Related papers: Dynamical fractalization of ring systems
The goal of this contribution is to introduce the Hamiltonian formalism of theoretical mechanics for analysing motion in generic linear and non-linear dynamical systems, including particle accelerators. This framework allows the derivation…
An overview of dynamical systems in accelerator physics is presented with a suggestion of a few issues to be addressed. Also mentioned are a few possible developments in the future. Technical details supporting the views are not presented.
The thermodynamics of rigidly rotating systems experience divergences when the system dimensions transverse to the rotation axis exceed the critical size imposed by the causality constraint. The rotation with imaginary angular frequency,…
Dynamics of regular clusters of many non-touching particles falling under gravity in a viscous fluid at low Reynolds number are analysed within the point-particle model. Evolution of two families of particle configurations is determined: 2…
The dynamics of systems of two and three planets, initially placed on circular and nearly coplanar orbits, is explored in the proximity of their stability limit. The evolution of a large number of systems is numerically computed and their…
The analytical generalization of the classical dynamical friction formula (derived under the assumption that all the field particles have the same mass) to the case in which the masses of the field particles are distributed with a mass…
We use the fractional integrals to describe fractal media. We consider the fractal media as special ("fractional") continuous media. We discuss the possible experimental testing of the continuous medium model for fractal media that is…
Chaotic transients occur in many experiments including those in fluids, in simulations of the plane Couette flow, and in coupled map lattices and they are a common phenomena in dynamical systems. Superlong chaotic transients are caused by…
A broad class of systems, including ecological, epidemiological, and sociological ones, are characterized by populations of individuals assigned to specific categories, e.g., a chemical species, an opinion or an epidemic state, that are…
We study the motion of test particles around a center of attraction represented by a monopole (with and without spheroidal deformation) surrounded by a ring, given as a superposition of Morgan & Morgan discs. We deal with two kinds of…
Evolution of coherent states is considered for a particle confined to a cylinder moving in a harmonic oscillator potential. Because of the discontinuous changes as time goes by of the phase representing the position of a particle on a…
The dynamics of an active walker in a harmonic potential is studied experimentally, numerically and theoretically. At odds with usual models of self-propelled particles, we identify two dynamical states for which the particle condensates at…
Despite several experiments on chaotic quantum transport in two-dimensional systems such as semiconductor quantum dots, corresponding quantum simulations within a real-space model have been out of reach so far. Here we carry out quantum…
The distribution of visible matter in the universe, such as galaxies and galaxy clusters, has its origin in the week fluctuations of density that existed at the epoch of recombination. The hierarchical distribution of the universe, with its…
We uncover a dynamical entanglement transition in a monitored quantum system that is heralded by a local order parameter. Classically, chaotic systems can be stochastically controlled onto unstable periodic orbits and exhibit controlled and…
Fractals are ubiquitous natural emergences that have gained increased attention in engineering applications, thanks to recent technological advancements enabling the fabrication of structures spanning across many spatial scales. We show how…
We study the interface dynamics of a binary particle mixture in a rotating cylinder numerically. By considering only the particle motion in axial direction, it is shown that the initial dynamics can be well described by a one-dimensional…
Studies of particle motion in vortical flows have mainly focused on point-like particles, either inertial or self-propelled. This approximation assumes that the velocity field that surrounds the particle is linear. We consider an…
A hybrid scheme between large-scale electronic structure calculations is developed and applied to nanocrystalline silicon with more than 10$^5$ atoms. Dynamical fracture processes are simulated under external loads in the [001] direction.…
This study is motivated by the observation, based on photographs from the Cassini mission, that Saturn's rings have a fractal structure in radial direction. Accordingly, two questions are considered: (1) What Newtonian mechanics argument in…