This paper presents a patch-wise low-rank based image denoising method with constrained variational model involving local and nonlocal regularization. On one hand, recent patch-wise methods can be represented as a low-rank matrix approximation problem whose convex relaxation usually depends on nuclear norm minimization (NNM). Here, we extend the NNM to the nonconvex schatten p-norm minimization...

Parameters of Gasser Leutwyler chiral Lagrangian are proved saturated by dynamical quark self energy Σ(k2) in a gauge invariant, nonlocal, dynamical quark model. Much of low-energy QCD can be encoded into a series parameters appearing in a chiral Lagrangian, expanded to some finite order of low energy expansion. Attempts have been made to understand these parameters: it is shown that low lying ...

We describe far-from-equilibrium nonlocal transport in a diffusive superconducting wire with a Zeeman splitting, taking into account different spin relaxation mechanisms. We demonstrate that due to the Zeeman splitting, an injection of current in a superconducting wire creates spin accumulation that can only relax via thermalization. This effect leads to a long-range spin accumulation detectabl...

It is essential to know the space-time structure of the nonlocal vacuum condensates for application to medium energy processes. Using the DysonSchwinger formalism in the rainbow approximation for the quark propagator, we study the nonlocal quark condensate and model forms for the nonperturbative gluon propagator constrained by fits to local condensates and deep inelastic scattering with nucleon...

We propose a new hybrid quasicontinuum model which captures both long and short-wave instabilities of crystal lattices and combines the advantages of weakly nonlocal (gradient) and strongly nonlocal continuum models. To illustrate the idea we consider a simple one-dimensional lattice exhibiting commensurate and incommensurate short-wave instabilities and compute stability limits for the homogen...

Nonlocal gradient operators are basic elements of nonlocal vector calculus that play important roles in nonlocal modeling and analysis. In this work, we extend earlier analysis on nonlocal gradient operators. In particular, we study a nonlocal Dirichlet integral that is given by a quadratic energy functional based on nonlocal gradients. Our main finding, which differs from claims made in previo...

In zonally averaged chemical transport models of the stratosphere, quasi-isentropic mixing is represented by diffusion in latitude. However, it is fairly certain that the real mixing is to some extent nonlocal, so that the diffusive representation is not formally justifiable. This issue is explored from a point of view that combines theory and empiricism. Several models of mixing are described ...

The work introduces a model for reciprocal connections in neural fields by a nonlocal feedback mechanism, while the neural field exhibits nonlocal interactions and intra-areal transmission delays. We study the speed of traveling fronts with respect to the transmission delay, the spatial feedback range, and the feedback delay for general axonal and feedback connectivity kernels. In addition, we ...

We investigate the propagation characteristics of superGaussian beam in highly nonlocal nonlinear media. The optical beam propagation has been modeled by well known nonlocal nonlinear Schrödinger equation. The variational method is employed to find the initial beam propagation parameters and then split step Fourier method is used for numerical simulations. A generalized exact analytical solutio...

A deformation of the wave equation on a two-dimensional black hole is considered as a toy-model for possible gravitational or stringy nonlocal effects. The deformed wave-equation allows for an initial-value problem despite being nonlocal. The singularity present in the classical geometry is resolved by the deformation, so that propagation of a wave-packet can be continued through the classicall...