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Fractional diffusion limit for collisional kinetic equations:A moments method
Kinetic equations linear Boltzmann equation asymptotic analysis diffusion limit anomalous diffusion limit fractional diffusion relaxation equation anomalous diffusive time scale
2015/10/15
This paper is devoted to hydrodynamic limits of linear kinetic equations. We consider situations in which the thermodynamical equilibrium is described by a heavy-tail distribution function rather than...
Anomalous diffusion limit for kinetic equations with degenerate collision frequency
Anomalous diffusion limit kinetic equations degenerate collision frequency
2015/10/15
This paper is devoted to hydrodynamic limits for collisional linear kinetic equations. It is a classical result that under certain conditions on the collision operator, the long time/small mean free p...
Fractional diffusion limit for collisional kinetic equations:a Hilbert expansion approach
Fractional diffusion limit collisional kinetic equations Hilbert expansion
2015/10/15
We develop a Hilbert expansion approach for the derivation of fractional diffusion equations from the linear Boltzmann equation with heavy tail equilibria.
The omega-limit sets of quadratic Julia sets
omega-limit sets of quadratic Julia sets Dynamical Systems
2012/5/9
In this paper we characterize $\w$-limit sets of dendritic Julia sets for quadratic maps. We use Baldwin's symbolic representation of these spaces as a non-Hausdorff itinerary space and prove that qua...
Fluid Dynamic Limit to the Riemann Solutions of Euler Equations: I. Superposition of rarefaction waves and contact discontinuity
Fluid Dynamic the Riemann Solutions of Euler Equations
2010/11/15
Fluid dynamic limit to compressible Euler equations from compressible Navier-Stokes equations and Boltzmann equation has been an active topic with limited success so far. In this paper, we consider t...
A generalized virial theorem and the balance of kinetic and potential energies in the semiclassical limit
Virial theorem semiclassical limit classically forbidden region
2010/12/1
We obtain two-sided bounds on kinetic and potential energies of a bound state of a quantum particle in the semiclassical limit, as the Planck constant ~ ! 0. Proofs of these results rely on the genera...
Bifurcation of limit cycles from quintic Hamiltonian with a double figure eight loop
动力系统 Conley理论 持续性 周期解 Abel积分
2008/4/25
Hilbert 16 问题的重要意义已是众所周知,但迄今尚未解决。为此，Arnold于1977年提出了弱Hilbert 16 问题，但也未解决。本项目首先研究与该问题有关的课题，讨论了三次和n次扰动的单参数Hamilton系统，得到了Abel积分的零点个数的上界估计。对具不变直线的二次系统极限环的唯一性定理，我们给出了完整的证明。对以柱面为首次积分的空间三次系统，我们得到在每个柱面上至多有三个周期...
A remark on the equivalence of isokinetic and isoenergetic thermostats in the thermodynamic limit
equivalence isokinetic isoenergetic thermostats the thermodynamic limit
2010/11/2
The Gaussian isokinetic and isoenergetic thermostats of Hoover and Evans are formally equivalent as remarked by Gallavotti, Rondoni and Cohen. But outside of equilibrium the fluctuations are uncontro...
