On the Mahler measure of hyperelliptic families

We prove Boyd’s “unexpected coincidence” of the Mahler measures for two families of two-variate polynomials defining curves of genus 2. We further equate the same measures to the Mahler measures of polynomials y³ − y + x³ − x + kxy whose zero loci define elliptic curves for k ≠ 0, ± 3

Dynamical properties of a family of collisionless models of elliptical galaxies

N-body simulations of collisionless collapse have offered important clues to the construction of realistic stellar dynamical models of elliptical galaxies. Such simulations confirm and quantify the qualitative expectation that rapid collapse of a self-gravitating collisionless system, initially cool and significantly far from equilibrium, leads to incomplete relaxation, that is to a quasi-equilibrium configuration characterized by isotropic, quasi-Maxwellian distribution of stellar orbits in the inner regions and by radially biased anisotropic pressure in the outer parts. In earlier studies, as illustrated in a number of papers several years ago (see Bertin et al. 1993 and references therein), the attention was largely focused on the successful comparison between the models (constructed under the qualitative clues offered by the N-body simulations mentioned above) and the observations. In this paper we revisit the problem of incomplete violent relaxation, by making a direct comparison between the detailed properties of a family of distribution functions and those of the products of collisionless collapse found in N-body simulations.Comment: to appear in "Plasmas in the Laboratory and in the Universe: new insights and new challenges", G. Bertin, D. Farina, R. Pozzoli eds., AIP Conference Proceedings, Vol. XXX, pp. YY

Dynamical models and numerical simulations of incomplete violent relaxation

N-body simulations of collisionless collapse have offered important clues to the construction of realistic stellar dynamical models of elliptical galaxies. Such simulations confirm and quantify the qualitative expectation that rapid collapse of a self-gravitating collisionless system, initially cool and significantly far from equilibrium, leads to incomplete relaxation. In this paper we revisit the problem, by comparing the detailed properties of a family of distribution functions derived from statistical mechanics arguments to those of the products of collisionless collapse found in N-body simulations.Comment: 4 pages, 2 figures, to appear in the proceedings of the 39th Rencontres de Moriond, "Exploring the Universe," La Thuile, Italy, March 28 - April 4, 200

Perception and reconstruction of two-dimensional, simulated ego-motion trajectories from optic flow.

A veridical percept of ego-motion is normally derived from a combination of visual, vestibular, and proprioceptive signals. In a previous study, blindfolded subjects could accurately perceive passively travelled straight or curved trajectories provided that the orientation of the head remained constant along the trajectory. When they were turned (whole-body, head-fixed) relative to the trajectory, errors occurred. We ask here whether vision allows for better path perception in similar tasks, to correct or complement vestibular perception. Seated, stationary subjects wore a head mounted display showing optic flow stimuli which simulated linear or curvilinear 2D trajectories over a horizontal ground plane. The observer's orientation was either fixed in space, fixed relative to the path, or changed relative to both. After presentation, subjects reproduced the perceived movement with a model vehicle, of which position and orientation were recorded. They tended to correctly perceive ego-rotation (yaw), but they perceived orientation as fixed relative to trajectory or (unlike in the vestibular study) to space. This caused trajectory misperception when body rotation was wrongly attributed to a rotation of the path. Visual perception was very similar to vestibular perception

The PROUST radar

The Stratosphere-Troposphere (ST) radar called PROUST works at 935 MHz using the same klystron and antenna as the coherent-scatter radar. The use of this equipment for ST work has required some important modifications of the transmitting system and the development of receiving, data processing and acquisition (1984,1985) equipment. The modifications are discussed

Relaxation of spherical systems with long-range interactions: a numerical investigation

The process of relaxation of a system of particles interacting with long-range forces is relevant to many areas of Physics. For obvious reasons, in Stellar Dynamics much attention has been paid to the case of 1/r^2 force law. However, recently the interest in alternative gravities emerged, and significant differences with respect to Newtonian gravity have been found in relaxation phenomena. Here we begin to explore this matter further, by using a numerical model of spherical shells interacting with an 1/r^alpha force law obeying the superposition principle. We find that the virialization and phase-mixing times depend on the exponent alpha, with small values of alpha corresponding to longer relaxation times, similarly to what happens when comparing for N-body simulations in classical gravity and in Modified Newtonian Dynamics.Comment: 6 pages, 3 figures, accepted in the International Journal of Bifurcation and Chao

The PROUST radar: First results

Two campaigns took place in 1984 with the PROUST Radar operating in a bistatic mode, the transmitting antenna pointing at the vertical and the receiving one, 1 deg. off the vertical axis. The antenna beam intersection covers an altitude range between 3 and 9 km. The first of these campaigns are analyzed. The results analyzed show the capability of the PROUST Radar to measure the turbulent parameters and study the turbulence-wave interaction. In its present configuration (bistatic mode and 600 m vertical resolution), it has been necessary to make some assumptions that are known not to be truly fulfilled: homogeneous turbulence and constant vertical wind intensity over a 600-m thickness. It is clear that a more detailed study of the interaction between wave and turbulence will be possible with the next version of PROUST Radar (30-m altitude resolution and monostatic mode) that will soon be achieved

Involutive constrained systems and Hamilton-Jacobi formalism

In this paper, we study singular systems with complete sets of involutive constraints. The aim is to establish, within the Hamilton-Jacobi theory, the relationship between the Frobenius' theorem, the infinitesimal canonical transformations generated by constraints in involution with the Poisson brackets, and the lagrangian point (gauge) transformations of physical systems

Hamilton-Jacobi formalism for Linearized Gravity

In this work we study the theory of linearized gravity via the Hamilton-Jacobi formalism. We make a brief review of this theory and its Lagrangian description, as well as a review of the Hamilton-Jacobi approach for singular systems. Then we apply this formalism to analyze the constraint structure of the linearized gravity in instant and front-form dynamics.Comment: To be published in Classical and Quantum Gravit

The Kovacs effect in model glasses

We discuss the `memory effect' discovered in the 60's by Kovacs in temperature shift experiments on glassy polymers, where the volume (or energy) displays a non monotonous time behaviour. This effect is generic and is observed on a variety of different glassy systems (including granular materials). The aim of this paper is to discuss whether some microscopic information can be extracted from a quantitative analysis of the `Kovacs hump'. We study analytically two families of theoretical models: domain growth and traps, for which detailed predictions of the shape of the hump can be obtained. Qualitatively, the Kovacs effect reflects the heterogeneity of the system: its description requires to deal not only with averages but with a full probability distribution (of domain sizes or of relaxation times). We end by some suggestions for a quantitative analysis of experimental results.Comment: 17 pages, 6 figures; revised versio