Related papers: Inelastic Collapse of Three Particles
Collisionless suspensions of inertial particles (finite-size impurities) are studied in 2D and 3D spatially smooth flows. Tools borrowed from the study of random dynamical systems are used to identify and to characterise in full generality…
A stochastic PDE, describing mesoscopic fluctuations in systems of weakly interacting inertial particles of finite volume, is proposed and analysed in any finite dimension $d\in\mathbb{N}$. It is a regularised and inertial version of the…
A method is provided for approximating random slow manifolds of a class of slow-fast stochastic dynamical systems. Thus approximate, low dimensional, reduced slow systems are obtained analytically in the case of sufficiently large time…
We have studied the general properties of the energy thresholds of stability for a three-particle system with short-range interaction. A wide region of the interaction constants and various ratios of the masses of particles are considered.…
We present a new general model for the prediction of the drag coefficient of non-spherical solid particles of regular and irregular shapes falling in gas or liquid valid for sub-critical particle Reynolds numbers (i.e. $Re < 3 \times…
The local gravitational instability of rotating discs is believed to be an important mechanism in different astrophysical processes, including the formation of gas and stellar clumps in galaxies. We aim to study in three dimensions the…
This article is a brief review of the results of studying the collapse of sound waves in media with positive dispersion, which is described in terms of the three-dimensional Kadomtsev-Petviashvili (KP) equation. The KP instability of…
We revisit the topic of shape evolution during the spherical collapse of an $N$-body system. Our main objective is to investigate the critical particle number below which, during a gravitational collapse, the amplification of triaxiality…
A brief review is given of some well-known and some very recent results obtained in studies of two- and three-dimensional (2D and 3D) solitons. Both zero-vorticity (fundamental) solitons and ones carrying vorticity S = 1 are considered.…
We study the stability of a zero temperature mixture of attractively interacting degenerate bosons and spin-polarized fermions in the absence of confinement. We demonstrate that higher order corrections to the standard mean-field energy can…
We compute the strengths of zero-th order (in eccentricity) three-body resonances for a co-planar and low eccentricity multiple planet system. In a numerical integration we illustrate that slowly moving Laplace angles are matched by…
When two non-relativistic particles scatter in one dimension, they can become entangled. This entanglement process is constrained by the symmetries of the scattering system and the boundary conditions on the incoming state. Applying these…
We comprehend the role of imperfections in materials consisting of interacting particles, arising from different origins on their universal features. Specifically, we report the static and dynamic responses in a cluster of Coulomb…
We discovered an oscillatory instability in a system of inelastically colliding hard spheres, driven by two opposite "thermal" walls at zero gravity. The instability, predicted by a linear stability analysis of the equations of granular…
Initially cold and spherically symmetric self-gravitating systems may give rise to a virial equilibrium state which is far from spherically symmetric, and typically triaxial. We focus here on how the degree of symmetry breaking in the final…
We study static packings of frictionless and frictional spheres in three dimensions, obtained via molecular dynamics simulations, in which we vary particle hardness, friction coefficient, and coefficient of restitution. Although…
The system of four point vortices in the plane has relative equilibria that behave as composite particles, in the case where three of the vortices have strength $-\Gamma/3$ and one of the vortices has strength $\Gamma$. These relative…
We consider a particle with a position-dependent mass, moving in a three-dimensional semi-infinite parallelepipedal or cylindrical channel under the influence of some hyperbolic potential. We show that the lack of uniformity in the…
The rapid collapse of a polymer, due to external forces or changes in solvent, yields a long-lived `crumpled globule.' The conjectured fractal structure shaped by hierarchical collapse dynamics has proved difficult to establish, even with…
Dynamics of inelastic gases are studied within the framework of random collision processes. The corresponding Boltzmann equation with uniform collision rates is solved analytically for gases, impurities, and mixtures. Generally, the energy…