The interrelations between weight-function upscaling (measurement) and the definition of various nonlocal operators is explored. Let < f > = f∗g where f∗g is the convolution product which represents the effect of upscaling via an instrument (defined by g) on a field variable f and its localized counterpart. Nonlocal field variables are defined and employed for upscaling. In this talk it will be...

Center for Concrete and Geomaterials, Northwestern University, Tech-241 0, Evanston, I L 60208 A recent nonlocal damage formulation, in which the spatially averaged quantity was the energy dissipated due to strain-softening, is extended to a more general form in which the strain remains local while any variable that controls strain-softening is nonlocal, In contrast to the original imbricate no...

aquaporins are integral membrane proteins from a larger family of major intrinsic proteins that formpores in the membrane of biological cells. aquaporins form tetramers in the cell membrane with eachmonomer acting as a water channel.in this research, the aqp4 tetramer was modeled from its pdbstructure file, then, we have performed the intraction of aquaporin4 in different temperatures (298k,300...

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...

We investigate some dynamical properties of nonlocal interaction equations. We consider sets of particles interacting pairwise via a potential W , as well as continuum descriptions of such systems. The typical potentials we consider are repulsive at short distances, but attractive at long distances. The main question we consider is whether an initially localized configuration remains localized ...

This paper describes the long wave scattering effect in gas saturated porous media using the homogenization method. To investigate the deviation from the continuum description, the multiscale asymptotic expansions are developed up to the third order. The leading (zeroth) order leads to the Biot-Allard continuum description. The correction of first order induces nonlocal terms in the dynamic Dar...

Electrostatic forces play many important roles in molecular biology, but are hard to model due to the complicated interactions between biomolecules and the surrounding solvent, a fluid composed of water and dissolved ions. Continuum model have been surprisingly successful for simple biological questions, but fail for important problems such as understanding the effects of protein mutations. In ...

Tunnel effect is a possible mechanism to explain the apparent large electric conductivity and nonlinear electric behavior of graphene-reinforced nanocomposites with polymer matrix. In this work, a numerical modeling framework is proposed to evaluate the effective electric conductivity in polymer composites reinforced with graphene sheets, taking into account the electrical tunneling effect, whi...