相关论文: Local amplitude equation from non-local dynamics

We study locking of the modulation frequency of a relative periodic orbit in a general $S^1$-equivariant system of ordinary differential equations under an external forcing of modulated wave type. Our main result describes the shape of the…

In this paper we study an aggregation equation with a general nonlocal flux. We study the local well-posedness and some conditions ensuring global existence. We are also interested in the differences arising when the nonlinearity in the…

A closed system of equations for the local Bloch vectors and spin correlation functions of three magnetic qudits, which are in an arbitrary, time-dependent, external magnetic field, is obtained using decomplexification of the Liouville-von…

We prove the local well-posedness for a nonlinear equation modeling the evolution of the free surface for waves of moderate amplitude in the shallow water regime.

We study how periodicity manifestations recently found in the turbulent globall coupled maps depend on the global feature of the couplings. We examine three non-locally coupled map models. In the first two, the all-to-all interaction is…

We prove an abstract compactness result for gradient flow lines of a non-local unregularized gradient flow equation on a scale Hilbert space. This is the first step towards Floer theory on scale Hilbert spaces.

A dynamical generalisation of the nonlocal coherent-potential approximation is derived based upon the functional integral approach to the interacting electron problem. The free energy is proven to be variational with respect to the…

The nonlinear dynamics of the free surface of an ideal dielectric liquid in a strong electric field is studied. The equation for the evolution of surface electrohydrodynamic waves is derived in the approximation of small surface-slope…

We consider an abstract second order linear equation with a strong dissipation, namely a friction term which depends on a power of the "elastic" operator. In the homogeneous case, we investigate the phase spaces in which the initial value…

A three dimensional small deformation theory is developed to examine the motion of a magnetic droplet in a uniform rotating magnetic field. The equations describing the droplet's shape evolution are derived using two different approaches -…

An essential property of magnetic devices is the relaxation rate in magnetic switching which depends strongly on the damping in the magnetisation dynamics. It was recently measured that damping depends on the magnetic texture and,…

In this short note, we derive a system of two nonlocal equations for the water-wave problem following the work of [AFM06]. Specifically, we consider a fluid with a one-dimensional free surface for an irrotational fluid both with, and…

We prove an explicit, non-local hydrodynamic closure for the linear one-dimensional kinetic equation independent on the size of the relaxation time. We compare this dynamical equation to the local approximations obtained from the…

The formation of local magnetic moments and its size effect in one- and three-dimension finite systems with magnetic impurity are investigated based on the Anderson hybridizing model in real space. By the exact diagonalization within the…

This paper addresses a wave equation on a exterior domain in R^{d}(d odd) with nonlinear time dependent dissipation. Under a microlocal geometric condition we prove that the decay rates of the local energy functional are obtained by solving…

In this paper, we study the long-time dynamics for the wave equation with nonlocal weak damping and sup-cubic nonlinearity in a bounded smooth domain of $\mathbb{R}^3.$ Based on the Strichartz estimates for the case of bounded domains, we…

We derive a general closed expression for the local pressure exerted onto the corrugated walls of a channel confining a fluid medium. When the fluid medium is at equilibrium the local pressure is a functional of the shape of the walls. It…

We derive amplitude equations for interface dynamics in pattern forming systems with long-range interactions. The basic condition for the applicability of the method developed here is that the bulk equations are linear and solvable by…

We study the model of a noninteracting spinless electron gas confined to the two-dimensional localized surface of a cone in the presence of external magnetic fields. The localized region is characterized by an annular radial potential. We…

Calculating by analytical theory the deformation of finite-sized elastic bodies in response to internally applied forces is a challenge. Here, we derive explicit analytical expressions for the amplitudes of modes of surface deformation of a…