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...

Today there is no programming model or language support which ooers a uniform programming methodology on a wide variety of parallel architectures. In this paper functional languages are proposed as such a methodology using an extension of the concept of skeletons | higher-order functions coupled with parallel implementation templates. An essential part of the proposed methodology is the use of ...

The finite element simulation of forming processes or vehicle crash scenarios involves multiaxial loading conditions in general. Thereby, damage and failure ductile steel sheets is triggered by void growth under hydrostatic tensile elongation within a narrow band shear dominated loading. These different mechanisms are considered stress state dependent continuum model. initiation represented cri...

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...

A model for spinodal decomposition must account for interface effects that include gradient and strain energy terms. The measurement of diffusion in the Cu-Ni(Fe) alloy for the special case of nanolaminate structured coatings is considered wherein the composition fluctuation is one-dimensional along <111>. An analytic approach is taken to model the kinetics of the transformation process that pr...

The object of interest in the present paper is a nonlocal nonlinear problem for a general second order elliptic operator. The problem under consideration represents a model of nonlocal reaction diffusion process. Furthermore, applications in computational biology are also available. The strong problem is reduced to a discrete minimization problem. The approximate problem is obtained by Lagrangi...

For a large class of variational quantum circuits, we show how arbitrary-order derivatives can be analytically evaluated in terms simple parameter-shift rules, i.e., by running the same circuit with different shifts parameters. As particular cases, obtain rules for Hessian an expectation value and metric tensor state, both which efficiently used to implement second-order optimization algorithms...