Related papers: On the geometry of a dislocated medium
A teleparallel geometrical description of the nematic phases of liquid crystals is proposed.In the case of the twisted geometry of nematics Cartan torsion is given by a spatial helical form which depends on the twist angle. Geodesics of a…
This article provides a gentle, visual introduction to the basic concepts of differential geometry appropriate for students familiar with special relativity. Visual methods are used to explain basics of differential geometry and build…
Motivated by research on contraction analysis and incremental stability/stabilizability the study of 'differential properties' has attracted increasing attention lately. Previously lifts of functions and vector fields to the tangent bundle…
We investigate structure formation in a one dimensional model of a matter-dominated universe using a quasi-newtonian formulation. In addition to dark matter, luminous matter is introduced to examine the potential bias in the distributions.…
We introduce an alternative formalization of curved spaces in which the concept of a pointwise affine space, as defined here, replaces that of a manifold. New or modified definitions of familiar notions from differential geometry such as…
A brief survey of real algebraic structures on topological spaces is given. This article is written for the Gokova Gemetry/Topology Conference proceedings.
We develop a fully coupled theoretical description of dislocation dynamics on deformable crystalline surfaces, using continuum modeling and the amplitude-phase-field crystal (APFC) framework extended to curved geometries. We derive a…
Basic issues of the general model-building framework of the mechanics of complex bodies are discussed. Attention is focused on the representation of the material elements, the conditions for the existence of ground states in conservative…
The aim of this text is to extend the theory of generalized ordinary differential equations to the setting of metric spaces. We present existence and uniqueness theorems that significantly improve previous results even when restricted back…
This note provides a variational description of the most basic differential geometric structures on a smooth manifold.
Differential forms provide a coordinate-free way to express many quantities and relations in mathematical physics. In particular, they are useful in plasma physics. This tutorial gives a guide so that you can read the plasma physics…
The kinetics of dislocations is studied with computer simulation at loadings of different intensity. It is established that the dislocations have a few different structural states. The dislocations "with the micropore" play important role…
A variety of models for the membrane-mediated interaction of particles in lipid membranes, mostly well-established in theoretical physics, is reviewed from a mathematical perspective. We provide mathematically consistent formulations in a…
Survey talk on certain aspects of the subject, stressing the neighbor relation as a basic notion in differential geometry.
The derivation of the equation of one-dimensional movement of a solitary shock wave is given. This derivation shows, that the differential equation of movement of a solitary plane shock wave in the channel with variable area, is exact, if…
A way to add an extra dimension is briefly discussed.
In this work we discuss the deformed relativistic wave equations, namely the Klein--Gordon and Dirac equations in a Doubly Special Relativity scenario. We employ what we call a geometric approach, based on the geometry of a curved momentum…
Geometrization of physical theories have always played an important role in their analysis and development. In this contribution we discuss various aspects concerning the geometrization of physical theories: from classical mechanics to…
The new approach to quantize the gravity based on the notion of differential algebra is suggested. It is shown that the differential geometry of this object can not be described in terms of points. The spatialization procedure giving rise…
We show that it is possible to represent various descriptions of Quantum Mechanics in geometrical terms. In particular we start with the space of observables and use the momentum map associated with the unitary group to provide an unified…