Related papers: On the geometry of a dislocated medium
We review the basic ideas lying at the foundation of the recently developed theory of twisted symmetries of differential equations, and some of its developments.
We investigate several topics of the geometry on real Cayley-Klein spaces. An important concern for us is to define a distance function on the projective space in such a way that the distance between two anisotropic subspaces of the same…
We consider the theory of \emph{twisted symmetries} of differential equations, in particular $\lambda$ and $\mu$-symmetries, and discuss their geometrical content. We focus on their interpretation in terms of gauge transformations on the…
In these lectures we review our present understanding of the fractal structure of two-dimensional Euclidean quantum gravity coupled to matter.
A class of congruences of principal Volterra-type effective dislocation lines associated with a dislocation density tensor is distinguished in order to investigate the kinematics of continuized defective crystals in terms of their…
In this letter we briefly investigate the mathematical structure of space-time in the framework of discretization. It is shown that the discreteness of space-time may result in a new mechanical system which differ from the usual quantum…
This chapter reviews the different methodological aspects of the ab ini-tio modeling of dislocations. Such simulations are now frequently used to study the dislocation core, i.e. the region in the immediate vicinity of the line defect where…
We investigate how exotic differential structures may reveal themselves in particle physics. The analysis is based on the A. Connes' construction of the standard model. It is shown that, if one of the copies of the spacetime manifold is…
We review understanding of kinetics of fluid phase separation in various space dimensions. Morphological differences, percolating or disconnected, based on overall composition in a binary liquid or density in a vapor-liquid system, have…
Distance Geometry is based on the inverse problem that asks to find the positions of points, in a Euclidean space of given dimension, that are compatible with a given set of distances. We briefly introduce the field, and discuss some open…
We review recent developments in differential topology with special concern for their possible significance to physical theories, especially general relativity. In particular we are concerned here with the discovery of the existence of…
Two-dimensional dilational materials, for which the only easy mode of deformation is a dilation are reviewed and connections are drawn between models previously proposed in the literature. Some models which appear to be dilational…
Organic molecular crystals encompass a vast range of materials from pharmaceuticals to organic optoelectronics and proteins to waxes in biological and industrial settings. Crystal defects from grain boundaries to dislocations are known to…
The geometries of spaces having as groups the real orthogonal groups and some of their contractions are described from a common point of view. Their central extensions and Casimirs are explicitly given. An approach to the trigonometry of…
Current problems in particle physics are reviewed from the viewpoint of theories possessing extra spatial dimensions.
We introduce a field theoretic formalism enabling the direct study of dislocation and interstitial dynamics. Explicit expressions for the energies of such defects are given. We provide links to earlier numerical, discrete elastic, time…
It is shown how the dimension of any arbitrary over-determined system of differential equations can be reduced, which makes the system suitable for numerical solution modeling. Specifically, over-determined equations of hydrodynamics are…
These notes are based on a series of five lectures given at the 2009 Villa de Leyva Summer School on Geometric and Topological Methods for Quantum Field Theory. The purpose of the lectures was to give an introduction to…
A three-dimensional continuum dislocation theory for single crystals containing curved dislocations is proposed. A set of governing equations and boundary conditions is derived for the true placement, plastic slips, and loop functions in…
We give detailed exposition of modern differential geometry from global coordinate independent point of view as well as local coordinate description suited for actual computations. In introduction, we consider Euclidean spaces and different…