partially random interactions and can be solved exactly…
We investigate the stochastic resonance phenomenon in a physical system based on a tunnel diode. The experimental control parameters are set to allow the control of the frequency and amplitude of the deterministic modulating signal over an…
Motivated by the recent contribution \cite{BB17} we study the scaling limit behavior of a class of one-dimensional stochastic differential equations which has a unique attracting point subject to a small additional repulsive perturbation.…
In [SIAM J. Appl. Dyn. Sys., 12(4):2068--2092, 2013], Widiasih proposed and analyzed a deterministic one-dimensional Budyko-Sellers energy-balance model with a moving ice-line. In this paper, we extend this model to the stochastic setting…