Related papers: On Weingarten-Volterra defects
We propose a discrete lattice model of the energy of dislocations in three-dimensional crystals which properly accounts for lattice symmetry and geometry, arbitrary harmonic interatomic interactions, elastic deformations and discrete…
We show the correspondence between a screw dislocation in gradient elasticity and a regularized vortex. The effective Burgers vector, nonsingular distortion and stress fields of a screw dislocation and the effective circulation, smoothed…
In this survey on local additive invariants of real and complex definable singular germs we systematically present classical or more recent invariants of different nature as emerging from a tame degeneracy principle. For this goal, we…
A recently developed viewpoint on the fundamentals of density-functional theory for finite interacting spin-lattice systems that centers around the notion of degeneracy regions is presented. It allows for an entirely geometrical description…
The Wheeler-DeWitt Equation represents a tool to study Quantum Gravity and Quantum Cosmology. Its solution in a very general context is, of course, impossible. To this purpose we consider some distortions of General Relativity like…
One of the least studied universal deformations of incompressible nonlinear elasticity, namely the straightening of a sector of a circular cylinder into a rectangular block, is revisited here and, in particular, issues of existence and…
We propose a simple method to compute the velocity difference statistics in forced Burgers turbulence in any dimension. Within a reasonnable assumption concerning the nucleation and coalescence of shocks, we find in particular that the…
While most strong-gravitational-lensing systems may be roughly modelled by a single massive object between the source and the observer, in the details all the structures near the light path contribute to the observed images. These…
It is first observed that the original formulation of the Volterra construction for dislocations and disclinations was related to the role that homotopy plays in strain compatibility, whereas the modern discussions are chiefly concerned…
While there is a well developed theory of locally solid topologies, many important convergences in vector lattice theory are not topological. Yet they share many properties with locally solid topologies. Building upon the theory of…
We study the deformation theory of nonsigular projective curves defined over algebraic closed fields of positive characteristic. We show that under some assumptions the local deformation problem for automorphisms of powerseries can be…
A systematic procedure for obtaining defect structures through cyclic deformation chains is introduced and explored in detail. The procedure outlines a set of rules for analytically constructing constraint equations that involve the finite…
New relations involving curvature components for the various connections appearing in the theory of almost product manifolds are given and the conformal behaviour of these connections are studied. New identities for the irreducible parts of…
This paper studies existence and uniqueness of solutions to generalized Volterra integral equations. Since our proof for existence and uniqueness does not make use of Banach fixed point theorem unlike the previous papers focused on this…
This paper derives new results for the analysis of nonlinear systems by extending contraction theory in the framework of vector distances. A new tool, vector contraction analysis utilizing a notion of the vector-valued norm which evidently…
We study the impact of a minimal length, implied by generalized uncertainty principles and quantum gravity models, on unbounded (scattering) trajectories in the Kepler problem. The analysis is based on the precession of the Hamilton vector,…
The existence of weak solutions is established for stochastic Volterra equations with time-inhomogeneous coefficients allowing for general kernels in the drift and convolutional or bounded kernels in the diffusion term. The presented…
In this paper we describe how relativistic field theories containing defects are equivalent to a class of boundary field theories. As a consequence previously derived results for boundaries can be directly applied to defects, these results…
Conformal field theory finds applications across diverse fields, from statistical systems at criticality to quantum gravity through the AdS/CFT correspondence. These theories are subject to strong constraints, enabling a systematic…
The aim of this paper is to show how a weakly dispersive perturbation of the inviscid Burgers equation improve (enlarge) the space of resolution of the local Cauchy problem. More generally we will review several problems arising from weak…