Related papers: Scaling invariance for the diffusion coefficient i…
We consider a two-dimensional Hamiltonian system perturbed by a small diffusion term, whose coefficient is state-dependent and non-degenerate. As a result, the process consists of the fast motion along the level curves and slow motion…
An ubiquitous property of biological sensory systems is adaptation: a step increase in stimulus triggers an initial change in a biochemical or physiological response, followed by a more gradual relaxation toward a basal, pre-stimulus level.…
The Pomeau-Manneville map is a paradigmatic intermittent dynamical system exhibiting weak chaos and anomalous dynamics. In this paper we analyse the parameter dependence of superdiffusion for the map lifted periodically onto the real line.…
We investigate some statistical properties of escaping particles in a billiard system whose boundary is described by two control parameters with a hole on its boundary. Initially, we analyze the survival probability for different hole…
We study the long time behaviour of a nonlinear oscillator subject to a random multiplicative noise with a spectral density (or power-spectrum) that decays as a power law at high frequencies. When the dissipation is negligible, physical…
The irreducible decomposition of successive restriction and induction of irreducible representations of a symmetric group gives rise to a Markov chain on Young diagrams keeping the Plancherel measure invariant. Starting from this Res-Ind…
Using a highly viscous magnetic fluid, the dynamics in the aftermath of the Rosensweig instability can be slowed down by more than 2000 times. In this way we expand the regime where the growth rate is predicted to scale linearly with the…
Using a numerical library for arbitrary precision arithmetic I study the irregular dependence of the diffusion coefficient on the slope of a piecewise linear map defining a dynamical system. I find that the graph of the diffusion…
We discuss a family of time-reversible, scale-invariant diffusions with singular coefficients. In analogy with the standard Gaussian theory, a corresponding family of generalized characteristic functions provides a useful tool for proving…
Deterministic diffusion in temporally oscillating convection is studied for particles with finite mass. The particles are assumed to obey a simple dissipative dynamical system and the particle diffusion is induced by the strange attractor.…
We consider a stochastically perturbed reaction diffusion equation in a bounded interval, with boundary conditions imposing the two stable phases at the endpoints. We investigate the asymptotic behavior of the front separating the two…
We consider the diffusion of independent particles experiencing random accelerations by a space- and time-dependent force as well as viscous damping. This model can exhibit several asymptotic behaviours, depending upon the limiting cases…
The value function of an optimal stopping problem for jump diffusions is known to be a generalized solution of a variational inequality. Assuming that the diffusion component of the process is nondegenerate and a mild assumption on the…
We study dimension theory for dissipative dynamical systems, proving a conditional variational principle for the quotients of Birkhoff averages restricted to the recurrent part of the system. On the other hand, we show that when the whole…
We study a system of particles which jump on the sites of the interval $[1,L]$ of $\mathbb Z$. The density at the boundaries is kept fixed to simulate the action of mass reservoirs. The evolution depends on two parameters $\lambda'\ge 0$…
In this paper, we prove the power-law in time upper bound for the diffusion of a 1D discrete nonlinear Anderson model. We remove completely the decaying condition restricted on the nonlinearity of Bourgain-Wang (Ann. of Math. Stud. 163:…
We consider the long-time behavior of a diffusion process on $\mathbb{R}^d$ advected by a stationary random vector field which is assumed to be divergence-free, dihedrally symmetric in law and have a log-correlated potential. A special case…
The reaction-diffusion processes in a growing domain involves a dilution term that modifies the properties of the homogeneous state that, in contrast to a fixed domain, depends on time. We study how the dilution term changes the steady…
The proper scale decomposition in flows with significant density variations is not as straightforward as in incompressible flows, with many possible ways to define a `length-scale.' A choice can be made according to the so-called…
In this paper, we investigate the long-time behavior of a passive scalar advected by a parallel shear flow in an infinite cylinder with unbounded cross section, in the regime where the viscosity coefficient satisfies $\nu \ll 1$, and in…