Related papers: A Generalized Nonlocal Calculus with Application t…
This note investigates the explicit convergence rates of nonlocal peridynamic operators to their classical (local) counterparts in $L^q$-norm. Previous results used Fourier series and hence were restricted to showing convergence in $L^2$.…
In this work we introduce a formulation for a non-local Hessian that combines the ideas of higher-order and non-local regularization for image restoration, extending the idea of non-local gradients to higher-order derivatives. By carefully…
The paper contains generalization of the renormgroup algorithm for boundary value problems of mathematical physics and related concept of the renormgroup symmetry, formulated earlier by authors with reference to models based on differential…
In this paper the generalisation of previous author's formulation of fractional continuum mechanics to the case of anisotropic non-locality is presented. The considerations include the review of competitive formulations available in…
Green-hyperbolic operators - partial differential operators on globally hyperbolic spacetimes that (together with their formal duals) possess advanced and retarded Green operators - play an important role in many areas of mathematical…
We present numerical techniques based on generalized functions adapted to nonlinear calculations. They concern main numerical engineering problems ruled by-or issued from-nonlinear equations of continuum mechanics. The aim of this text is…
Identification in errors-in-variables regression models was recently extended to wide models classes by S. Schennach (Econometrica, 2007) (S) via use of generalized functions. In this paper the problems of non- and semi- parametric…
We study an integral equation that extends the problem of anti-differentiation. We formulate this equation by replacing the classical derivative with a known nonlocal operator similar to those applied in fracture mechanics and nonlocal…
This study presents the application of variable-order (VO) fractional calculus to the modeling of nonlocal solids. The reformulation of nonlocal fractional-order continuum mechanic framework, by means of VO kinematics, enables a unique…
We introduce a general approach to traces that we consider as linear continuous functionals on some function space where we focus on some special choices for that space. This leads to an integral calculus for the computation of the precise…
This study presents a physically consistent displacement-driven reformulation of the concept of action-at-a-distance, which is at the foundation of nonlocal elasticity. In contrast to existing approaches that adopts an integral…
This paper considers uncertainty quantification for an elliptic nonlocal equation. In particular, it is assumed that the parameters which define the kernel in the nonlocal operator are uncertain and a priori distributed according to a…
We consider a class of nonconvex energy functionals that lies in the framework of the peridynamics model of continuum mechanics. The energy densities are functions of a nonlocal strain that describes deformation based on pairwise…
The derivation of nonlocal strong forms for many physical problems remains cumbersome in traditional methods. In this paper, we apply the variational principle/weighted residual method based on nonlocal operator method for the derivation of…
The present work is devoted to the study of fractional powers of vector operators, with particular emphasis on the gradient operator with non-constant coefficients. Within the setting of Clifford algebra $\mathbb{R}_n$, this operator turns…
We study a simple nonlocal-in-time dynamic system proposed for the effective modeling of complex diffusive regimes in heterogeneous media. We present its solutions and their commonly studied statistics such as the mean square distance. This…
New universal invariant operators are introduced in a class of geometries which include the quaternionic structures and their generalisations as well as 4-dimensional conformal (spin) geometries. It is shown that, in a broad sense, all…
Motivated by Popescu's example of hidden nonlocality, we elaborate on the conjecture that quantum states that are intuitively nonlocal, i.e., entangled, do not admit a local causal hidden variables model. We exhibit quantum states which…
Following the guidelines of classical differential geometry the `building material' for the tensor calculus in non-commutative geometry is suggested. The algebraic account of moduli of vectors and covectors is carried out.
In the paper we study nonlocal functionals whose kernels are homogeneous generalized functions. We also use such functionals to solve the Korteweg-de Vries , the nonlinear Schr\"odinger and the Davey-Stewartson equations.