Related papers: The speed of Arnold diffusion
The self-consistent theory of Anderson localization of quantum particles or classical waves in disordered media is reviewed. After presenting the basic concepts of the theory of Anderson localization in the case of electrons in disordered…
The genericity of Arnold diffusion in the analytic category is an open problem. In this paper, we study this problem in the following a priori unstable Hamiltonian system with a time-periodic perturbation…
In this paper, a generalized Brownian motion model has been applied to describe the relative particle dispersion problem in more realistic turbulent flows. The fluctuating pressure forces acting on a fluid particle are taken to be a colored…
An outline of theoretical estimates is given regarding the dependence of the value of the diffusion coefficient $D$ on the size $R$ of the remainder of the normal form in doubly or simply resonant domains of the action space of 3dof…
When particles/molecules diffuse in systems that contain obstacles, the steady-state regime (during which the mean-square displacement scales linearly with time, $\left< r^2 \right> \sim t$) is preceded by a transient regime. It is common…
This paper presents a methodology and numerical algorithms for constructing accelerated gradient flows on the space of probability distributions. In particular, we extend the recent variational formulation of accelerated gradient methods in…
We study the link between relaxation to the equilibrium and anomalous superdiffusive motion in a classical N-body hamiltonian system with long-range interaction showing a second-order phase-transition in the canonical ensemble. Anomalous…
We study the one-dimensional diffusion process which takes place between two reflecting boundaries and which is acted upon by a time-dependent and spatially-constant force. The assumed force possesses both the harmonically oscillating and…
We provide stability estimates, obtained by implementing the Nekhoroshev theorem, in reference to the orbital motion of a small body (satellite or space debris) around the Earth. We consider a Hamiltonian model, averaged over fast angles,…
We introduce order-based diffusion processes as the solutions to multidimensional stochastic differential equations, with drift coefficient depending only on the ordering of the coordinates of the process and diffusion matrix proportional…
Local integrability of hyperbolic oscillators is discussed to provide an introductory example of the Arnold's diffusion phenomenon in a forced pendulum. This is a text prepared for the the ISI summer school of June 1997 and deals with…
Constraints can affect dramatically the behavior of diffusion processes. Recently, we analyzed a natural and a technological system and reported that they perform diffusion-like discrete steps displaying a peculiar constraint, whereby the…
We consider a diffusion on a bounded domain, assuming that the system is irreducible inside the domain and that the diffusion has varying degree of degeneracy on the domain's boundary. The long-term statistical properties of typical…
Diffusive transport is among the most common phenomena in nature [1]. However, as predicted by Anderson [2], diffusion may break down due to interference. This transition from diffusive transport to localization of waves should occur for…
We survey recent results of normal and anomalous diffusion of two types of random motions with long memory in ${\Bbb R}^d$ or ${\Bbb Z}^d$. The first class consists of random walks on ${\Bbb Z}^d$ in divergence-free random drift field,…
High energy diffraction and soft QCD span exciting final state topologies and fluctuations which have not yet been measured or characterized in a fully exhaustive way. In this work, we go beyond the standard measures and formulate a new…
We consider nearly-integrable Hamiltonian systems defined over a non-resonant domain. In the neighborhood of resonances, we use Nekhoroshev-like estimates to provide effective stability bounds for the action variables over long time. The…
This article includes a short survey of selected averaging and dimension reduction techniques for deterministic fast-slow systems. This survey includes, among others, classical techniques, such as the WKB approximation or the averaging…
Considering a real-valued diffusion, a real-valued reward function and a positive discount rate, we provide an algorithm to solve the optimal stopping problem consisting in finding the optimal expected discounted reward and the optimal…
We consider a family of one-dimensional diffusions, in dynamical Wiener mediums, which are random perturbations of the Ornstein-Uhlenbeck diffusion process. We prove quenched and annealed convergences in distribution and under weighted…