相关论文: Functional Methods and Effective Potentials for No…

We use a power expansion representation of plane elasticity complex potentials due to Kolossov and Muskhelishvili, to compute the elastic fields induced by a localized plastic deformation event. Far from its center, the dominant…

This paper presents a combined numerical-theoretical study of the macroscopic behavior and local field distributions in a special class of two-dimensional periodic composites with viscoplastic phases. The emphasis is on strongly nonlinear…

In this article, we propose a new method to compute the effective properties of non-linear disordered media. We use the fact that the effective constants can be defined through the minimum of an energy functional. We express this minimum in…

We discuss variational formulas for the limits of certain models of motion in a random medium: namely, the limiting time constant for last-passage percolation and the limiting free energy for directed polymers. The results are valid for…

The optimized effective potential method is formulated as a convex minimization problem. This formulation does not require assumptions about $v$-representability nor functional differentiability. The formulation provides a natural framework…

Starting from a general classical model of many interacting particles we present a well defined step by step procedure to derive the continuum-mechanics equations of nonlinear elasticity theory with fluctuations which describe the…

The method for the recursive calculation of the effective potential is applied successfully in case of weak coupling limit (g tend to zero) to a multidimensional complex cubic potential. In strong-coupling limit (g tend to infinity), the…

In this master thesis, a new approximation scheme to non-relativistic potential scattering is developed and discussed. The starting points are two exact path integral representations of the T-matrix, which permit the application of the…

We present a formalism for local composite operators. The corresponding effective potential is unique, multiplicatively renormalizable, it is the sum of 1PI diagrams and can be interpreted as an energy-density. First we apply this method to…

We investigate the effective elastic properties of periodic dilute two-phase composites consisting of an homogeneous isotropic matrix and a periodic array of rigid inclusions. We assume the rigid inclusion in a unit cell is a simply…

We study the effective potential for composite operators. Introducing a source coupled to the composite operator, we define the effective potential by a Legendre transformation. We find that in three or fewer dimensions, one can use the…

A bivariate perspective on Kohn-Sham density functional theory is proposed, treating potential and density as simultaneous independent variables, and used to make fruitful connection between Lieb's rigorous foundational framework and…

A variational modeling framework for hydraulically induced fracturing of elastic-plastic solids is developed in the present work. The developed variational structure provides a global minimization problem. While fracture propagation is…

We present a formalism for obtaining the statistical properties of functionals and inverse functionals of the paths of a particle diffusing in a one-dimensional quenched random potential. We demonstrate the implementation of the formalism…

We address the statistical estimation of composite functionals which may be nonlinear in the probability measure. Our study is motivated by the need to estimate coherent measures of risk, which become increasingly popular in finance,…

Microstructure reconstruction and compression techniques are designed to find a microstructure with desired properties. While the microstructure reconstruction searches for a microstructure with prescribed statistical properties, the…

We investigate a class of composite nonconvex functions, where the outer function is the sum of univariate extended-real-valued convex functions and the inner function is the limit of difference-of-convex functions. A notable feature of…

The problem of evaluating potential integrals on planar triangular elements has been addressed using a polar coordinate decomposition. The resulting formulae are general, exact, easily implemented, and have only one special case, that of a…

The variational discrete element method developed in [28] for dynamic elasto-plastic computations is adapted to compute the deformation of elastic Cosserat materials. In addition to cellwise displacement degrees of freedom (dofs), cellwise…

We derive, by means of variational techniques, a limiting description for a class of integral functionals under linear differential constraints. The functionals are designed to encode the energy of a high-contrast composite, that is, a…