Transport properties in chaotic and non-chaotic many particles systems

Two deterministic models for Brownian motion are investigated by means of numerical simulations and kinetic theory arguments. The first model consists of a heavy hard disk immersed in a rarefied gas of smaller and lighter hard disks acting as a thermal bath. The second is the same except for the shape of the particles, which is now square. The basic difference of these two systems lies in the interaction: hard core elastic collisions make the dynamics of the disks chaotic whereas that of squares is not. Remarkably, this difference is not reflected in the transport properties of the two systems: simulations show that the diffusion coefficients, velocity correlations and response functions of the heavy impurity are in agreement with kinetic theory for both the chaotic and the non-chaotic model. The relaxation to equilibrium, however, is very sensitive to the kind of interaction. These observations are used to reconsider and discuss some issues connected to chaos, statistical mechanics and diffusion.Comment: 23 pgs with 8 Figure

Weighing the Milky Way

We describe an experiment to measure the mass of the Milky Way galaxy. The experiment is based on calculated light travel times along orthogonal directions in the Schwarzschild metric of the Galactic center. We show that the difference is proportional to the Galactic mass. We apply the result to light travel times in a 10cm Michelson type interferometer located on Earth. The mass of the Galactic center is shown to contribute 10^-6 to the flat space component of the metric. An experiment is proposed to measure the effect.Comment: 10 pages, 1 figur

Macroscopic equations for the adiabatic piston

A simplified version of a classical problem in thermodynamics -- the adiabatic piston -- is discussed in the framework of kinetic theory. We consider the limit of gases whose relaxation time is extremely fast so that the gases contained on the left and right chambers of the piston are always in equilibrium (that is the molecules are uniformly distributed and their velocities obey the Maxwell-Boltzmann distribution) after any collision with the piston. Then by using kinetic theory we derive the collision statistics from which we obtain a set of ordinary differential equations for the evolution of the macroscopic observables (namely the piston average velocity and position, the velocity variance and the temperatures of the two compartments). The dynamics of these equations is compared with simulations of an ideal gas and a microscopic model of gas settled to verify the assumptions used in the derivation. We show that the equations predict an evolution for the macroscopic variables which catches the basic features of the problem. The results here presented recover those derived, using a different approach, by Gruber, Pache and Lesne in J. Stat. Phys. 108, 669 (2002) and 112, 1177 (2003).Comment: 13 pages, 7 figures (revTeX4) The paper has been completely rewritten with new derivation and results, supplementary information can be found at http://denali.phys.uniroma1.it/~cencini/Papers/cppv07_supplements.pd

The production rate of the coarse grained Gibbs entropy and the Kolmogorov-Sinai entropy: a real connection ?

We discuss the connection between the Kolmogorov-Sinai entropy, $h_{KS}$, and the production rate of the coarse grained Gibbs entropy, $r_G$. Detailed numerical computations show that the (often accepted) identification of the two quantities does not hold in systems with intermittent behavior and/or very different characteristic times and in systems presenting pseudo-chaos. The basic reason of this fact is in the asymptotic (with respect to time) nature of $h_{KS}$, while $r_G$ is a quantity related to short time features of a system.Comment: 8 pages, 5 figures Submitted to PR

A Process for Improving Course Quality based on Mid-Semester Feedback

Proceedings of: First International Conference on Reforming Education, Quality of Teaching and Technology-Enhanced Learning: Learning Technologies, Quality of Education, Educational Systems, Evaluation, Pedagogies (TECH-EDUCATION 2010). Athens, Greece, May 19-21, 2010.Quality control mechanisms are becoming more important in higher educational institutions. Student evaluation of teaching is typically used to obtain feedback from students about a learning experience but its effect in the course may take too long. Fast feedback mechanisms, in exchange, look at obtaining feedback in order to apply corrective measures quickly. In this paper a process is described to obtain feedback from the students about a course, analyze the received results, and identify the most significant aspects. The process has been applied to a course and led to some adjustments that had immediate impact on the course.The authors are truly indebted to Miguel Valero for his guidance during the design of this process. Work partially funded by the Learn3 project, “Plan Nacional de I+D+I TIN2008-05163/TSI”, the Best Practice Network ICOPER (Grant No. ECP-2007-EDU-417007), the Flexo Project “Plan Nacional de Investigación Científica, Desarrollo e Innovación Tecnológica” (Ref. TSI-020301-2008-19), and the “Emadrid: Investigación y desarrollo de tecnologías para el e-learning en la Comunidad de Madrid” project (S2009/TIC-1650).Publicad

BeppoSAX Observations of the Maser Sy2 Galaxy: ESO103-G35

We have made BeppoSAX observations of the Seyfert 2/1.9 galaxy ESO103-G35, which contains a nuclear maser source and is known to be heavily absorbed in the X-rays. Analysis of the X-ray spectra observed by SAX in October 1996 and 1997 yields a spectral index 0.74+/-0.07, typical of Seyfert galaxies and consistent with earlier observations of this source. The strong, soft X-ray absorption has column density 1.79E(23)/cm^2, again consistent with earlier results. The best fitting spectrum is that of a power law with a high energy cutoff at 29+/-10 keV, a cold, marginally resolved Fe Kalpha line with EW 290 eV (1996) and a mildly ionized Fe K-edge at 7.37 keV. The Kalpha line and cold absorption are consistent with origin in a accretion disk/torus through which our line-of-sight passes at a radial distance of $\sim 50$ pc. The Fe K-edge is mildly ionized suggesting the presence of ionized gas probably in the inner accretion disk, close to the central source or in a separate warm absorber. The data quality is too low to distinguish between these possibilities but the edge-on geometry implied by the water maser emission favors the former. Comparison with earlier observations of ESO103-G35 shows little/no change in spectral parameters while the flux changes by factors of a few on timescales of a few months. The 2--10 keV flux decreased by a factor of 2.7 between Oct 1996 and Oct 1997 with no detectable change in the count rate >20 keV suggesting a constant or delayed response reflection component. The high energy cutoff is lower than the typical 300keV values seen in Seyfert galaxies. A significant subset of similar sources would affect current models of the AGN contribution to the cosmic X-ray background which generally assume a high energy cutoff of 300 keV.Comment: 22 pages, postscript file, accepted for publication in Ap

