Many atomistic/continuum coupling algorithms utilize an overlapping subdomain method, where boundary data for local solves in atomistic and discretized continuum subdomains is provided from local solves in neighboring subdomains. Such coupling algorithms are closely related to the classical alternating Schwarz domain decomposition method, although little to no convergence or error analysis exis...

By examining the analyticity of a sequence of topologically-proper lattice Dirac operators, we show that they tend to a nonlocal Dirac operator. This implies that a nonlocal lattice Dirac operator can have exact zero modes satisfying the Atiyah-Singer index theorem, in gauge backgrounds with nonzero topological charge. PACS numbers: 11.15.Ha, 11.30.Rd, 11.30.Fs It is well known that all fundame...

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 ...

By examining the analyticity of a sequence of topologically-proper lattice Dirac operators, we show that they tend to a nonlocal Dirac operator. This implies that a nonlocal lattice Dirac operator can have exact zero modes satisfying the Atiyah-Singer index theorem, in gauge backgrounds with nonzero topological charge. PACS numbers: 11.15.Ha, 11.30.Rd, 11.30.Fs It is well known that all fundame...

A method used recently to obtain a discrete formalism for classical fields with nonlocal actions preserving chiral symmetry and uniqueness of fermion fields yields a discrete version of Huygens’ principle with free discrete propagators that recover their continuum forms in certain limit.

The paper deals with the problem of nonlocal generalization of constitutive models such as microplane model M4 for concrete, in which the yield limits, called stress–strain boundaries, are softening functions of the total strain. Such constitutive models call for a different nonlocal generalization than those for continuum damage mechanics, in which the total strain is reversible, or for plasti...

Geometric methods based on PDEs have revolutionized the field of image processing and image analysis. I will discuss recent work to develop these ideas for machine learning applications involving “big data”. The main idea is to pose variational problems involving graph cuts in terms of total variation minimization problems. We then develop both phase field and mean curvature methods to solve th...

In this paper nonlocal boundary conditions for the Navier–Stokes equations are derived, starting from the Boltzmann equation in the hydrodynamic limit. Basing on phenomenological arguments, two scattering kernels which model non–local interactions between the gas molecules and the wall boundary are proposed. They satisfy the global mass conservation and a generalized reciprocity relation. The a...

INTRODUCTION Investigations of bone stiffness and strength based on continuum finite element (FE) models have big advantages in terms of computational cost when compared to micro FE models. A nonlocal elastoplastic constitutive law with damage that leads to softening has recently been developed for the compressive behavior of trabecular bone [1]. Mechanical tests on human trabecular bone biopsi...