Well-posedness results for the state-based peridynamic nonlocal continuum model of solid mechanics are established with the help of a nonlocal vector calculus. The peridynamic strain energy density for an elastic constitutively linear anisotropic heterogenous solid is expressed in terms of the field operators of that calculus, after which a variational principle for the equilibrium state is def...

SOLIDS THAT I:XHIUIT localization of deformation (in the form of shear bands) at sufficiently high levels of strain, are ftrcquently modeled by gradient type non-local constitutive laws. i.e. continuum theories that include higher order deformation gradients. These models incorporate a length scale for the localized deformation zone and are either postulated or justified from micromechanical co...

Abstract In this paper, we define a family of functionals generalizing the Yang–Mills–Higgs on closed Riemannian manifold. Then prove short-time existence corresponding gradient flow by gauge-fixing technique. The lack maximum principle for higher order operator brings us lot inconvenience during estimates Higgs field. We observe that $L^2$ -bound field is enough energy in four dimensions and s...

Recent developments in modeling and analysis of nanostructures are illustrated discussed this paper. Starting with the early theories nonlocal elastic continua, a thorough investigation continuum nano-mechanics is provided. Two-phase local/nonlocal models shown as possible to recover consistency strain-driven purely integral theory, provided that mixture parameter not vanishing. Ground-breaking...

We prove that the isotropic Landau equation equipped with Coulomb potential introduced by Krieger-Strain and Gualdani-Guillen can be identified gradient flow of entropy in probability space respect to a Riemannian metric tensor nonlocal mobility. give characterizations corresponding geodesics equations present convergence rate result estimating its Hessian operator.