Single Channel Analysis of Conductance and Rectification in Cation-selective, Mutant Glycine Receptor Channels

Members of the ligand-gated ion channel superfamily mediate fast synaptic transmission in the nervous system. In this study, we investigate the molecular determinants and mechanisms of ion permeation and ion charge selectivity in this family of channels by characterizing the single channel conductance and rectification of α1 homomeric human glycine receptor channels (GlyRs) containing pore mutations that impart cation selectivity. The A-1'E mutant GlyR and the selectivity double mutant ([SDM], A-1'E, P-2'Δ) GlyR, had mean inward chord conductances (at −60 mV) of 7 pS and mean outward conductances of 11 and 12 pS (60 mV), respectively. This indicates that the mutations have not simply reduced anion permeability, but have replaced the previous anion conductance with a cation one. An additional mutation to neutralize the ring of positive charge at the extracellular mouth of the channel (SDM+R19'A GlyR) made the conductance–voltage relationship linear (14 pS at both 60 and −60 mV). When this external charged ring was made negative (SDM+R19'E GlyR), the inward conductance was further increased (to 22 pS) and now became sensitive to external divalent cations (being 32 pS in their absence). The effects of the mutations to the external ring of charge on conductance and rectification could be fit to a model where only the main external energy barrier height for permeation was changed. Mean outward conductances in the SDM+R19'A and SDM+R19'E GlyRs were increased when internal divalent cations were absent, consistent with the intracellular end of the pore being flanked by fixed negative charges. This supports our hypothesis that the ion charge selectivity mutations have inverted the electrostatic profile of the pore by introducing a negatively charged ring at the putative selectivity filter. These results also further confirm the role of external pore vestibule electrostatics in determining the conductance and rectification properties of the ligand-gated ion channels

Minimal Stochastic Model for Fermi's Acceleration

We introduce a simple stochastic system able to generate anomalous diffusion both for position and velocity. The model represents a viable description of the Fermi's acceleration mechanism and it is amenable to analytical treatment through a linear Boltzmann equation. The asymptotic probability distribution functions (PDF) for velocity and position are explicitly derived. The diffusion process is highly non-Gaussian and the time growth of moments is characterized by only two exponents $\nu_x$ and $\nu_v$. The diffusion process is anomalous (non Gaussian) but with a defined scaling properties i.e. $P(|{\bf x}|,t) = 1/t^{\nu_x}F_x(|{\bf x}|/t^{\nu_x})$ and similarly for velocity.Comment: RevTeX4, 4 pages, 2 eps-figures (minor revision

Recoherence in the entanglement dynamics and classical orbits in the N-atom Jaynes-Cummings model

The rise in linear entropy of a subsystem in the N-atom Jaynes-Cummings model is shown to be strongly influenced by the shape of the classical orbits of the underlying classical phase space: we find a one-to-one correspondence between maxima (minima) of the linear entropy and maxima (minima) of the expectation value of atomic excitation J_z. Since the expectation value of this operator can be viewed as related to the orbit radius in the classical phase space projection associated to the atomic degree of freedom, the proximity of the quantum wave packet to this atomic phase space borderline produces a maximum rate of entanglement. The consequence of this fact for initial conditions centered at periodic orbits in regular regions is a clear periodic recoherence. For chaotic situations the same phenomenon (proximity of the atomic phase space borderline) is in general responsible for oscillations in the entanglement properties.Comment: 15 pages (text), 6 figures; to be published in Physical Review

The evolution of ultraviolet emission lines from the circumstellar material surrounding SN 1987A

The presence of narrow high-temperature emission lines from nitrogen-rich gas close to SN 1987A has been the principal observational constraint on the evolu- tionary status of the supernova's progenitor. A new analysis of the complete five-year set of low and high resolution IUE ultraviolet spectra of SN 1987A (1987.2--1992.3) provide fluxes for the N V 1240, N IV] 1486, He II 1640, OIII] 1665, NIII] 1751, and CIII] 1908 lines with significantly reduced random and systematic errors and reveals significant short-term fluctuations in the light curves. The N V, N IV] and N III] lines turn on sequentially over 15 to 20 days and show a progression from high to low ionization potential, implying an ioni- zation gradient in the emitting region. The line emission turns on suddenly at 83+/-4 days after the explosion, as defined by N IV]. The N III] line reaches peak luminosity at 399+/-15 days. A ring radius of (6.24+/-0.20)E{17} cm and inclination of 41.0+/-3.9 is derived from these times, assuming a circular ring. The probable role of resonant scattering in the N V light curve introduces systematic errors that leads us to exclude this line from the timing analysis. A new nebular analysis yields improved CNO abundance ratios N/C=6.1+/-1.1 and N/O=1.7+/-0.5, confirming the nitrogen enrichment found in our previous paper. From the late-time behavior of the light curves we find that the emission origi- nates from progressively lower density gas. We estimate the emitting mass near maximum (roughly 400 days) to be roughly 4.7E{-2} solar masses, assuming a filling factor of unity and an electron density of 2.6E4 cm^{-3}. These results are discussed in the context of current models for the emission and hydrodynamics of the ring.Comment: 38 pages, AASTeX v.4.0, 13 Postscript figures; ApJ, in pres