Related papers: Collapse of n vortices
A system of three point vortices in an unbounded plane has a special family of self-similarly contracting or expanding solutions: during the motion, vortex triangle remains similar to the original one, while its area decreases (grows) at a…
We study self-similar solutions of the point-vortex system. The explicit formula for self-similar solutions has been obtained for the three point-vortex problem and for a specific example of the four and five point-vortex problems. We see…
In this article we considered the integrable problems of three vortices on a plane and sphere for noncompact case. We investigated explicitly the problems of a collapse and a scattering of vortices and obtained the conditions of its…
We investigate the dynamics of $N$ point vortices in the plane, in the limit of large $N$. We consider {\em relative equilibria}, which are rigidly rotating lattice-like configurations of vortices. These configurations were observed in…
The gravitational collapse of cylindrically distributed perfect fluid is studied. We assume the collapsing speed of fluid is very large and investigate such a situation by recently proposed high-speed approximation scheme. We show that if…
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 obtained new periodic solutions in the problems of three and four point vortices moving on a plane. In the case of three vortices, the system is reduced to a Hamiltonian system with one degree of freedom, and it is integrable. In the…
A self-gravitating homogeneous ball of a fluid with pressure zero where the fluid particles are initially at rest collapses to a point in finite time. We prove that this gravitational collapse can be approximated arbitrarily closely by…
A system of three particles undergoing inelastic collisions in arbitrary spatial dimensions is studied with the aim of establishing the domain of ``inelastic collapse''---an infinite number of collisions which take place in a finite time.…
We give a method to determine relative periodic orbits in point vortex systems: it consists mainly into perform a symplectic reduction on a fixed point submanifold in order to obtain a two-dimensional reduced phase space. The method is…
We consider 2D point vortex systems and, under certain conditions on the masses of the point vortices, prove that collapse is impossible and provide bounds on the growth of the system. The bounds are typically of the form $O(t^a)$ for some…
A long-standing quantum-mechanical puzzle is whether the collapse of the wave function is a real physical process or simply an epiphenomenon. This puzzle lies at the heart of the measurement problem. One way to choose between the…
Emergence of singularity of vorticity at a single point, not related to any symmetry of the initial distribution, has been demonstrated numerically for the first time. Behavior of the maximum of vorticity near the point of collapse closely…
We offer a new method of reduction for a system of point vortices on a plane and a sphere. This method is similar to the classical node elimination procedure. However, as applied to the vortex dynamics, it requires substantial modification.…
Topological techniques are used to study the motions of systems of point vortices in the infinite plane, in singly-periodic arrays, and in doubly-periodic lattices. The reduction of each system using its symmetries is described in detail.…
This article studies the N-vortex problem in the plane with positive vorticities. After an investigation of some properties for normalised relative equilibria of the system, we use symplectic capacity theory to show that, there exist…
We numerically investigate the erosion potential of a cavitating liquid jet by means of high-resolution finite volume simulations. As thermodynamic model, we employ a barotropic equilibrium cavitation approach, embedded into a homogeneous…
We investigate the dynamics of self-gravitating, spherically-symmetric distributions of fluid through numerical means. In particular, systems involving neutron star models driven far from equilibrium in the strong-field regime of general…
The gravitational collapse of spherical, barotropic perfect fluids is analyzed here. For the first time, the final state of these systems is studied without resorting to simplifying assumptions - such as self-similarity - using a new…
Collapse models implement a progressive loss of quantum coherence when the mass and the complexity of quantum systems increase. We will review such models and the current attempts to test their predicted loss of quantum coherence.