108 research outputs found
Homogeneous Relaxation at Strong Coupling from Gravity
Homogeneous relaxation is a ubiquitous phenomenon in semiclassical kinetic
theories where the quasiparticles are distributed uniformly in space, and the
equilibration involves only their velocity distribution. For such solutions,
the hydrodynamic variables remain constant. We construct asymptotically AdS
solutions of Einstein's gravity dual to such processes at strong coupling,
perturbatively in the amplitude expansion, where the expansion parameter is the
ratio of the amplitude of the non-hydrodynamic shear-stress tensor to the
pressure. At each order, we sum over all time derivatives through exact
recursion relations. We argue that the metric has a regular future horizon,
order by order in the amplitude expansion, provided the shear-stress tensor
follows an equation of motion. At the linear order, this equation of motion
implies that the metric perturbations are composed of zero wavelength
quasinormal modes. Our method allows us to calculate the non-linear corrections
to this equation perturbatively in the amplitude expansion. We thus derive a
special case of our previous conjecture on the regularity condition on the
boundary stress tensor that endows the bulk metric with a regular future
horizon, and also refine it further. We also propose a new outlook for
heavy-ion phenomenology at RHIC and ALICE.Comment: 60 pages, a section titled "Outlook for RHIC and ALICE" has been
added, accepted for publication in Physical Review
Dynamics of Air-Fluidized Granular System Measured by the Modulated Gradient Spin-echo
The power spectrum of displacement fluctuation of beads in the air-fluidized
granular system is measured by a novel NMR technique of modulated gradient
spin-echo. The results of measurement together with the related spectrum of the
velocity fluctuation autocorrelation function fit well to an empiric formula
based on to the model of bead caging between nearest neighbours; the cage
breaks up after a few collisions \cite{Menon1}. The fit yields the
characteristic collision time, the size of bead caging and the diffusion-like
constant for different degrees of system fluidization. The resulting mean
squared displacement increases proportionally to the second power of time in
the short-time ballistic regime and increases linearly with time in the
long-time diffusion regime as already confirmed by other experiments and
simulations.Comment: 4 figures. Submited to Physical Review Letters, April 200
Non equilibrium inertial dynamics of colloidal systems
We consider the properties of a one dimensional fluid of brownian inertial
hard-core particles, whose microscopic dynamics is partially damped by a
heat-bath. Direct interactions among the particles are represented as binary,
instantaneous elastic collisions. Collisions with the heath bath are accounted
for by a Fokker-Planck collision operator, whereas direct collisions among the
particles are treated by a well known method of kinetic theory, the Revised
Enskog Theory. By means of a time multiple time-scale method we derive the
evolution equation for the average density. Remarkably, for large values of the
friction parameter and/or of the mass of the particles we obtain the same
equation as the one derived within the dynamic density functional theory (DDF).
In addition, at moderate values of the friction constant, the present method
allows to study the inertial effects not accounted for by DDF method. Finally,
a numerical test of these corrections is provided.Comment: 13 pages+ 3 Postscript figure
Transport Equations from Liouville Equations for Fractional Systems
We consider dynamical systems that are described by fractional power of
coordinates and momenta. The fractional powers can be considered as a
convenient way to describe systems in the fractional dimension space. For the
usual space the fractional systems are non-Hamiltonian. Generalized transport
equation is derived from Liouville and Bogoliubov equations for fractional
systems. Fractional generalization of average values and reduced distribution
functions are defined. Hydrodynamic equations for fractional systems are
derived from the generalized transport equation.Comment: 11 pages, LaTe
Phase-space approach to dynamical density functional theory
We consider a system of interacting particles subjected to Langevin inertial
dynamics and derive the governing time-dependent equation for the one-body
density. We show that, after suitable truncations of the
Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy, and a multiple time scale
analysis, we obtain a self-consistent equation involving only the one-body
density. This study extends to arbitrary dimensions previous work on a
one-dimensional fluid and highlights the subtelties of kinetic theory in the
derivation of dynamical density functional theory
A Vehicular Traffic Flow Model Based on a Stochastic Acceleration Process
A new vehicular traffic flow model based on a stochastic jump process in
vehicle acceleration and braking is introduced. It is based on a master
equation for the single car probability density in space, velocity and
acceleration with an additional vehicular chaos assumption and is derived via a
Markovian ansatz for car pairs. This equation is analyzed using simple driver
interaction models in the spatial homogeneous case. Velocity distributions in
stochastic equilibrium, together with the car density dependence of their
moments, i.e. mean velocity and scattering and the fundamental diagram are
presented.Comment: 27 pages, 6 figure
The dynamics of thin vibrated granular layers
We describe a series of experiments and computer simulations on vibrated
granular media in a geometry chosen to eliminate gravitationally induced
settling. The system consists of a collection of identical spherical particles
on a horizontal plate vibrating vertically, with or without a confining lid.
Previously reported results are reviewed, including the observation of
homogeneous, disordered liquid-like states, an instability to a `collapse' of
motionless spheres on a perfect hexagonal lattice, and a fluctuating,
hexagonally ordered state. In the presence of a confining lid we see a variety
of solid phases at high densities and relatively high vibration amplitudes,
several of which are reported for the first time in this article. The phase
behavior of the system is closely related to that observed in confined
hard-sphere colloidal suspensions in equilibrium, but with modifications due to
the effects of the forcing and dissipation. We also review measurements of
velocity distributions, which range from Maxwellian to strongly non-Maxwellian
depending on the experimental parameter values. We describe measurements of
spatial velocity correlations that show a clear dependence on the mechanism of
energy injection. We also report new measurements of the velocity
autocorrelation function in the granular layer and show that increased
inelasticity leads to enhanced particle self-diffusion.Comment: 11 pages, 7 figure
Condensation of Hard Spheres Under Gravity: Exact Results in One Dimension
We present exact results for the density profile of the one dimensional array
of N hard spheres of diameter D and mass m under gravity g. For a strictly one
dimensional system, the liquid-solid transition occurs at zero temperature,
because the close-pakced density, , is one. However, if we relax this
condition slightly such that , we find a series of critical
temperatures T_c^i=mgD(N+1-i)/\mu_o with \mu_o=const, at which the i-th
particle undergoes the liquid-solid transition. The functional form of the
onset temperature, T_c^1=mgDN/\mu_o, is consistent with the previous result
[Physica A 271, 192 (1999)] obtained by the Enskog equation. We also show that
the increase in the center of mass is linear in T before the transition, but it
becomes quadratic in T after the transition because of the formation of solid
near the bottom
The Enskog Process
The existence of a weak solution to a McKean-Vlasov type stochastic
differential system corresponding to the Enskog equation of the kinetic theory
of gases is established under natural conditions. The distribution of any
solution to the system at each fixed time is shown to be unique. The existence
of a probability density for the time-marginals of the velocity is verified in
the case where the initial condition is Gaussian, and is shown to be the
density of an invariant measure.Comment: 38 page
Liquid-Solid Transition of Hard Spheres Under Gravity
We investigate the liquid-solid transition of two dimensional hard spheres in
the presence of gravity. We determine the transition temperature and the
fraction of particles in the solid regime as a function of temperature via
Even-Driven molecular dynamics simulations and compare them with the
theoretical predictions. We then examine the configurational statistics of a
vibrating bed from the view point of the liquid-solid transition by explicitly
determining the transition temperature and the effective temperature, T, of the
bed, and present a relation between T and the vibration strength.Comment: 14 total pages, 4 figure
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