The hysteretic behavior of many-particle systems with non-convex free energy can be modeled by nonlocal Fokker-Planck equations that involve two small parameters and are driven by a timedependent constraint. In this paper we consider the fast reaction regime related to Kramers-type phase transitions and prove that the dynamics in the small-parameter limit can be described by a rate-independent ...

functionally gradedpoisson’s ratio structures have been developed for critical protection. in thispaper, the static bending and buckling of fgpr nanoscale beam are studied basedon the nonlocal timoshenko beam model, in which both young’s modulus andpoisson’s ratio are assumed to vary continuously in the thickness direction. byutilizing total potential energy principle, equilibrium equations are...

Abstract. In this paper we present the first results on substructuring methods for nonlocal operators, specifically, an instance of the nonlocal p-Laplace operator. We present a nonlocal variational formulation of this operator, proving a nonlocal Poincaré inequality and upper bound to establish a spectral equivalence. We then introduce a nonlocal two-domain variational formulation utilizing no...

in this research, the buckling and bending behaviour of smart nanocomposite plate reinforced by single- walled carbon nanotubes (swcnts) under electro-magneto-mechanical loadings is studied. the extended mixture rule approach is used to determine the elastic properties of nanocomposite plate. equilibrium equations of smart nanocomposite plate are derived using the hamilton’s principle based on ...

A construction of W-symmetries is given only in terms of the nonlocal fields (parafermions ψ α), which take values on the homogeneous space G/U (1) r , where G is a simply connected compact Lie group manifold (its accompanying Lie algebra G is a simple one of rank r). Only certain restriction of the root set of Lie algebra on which the parafermionic fields take values are satisfied, then a cons...