Related papers: Symmetric Molecular Dynamics
The motion of an incompressible fluid in Lagrangian coordinates involves infinitely many symmetries generated by the left Lie algebra of group of volume preserving diffeomorphisms of the three dimensional domain occupied by the fluid.…
As "2D" materials (i.e. materials just a few atoms thick) continue to gain prominence, understanding their symmetries is critical for unlocking their full potential. In this work, we present comprehensive tables that tabulate the rod group…
The planar dynamics of spin-1/2 quantum relativistic particles is important for several physical systems. In this paper we derive, by a simple method, the generators for the continuous symmetries of the 3+1 Dirac equation for planar motion,…
Crystal symmetry plays a fundamental role in determining its physical, chemical, and electronic properties such as electrical and thermal conductivity, optical and polarization behavior, and mechanical strength. Almost all known crystalline…
We formulate a geometric measurement theory of dynamical classical systems possessing both continuous and discrete degrees of freedom. The approach is covariant with respect to choices of clocks and canonically incorporates laboratories.…
Let a finite set of interacting particles be given, together with a symmetry Lie group $G$. Here we describe all possible dynamics that are jointly equivariant with respect to the action of $G$. This is relevant e.g., when one aims to…
This lecture series consists of mostly independent three parts: Part 1: a tour of basic 4d N=1 supersymmetric dynamics, covering the pure super Yang-Mills, the Seiberg duality for classical groups, the supersymmetric index on S^3, and the…
We construct a generalized dynamics for particles moving in a symmetric space-time, i.e. a space-time admitting one or more Killing vectors. The generalization implies that the effective mass of particles becomes dynamical. We apply this…
We consider dynamics of massless particle in 2d spacetimes with constant curvature. We analyze different examples of spacetime. Dynamical integrals are constructed from spacetime symmetry related to $sl(2.{\bf R})$ algebra. Mass-shell…
We summarise some recent results on solution landscapes for two-dimensional (2D) problems in the Landau--de Gennes theory for nematic liquid crystals. We study energy-minimizing and non energy-minimizing solutions of the Euler--Lagrange…
It is shown that all spherical symmetric potentials are capable of producing dynamical symmetries in classical one-body motions, thanks to the inevitable existence of symmetry axes associated with turning points for corresponding…
The symmetry of a crystal structure with a three-dimensional (3D) lattice can be classified by one of the 230 space group types. For some types of crystals, e.g. crystalline films, surfaces, or planar interfaces, it is more appropriate to…
The study of granular crystals, metamaterials that consist of closely packed arrays of particles that interact elastically, is a vibrant area of research that combines ideas from disciplines such as materials science, nonlinear dynamics,…
Generating novel crystalline materials has the potential to lead to advancements in fields such as electronics, energy storage, and catalysis. The defining characteristic of crystals is their symmetry, which plays a central role in…
The optimal conversion of a continuous inter-particle potential to a discrete equivalent is considered here. Existing and novel algorithms are evaluated to determine the best technique for creating accurate discrete forms using the minimum…
A fundamental objective of materials modeling is identifying atomic structures that align with experimental observables. Conventional approaches for disordered materials involve sampling from thermodynamic ensembles and hoping for an…
The spatial symmetry of matter - including finite objects like molecules or atomic clusters, and extended objects like periodic or aperiodic crystals - is described using point groups and space groups. Magnetic point groups and space groups…
We extend the phase field crystal model to accommodate exact atomic configurations and vacancies by requiring the order parameter to be non-negative. The resulting theory dictates the number of atoms and describes the motion of each of…
Classical model S_{Dcl} of the Dirac particle S_D is constructed. S_D is the dynamic system described by the Dirac equation. For investigation of S_D and construction of S_{Dcl} one uses a new dynamic method: dynamic disquantization. This…
Crystals form regular and robust structures that under extreme conditions can melt and recrystallize into different arrangements in a process that is called crystal metamorphism. While crystals exist due to the breaking of a continuous…