Related papers: Stability of trajectories for N -particles dynamic…
We model the phase oscillations of electrons in race-track microtrons by means of an area preserving map with a fixed point at the origin, which represents the synchronous trajectory of a reference particle in the beam. We study the…
In this paper, we consider $N$ clusters of pairs of particles sedimenting in a viscous fluid. The particles are assumed to be rigid spheres and inertia of both particles and fluid are neglected. The distance between each two particles…
We investigate the behaviour of a chain of interacting Brownian particles with one end fixed and the other moving away at slow speed, in the limit of small noise. The interaction between particles is through a pairwise potential with finite…
Stability is a fundamental notion in dynamical systems and control theory that, traditionally understood, describes asymptotic behavior of solutions around an equilibrium point. This notion may be characterized abstractly as continuity of a…
The stability of the orbital motion of two long cylindrical magnets interacting exclusively with magnetic forces is described. To carry out analytical studies a model of magnetically interacting symmetric tops [1] is used. The model was…
We consider N run and tumble particles in one dimension interacting via a linear 1D Coulomb potential, an active version of the rank diffusion problem. It was solved previously for N = 2 leading to a stationary bound state in the attractive…
We consider systems of n particles that move with constant velocity between collisions. Their total momentum but not necessarily their kinetic energy is preserved at collisions. As there are no further constraints, these systems are…
Studying the orbital stability of multi-planet systems is essential to understand planet formation, estimate the stable time of an observed planetary system, and advance population synthesis models. Although previous studies have primarily…
In this paper we provide an analytical investigation of the entanglement dynamics of moving qubits dissipating into a common and (in general) non-Markovian environment for both weak and strong coupling regimes. We first consider the case of…
The exceptionally long lifetime of surface nanobubbles remains one of the biggest questions in the field. One of the proposed mechanisms for the stability is the \emph{dynamic equilibrium} model, which describes a constant flux of gas in…
We investigate a diffusive motion of a system of interacting Brownian particles in quasi-one-dimensional micropores. In particular, we consider a semi-infinite 1D geometry with a partially absorbing boundary and the hard-core inter-particle…
In this paper we study the dynamics of self gravitating spherically symmetric thin shells of counter rotating particles. We consider all possible velocity distributions for the particles, and show that the equations of motion by themselves…
We follow the time sequence of binary elastic collisions in a small collection of hard-core particles. Intervals between the collisions are characterized by the numbers of collisions of different pairs in a given time. It was shown…
We prove H\"{o}lder regularity for the trajectories of an interacting particle system. The particle velocities are given by the nonlocal and singular interactions with the other particles. Particle collisions occur in finite time. Prior to…
We study a system of particles moving on a line in the same direction. Passing is allowed and when a fast particle overtakes a slow particle, it acquires a new velocity drawn from a distribution P_0(v), while the slow particle remains…
For the classical N-body problem, an approach is proposed based on the introduction of some natural in the physical sense optimization problems of mathematical programming for finding a conditional minimum for the characteristics of the…
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…
We present numerical and experimental results for the development of islands of stability in atom-optics billiards with soft walls. As the walls are soften, stable regions appear near singular periodic trajectories in converging (focusing)…
Circular orbits of spinning test particles and their stability in Schwarzschild-like backgrounds are investigated. For these space-times the equations of motion admit solutions representing circular orbits with particles spins being…
We analyze the dynamics of a quantum particle in a one-dimensional bistable potential within the framework of Bohm's quantum mechanics. We give arguments that evidence the fallacy of certain claims found in the literature dealing with the…