Related papers: Interacting Geodesics on Discrete Manifolds
Geometric evolution represents a fundamental aspect of many physical phenomena. In this paper we consider the geometric evolution of structures that undergo topological changes. Topological changes occur when the shape of an object evolves…
We investigate the geodesic motions of a massive particle and light ray in the hyperplane orthogonal to the symmetry axis in the 5-dimensional hypercylindrical spacetime. The class of the solutions depends on one constant a which is the…
The geodesic deviation equation is generalized to worldline deviation equations describing the relative accelerations of charged spinning particles in the framework of Dixon-Souriau equations of motion.
We propose a new model for the description of complex granular particles and their interaction in molecular dynamics simulations of granular material in two dimensions. The grains are composed of triangles which are connected by deformable…
We study a system of interacting particles in a periodically moving external potential, within the simplest possible description of paradigmatic symmetric exclusion process on a ring. The model describes diffusion of hardcore particles…
We study confined solutions of certain evolutionary partial differential equations (pde) in 1+1 space-time. The pde we study are Lie-Poisson Hamiltonian systems for quadratic Hamiltonians defined on the dual of the Lie algebra of vector…
We investigate motion of test particles in exact spacetimes with an expanding impulsive gravitational wave which propagates in Minkowski, de Sitter or anti-de Sitter universe. Using the continuous form of these metrics we derive explicit…
In this paper we relate the study of actions of discrete groups over connected manifolds to that of their orbit spaces seen as differentiable stacks. We show that the orbit stack of a discrete dynamical system on a simply connected manifold…
We develop a formulation of the strong deflection limit for the scattering of particles following timelike geodesics in asymptotically flat, static, and spherically symmetric spacetimes. For fixed specific energy, as the angular momentum…
The features of the scattering of massive neutral particles propagating in the field of a gravitational plane wave are compared with those characterizing their interaction with an electromagnetic radiation field. The motion is geodesic in…
We describe simulations of active Brownian particles carried out to explore how dynamics and clustering are influenced by particle shape. Our particles are composed of four disks, held together by springs, whose relative size can be varied.…
A Quincke roller is a unique active particle that can run and tumble freely on a flat plate due to the torque generated by a uniform DC electric field applied perpendicular to the plate. A system involving many such particles exhibits a…
The displacement and deviation vectors in spaces (manifolds), the tangent bundle of which is endowed with a transport along paths, are introduced. In case these spaces are equipped with a linear connection, the deviation equations (between…
We study the dynamics of a small solid particle arising from the dewetting of a thin film on a curved substrate driven by capillarity, where mass transport is controlled by surface diffusion. We consider the case when the size of the…
An algebraic formalism for description of quantum states of charged particle with spin moving in two-dimensional space under influence of singular magnetic field is developed in terms of graded algebras. The fundamental assumption is that…
We consider the dynamics of Dirac particles moving in the curved spaces with one coordinate subjected to compactification and thus interpolating smoothly between three- and two-dimensional spaces. We use the model of compactification, which…
A discrete system constituted of particles interacting by means of a centroid-based law is numerically investigated. The elements of the system move in the plane, and the range of the interaction can be varied from a more local form…
We study a class of interacting particle systems in which $n$ signed particles move on the real line. At close range particles with the same sign repel and particles with opposite sign attract each other. The repulsion and attraction are…
Topological phenomena typically govern the behavior of delocalized waves, giving rise to robust transport in electronic, photonic, and mechanical systems. Whether similar principles can directly control the motion of a localized particle,…
We study the dynamics of two particles that interact only when in contact. In this sense, although not in every particular, the interactions mimic those in granular materials. The detailed solution of the dynamics allows an analysis of the…