44 research outputs found
Globule transitions of a single homopolymer: A Wang-Landau Monte Carlo study
The temperature-independent Wang-Landau Monte Carlo approach is implemented for an off-lattice model of flexible homopolymers and applied to the coil-globule and solidification transitions based on chain sizes up to N=300. An intermediate transformation from low-density liquid globule to high-density liquid globule is suggested. A scheme for identifying polymer structures representative of particular temperatures in the course of the simulation is presented and applied to illustrate intermediate states in the coil-globule transition. Transition temperatures are calculated and used to obtain a theta point of at least Î=1.96, distinctly higher than the solid-liquid transition temperature TM =1.26
The second and third Sonine coefficients of a freely cooling granular gas revisited
In its simplest statistical-mechanical description, a granular fluid can be
modeled as composed of smooth inelastic hard spheres (with a constant
coefficient of normal restitution ) whose velocity distribution
function obeys the Enskog-Boltzmann equation. The basic state of a granular
fluid is the homogeneous cooling state, characterized by a homogeneous,
isotropic, and stationary distribution of scaled velocities, .
The behavior of in the domain of thermal velocities ()
can be characterized by the two first non-trivial coefficients ( and
) of an expansion in Sonine polynomials. The main goals of this paper are
to review some of the previous efforts made to estimate (and measure in
computer simulations) the -dependence of and , to report new
computer simulations results of and for two-dimensional systems,
and to investigate the possibility of proposing theoretical estimates of
and with an optimal compromise between simplicity and accuracy.Comment: 12 pages, 5 figures; v2: minor change
Exact steady state solution of the Boltzmann equation: A driven 1-D inelastic Maxwell gas
The exact nonequilibrium steady state solution of the nonlinear Boltzmann
equation for a driven inelastic Maxwell model was obtained by Ben-Naim and
Krapivsky [Phys. Rev. E 61, R5 (2000)] in the form of an infinite product for
the Fourier transform of the distribution function . In this paper we
have inverted the Fourier transform to express in the form of an
infinite series of exponentially decaying terms. The dominant high energy tail
is exponential, , where and the amplitude is given in terms of a converging
sum. This is explicitly shown in the totally inelastic limit ()
and in the quasi-elastic limit (). In the latter case, the
distribution is dominated by a Maxwellian for a very wide range of velocities,
but a crossover from a Maxwellian to an exponential high energy tail exists for
velocities around a crossover velocity , where .
In this crossover region the distribution function is extremely small, .Comment: 11 pages, 4 figures; a table and a few references added; to be
published in PR
Survival-Time Distribution for Inelastic Collapse
In a recent publication [PRL {\bf 81}, 1142 (1998)] it was argued that a
randomly forced particle which collides inelastically with a boundary can
undergo inelastic collapse and come to rest in a finite time. Here we discuss
the survival probability for the inelastic collapse transition. It is found
that the collapse-time distribution behaves asymptotically as a power-law in
time, and that the exponent governing this decay is non-universal. An
approximate calculation of the collapse-time exponent confirms this behaviour
and shows how inelastic collapse can be viewed as a generalised persistence
phenomenon.Comment: 4 pages, RevTe
Fluctuation-Dissipation relations in Driven Granular Gases
We study the dynamics of a 2d driven inelastic gas, by means of Direct
Simulation Monte Carlo (DSMC) techniques, i.e. under the assumption of
Molecular Chaos. Under the effect of a uniform stochastic driving in the form
of a white noise plus a friction term, the gas is kept in a non-equilibrium
Steady State characterized by fractal density correlations and non-Gaussian
distributions of velocities; the mean squared velocity, that is the so-called
{\em granular temperature}, is lower than the bath temperature. We observe that
a modified form of the Kubo relation, which relates the autocorrelation and the
linear response for the dynamics of a system {\em at equilibrium}, still holds
for the off-equilibrium, though stationary, dynamics of the systems under
investigation. Interestingly, the only needed modification to the equilibrium
Kubo relation is the replacement of the equilibrium temperature with an
effective temperature, which results equal to the global granular temperature.
