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We extend and apply a recently developed approach to the study of dynamic bifurcations in PDEs based on the geometric blow-up method. We show that this approach, which has so far only been applied to study a dynamic Turing bifurcation in a…
The traditional goal of inverse self-assembly is to design interactions that drive particles toward a desired target structure. However, achieving successful self-assembly also requires tuning the thermodynamic conditions under which the…
The propagation of waves through microstructured media with periodically arranged inclusions has applications in many areas of physics and engineering, stretching from photonic crystals through to seismic metamaterials. In the…
Using concepts of physics of elementary particles concerning the breaking of symmetry and grannd unified theory we propose to study with the algebraic approximation the degeneracy finded in the genetic code with the incorporation of a…
Algebraic topology (homology) is used to analyze the weakly turbulent state of spiral defect chaos in both laboratory experiments and numerical simulations of Rayleigh-Benard convection.The analysis reveals topological asymmetries that…
This manuscript introduces novel approaches to three phenomena. First, we extend the algebraic formulation of kinetic theory within the contact framework by making explicit the gauge freedom, thereby obtaining a formulation in which the…
A model in statistical mechanics, characterised by the corresponding Gibbs measure, is a subset of the totality of probability distributions on the phase space. The shape of this subset, i.e., the geometry, then plays an important role in…
This paper describes an interdisciplinary approach to geometry modeling of geospatial boundaries. The objective is to extract surfaces from irregular spatial patterns using differential geometry and obtain coherent directional predictions…
We give a self-contained survey of some approaches aimed at a global description of the geometry underlying double field theory. After reviewing the geometry of Courant algebroids and their incarnations in the AKSZ construction, we develop…
We provide a consistent statistical-mechanical treatment for describing the thermodynamics and the structure of fluids embedded in the hyperbolic plane. In particular, we derive a generalization of the virial equation relating the bulk…
Artificial intelligence for scientific discovery has recently generated significant interest within the machine learning and scientific communities, particularly in the domains of chemistry, biology, and material discovery. For these…
We give an introduction to the study of algebraic hypersurfaces, focusing on the problem of when two hypersurfaces are isomorphic or close to being isomorphic. Working with hypersurfaces and emphasizing examples makes it possible to discuss…
The two particle interferometry method to determine the size of the emitting source after a heavy ion collision is extended. Following the extension of the method to spherical expansion dynamics, here we extend the method to rotating…
Manifolds occur naturally as configuration spaces of robotic systems. They provide global descriptions of local coordinate systems that are common tools in expressing positions of robots. The purpose of this survey is threefold. Firstly, we…
The microscopic structure of several amorphous substances often reveals complex patterns such as medium- or long-range order, spatial heterogeneity, and even local polycrystallinity. To capture all these features, models usually incorporate…
The formal structure of geometrical thermodynamics is reviewed with particular emphasis on the geometry of equilibria submanifolds. On these submanifolds thermodynamic metrics are defined as the Hessian of thermodynamic potentials. Links…
Several cellular activities, such as directed cell migration, are coordinated by an intricate network of biochemical reactions which lead to a polarised state of the cell, in which cellular symmetry is broken, causing the cell to have a…
Models that involve coupled dynamics in a mixed-dimensional geometry are of increasing interest in several applications. Here, we describe the development of a simulation model for flow in fractured porous media, where the fractures and…
We consider the demixing of a binary fluid mixture, under gravity, which is steadily driven into a two phase region by slowly ramping the temperature. We assume, as a first approximation, that the system remains spatially isothermal, and…
A stochastic method is introduced for geometric modeling aerosol surface roughness with random field and discrete differential geometry theory. Optical scattering properties are computed for randomly oriented spheroidal particles with…