We describe an approach to nonlocal, nonlinear advection in one dimension that extends the usual pointwise concepts to account for nonlocal contributions to the flux. The spatially nonlocal operators we consider do not involve derivatives. Instead, the spatial operator involves an integral that, in a distributional sense, reduces to a conventional nonlinear advective operator. In particular, we...

We are interested in the mathematical modeling of the deformation of the human lung tissue, called the lung parenchyma, during the respiration process. The parenchyma is a foam–like elastic material containing millions of air–filled alveoli connected by a tree– shaped network of airways. In this study, the parenchyma is governed by the linearized elasticity equations and the air movement in the...

In this article, the nonlocal biaxial buckling load and bending analysis of polymeric piezoelectric nanoplate reinforced by carbon nanotube (CNT) considering the surface stress effect is presented. This plate is subjected to electro-magneto-mechanical loadings. Eshelby-Mori-Tanaka approach is used for defining the piezoelectric nanoplate material properties. Navier’s type solution is employed t...

We discuss the formation of a vortex polycrystal in type II superconductors from the competition between pinning and elastic forces. We compute the elastic energy of a deformed grain boundary, which is strongly nonlocal, and obtain the depinning stress for weak and strong pinning. Our estimates for the grain size dependence on the magnetic field strength are in good agreement with previous expe...

despite its numerous potential applications, two-dimensional monolayer graphyne, a novel form of carbon allotropes with sp and sp2 carbon atoms, has received little attention so far, perhaps as a result of its unknown properties. especially, determination of the exact values of its elastic properties can pave the way for future studies on this nanostructure. hence, this article describes a dens...

In this paper we design high-order local artificial boundary conditions and present error bounds for the finite element approximation of an incompressible elastic material in an unbounded domain. The finite element approximation is formulated in a bounded computational domain using a nonlocal approximate artificial boundary condition or a local one. In fact there are a family of nonlocal approx...

We describe an approach to nonlocal, nonlinear advection in one dimension that extends the usual pointwise concepts to account for nonlocal contributions to the flux. The spatially nonlocal operators we consider do not involve derivatives. Instead, the spatial operator involves an integral that, in a distributional sense, reduces to a conventional nonlinear advective operator. In particular, we...

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 present paper investigates the potential application of graphene sheets with attached nanoparticles as resonant sensors by introducing a nonlocal shear deformation plate model. To take into account an elastic connection between the nanoplate and the attached nanoparticle, the nanoparticle is considered as a mass-spring system. Then, a combination of pseudo-spectral and integral quadrature m...