85 research outputs found
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
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
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
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
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
Correlations and Renormalization in Lattice Gases
A complete formulation is given of an exact kinetic theory for lattice gases.
This kinetic theory makes possible the calculation of corrections to the usual
Boltzmann / Chapman-Enskog analysis of lattice gases due to the buildup of
correlations. It is shown that renormalized transport coefficients can be
calculated perturbatively by summing terms in an infinite series. A
diagrammatic notation for the terms in this series is given, in analogy with
the diagrammatic expansions of continuum kinetic theory and quantum field
theory. A closed-form expression for the coefficients associated with the
vertices of these diagrams is given. This method is applied to several standard
lattice gases, and the results are shown to correctly predict experimentally
observed deviations from the Boltzmann analysis.Comment: 94 pages, pure LaTeX including all figure
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
The non-ergot derived dopamine agonist quinagolide in prevention of early ovarian hyperstimulation syndrome in IVF patients: a randomized, double-blind, placebo-controlled trial†
Global validity of the Master kinetic equation for hard-sphere systems
Following the recent establishment of an exact kinetic theory realized by the Master kinetic equation
which describes the statistical behavior of the Boltzmann-Sinai Classical Dynamical System (CDS), in
this paper the problem is posed of the construction of the related global existence and regularity theorems.
For this purpose, based on the global prescription of the same CDS for arbitrary single- and multiplecollision
events, first global existence is extablished for the N-body Liouville equation which is written
in Lagrangian differential and integral forms. This permits to reach the proof of global existence both
of generic N-body probability density functions (PDF) as well as of particular solutions which maximize
the statistical Boltzmann-Shannon entropy and are factorized in terms of the corresponding 1-body PDF.
The latter PDF is shown to be uniquely defined and to satisfy the Master kinetic equation globally in the
extended 1-body phase space. Implications concerning the global validity of the asymptotic Boltzmann
equation and Boltzmann H-theorem are discussed
A new surgical technique of uterine auto-transplantation in cynomolgus monkey: preliminary report about two cases
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