186,323 research outputs found
Cucker–Smale Type Dynamics of Infinitely Many Individuals with Repulsive Forces
No full textWe study the existence and uniqueness of the time evolution of a system of infinitely many individuals, moving in a tunnel and subjected to a Cucker–Smale type alignment dynamics with compactly supported communication kernels and to short-range repulsive interactions to avoid collisions
Time Evolution of Concentrated Vortex Rings
No full textWe study the time evolution of an incompressible fluid with axisymmetry without swirl when the vorticity is sharply concentrated. In particular, we consider N disjoint vortex rings of size ε and intensity of the order of | log ε| - 1. We show that in the limit ε→ 0 , when the density of vorticity becomes very large, the movement of each vortex ring converges to a simple translation, at least for a small but positive time
A stochastic particle system approximating the BGK equation
No full textWe consider a stochastic N-particle system on a torus in which each particle moving freely can instantaneously thermalize according to the particle configuration at that instant. Following [2], we show that the propagation of chaos does hold and that the one-particle distribution converges to the solution of the BGK equation. The improvement with respect to [2] consists in the fact that here, as suggested by physical considerations, the thermalizing transition is driven only by the restriction of the particle configuration in a small neighborhood of the jumping particle. In other words, the Maxwellian distribution of the outgoing particle is computed via the empirical hydrodynamical fields associated to the fraction of particles sufficiently close to the test particle and not, as in [2], via the whole particle configuration
Global time evolution of concentrated vortex rings
No full textWe study the time evolution of an incompressible fluid with axial symmetry without swirl, assuming initial data such that the initial vorticity is very concentrated inside N small disjoint rings of thickness ε and vorticity mass of the order of | log ε| - 1. When ε→ 0 , we show that the motion of each vortex ring converges to a simple translation with constant speed (depending on the single ring) along the symmetry axis. We obtain a sharp localization of the vorticity support at time t in the radial direction, whereas we state only a concentration property in the axial direction. This is obtained for arbitrary (but fixed) intervals of time. This study is the completion of a previous paper [5], where a sharp localization of the vorticity support was obtained both along the radial and axial directions, but the convergence for ε→ 0 worked only for short times
On the dynamics of infinitely many charged particles with magnetic confinement
No full textWe study the time evolution of a system of infinitely many charged particles confined by an external magnetic field in an unbounded cylindrical conductor and mutually interacting via the Coulomb force. We prove the existence, uniqueness and quasi-locality of the motion. Moreover, we give some nontrivial bounds on its long time behavior
Kac polymers
No full textWe show how a polymer in two dimensions with a self-repelling interaction of Kac type exhibits a diffusive-ballistic transition if considered on the appropriate scale
Computing the Structured Pseudospectrum of a Toeplitz Matrix and Its Extreme Points.
No full textThe computation of the structured pseudospectral abscissa and radius (with respect to the Frobenius norm) of a Toeplitz matrix is discussed and two algorithms based on a low-rank property to construct extremal perturbations are presented. The algorithms are inspired by those considered in [N. Guglielmi and M. Overton, SIAM J. Matrix Anal. Appl., 32 (2011), pp. 1166--1192] for the unstructured case, but their extension to structured pseudospectra and analysis presents several difficulties. Natural generalizations of the algorithms, allowing us to draw significant sections of the structured pseudospectra in proximity of extremal points, are also discussed. Since no algorithms are available in the literature to draw such structured pseudospectra, the approach we present seems promising to extend existing software tools (Eigtool, Seigtool) to structured pseudospectra representation for Toeplitz matrices. We discuss local convergence properties of the algorithms and show some applications to a few illustrative examples
Slow motion and metastability for a non local evolution equation
No full textIn this paper we consider a nonlocal evolution equation in one dimension,
which describes the dynamics of a ferromagnetic system in the mean field
approximation. In the presence of a small magnetic field, it admits two stationary
and homogeneous solutions, representing the stable and metastable phases
of the physical system. We prove the existence of an invariant, one dimensional
manifold connecting the stable and metastable phases. This is the unstable
manifold of a distinguished, spatially nonhomogeneous, stationary solution,
called the critical droplet.(4, 10) We show that the points on the manifold are
droplets longer or shorter than the critical one, and that their motion is very
slow in agreement with the theory of metastable patterns. We also obtain a new
proof of the existence of the critical droplet, which is supplied with a local
uniqueness result
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