In this study we model early times dynamics of the system produced in relativistic heavy ion collisions by an initial color electric field which then decays to a plasma by the Schwinger mechanism, coupling the dynamical evolution of the initial color
field to the dynamics of the many particles system produced by the decay. The latter is described by relativistic kinetic theory in which we fix the ratio $eta/s$ rather than insisting on specific microscopic processes. We study isotropization and thermalization of the system produced by the field decay for a static box and for a $1+1$D expanding geometry. We find that regardless of the viscosity of the produced plasma, the initial color electric field decays within $1$ fm/c; however in the case $eta/s$ is large, oscillations of the field are effective along all the entire time evolution of the system, which affect the late times evolution of the ratio between longitudinal and transverse pressure. In case of small $eta/s$ ($eta/slesssim0.3$) we find $tau_{isotropization}approx 0.8$ fm/c and $tau_{thermalization}approx 1$ fm/c in agreement with the common lore of hydrodynamics. Moreover we have investigated the effect of turning from the relaxation time approximation to the Chapman-Enskog one: we find that this improvement affects mainly the early times evolution of the physical quantities, the effect being milder in the late times evolution.
The interplay between Coulomb friction and random excitations is studied experimentally by means of a rotating probe in contact with a stationary granular gas. The granular material is independently fluidized by a vertical shaker, acting as a heat ba
th for the Brownian-like motion of the probe. Two ball bearings supporting the probe exert nonlinear Coulomb friction upon it. The experimental velocity distribution of the probe, autocorrelation function, and power spectra are compared with the predictions of a linear Boltzmann equation with friction, which is known to simplify in two opposite limits: at high collision frequency, it is mapped to a Fokker-Planck equation with nonlinear friction, whereas at low collision frequency, it is described by a sequence of independent random kicks followed by friction-induced relaxations. Comparison between theory and experiment in these two limits shows good agreement. Deviations are observed at very small velocities, where the real bearings are not well modeled by Coulomb friction.
The new 8.4m LBT adaptive secondary AO system, with its novel pyramid wavefront sensor, was used to produce very high Strehl (75% at 2.16 microns) near infrared narrowband (Br gamma: 2.16 microns and [FeII]: 1.64 microns) images of 47 young (~1 Myr)
Orion Trapezium theta1 Ori cluster members. The inner ~41x53 of the cluster was imaged at spatial resolutions of ~0.050 (at 1.64 microns). A combination of high spatial resolution and high S/N yielded relative binary positions to ~0.5 mas accuracies. Including previous speckle data, we analyse a 15 year baseline of high-resolution observations of this cluster. We are now sensitive to relative proper motions of just ~0.3 mas/yr (0.6 km/s at 450 pc) this is a ~7x improvement in orbital velocity accuracy compared to previous efforts. We now detect clear orbital motions in the theta1 Ori B2/B3 system of 4.9+/-0.3 km/s and 7.2+/-0.8 km/s in the theta1 Ori A1/A2 system (with correlations of PA vs. time at >99% confidence). All five members of the theta1 Ori B system appear likely as a gravitationally bound mini-cluster. The very lowest mass member of the theta1 Ori B system (B4; mass ~0.2 Msun) has, for the first time, a clearly detected motion (at 4.3+/-2.0 km/s; correlation=99.7%) w.r.t B1. However, B4 is most likely in an long-term unstable (non-hierarchical) orbit and may soon be ejected from this mini-cluster. This ejection process could play a major role in the formation of low mass stars and brown dwarfs.
Velocity and density structure factors are measured over a hydrodynamic range of scales in a horizontal quasi-2d fluidized granular experiment, with packing fractions $phiin[10%,40%]$. The fluidization is realized by vertically vibrating a rough plat
e, on top of which particles perform a Brownian-like horizontal motion in addition to inelastic collisions. On one hand, the density structure factor is equal to that of elastic hard spheres, except in the limit of large length-scales, as it occurs in the presence of an effective interaction. On the other hand, the velocity field shows a more complex structure which is a genuine expression of a non-equilibrium steady state and which can be compared to a recent fluctuating hydrodynamic theory with non-equilibrium noise. The temporal decay of velocity modes autocorrelations is compatible with linear hydrodynamic equations with rates dictated by viscous momentum diffusion, corrected by a typical interaction time with the thermostat. Equal-time velocity structure factors display a peculiar shape with a plateau at large length-scales and another one at small scales, marking two different temperatures: the bath temperature $T_b$, depending on shaking parameters, and the granular temperature $T_g<T_b$, which is affected by collisions. The two ranges of scales are separated by a correlation length which grows with $phi$, after proper rescaling with the mean free path.
We study a general model of granular Brownian ratchet consisting of an asymmetric object moving on a line and surrounded by a two-dimensional granular gas, which in turn is coupled to an external random driving force. We discuss the two resulting Bol
tzmann equations describing the gas and the object in the dilute limit and obtain a closed system for the first few moments of the system velocity distributions. Predictions for the net ratchet drift, the variance of its velocity fluctuations and the transition rates in the Markovian limit, are compared to numerical simulations and a fair agreement is observed.
We consider a massive inelastic piston, whose opposite faces have different coefficients of restitution, moving under the action of an infinitely dilute gas of hard disks maintained at a fixed temperature. The dynamics of the piston is Markovian and
obeys a continuous Master Equation: however, the asymmetry of restitution coefficients induces a violation of detailed balance and a net drift of the piston, as in a Brownian ratchet. Numerical investigations of such non-equilibrium stationary state show that the velocity fluctuations of the piston are symmetric around the mean value only in the limit of large piston mass, while they are strongly asymmetric in the opposite limit. Only taking into account such an asymmetry, i.e. including a third parameter in addition to the mean and the variance of the velocity distribution, it is possible to obtain a satisfactory analytical prediction for the ratchet drift velocity.
A driven granular material, e.g. a vibrated box full of sand, is a stationary system which may be very far from equilibrium. The standard equilibrium statistical mechanics is therefore inadequate to describe fluctuations in such a system. Here we pre
sent numerical and analytical results concerning energy and injected power fluctuations. In the first part we explain how the study of the probability density function (pdf) of the fluctuations of total energy is related to the characterization of velocity correlations. Two different regimes are addressed: the gas driven at the boundaries and the homogeneously driven gas. In a granular gas, due to non-Gaussianity of the velocity pdf or lack of homogeneity in hydrodynamics profiles, even in the absence of velocity correlations, the fluctuations of total energy are non-trivial and may lead to erroneous conclusions about the role of correlations. In the second part of the chapter we take into consideration the fluctuations of injected power in driven granular gas models. Recently, real and numerical experiments have been interpreted as evidence that the fluctuations of power injection seem to satisfy the Gallavotti-Cohen Fluctuation Relation. We will discuss an alternative interpretation of such results which invalidates the Gallavotti-Cohen symmetry. Moreover, starting from the Liouville equation and using techniques from large deviation theory, the general validity of a Fluctuation Relation for power injection in driven granular gases is questioned. Finally a functional is defined using the Lebowitz-Spohn approach for Markov processes applied to the linear inelastic Boltzmann equation relevant to describe the motion of a tracer particle. Such a functional results to be different from injected power and to satisfy a Fluctuation Relation.
