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...

We study a nonlocal evolution equation generalising model introduced by Shigeru Kondo to explain colour patterns on skin of guppy fish. prove the existence stationary solutions using either bifurcation theory or Schauder fixed‐point theorem. also present numerical studies this and show that it exhibits similar those modelled well‐known reaction‐diffusion equations.

For dynamic analyses of railway track structures, the algorithm of solution is very important. For estimating the important problems in the railway tracks such as the effects of rail joints, rail supports, rail modeling in the nearness of bridge and other problems, the models of the axially beam model on the elastic foundation can be utilized. For studying the effects of axially beam on the ela...

this paper proposed analytical solutions for the buckling analysis of rectangular single-layered graphene sheets under in-plane loading on all edges simply is supported. the characteristic equations of the graphene sheets are derived and the analysis formula is based on the nonlocal mindlin plate. this theory is considering both the small length scale effects and transverse shear deformation ef...

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...