相关论文: Local amplitude equation from non-local dynamics
The classical equations of irrotational water waves have recently been reformulated as a system of two equations, one of which is an explicit non-local equation for the wave height and for the velocity potential evaluated on the free…
In this work we study a general shape optimization problem where the state equation is given in terms of a nonlocal operator. Examples of the problems considered are monotone combinations of fractional eigenvalues. Moreover, we also analyze…
A novel model of incompressible magnetohydrodynamic turbulence in the presence of a strong external magnetic field is proposed for explanation of recent numerical results. According to the proposed model, in the presence of the strong…
Direct comparison is made of the steady-sates and coarsening dynamics in a local system and its nonlocal generalization. The example system is the surface of a solid film in a strong electric field; the morphological evolution of the…
Non-local reaction-diffusion partial differential equations (PDEs) involving the fractional Laplacian have arisen in a wide variety of applications. One common tool to analyse the dynamics of classical local PDEs near instability is to…
Amplitude equations are used to describe the onset of instability in wide classes of partial differential equations (PDEs). One goal of the field is to determine simple universal/generic PDEs, to which many other classes of equations can be…
We present a systematic approach to deriving normal forms and related amplitude equations for flows and discrete dynamics on the center manifold of a dynamical system at local bifurcations and unfoldings of these. We derive a general,…
Among hyperbolic Initial Boundary Value Problems (IBVP), those coming from a variational principle 'generically' admit linear surface waves, as was shown by Serre [J. Funct. Anal. 2006]. At the weakly nonlinear level, the behavior of…
We report on three-dimensional direct numerical simulation of wave turbulence on the free surface of a magnetic fluid subjected to an external horizontal magnetic field. A transition from capillarywave turbulence to anisotropic…
Aim of the paper is to study non-local dynamic boundary conditions of reactive-diffusive type for the Laplace equation from analytic and probabilistic point of view. In particular, we provide compact and probabilistic representation of the…
We present a local Master equation for open system dynamics in two forms: Markovian and non-Markovian. Both have a wider range of validity than the Lindblad equation investigated by Davies. For low temperatures, they do not require coupling…
When canonical Hamiltonians of local quantum field theories are transformed using a renormalization group procedure for effective particles, the resulting interaction terms are non-local. The range of their non-locality depends on the…
The nonlinear amplitude modulation of known electrostatic plasma modes is examined in a generic manner, by applying a collisionless fluid model. Both cold (zero-temperature) and warm fluid descriptions are discussed and the results are…
Filled rubber-like materials are widely used in engineering applications and are well known to exhibit the Mullins effect. In this work, an established local constitutive model from the literature is extended to a non-local setting to…
The apparent nonlocality of the Coulomb gauge external field problem in electrodynamics is illustrated with an example in which nonlocality is especially striking. Explanation of this apparent nonlocal behaviour based on a purely local…
This work is devoted to the study of non-Newtonian fluids of grade three on two-dimensional and three-dimensional bounded domains, driven by a nonlinear multiplicative Wiener noise. More precisely, we establish the existence and uniqueness…
In this paper a general approach to reconstruct three dimensional field solutions in particle accelerator magnets from distributed magnetic measurements is presented. To exploit the locality of the measurement operation a special…
In this paper the local regularity of the Hilbert transform is considered, and local smoothness and real analyticity results are obtained.
A closed system of the equations for the local Bloch vectors and spin correlation functions is obtained by decomplexification of the Liouville-von Neumann equation for three magnetic qubits with the exchange interaction, that takes place in…
The Rosensweig instability has a special character among the frequently discussed instabilities. One distinct property is the necessary presence of a deformable surface, and another very important fact is, that the driving force acts purely…