We model pacemaker effects of an algebraically localized heterogeneity in a 1 dimensional array of oscillators with nonlocal coupling. We assume the oscillators obey simple phase dynamics and that the array is large enough so that it can be approximated by a continuous nonlocal evolution equation. We concentrate on the case of heterogeneities with positive average and show that steady solutions...

We compare two models describing the dynamics of phase separation of incompressible mixtures: A local model proposed by de Gennes, and a nonlocal model proposed by E and Palffy-Muhoray. We find that in the interfacial regime, the local model gives rise to interfacial motion via the Mullins-Sekerka law for moderate quenches, and surface diffusion for deep quenches. The interface dynamics is slow...

We wish to recover an image corrupted by blur and Gaussian or impulse noise, in a variational framework. We use two data-fidelity terms depending on the noise, and several local and nonlocal regularizers. Inspired by Buades-Coll-Morel, Gilboa-Osher, and other nonlocal models, we propose nonlocal versions of the Ambrosio-Tortorelli and Shah approximations to Mumford-Shah-like regularizing functi...

Bell's theorem guarantees that no model based on local variables can reproduce quantum correlations. Also, some models based on nonlocal variables, if subject to apparently "reasonable" constraints, may fail to reproduce quantum physics. In this Letter, we introduce a family of inequalities, which use a finite number of measurement settings, and which therefore allow testing Leggett's nonlocal ...

A polyadic dynamic logic is introduced in which a model-theoretic version of nonlocal multicomponent tree-adjoining grammar can be formulated. It is shown to have a low polynomial time model checking procedure. This means that treebanks for nonlocal MCTAG, incl. all weaker extensions of TAG, can be efficiently corrected and queried. Our result is extended to HPSG treebanks (with some qualificat...

The classical phase-field model represents a coupling of an Allen-Cahn type nonlinear equation with a standard diffusion equation and has been proposed to describe uniform phase separation in a pure substance. This research considers an extension of that model which incorporates a more accurate approximation to the diffuse interface between states of matter through the use of a nonlocal operato...

Biological aggregations such as insect swarms and bird flocks may arise from a combination of social interactions and environmental cues. We focus on nonlocal continuum equations, which are often used to model aggregations, and yet which pose significant analytical and computational challenges. Beginning with a particular nonlocal aggregation model [Topaz et al., Bull. Math. Bio., 2006], we der...

We compare two models describing the dynamics of phase separation of incompressible mixtures: A local model proposed by de Gennes, and a nonlocal model proposed by E and Pally-Muhoray. We nd that in the interfacial regime, the local model gives rise to interfacial motion via the Mullins-Sekerka law for moderate quenches, and surface diiusion for deep quenches. The interface dynamics is slowed d...