Related papers: Geometric evolution as a source of discontinuous b…
Evolutionary dynamics is often viewed as a subtle process of change accumulation that causes a divergence among organisms and their genomes. However, this interpretation is an inheritance of a gradualistic view that has been challenged at…
In the present work, we discuss how the functional form of thermodynamic observables can be deduced from the geometric properties of subsets of phase space. The geometric quantities taken into account are mainly extrinsic curvatures of the…
Significant advances in numerical simulations of black-hole binaries have recently been achieved using the puncture method. We examine how and why this method works by evolving a single black hole. The coordinate singularity and hence the…
This paper considers generalised network, intended as networks where (a) the edges connecting the nodes are nonlinear, and (b) stochastic processes are continuously indexed over both vertices and edges. Such topological structures are…
The dynamical ellipticity of a planet expresses the departure of its mass distribution from spherical symmetry. It enters as a parameter in the description of a planet's precession and nutation, as well as other rotational normal modes. In…
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…
Topological defects are thought to be left behind by the cosmological phase transitions which occur as the universe expands and cools. Similar processes can be studied in the phase transitions which take place in the laboratory:…
We study the evolution of graphs densifying by adding edges: Two vertices are chosen randomly, and an edge is (i) established if each vertex belongs to a tree; (ii) established with probability $p$ if only one vertex belongs to a tree;…
On the basis of the principle that topological quantum phases arise from the scattering around space-time defects in higher dimensional unification, a geometric model is presented that associates with each quantum phase an element of a…
A monitored quantum system undergoing a cyclic evolution of the parameters governing its Hamiltonian accumulates a geometric phase that depends on the quantum trajectory followed by the system on its evolution. The phase value will be…
The topological properties of a material depend on its symmetries, parameters, and spatial dimension. Changes in these properties due to parameter and symmetry variations can be understood by computing the corresponding topological…
Cities are living organisms. They are out of equilibrium, open systems that never stop developing and sometimes die. The local geography can be compared to a shell constraining its development. In brief, a city's current layout is a step in…
We study the asymptotic nature of geometric structures formed from a point cloud of observations of (generally heavy tailed) distributions in a Euclidean space of dimension greater than one. A typical example is given by the Betti numbers…
Dislocations, as topological defects in crystal lattices, are fundamental to understanding plasticity in materials. Similar periodic structures also arise in continuum field theories, such as chiral soliton lattices (CSLs), which appear in…
Networks are important representations in computer science to communicate structural aspects of a given system of interacting components. The evolution of a network has several topological properties that can provide us information on the…
We introduce a new geometric framework for relativistic particle dynamics based on contact geometry and suitable for treating dissipative processes like particle decay. The dynamics is formulated on a nine--dimensional extended phase space…
This text surveys different probabilistic aspects of a model which is used to describe the evolution of an object that falls apart randomly as time passes. Each point of view yields useful techniques to establish properties of such random…
We show that gravity theories involving disformally transformed metrics in their matter coupling lead to spontaneous growth of various fields in a similar fashion to the spontaneous scalarization scenario in scalar-tensor theories.…
The approach to incorporate quantum effects in gravity by replacing free particle geodesics with Bohmian non-geodesic trajectories has an equivalent description in terms of a conformally related geometry, where the motion is force free,…
We study a 2D scalar harmonic wave transmission problem between a classical dielectric and a medium with a real-valued negative permittivity/permeability which models a metal at optical frequency or an ideal negative metamaterial. We…