Related papers: Differential Complexes in Continuum Mechanics
This paper is concerned with the derivation and properties of differential complexes arising from a variety of problems in differential equations, with applications in continuum mechanics, relativity, and other fields. We present a…
We look at several problems in even dimensional conformal geometry based around the de Rham complex. A leading and motivating problem is to find a conformally invariant replacement for the usual de Rham harmonics. An obviously related…
Diffusive transport is characterized by a diffusivity tensor which may, in general, contain both a symmetric and an antisymmetric component. Although the latter is often neglected, we derive Green-Kubo relations showing it to be a general…
We extend previous work on conformally covariant differential operators to consider the case of second order operators acting on symmetric traceless tensor fields. The corresponding flat space Green function is explicitly constructed and…
The norms associated with the gradients of the two non-differential invariants of the Kerr vacuum are examined. Whereas both locally single out the horizons, their global behavior is more interesting. Both reflect the background angular…
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…
Derivation-based differential calculi are of great importance in noncommutative geometry, noncommutative gauge theory and integrable systems. In this paper, we propose the connection and curvature from a class of deformed derivation-based…
We study classical scalar field theories on noncommutative curved spacetimes. Following the approach of Wess et al. [Classical Quantum Gravity 22 (2005), 3511 and Classical Quantum Gravity 23 (2006), 1883], we describe noncommutative…
We derive a general expression for the deformation-gradient tensor by invoking the standard definition of a gradient of a vector field in curvilinear coordinates. This expression shows the connection between the standard definition of a…
A continuum model to study the influence of dislocations on the electronic properties of condensed matter systems is described and analyzed. The model is based on a geometrical formalism that associates a density of dislocations with the…
The purpose of this work is the development and determination of higher-order continuum-like kinematic measures which characterize discrete kinematic data obtained from experimental measurement (e.g., digital image correlation) or kinematic…
The geometry of parallelizable manifolds (i.e., teleparallelism) is summarized in the language of local frame fields. Some problems in continuum mechanics that relate to the couple-stresses that are produced in the bending and twisting of…
Continuum equations are ubiquitous in physical modelling of elastic, viscous, and viscoelastic systems. The equations of continuum mechanics take nontrivial forms on curved surfaces. Although the curved surface formulation of the continuum…
Discretizing variational principles, as opposed to discretizing differential equations, leads to discrete-time analogues of mechanics, and, systematically, to geometric numerical integrators. The phase space of such variational…
We investigate the dynamical coupling between the motion and the deformation of a single self-propelled domain based on two different model systems in two dimensions. One is represented by the set of ordinary differential equations for the…
For an n-dimensional bounded domain we derive some inequalities bounding the norm of a square tensor field. Concerning the Div-Dev-inequality the bound is given by the trace-free part and the divergence and the tensor. In the case of the…
The paper deals with systems of ordinary differential equations containing in the right-hand side controls which are discontinuous in phase variables. These controls cause the occurrence of sliding modes. If one uses one of the well-known…
In this article we survey recent results on rigid dualizing complexes over commutative algebras. We begin by recalling what are dualizing complexes. Next we define rigid complexes, and explain their functorial properties. Due to the…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…
In this thesis, I investigate how to construct a self-consistent model of deformed general relativity using canonical methods and metric variables. The specific deformation of general covariance is predicted by some studies into loop…