Related papers: Geometric Aspects of Singular Dislocations

In the author's earlier work there appeared a new way to specify any smooth closed 4-manifold by a surface diagram, which consists of an orientable surface decorated with simple closed curves. These curves are cyclically indexed, and each…

This thesis studies moduli spaces of singular connections on 3-manifolds and manifolds with cylindrical ends. A Chern-Simons functional is defined for singular connections on 3-manifolds which are singular along a knot. The critical points…

We show that the equations of motion governing the dynamics of strings in a compact internal space can be written as dispersion relations, with a local speed that depends on the velocity and curvature of the string in the large dimensions.…

Standard singularity theorems are proven in Lorentzian manifolds of arbitrary dimension n if they contain closed trapped submanifolds of arbitrary co-dimension. By using the mean curvature vector to characterize trapped submanifolds, a…

The theory of linear transports along paths in vector bundles, generalizing the parallel transports generated by linear connections, is developed. The normal frames for them are defined as ones in which their matrices are the identity…

Given a manifold M with a submanifold N, the deformation space D(M,N) is a manifold with a submersion to R whose zero fiber is the normal bundle, and all other fibers are equal to M. This article uses deformation spaces to study the local…

This paper presents a gentle introduction to cohomology vanishing theorems, largely based on the paper work of Hongshan Li. It offers an insightful exploration of unitary local systems on complex manifolds, particularly focusing on their…

Mechanical fields over thin elastic surfaces can develop singularities at isolated points and curves in response to constrained deformations (e.g., crumpling and folding of paper), singular body forces and couples, distributions of isolated…

We present a rigorous homogenization theorem for distributed dislocations. We construct a sequence of locally-flat Riemannian manifolds with dislocation-type singularities. We show that this sequence converges, as the dislocations become…

Dislocation based modeling of plasticity is one of the central challenges at the crossover of materials science and continuum mechanics. Developing a continuum theory of dislocations requires the solution of two long standing problems: (i)…

We investigate the dynamics of the geometric transitions associated to compactified spacetimes. By including the dynamics of gravity we are able to follow the evolution of collapsing cycles as they attempt to undergo a topology changing…

Although continuum theory has been widely used to describe the long-range elastic behavior of dislocations, it is limited in its ability to describe mechanical behaviors that occur near dislocation cores. This limit of the continuum theory…

We study the mechanics and statistical physics of dislocations interacting on cylinders, motivated by the elongation of rod-shaped bacterial cell walls and cylindrical assemblies of colloidal particles subject to external stresses. The…

Phase singularities appear ubiquitously in wavefields, regardless of the wave equation. Such topological defects can lead to wavefront dislocations, as observed in a humongous number of classical wave experiments. Phase singularities of…

Theoretical results on the dynamics of dislocations in Rayleigh-B\'enard convection are reported both for Swift-Hohenberg models and the Boussinesq equations. For intermediate Prandtl numbers the motion of dislocations is found to be driven…

The continuum mechanics of line defects representing singularities due to terminating discontinuities of the elastic displacement and its gradient field is developed. The development is intended for application to coupled phase…

Dislocations are the main carriers of the permanent deformation of crystals. For simulations of engineering applications, continuum models where material microstructures are represented by continuous density distributions of dislocations…

In this paper we propose a new treatment about infinite dimensional manifolds, using the language of category and functor. Our definition of infinite dimensional manifolds is a natural generalization of finite dimensional manifolds in the…

Spectral subspaces of a linear dynamical system identify a large class of invariant structures that highlight/isolate the dynamics associated to select subsets of the spectrum. The corresponding notion for nonlinear systems is that of…

This paper develops a geometrical model of dislocations and disclinations in single crystals at the mesoscopic scale. In the continuation of previous work the distribution theory is used to represent concentrated effects in the defect lines…