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

We make use of point transformations to introduce new canonical variables for systems defined on a finite interval and on the half-line so that new position variables should take all real values from $-\infty$ to $\infty$. The completeness…

We calculate the two-particle irreducible (2PI) effective potential of the O(N) linear sigma model in 1+1 dimensions. The approximations we use are the next-to-leading order of a 1/N expansion (for arbitrary N) and a kind of "resummed loop…

Fractional dissipation is a powerful tool to study non-local physical phenomena such as damping models. The design of geometric, in particular, variational integrators for the numerical simulation of such systems relies on a variational…

We present a numerical study of the spatial correlations of a quasi-two-dimensional granular fluid kept in a non-static steady state via vertical shaking. The simulations explore a wide range of packing fractions, vertical accelerations and…

The spectral representation separates the contributions of geometrical arrangement (topology) and intrinsic constituent properties in a composite. The aim of paper is to present a numerical algorithm based on the Monte Carlo integration and…

It is discussed that the classical effective medium theory for the elastic properties of random heterogeneous materials is not congruous with the effective medium theory for the electrical conductivity. In particular, when describing the…

This work proposes an implementable proximal-type method for a broad class of optimization problems involving nonsmooth and nonconvex objective and constraint functions. In contrast to existing methods that rely on an ad hoc model…

The rational function approximation method, density functional theory, and NVT Monte Carlo simulation are used to obtain the density profiles of multicomponent hard-sphere mixtures near a planar hard wall. Binary mixtures with a size ratio…

We present a computational framework for two-scale asymptotic homogenization to determine the intrinsic magnetic permeability of composites. To this end, considering linear magnetostatics, both vector and scalar potential formulations are…

Starting from the Abrikosov-Ryzhkin formulation of the 1D random potential problem I find closed functional representations for various physical quantities. These functional integrals are calculated exactly without the use of any…

We develop a new paradigm for finding bifurcations of solutions of nonlinear problems, which is based on the detection of extreme values of new type of variational functional associated with the considering problem. The variational…

In this note, we consider a Robin-type traction problem for a linearly elastic body occupying an infinite periodically perforated domain. After proving the uniqueness of the solution we use periodic elastic layer potentials to show that the…

We consider minimization of functions that are compositions of convex or prox-regular functions (possibly extended-valued) with smooth vector functions. A wide variety of important optimization problems fall into this framework. We describe…

Dilute or semi-dilute solutions of non-intersecting self-avoiding walk (SAW) polymer chains are mapped onto a fluid of ``soft'' particles interacting via an effective pair potential between their centers of mass. This mapping is achieved by…

Derivatives and integrals of non-integer order may have a wide application in describing complex properties of materials including long-term memory, non-locality of power-law type and fractality. In this paper we consider extensions of…

The one-loop effective potential calculated for a generic model that originates from 5-dimensional theory reduced down to 4 dimensions is considered. The cut-off and dimensional regularization schemes are discussed and compared. It is…

We present a novel way to compute the one-loop ring-improved effective potential numerically, which avoids the spurious appearence of complex expressions and at the same time is free from the renormalization ambiguities of the…

The nonlinear conjugate gradient methods are known to be an effective approach for standard unconstrained optimization problems especially for large-scale problems. This paper proposes a proximal nonlinear conjugate gradient method, which…

In the context of functional data analysis, probability density functions as non-negative functions are characterized by specific properties of scale invariance and relative scale which enable to represent them with the unit integral…

We extend the density functional perturbation theory formalism to the case of non-collinear magnetism. The main problem comes with the exchange-correlation (XC) potential derivatives, which are the only ones that are affected by the…