We present two independent numerical experiment, i.e. two different observables
are studied: (a) the staggered density current, whose response to an impulsive
shear is proportional to its autocorrelation in the unperturbed system and (b)
the response of a tracer to a small constant force, switched on at time ,
which is proportional to the mean-square displacement in the unperturbed
system. Both measures confirm the validity of Kubo's formula, provided that the
granular temperature is used as the proportionality factor between response and
autocorrelation, at least for not too large inelasticities.Comment: 11 pages, 7 figures, submitted for publicatio
Granular fluid thermostatted by a bath of elastic hard spheres
The homogeneous steady state of a fluid of inelastic hard spheres immersed in
a bath of elastic hard spheres kept at equilibrium is analyzed by means of the
first Sonine approximation to the (spatially homogeneous) Enskog--Boltzmann
equation. The temperature of the granular fluid relative to the bath
temperature and the kurtosis of the granular distribution function are obtained
as functions of the coefficient of restitution, the mass ratio, and a
dimensionless parameter measuring the cooling rate relative to the
friction constant. Comparison with recent results obtained from an iterative
numerical solution of the Enskog--Boltzmann equation [Biben et al., Physica A
310, 308 (202)] shows an excellent agreement. Several limiting cases are also
considered. In particular, when the granular particles are much heavier than
the bath particles (but have a comparable size and number density), it is shown
that the bath acts as a white noise external driving. In the general case, the
Sonine approximation predicts the lack of a steady state if the control
parameter is larger than a certain critical value that
depends on the coefficient of restitution and the mass ratio. However, this
phenomenon appears outside the expected domain of applicability of the
approximation.Comment: 16 pages, 7 figures; minor changes; to be published in Phys. Rev.
Bifurcations of a driven granular system under gravity
Molecular dynamics study on the granular bifurcation in a simple model is
presented. The model consists of hard disks, which undergo inelastic
collisions; the system is under the uniform external gravity and is driven by
the heat bath. The competition between the two effects, namely, the
gravitational force and the heat bath, is carefully studied. We found that the
system shows three phases, namely, the condensed phase, locally fluidized
phase, and granular turbulent phase, upon increasing the external control
parameter. We conclude that the transition from the condensed phase to the
locally fluidized phase is distinguished by the existence of fluidized holes,
and the transition from the locally fluidized phase to the granular turbulent
phase is understood by the destabilization transition of the fluidized holes
due to mutual interference.Comment: 35 pages, 17 figures, to be published in PR
Detector Description and Performance for the First Coincidence Observations between LIGO and GEO
For 17 days in August and September 2002, the LIGO and GEO interferometer
gravitational wave detectors were operated in coincidence to produce their
first data for scientific analysis. Although the detectors were still far from
their design sensitivity levels, the data can be used to place better upper
limits on the flux of gravitational waves incident on the earth than previous
direct measurements. This paper describes the instruments and the data in some
detail, as a companion to analysis papers based on the first data.Comment: 41 pages, 9 figures 17 Sept 03: author list amended, minor editorial
change
Search for Gravitational Waves from Primordial Black Hole Binary Coalescences in the Galactic Halo
We use data from the second science run of the LIGO gravitational-wave
detectors to search for the gravitational waves from primordial black hole
(PBH) binary coalescence with component masses in the range 0.2--.
The analysis requires a signal to be found in the data from both LIGO
observatories, according to a set of coincidence criteria. No inspiral signals
were found. Assuming a spherical halo with core radius 5 kpc extending to 50
kpc containing non-spinning black holes with masses in the range 0.2--, we place an observational upper limit on the rate of PBH coalescence
of 63 per year per Milky Way halo (MWH) with 90% confidence.Comment: 7 pages, 4 figures, to be submitted to Phys. Rev.
Single chains of block copolymers in poor solvents: Handshake, spiral, and lamellar globules formed by geometric frustration
A single multiblock copolymer chain in poor solvent undergoes microphase separation within its own globule, driven by the same kind of forces operating in the bulk system. However, the necessity of packing a large AB interface into a small volume leads to novel convoluted geometries. Long block lengths form a double droplet. Very short block lengths exhibit bulk behavior, forming a lamellar globule. With intermediate block lengths, the AB interface buckles to form a hand shake or spiral dicluster. An order-disorder transition is reported for short block lengths