Boltzmann equation for dissipative gases in homogeneous states with nonlinear friction

Combining analytical and numerical methods, we study within the framework of the homogeneous non-linear Boltzmann equation, a broad class of models relevant for the dynamics of dissipative fluids, including granular gases. We use the new method presented in a previous paper [J. Stat. Phys. 124, 549 (2006)] and extend our results to a different heating mechanism, namely a deterministic non-linear friction force. We derive analytically the high energy tail of the velocity distribution and compare the theoretical predictions with high precision numerical simulations. Stretched exponential forms are obtained when the non-equilibrium steady state is stable. We derive sub-leading corrections and emphasize their relevance. In marginal stability cases, power-law behaviors arise, with exponents obtained as the roots of transcendental equations. We also consider some simple BGK (Bhatnagar, Gross, Krook) models, driven by similar heating devices, to test the robustness of our predictions

Tapping Spin Glasses

We consider a tapping dynamics, analogous to that in experiments on granular media, on spin glasses and ferromagnets on random thin graphs. Between taps, zero temperature single spin flip dynamics takes the system to a metastable state. Tapping, corresponds to flipping simultaneously any spin with probability $p$. This dynamics leads to a stationary regime with a steady state energy $E(p)$. We analytically solve this dynamics for the one dimensional ferromagnet and $\pm J$ spin glass. Numerical simulations for spin glasses and ferromagnets of higher connectivity are carried out, in particular we find a novel first order transition for the ferromagnetic systems.Comment: 5 pages, 3 figures, RevTe

The Diderot meteorite: The second chassignite

The Diderot meteorite is a dunite discovered in Sahara. The martian origin is unambiguous and Diderot shares strong petrographical similarities with Chassigny

Random inelasticity and velocity fluctuations in a driven granular gas

We analyze the deviations from Maxwell-Boltzmann statistics found in recent experiments studying velocity distributions in two-dimensional granular gases driven into a non-equilibrium stationary state by a strong vertical vibration. We show that in its simplest version, the ``stochastic thermostat'' model of heated inelastic hard spheres, contrary to what has been hitherto stated, is incompatible with the experimental data, although predicting a reminiscent high velocity stretched exponential behavior with an exponent 3/2. The experimental observations lead to refine a recently proposed random restitution coefficient model. Very good agreement is then found with experimental velocity distributions within this framework, which appears self-consistent and further provides relevant probes to investigate the universality of the velocity statistics.Comment: 5 pages, 5 eps figure

Generic Absorbing Transition in Coevolution Dynamics

We study a coevolution voter model on a network that evolves according to the state of the nodes. In a single update, a link between opposite-state nodes is rewired with probability $p$, while with probability $1-p$ one of the nodes takes its neighbor's state. A mean-field approximation reveals an absorbing transition from an active to a frozen phase at a critical value $p_c=\frac{\mu-2}{\mu-1}$ that only depends on the average degree $\mu$ of the network. The approach to the final state is characterized by a time scale that diverges at the critical point as $\tau \sim |p_c-p|^{-1}$. We find that the active and frozen phases correspond to a connected and a fragmented network respectively. We show that the transition in finite-size systems can be seen as the sudden change in the trajectory of an equivalent random walk at the critical rewiring rate $p_c$, highlighting the fact that the mechanism behind the transition is a competition between the rates at which the network and the state of the nodes evolve.Comment: 5 pages, 4 figure

Estimating the epidemic risk using non-uniformly sampled contact data

Many datasets describing contacts in a population suffer from incompleteness due to population sampling and underreporting of contacts. Data-driven simulations of spreading processes using such incomplete data lead to an underestimation of the epidemic risk, and it is therefore important to devise methods to correct this bias. We focus here on a non-uniform sampling of the contacts between individuals, aimed at mimicking the results of diaries or surveys, and consider as case studies two datasets collected in different contexts. We show that using surrogate data built using a method developed in the case of uniform population sampling yields an improvement with respect to the use of the sampled data but is strongly limited by the underestimation of the link density in the sampled network. We put forward a second method to build surrogate data that assumes knowledge of the density of links within one of the groups forming the population. We show that it gives very good results when the population is strongly structured, and discuss its limitations in the case of a population with a weaker group structure. These limitations highlight the interest of measurements using wearable sensors able to yield accurate information on the structure and durations of contacts

On the Einstein relation in a heated granular gas

Recent computer simulation results [Barrat {\em et al.}, Physica A 334 (2004) 513] for granular mixtures subject to stochastic driving have shown the validity of the Einstein relation $\epsilon\equiv D/(T_0\lambda)=1$ between the diffusion $D$ and mobility $\lambda$ coefficients when the temperature of the gas $T$ is replaced by the temperature of the impurity $T_0$ in the usual Einstein relation. This problem is analyzed in this paper by solving analytically the Boltzmann-Lorentz equation from the Chapman-Enskog method. The gas is heated by the action of an external driving force (thermostat) which does work to compensate for the collisional loss of energy. Two types of thermostats are considered: (a) a deterministic force proportional to the particle velocity (Gaussian thermostat), and (b) a white noise external force (stochastic thermostat). The diffusion and mobility coefficients are given in terms of the solutions of two linear integral equations, which are approximately solved up to the second order in a Sonine polynomial expansion. The results show that the violation of the Einstein relation ($\epsilon\neq 1$) is only due to the non-Maxwellian behavior of the impurity velocity distribution function (absence of the Gibbs state). At a quantitative level, the kinetic theory results also show that the deviation of $\epsilon$ from 1 is more significant in the case of the Gaussian thermostat than in the case of the stochastic one, in which case the deviation of the Einstein relation is in general smaller than 1%. This conclusion agrees quite well with the results found in computer simulations.Comment: 7 figures. to appear in Physica

Level-crossing spectroscopy of the 7, 9, and 10D_5/2 states of 133Cs and validation of relativistic many-body calculations of the polarizabilities and hyperfine constants

We present an experimental and theoretical investigation of the polarizabilities and hyperfine constants of D_J states in 133Cs for J=3/2 and J=5/2. New experimental values for the hyperfine constant A are obtained from level-crossing signals of the (7,9,10)D_5/2 states of 133Cs and precise calculations of the tensor polarizabilities alpha_2. The results of relativistic many-body calculations for scalar and tensor polarizabilities of the (5-10)D_3/2 and (5-10)D_5/2 states are presented and compared with measured values from the literature. Calculated values of the hyperfine constants A for these states are also presented and checked for consistency with experimental values.Comment: 12 pages, revtex4, 11 figure file

Hydrodynamic profiles for an impurity in a open vibrated granular gas

The hydrodynamic state of an impurity immersed in a low density granular gas is analyzed. Explicit expressions for the temperature and density fields of the impurity in terms of the hydrodynamic fields of the gas are derived. It is shown that the ratio between the temperatures of the two components, measuring the departure from energy equipartition, only depends on the mechanical properties of the particles, being therefore constant in the bulk of the system. This ratio plays an important role in determining the density profile of the intruder and its position with respect to the gas, since it determines the sign of the pressure diffusion coefficient. The theoretical predictions are compared with molecular dynamics simulation results for the particular case of the steady state of an open vibrated granular system in absence of macroscopic fluxes, and a satisfactory agreement is found