We introduce the nonlocal Cattaneo-Vernotte equation by including a relaxation effect in the nonlocal diffusion equation, both of which are models for anomalous diffusion. This equation has two different interpretations: as a generalization of Fick’s first law in terms of a nonlocal flux and memory kernel and as an equation arising from the generalized master equation for a continuous time rand...

This is a study of a class of nonlocal nonlinear diffusion equations (NNDEs). We present several new qualitative results for nonlocal Dirichlet problems. It is shown that solutions with positive initial data remain positive through time, even for nonlinear problems; in addition, we prove that solutions to these equations obey a strong maximum principle. A striking result shows that nonlocal sol...

Prediction of Peierls stress associated with dislocation glide is of fundamental concern in understanding and designing the plasticity and mechanical properties of crystalline materials. Here, we develop a nonlocal semi-discrete variational Peierls-Nabarro (SVPN) model by incorporating the nonlocal atomic interactions into the semi-discrete variational Peierls framework. The nonlocal kernel is ...

We investigate the effects of hydrodynamic nonlocal response in hyperbolic metamaterials (HMMs), focusing on the experimentally realizable parameter regime where unit cells are much smaller than an optical wavelength but much larger than the wavelengths of the longitudinal pressure waves of the free-electron plasma in the metal constituents. We derive the nonlocal corrections to the effective m...

Orbital-free density-functional theory (OF-DFT) with modern kinetic-energy density functionals (KEDFs) is a linear scaling technique that accurately describes nearly-free-electron-like (main group) metals. In an attempt towards extending OF-DFT to transition metals, here we consider whether OF-DFT can be used effectively to study Ag, a metal with a localized d shell. OF-DFT has two approximatio...

A key challenge to planning in multiagent systems is to deal with uncertainty related to coordination, which means to manage the interdependencies between agent activities. Typically, a decentralized agent has only partial knowledge of the system and must deal with nondeterministic outcomes of both local and nonlocal actions. While there are many multiagent planning approaches, the issue of unc...

In this article, the thermoelastic interactions in an isotropic and homogeneous semi-infinite medium with variable thermal conductivity caused by an ultra-short pulsed laser heating based on the linear nonlocal theory of elasticity has been considered. We consider that the thermal conductivity of the material is dependent on the temperature. The surface of the surrounding plane of the medium is...

abstract: in this paper, nonlocal euler–bernoulli beam theory is employed for transverse vibration analysis of an initially pre-stressed size-dependent rotating nanotube. the nonlocal eringen theory takes into account the effect of small size, which enables the present model to become effective in the analysis and design of nanosensors and nanoactuators. governing equations are derived through ...

We show that standard nonlocal boxes, also known as PopescuRohrlich machines, are not sufficient to simulate any nonlocal correlations that do not allow signalling. This was known in the multipartite scenario, but we extend the result to the bipartite case. We then generalize this result further by showing that no finite set containing any finite-output-alphabet nonlocal boxes can be a universa...

In this paper, nonlocal mathematical morphology operators are introduced as a natural extension of nonlocal-means in the max-plus algebra. Firstly, we show that nonlocal morphology is a particular case of adaptive morphology. Secondly, we present the necessary properties to have algebraic properties on the associated pair of transformations. Finally, we recommend a sparse version to introduce a...