相关论文: Quasinonlocal coupling of nonlocal diffusions

For a class of interacting particle systems in continuous space, we show that finite-volume approximations of the bulk diffusion matrix converge at an algebraic rate. The models we consider are reversible with respect to the Poisson…

This study investigates chaotic diffusion in multi-scale turbulence driven by nonlinear wave-particle resonance coupling. Turbulent waves with distinct characteristic wavelengths across scales coherently interact with charged particles when…

Franson-type nonlocal quantum correlation based on the particle nature of quantum mechanics has been intensively studied for both fundamental physics and potential applications of quantum key distribution between remotely separated parties…

We analyze the effect of adding a weak, localized, inhomogeneity to a two dimensional array of oscillators with nonlocal coupling. We propose and also justify a model for the phase dynamics in this system. Our model is a generalization of a…

Coupled mode theory (CMT) is a powerful framework for decomposing interactions between electromagnetic waves and scattering bodies into resonances and their couplings with power-carrying channels. It has widespread use in few-resonance,…

We develop a framework for localized source detection in dynamical systems governed by nonlinear partial differential equations based on first and second-order sensitivity analysis. Building on the standard adjoint formulation, which…

A space fractional diffusion-like equation is introduced, which embodies the nonlocality in time, represented by the memory kernel and the non-locality in space. A specific example of the nonlocal term is considered in combination with…

We consider models of open quantum spin systems with irreversible dynamics and show that general quasi-locality results for long-range models, e.g. as proven for the Heisenberg dynamics associated to quantum systems in [27], naturally…

We develop a direct Lyapunov method for the almost sure open-loop stabilizability and asymptotic stabilizability of controlled degenerate diffusion processes. The infinitesimal decrease condition for a Lyapunov function is a new form of…

We are concerned with fully-discrete schemes for the numerical approximation of diffusive-dispersive hyperbolic conservation laws with a discontinuous flux function in one-space dimension. More precisely, we show the convergence of…

This paper proposes a novel reaction-diffusion system approximation tailored for singular diffusion problems, typified by the fast diffusion equation. While such approximation methods have been successfully applied to degenerate parabolic…

Quantum nonlocality, pioneered in Bell's seminal work and subsequently verified through a series of experiments, has drawn substantial attention due to its practical applications in various protocols. Evaluating and comparing the extent of…

For some spatially nonlocal diffusion models with a finite range of nonlocal interactions measured by a positive parameter $\delta$, we review their formulation defined on a bounded domain subject to various conditions that correspond to…

Conventional phase-field models often drive solid-solid interfaces to coalesce when in close proximity. This feature limits their use for processes like diffusion bonding, where the interfaces might need to remain distinct under certain…

Bell's theorem shows that local measurements on entangled states give rise to correlations incompatible with local hidden variable models. The degree of quantum nonlocality is not maximal though, as there are even more nonlocal theories…

We investigate superdiffusion for stochastic processes generated by nonuniformly hyperbolic system models, in terms of the convergence of rescaled distributions to the normal distribution following the abnormal central limit theorem, which…

We present a Petrov-Gelerkin (PG) method for a class of nonlocal convection-dominated diffusion problems. There are two main ingredients in our approach. First, we define the norm on the test space as induced by the trial space norm, i.e.,…

We present an approach to handle Dirichlet type nonlocal boundary conditions for nonlocal diffusion models with a finite range of nonlocal interactions. Our approach utilizes a linear extrapolation of prescribed boundary data. A novelty is,…

We consider a problem of optimal distribution of conductivities in a system governed by a non-local diffusion law. The problem stems from applications in optimal design and more specifically topology optimization. We propose a novel…

We consider a nonlinear microcavity separating a waveguide channel into two parts so as the coupling between them is possible only due to the resonant properties of the microcavity. We provide a rigorous derivation of the equations used in…