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...

At what characteristic length scale does classical continuum elasticity cease to accurately describe small deformation mechanical behavior? The two dominant physical mechanisms that lead to size dependency of elastic behavior at the nanoscale are surface energy effects and nonlocal interactions. The latter arises due to the discrete structure of matter and the fluctuations in the interatomic fo...

The respective roles of local and nonlocal interactions in the thermodynamic cooperativity of proteins are investigated using continuum (off-lattice) native-centric Gō-like models with a coarse-grained Ca chain representation. We study a series of models in which the (local) bondand torsion-angle terms have different strengths relative to the (nonlocal) pairwise contact energy terms. Conformati...

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...

A microscopic, nonlocal response theory is developed to model the interaction of electromagnetic radiation with inhomogeneous nanoscale clusters. The breakdown of classical continuum-field Mie theory is demonstrated at a critical coarse-graining threshold, below which macroscopic plasmon resonances are replaced by molecular excitations with suppressed spectral intensity.

In this article, the free vibration behavior of nanoscale FG rectangular plates is studied within the framework of the refined plate theory (RPT) and small-scale effects are taken into account. Using the nonlocal elasticity theory, the governing equations are derived for single-layered FG nanoplate. The Navier’s method is employed to obtain closed-form solutions for rectangular nanoplates assum...

In this research, a control feedback system is used to study the free vibration response of rectangular plate made of magnetostrictive material (MsM) for the first time. A new trigonometric higher order shear deformation plate theory are utilized and the results of them are compared with two theories in order to clarify their accuracy and errors. Pasternak foundation is selected to modelling of...

We consider dynamics driven by interaction energies on graphs. introduce graph analogues of the continuum nonlocal-interaction equation and interpret them as gradient flows with respect to a Wasserstein distance. The particular distance we arises from analogue Benamou-Brenier formulation where continuity uses an upwind interpolation define density along edges. While this approach has both theor...