Related papers: Umbral Deformations on Discrete Spacetime
Plastic deformation In crystalline materials is controlled by the motion and interactions of dislocations [AND 17]. Discrete Dislocation Dynamics (DDD) simulations have now existed for about 25 years to investigate plastic flow at the…
Inspired by the work of Wheeler among others, we have studied the problem of quantum measurements of space-time distances by applying the general principles of quantum mechanics as well as those of general relativity. Contrary to the…
A discretisation scheme that preserves topological features of a physical problem is extended so that differential geometric structures can be approximated in a consistent way thus giving access to the study of physical systems which are…
This article deals with universal deformations of dihedral representations with a particular focus on the question when the universal deformation is dihedral. Results are obtained in three settings: (1) representation theory, (2) algebraic…
We develop a unified theory for continuous in time finite element discretisations of partial differential equations posed in evolving domains including the consideration of equations posed on evolving surfaces and bulk domains as well…
The WKB approximation for deformed space with minimal length is considered. The Bohr-Sommerfeld quantization rule is obtained. A new interesting feature in presence of deformation is that the WKB approximation is valid for intermediate…
In a previous work we proved the uniqueness and functoriality of primary unfoldings on simple Thom-Mather spaces, which is a functor to the category of smooth manifolds. In this article we extend these results for any stratified Thom-Mather…
For a conformal theory it is natural to seek the conformal moduli space, M_c to which it belongs, generated by the exactly marginal deformations. By now we should have the tools to determine M_c in the presence of enough supersymmetry. Here…
The stationary points of the total scalar curvature functional on the space of unit volume metrics on a given closed manifold are known to be precisely the Einstein metrics. One may consider the modified problem of finding stationary points…
Noncommutativity of the spacetime coordinates has been explored in several contexts, mostly associated to phenomena at the Planck length scale. However, approaching this question through deformation theory and the principle of stability of…
The possibility that global discrete dilation invariance is a fundamental symmetry principle of nature is explored. If the discrete self-similarity observed in nature is exact, then the Principle of General Covariance needs to be broadened…
We show that quantum mechanics and general relativity imply the existence of a minimal length. To be more precise, we show that no operational device subject to quantum mechanics, general relativity and causality could exclude the…
We study the process of compactification as a topology change. It is shown how the mediating spacetime topology, or cobordism, may be simplified through surgery. Within the causal Lorentzian approach to quantum gravity, it is shown that any…
This paper describes a generalization of decomposition in orbifolds. In general terms, decomposition states that two-dimensional orbifolds and gauge theories whose gauge groups have trivially-acting subgroups decompose into disjoint unions…
Discrete element modelling (DEM) is one of the most efficient computational approaches to the fracture processes of heterogeneous materials on mesoscopic scales. From the dynamics of single crack propagation through the statistics of crack…
The purpose of this paper is to discuss a generalization of the bubble transform to differential forms. The bubble transform was discussed in a previous paper by the authors for scalar valued functions, or zero-forms, and represents a new…
Several proposals for Quantum Gravity involve length and area operators with discrete eigenvalues. I show that the analyses of some simple procedures for the measurement of areas and lengths suggest that this discreteness characterizing the…
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
Diffusion-driven patterns appear on curved surfaces in many settings, initiated by unstable modes of an underlying Laplacian operator. On a flat surface or perfect sphere, the patterns are degenerate, reflecting translational/rotational…
In this short note we briefly review some recent developments in understanding discrete torsion. Specifically, we give a short overview of the highlights of a group of recent papers which give the basic understanding of discrete torsion.…