相关论文: On the geometry of a dislocated medium

We propose a geometrical approach to the investigation of Hamiltonian systems on (Pseudo) Riemannian manifolds. A new geometrical criterion of instability and chaos is proposed. This approach is more generic than well known reduction to the…

We study diffusion processes in anomalous spacetimes regarded as models of quantum geometry. Several types of diffusion equation and their solutions are presented and the associated stochastic processes are identified. These results are…

It is shown that properties of a discrete space-time geometry distinguish from properties of the Riemannian space-time geometry. The discrete geometry is a physical geometry, which is described completely by the world function. The discrete…

A new field of discrete differential geometry is presently emerging on the border between differential and discrete geometry. Whereas classical differential geometry investigates smooth geometric shapes (such as surfaces), and discrete…

A number of topics involving metrics and measures are discussed, including some of the special structure associated with ultrametrics.

This work introduces ``generalized meshes", a type of meshes suited for the discretization of partial differential equations in non-regular geometries. Generalized meshes extend regular simplicial meshes by allowing for overlapping elements…

For any real diagonalizable matrix with complex eigenvalues we provide a real, coordinate free decomposition with a clear geometric interpretation.

We study ray optics in the context of double mirror systems, in the limit as the two mirrors approach one another (thin films). This leads to a novel set of differential equations on a mirror surface which have interesting structure as seen…

A discrete model describing defects in crystal lattices and having the standard linear anisotropic elasticity as its continuum limit is proposed. The main ingredients entering the model are the elastic stiffness constants of the material…

We study evolutes and involutes of space curves. Although much of the material presented is not new and can be found in classic treatises, we believe that a modern and unified treatment, complemented with several novel observations, may be…

Discrete models of dislocations in cubic crystal lattices having one or two atoms per unit cell are proposed. These models have the standard linear anisotropic elasticity as their continuum limit and their main ingredients are the elastic…

This text is a survey of derived algebraic geometry. It covers a variety of general notions and results from the subject with a view on the recent developments at the interface with deformation quantization.

Basic concepts and definitions in differential geometry and topology which are important in the theory of solitons and instantons are reviewed. Many examples from soliton theory are discussed briefly, in order to highlight the application…

Understanding, finding, or even deciding on the existence of real solutions to a system of equations is a very difficult problem with many applications. While it is hopeless to expect much in general, we know a surprising amount about these…

The closure conditions of the inexact exterior differential form and dual form (an equality to zero of differentials of these forms) can be treated as a definition of some differential-geometrical structure. Such a connection discloses the…

This is a short presentation of some classical results on finite dimensional complex Lie algebras (classification of nilpotent Lie algebras, deformations and perturbations, contractions and rigidity). We present some applications to…

The purpose of the paper is to study the relationship between differential equations, Pfaffian systems and geometric structures, via the method of moving frames of E.Cartan. We show a local structure theorem. The Lie algebra aspects…

A variational model for epitaxially strained films accounting for the presence of dislocations is considered. Existence, regularity and some qualitative properties of solutions are addressed.

The classifying space of inertial reference frames in special relativity is naturally hyperbolic. There is a remarkable interplay between central elements of hyperbolic geometry and those of special relativity -- which, to a certain extent,…

Algebras of generalized functions offer possibilities beyond the purely distributional approach in modelling singular quantities in non-smooth differential geometry. This article presents an introductory survey of recent developments in…