Probing an nonequilibrium Einstein relation in an aging colloidal glass

We present a direct experimental measurement of an effective temperature in a colloidal glass of Laponite, using a micrometric bead as a thermometer. The nonequilibrium fluctuation-dissipation relation, in the particular form of a modified Einstein relation, is investigated with diffusion and mobility measurements of the bead embedded in the glass. We observe an unusual non-monotonic behavior of the effective temperature : starting from the bath temperature, it is found to increase up to a maximum value, and then decreases back, as the system ages. We show that the observed deviation from the Einstein relation is related to the relaxation times previously measured in dynamic light scattering experiments.Comment: 4 pages, 4 figures, corrected references, published in Phys. Rev. Lette

On chaotic behavior of gravitating stellar shells

Motion of two gravitating spherical stellar shells around a massive central body is considered. Each shell consists of point particles with the same specific angular momenta and energies. In the case when one can neglect the influence of gravitation of one ("light") shell onto another ("heavy") shell ("restricted problem") the structure of the phase space is described. The scaling laws for the measure of the domain of chaotic motion and for the minimal energy of the light shell sufficient for its escape to infinity are obtained.Comment: e.g.: 12 pages, 8 figures, CHAOS 2005 Marc

Escaping from nonhyperbolic chaotic attractors

We study the noise-induced escape process from chaotic attractors in nonhyperbolic systems. We provide a general mechanism of escape in the low noise limit, employing the theory of large fluctuations. Specifically, this is achieved by solving the variational equations of the auxiliary Hamiltonian system and by incorporating the initial conditions on the chaotic attractor unambiguously. Our results are exemplified with the H{\'e}non and the Ikeda map and can be implemented straightforwardly to experimental data.Comment: replaced with published versio

Solving procedure for a twenty-five diagonal coefficient matrix: direct numerical solutions of the three dimensional linear Fokker-Planck equation

We describe an implicit procedure for solving linear equation systems resulting from the discretization of the three dimensional (seven variables) linear Fokker-Planck equation. The discretization of the Fokker-Planck equation is performed using a twenty-five point molecule that leads to a coefficient matrix with equal number of diagonals. The method is an extension of Stone's implicit procedure, includes a vast class of collision terms and can be applied to stationary or non stationary problems with different discretizations in time. Test calculations and comparisons with other methods are presented in two stationary examples, including an astrophysical application for the Miyamoto-Nagai disk potential for a typical galaxy.Comment: 20 pages, RevTex, no proofreading, accepted in Journal of Computational Physic

Quadratic Volume Preserving Maps

We study quadratic, volume preserving diffeomorphisms whose inverse is also quadratic. Such maps generalize the Henon area preserving map and the family of symplectic quadratic maps studied by Moser. In particular, we investigate a family of quadratic volume preserving maps in three space for which we find a normal form and study invariant sets. We also give an alternative proof of a theorem by Moser classifying quadratic symplectic maps.Comment: Ams LaTeX file with 4 figures (figure 2 is gif, the others are ps

Core Collapse via Coarse Dynamic Renormalization

In the context of the recently developed "equation-free" approach to computer-assisted analysis of complex systems, we extract the self-similar solution describing core collapse of a stellar system from numerical experiments. The technique allows us to side-step the core "bounce" that occurs in direct N-body simulations due to the small-N correlations that develop in the late stages of collapse, and hence to follow the evolution well into the self-similar regime.Comment: 5 pages, 3 figure

Nambu-Hamiltonian flows associated with discrete maps

For a differentiable map $(x_1,x_2,..., x_n)\to (X_1,X_2,..., X_n)$ that has an inverse, we show that there exists a Nambu-Hamiltonian flow in which one of the initial value, say $x_n$, of the map plays the role of time variable while the others remain fixed. We present various examples which exhibit the map-flow correspondence.Comment: 19 page

Chaos and Rotating Black Holes with Halos

The occurrence of chaos for test particles moving around a slowly rotating black hole with a dipolar halo is studied using Poincar\'e sections. We find a novel effect, particles with angular momentum opposite to the black hole rotation have larger chaotic regions in phase space than particles initially moving in the same direction.Comment: 9 pages, 4 Postscript figures. Phys. Rev. D, in pres

The Tidal Tails of the Ultra-Faint Globular Cluster Palomar 1

Using the Optimal Filter Technique applied to Sloan Digital Sky Survey photometry, we have found extended tails stretching about 1 degree (or several tens of half-light radii) from either side of the ultra-faint globular cluster Palomar 1. The tails contain roughly as many stars as does the cluster itself. Using deeper Hubble Space Telescope data, we see that the isophotes twist in a chacteristic S-shape on moving outwards from the cluster centre to the tails. We argue that the main mechanism forming the tails may be relaxation driven evaporation and that Pal 1 may have been accreted from a now disrupted dwarf galaxy ~500 Myr ago.Comment: 6 figures, accepted for publication in MNRAS Letters Changes in v2: Merged previous figures 3 and 5 and slightly expanded discussio