Related papers: Geometric evolution as a source of discontinuous b…
Many particle physics models of matter admit solutions corresponding to stable or long-lived topological defects. In the context of standard cosmology it is then unavoidable that such defects will form during phase transitions in the very…
This paper brings together three distinct theories with the goal of quantifying shape textures with complex morphologies. Distance fields are central objects in shape representation, while topological data analysis uses algebraic topology…
Conformational transitions are ubiquitous in biomolecular systems, have significant functional roles and are subject to evolutionary pressures. Here we provide a first theoretical framework for topological transition, i.e. conformational…
Topology transcends boundaries that conventionally delineate physical, biological and engineering sciences. Our ability to mathematically describe topology, combined with our access to precision tracking and manipulation approaches, has…
We perform the discrete-to-continuum limit passage for a microscopic model describing the time evolution of dislocations in a one dimensional setting. This answers the related open question raised by Geers et al. in [GPPS13]. The proof of…
Geological materials are often seen as the antithesis of soft; rocks are hard. However, during the formation of minerals and rocks, all the systems we shall discuss, indeed geological materials in general, pass through a stage where they…
The Topological Hypothesis states that phase transitions should be related to changes in the topology of configuration space. The necessity of such changes has already been demonstrated. We characterize exactly the topology of the…
We show that thermodynamics can be formulated naturally from the intrinsic geometry of phase space alone-without postulating an ensemble, which instead emerges from the geometric structure itself. Within this formulation, phase transitions…
We calculate the geometric phase associated to the evolution of a system subjected to decoherence through a quantum-jump approach. The method is general and can be applied to many different physical systems. As examples, two main source of…
To analyze the evolutionary emergence of structural complexity in physical processes we introduce a general, but tractable, model of objects that interact to produce new objects. Since the objects--\emph{$epsilon$-machines}--have well…
In the literature, it has been shown that the evolution of the known explicit 3D surface to the target one can be learned from 2D images using the instantaneous flow field, where the known and target 3D surfaces may largely differ in…
Geometric torsions are torsions of acyclic complexes of vector spaces which consist of differentials of geometric quantities assigned to the elements of a manifold triangulation. We use geometric torsions to construct invariants for a…
We introduce a theoretical framework for differentiable surface evolution that allows discrete topology changes through the use of topological derivatives for variational optimization of image functionals. While prior methods for inverse…
For atoms and crystals with an ideal symmetry, the optical selection rules for electronic transitions are well covered in physics textbooks. However, in studies of material systems one often encounters systems with a weakly distorted…
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…
We study a three matrix model with global SO(3) symmetry containing at most quartic powers of the matrices. We find an exotic line of discontinuous transitions with a jump in the entropy, characteristic of a 1st order transition, yet with…
Topological data analysis is an emerging area in exploratory data analysis and data mining. Its main tool, persistent homology, has become a popular technique to study the structure of complex, high-dimensional data. In this paper, we…
Liquid crystals generally support orientational singularities of the director field known as topological defects. These latter modifiy transport properties in their vicinity as if the geometry was non-Euclidean. We present a state of the…
The theory of persistence modules is an emerging field of algebraic topology which originated in topological data analysis. In these notes we provide a concise introduction into this field and give an account on some of its interactions…
Properties of the geometric phase for a nonstatic coherent light-wave arisen in a static environment are analyzed from various angles. The geometric phase varies in a regular nonlinear way, where the center of its variation increases…