相关论文: A crystallographic approach to symmetry-breaking i…

Modeling symmetry breaking is essential for understanding the fundamental changes in the behaviors and properties of physical systems, from microscopic particle interactions to macroscopic phenomena like fluid dynamics and cosmic…

These lectures focus on bifurcation analysis as a tool for studying phase transitions that occur in models of liquid-crystalline systems. We show how this approach bridges the gap between the phenomenological Landau theory and the --- often…

Granular hydrodynamics predicts symmetry-breaking instability in a two-dimensional (2D) ensemble of nearly elastically colliding smooth hard spheres driven, at zero gravity, by a rapidly vibrating sidewall. Super- and subcritical…

In this work we investigate symmetry breaking in the presence of a turbulent environment. The transition from a symmetric state to a symmetry-breaking state is demonstrated using two examples: (i) the transition of a two-dimensional flow to…

Symmetry is fundamental to understanding physical systems and can improve performance and sample efficiency in machine learning. Both pursuits require knowledge of the underlying symmetries in data, yet discovering these symmetries…

Nucleation is an activated process in which the system has to overcome a free energy barrier in order for a first-order phase transition between the metastable and the stable phases to take place. In the liquid-to-solid transition the…

We use a bifurcation theory due to Crandall and Rabinowitz to show the existence of a symmetry breaking bifurcation of a specific one parameter family of axially symmetric disc type solutions of a membrane equation with fixed boundary. In…

Herein, fundamentals of topology and symmetry breaking are used to understand crystallization and geometrical frustration in topologically close-packed structures. This frames solidification from a new perspective that is unique from…

Lie symmetry group method is applied to study the boundary-layer equations for two-dimensional steady flow of an incompressible, viscous fluid near a stagnation point at a heated stretching sheet placed in a porous medium equation. The…

The spontaneous symmetry breaking in a vibro-fluidized low-density granular gas in three connected compartments is investigated. When the total number of particles in the system becomes large enough, particles distribute themselves…

Despite the simplicity of its molecular unit, water is a challenging system because of its uniquely rich polymorphism and predicted but yet unconfirmed features. Introducing a novel space of generalized coordinates that capture changes in…

A generalization of scalar electrodynamics called fluid electrodynamics is presented. In this theory a fluid replaces the Higgs scalar field. Fluid electrodynamics might have application to the theory of low temperature Helium superfluids,…

The tasks of identifying separation structures and clusters in flow data are fundamental to flow visualization. Significant work has been devoted to these tasks in flow represented by vector fields, but there are unique challenges in…

Lie symmetry group method is applied to study Newtonian incompressible fluid's equations flow in turbulent boundary layers. The symmetry group and its optimal system are given, and group invariant solutions associated to the symmetries are…

Dipole-conserving fluids serve as examples of kinematically constrained systems that can be understood on the basis of symmetry. They are known to display various exotic features including glassylike dynamics, subdiffusive transport, and…

We show that some pieces of cylinders bounded by two parallel straight-lines bifurcate in a family of periodic non-rotational surfaces with constant mean curvature and with the same boundary conditions. These cylinders are initial…

We study the structure and morphological changes of fluids that are in contact with solid composites formed by alternating and microscopically wide stripes of two different materials. One type of the stripes interacts with the fluid via…

The issue of symmetry and symmetry breaking is fundamental in all areas of science. Symmetry is often assimilated to order and beauty while symmetry breaking is the source of many interesting phenomena such as phase transitions,…

Bifurcation theory is the usual analytic approach to study the parameter space of a dynamical system. Despite the great power of prediction of these techniques, fundamental limitations appear during the study of a given problem. Nonlinear…

This study introduces a modeling approach aimed at elucidating the pivotal role of symmetry in phase transitions, focusing specifically on the isotropic-nematic (I-N) transition characteristic of liquid crystal systems. By leveraging…