Related papers: Global Dynamics in the Singular Logarithmic Potent…
We built three models for the gravitational field of the Galactic bar. These models are an inhomogeneous ellipsoid, an inhomogeneous prolate spheroid, and a superposition of four inhomogeneous ellipsoids. Among the three models, the…
The aim of this work is to prove the global-in-time existence of weak solutions for a viscoelastic phase separation model in three space dimensions. To this end we apply the relative energy concept provided by [3]. We consider the case of…
Luminous galaxies and their dark halos are likely to have triaxial shapes. The construction of distribution functions for triaxial systems is a hard problem, due to the existence of only one exact integral of motion, the energy $E$. Even…
We study the dynamics near the unstable Lagrangian points in galactic bar models using dynamical system tools in order to determine the global morphology of a barred galaxy. We aim at the case of non-autonomous models, in particular with…
Locomotion is essential for living cells. It enables bacteria and algae to explore space for food, cancer to spread, and immune system to fight infections. Motile cells display trajectories of intriguing complexity, from regular (e.g.…
Absolute proper motions for six new globular clusters have recently been determined. This motivated us to obtain the Galactic orbits of these six clusters both in an axisymmetric Galactic potential and in a barred potential, such as the one…
The spherical reduction of the rational Calogero model (of type $A_{n-1}$ and after removing the center of mass) is considered as a maximally superintegrable quantum system, which describes a particle on the $(n{-}2)$-sphere subject to a…
Dynamics of charged particles in the vicinity of a rotating black hole embedded in the external large-scale magnetic field is numerically investigated. In particular, we consider a non-axisymmetric model in which the asymptotically uniform…
Revisiting canonical integration of the classical solid near a uniform rotation, canonical action angle coordinates, hyperbolic and elliptic, are constructed in terms of various power series with coefficients which are polynomials in a…
It is shown that nonzero orbital momentum in the vertex of secondary interaction in the triangle graph leads to a more clear picture corresponding to the moving complex singularity compared with the case of constant vertex. The peak in the…
Conformal gravity theory can explain observed flat rotation curves of galaxies without invoking hypothetical dark matter. Within this theory, we obtain a generic formula for the sizes of galaxies exploiting the stability criterion of…
We consider particle dynamics in singular gravitational field. In 2d spacetime the system splits into two independent gravitational systems without singularity. Dynamical integrals of each system define $sl(2,R)$ algebra, but the…
We present a detailed theoretical analysis of micro-motion in a time-averaged orbiting potential trap. Our treatment is based on the Gross-Pitaevskii equation, with the full time dependent behaviour of the trap systematically approximated…
We use Laskar's frequency mapping technique to study the dynamics of triaxial galaxies with central density cusps and nuclear black holes. For ensembles of 10^4 orbits, we numerically compute the three fundamental frequencies of the motion,…
Studies of the dynamics of globular clusters assume different values of bar parameters (mass, velocity, size) and analyse the results of orbit classifications over the range of the chosen values. It is also a usual thing that a spherical…
Common noise acting on a population of identical oscillators can synchronize them. We develop a description of this process which is not limited to the states close to synchrony, but provides a global picture of the evolution of the…
The study of self-gravitating stellar systems has provided important hints to develop tools of analytical mechanics. In the present contribution we review how to exploit detuned resonant normal forms to extract information on several…
This paper introduces a new global dynamics and chaos indicator based on the method of Lagrangian Descriptor apt for discriminating ordered and deterministic chaotic motions in multidimensional systems. The selected implementation of this…
Low-dimensional, complex systems are often characterized by logarithmically slow dynamics. We study the generic motion of a labeled particle in an ensemble of identical diffusing particles with hardcore interactions in a strongly…
Slow dynamic nonlinearity is ubiquitous amongst brittle materials, such as rocks and concrete, with cracked microstructures. A defining feature of the behavior is the logarithmic-in-time recovery of stiffness after a mechanical…