相关论文: Relaxation of the kinematic dynamo equations

We use the methods of commutator and fundamental solutions to establish averaging lemmas and hypoelliptic estimates for purely kinetic transport equations. Assuming certain amount of velocity regularity for solutions, we extend our analysis…

On the basis of physical considerations we propose a one-dimensional discrete lattice model for the density relaxation of granular materials under tapping. Solving the difference equation numerically, we find a logarithmic time-dependence…

General Successive Convex Relaxation Methods (SRCMs) can be used to compute the convex hull of any compact set, in an Euclidean space, described by a system of quadratic inequalities and a compact convex set which is not very complicated.…

Quadratically constrained quadratic programs (QCQPs) are a highly expressive class of nonconvex optimization problems. While QCQPs are NP-hard in general, they admit a natural convex relaxation via the standard semidefinite program (SDP)…

Kinetic approaches, i.e., methods based on the lattice Boltzmann equations, have long been recognized as an appealing alternative for solving incompressible Navier-Stokes equations in computational fluid dynamics. However, such approaches…

Motivated by the motion of biopolymers and membranes in solution, this article presents a formulation of the equations of motion for curves and surfaces in a viscous fluid. We focus on geometrical aspects and simple variational methods for…

The recently-introduced relaxation approach for Runge-Kutta methods can be used to enforce conservation of energy in the integration of Hamiltonian systems. We study the behavior of implicit and explicit relaxation Runge-Kutta methods in…

In this paper a symplectic realization for the Maxwell-Bloch equations with the rotating wave approximation is given, which also leads to a Lagrangian formulation. We show how Lie point symmetries generate a third constant of motion for the…

In this paper, we investigate the similarity solutions for a steady laminar incompressible boundary layer equations governing the Magnetohydrodynamic (MHD) flow near the forward stagnation point of two-dimensional and axisymmetric bodies.…

In this paper, we present convex hull formulations for a mixed-integer, multilinear term/function (MIMF) that features products of multiple continuous and binary variables. We develop two equivalent convex relaxations of an MIMF and study…

Exact relaxation times and eigenfunctions for a simple mechanical model of polymer dynamics are obtained using supersymmetry methods of quantum mechanics. The model includes the finite extensibility of the molecule and does not make use of…

We provide explicit conditions for uniform stability, global asymptotic stability and uniform exponential stability for dynamic equations with a single delay and a nonnegative coefficient. Some examples on nonstandard time scales are also…

A closure for the effective relaxation time of the Boltzmann-BGK kinetic equation for fluid turbulence is presented, based on a double-averaging procedure over both kinetic and turbulent fluctuations. The resulting effective relaxation time…

The aim of this paper is to study, via theoretical analysis and numerical simulations, the dynamics of Whitham and related equations. In particular we establish rigorous bounds between solutions of the Whitham and KdV equations and provide…

We consider polyhedral approximations of strictly convex compacta in finite dimensional Euclidean spaces (such compacta are also uniformly convex). We obtain the best possible estimates for errors of considered approximations in the…

We have studied the approach to equilibrium of islands and pores in two dimensions. The two-regime scenario observed when islands evolve according to a set of particular rules, namely relaxation by steps at low temperature and smooth at…

We analyse the linear response properties of the uniformly heated granular gas. The intensity of the stochastic driving fixes the value of the granular temperature in the non-equilibrium steady state reached by the system. Here, we…

We consider an out-of-equilibrium one-dimensional model for two electrical double-layers. With a combination of exact calculations and Brownian Dynamics simulations, we compute the relaxation time ($\tau$) for an electroneutral salt-free…

Upon quenching the forcing, a turbulent system tends to attain the state of stable equilibrium through the process of turbulent relaxation. Such relaxation in binary fluids is of surmount interest for both fundamental science understanding…

The relaxation rates to the invariant density in the chaotic phase space component of the kicked rotor (standard map) are calculated analytically for a large stochasticity parameter, $K$. These rates are the logarithms of the poles of the…