Related papers: Multiple regimes of diffusion
We consider high-dimensional estimation problems where the number of parameters diverges with the sample size. General conditions are established for consistency, uniqueness, and asymptotic normality in both unpenalized and penalized…
We examine characteristic properties of deterministic and stochastic diffusion in low-dimensional chaotic dynamical systems. As an example, we consider a periodic array of scatterers defined by a simple chaotic map on the line. Adding…
The diffusion of a particle in a crowded environment typically proceeds through three regimes: for very short times the particle diffuses freely until it collides with an obstacle for the first time, while for very long times diffusion the…
We study the problem of evolution of a density pulse of one-dimensional interacting fermions with a non-linear single-particle spectrum. We show that, despite non-Fermi-liquid nature of the problem, non-equilibrium phenomena can be…
We analyze a simple model of deterministic diffusion. The model consists of a one-dimensional periodic array of scatterers in which point particles move from cell to cell as defined by a piecewise linear map. The microscopic chaotic…
The propagation of an electrostatic wave packet inside a collisionless and initially Maxwellian plasma is always dissipative because of the irreversible acceleration of the electrons by the wave. Then, in the linear regime, the wave packet…
Droplet breakup is important in many natural and industrial processes, but the current classification of breakup regimes, especially the intermediate breakup regime, is ambiguous. In this study, the transitions of breakup regimes for…
We analyze the spreading of wavepackets in two-dimensional quasiperiodic and random tilings as a function of their codimension, i.e. of their topological complexity. In the quasiperiodic case, we show that the diffusion exponent that…
The effects of quenched disorder on a single and many active run-and-tumble particles is studied in one dimension. For a single particle, we consider both the steady-state distribution and the particle's dynamics subject to disorder in…
We prove a central limit theorem for the momentum distribution of a particle undergoing an unbiased spatially periodic random forcing at exponentially distributed times without friction. The start is a linear Boltzmann equation for the…
We consider model of a complex particle that consists of a rigid shell and a nucleus with spatial asymmetric interaction. The particle's dynamics with the nucleus driven by a periodic excitation is considered. It is shown that…
We study a continuum model of overdamped self-propelled particles with an aligning interaction in two dimensions. By combining analytical and numerical work, we map out the phase diagram for generic parameters. We find that the system…
A survey is given on asymptotic diffusion coefficients of particles in lattices with random transition rates. Exact and approximate results for single particles are reviewed. A recent exact expression in $d = 1$ which includes occupation…
We investigate the dynamics of a kicked particle in an infinite square well undergoing frequent measurements of energy. For a large class of periodic kicking force, constant diffusion is found in such a non-KAM system. The influence of…
For a class of particle systems in continuous space with local interactions, we show that the asymptotic diffusion matrix is an infinitely differentiable function of the density of particles. Our method allows us to identify relatively…
We analyze circumstances under which the microscopic dynamics of particles which are driven by a forced, gradient-type flow can be consistently interpreted as a Markovian diffusion process. Special attention is paid to discriminating…
This letter investigates the molecular dynamics of inelastic disks without external forcing. By introducing a new observation frame with a rescaled time, we observe the virtual steady states converted from asymptotic energy dissipation…
We develop several statistical tests of the determinant of the diffusion coefficient of a stochastic differential equation, based on discrete observations on a time interval $[0,T]$ sampled with a time step $\Delta$. Our main contribution…
When the pressure of particles accelerated at shock waves is no longer negligible compared to the kinetic pressure of the gas, the linear theory of diffusive shock acceleration breaks down. This is expected in particular when the shock…
The dynamics of a test particle interacting with diffusing impurities in one dimension is investigated analytically and numerically. In the absence of an applied external force, the dynamics of the particle can be characterized by a…