Related papers: On the geometry of a dislocated medium
In this paper, we study the differential smoothness of diffusion algebras.
The purpose of this paper is to study the shapes and stabilities of bio-membranes within the framework of exterior differential forms. After a brief review of the current status in theoretical and experimental studies on the shapes of…
We determine the scaling properties of geometric operators such as lengths, areas, and volumes in models of higher derivative quantum gravity by renormalizing appropriate composite operators. We use these results to deduce the fractal…
We discuss the theoretical solution to the differential equations governing accelerating edge dislocations in anisotropic crystals. This is an important prerequisite to understanding high speed dislocation motion, including an open question…
One considers geometry with the intransitive equaivalence relation. Such a geometry is a physical geometry, i.e. it is described completely by the world function, which is a half of the squared distance function. The physical geometry…
A computational approach has been developed for the analysis of the properties of 3D dislocation substructures generated by the vector density continuum dislocation dynamics (CDD), within the framework of crystal plasticity. In the CDD…
In 3D nematic liquid crystals, disclination lines have a range of geometric structures. Locally, they may resemble $+1/2$ or $-1/2$ defects in 2D nematic phases, or they may have 3D twist. Here, we analyze the structure in terms of the…
We investigate geometrical properties and inequalities satisfied by the complex difference body, in the sense of studying which of the classical ones for the difference body have an analog in the complex framework. Among others we give an…
These notes are designed for those who either plan to work in differential geometry, or at least want to have a good reason not to do it. We discuss smooth curves and surfaces -- the main gate to differential geometry. We focus on the…
Research in the field of Materials Science and Engineering focuses on the design, synthesis, properties, and performance of materials. An important class of materials that is widely investigated are crystalline materials, including metals…
A differential geometrical and topological structure of Delsarte transmutation operators in multidimension is studied, the relationships with De Rham-Hodge-Skrypnik theory of generalized differential complexes is stated.
Lie groupoids and their associated algebroids arise naturally in the study of the constitutive properties of continuous media. Thus, Continuum Mechanics and Differential Geometry illuminate each other in a mutual entanglement of theory and…
For materials science, diamond crystals are almost unrivaled for hardness and a range of other properties. Yet, when simply abstracting the carbon bonding structure as a geometric bar-and-joint periodic framework, it is far from rigid. We…
A continuum mechanical framework for the description of the geometry and kinematics of defects in material structure is proposed. The setting applies to a body manifold of any dimension which is devoid of a Riemannian or a parallelism…
The surrounding world surprises us by the beauty and variety of complex shapes that emerge from nanometric to macroscopic scales. Natural or manufactured materials (sandstones, sedimentary rocks and cement), colloidal solutions (proteins…
Integrable systems in low dimensions, constructed through the symmetry reduction method, are studied using phase portrait and variable separation techniques. In particular, invariant quantities and explicit periodic solutions are…
Given a compact pseudo-metric space, we associate to it upper and lower dimensions, depending only on the metric. Then we construct a doubling metric for which the measure of a dillated ball is closely related to these dimensions.
Although glassy relaxation is typically associated with disorder, here we report on a new type of glassy dynamics relating to dislocations within 2-D crystals of colloidal dimers. Previous studies have demonstrated that dislocation motion…
We describe the duality between different geometries which arises by considering the classical and quantum harmonic map problem. To appear in ``Essays on Mirror Manifolds II''.
Starting from a model of an elastic medium, partial differential equations with the form of the coupled Einstein-Dirac-Maxwell equations are derived. The form of these equations describes particles with mass and spin coupled to…