106 research outputs found
Self-diffusion in sheared colloidal suspensions: violation of fluctuation-dissipation relation
Using memory-function formalism we show that in sheared colloidal suspensions
the fluctuation-dissipation theorem for self-diffusion, i.e. Einstein's
relation between self-diffusion and mobility tensors, is violated and propose a
new way to measure this violation in Brownian Dynamics simulations. We derive
mode-coupling expressions for the tagged particle friction tensor and for an
effective, shear-rate dependent temperature
Dynamic glass transition: bridging the gap between mode-coupling theory and the replica approach
We clarify the relation between the ergodicity breaking transition predicted
by mode-coupling theory and the so-called dynamic transition predicted by the
static replica approach. Following Franz and Parisi [Phys. Rev. Lett. 79, 2486
(1997)], we consider a system of particles in a metastable state characterized
by non-trivial correlations with a quenched configuration. We show that the
assumption that in a metastable state particle currents vanish leads to an
expression for the replica off-diagonal direct correlation function in terms of
a replica off-diagonal static four-point correlation function. A factorization
approximation for this function results in an approximate closure for the
replica off-diagonal direct correlation function. The replica off-diagonal
Ornstein-Zernicke equation combined with this closure coincides with the
equation for the non-ergodicity parameter derived using the mode-coupling
theory.Comment: revised version; to be published in EP
Gaussian density fluctuations, mode coupling theory, and all that
We consider a toy model for glassy dynamics of colloidal suspensions: a
single Brownian particle diffusing among immobile obstacles. If Gaussian
factorization of static density fluctuations is assumed, this model can be
solved without factorization approximation for any dynamic correlation
function. The solution differs from that obtained from the ideal mode coupling
theory (MCT). The latter is equivalent to including only some, positive
definite terms in an expression for the memory function. An approximate
re-summation of the complete expression suggests that, under the assumption of
Gaussian factorization of static fluctuations, mobile particle's motion is
always diffusive. In contrast, MCT predicts that the mobile particle becomes
localized at a high enough obstacle density. We discuss the implications of
these results for models for glassy dynamics.Comment: to be published in Europhys. Let
Tagged particle in a sheared suspension: effective temperature determines density distribution in a slowly varying external potential beyond linear response
We consider a sheared colloidal suspension under the influence of an external
potential that varies slowly in space in the plane perpendicular to the flow
and acts on one selected (tagged) particle of the suspension. Using a
Chapman-Enskog type expansion we derive a steady state equation for the tagged
particle density distribution. We show that for potentials varying along one
direction only, the tagged particle distribution is the same as the equilibrium
distribution with the temperature equal to the effective temperature obtained
from the violation of the Einstein relation between the self-diffusion and
tagged particle mobility coefficients. We thus prove the usefulness of this
effective temperature for the description of the tagged particle behavior
beyond the realm of linear response. We illustrate our theoretical predictions
with Brownian dynamics computer simulations.Comment: Accepted for publication in Europhys. Let
Microscopic theory for the glass transition in a system without static correlations
We study the orientational dynamics of infinitely thin hard rods of length L,
with the centers-of-mass fixed on a simple cubic lattice with lattice constant
a.We approximate the influence of the surrounding rods onto dynamics of a pair
of rods by introducing an effective rotational diffusion constant D(l),l=L/a.
We get D(l) ~ [1-v(l)], where v(l) is given through an integral of a
time-dependent torque-torque correlator of an isolated pair of rods. A glass
transition occurs at l_c, if v(l_c)=1. We present a variational and a
numerically exact evaluation of v(l).Close to l_c the diffusion constant
decreases as D(l) ~ (l_c-l)^\gamma, with \gamma=1. Our approach predicts a
glass transition in the absence of any static correlations, in contrast to
present form of mode coupling theory.Comment: 6 pages, 3 figure
Glass transition in systems without static correlations: a microscopic theory
We present a first step toward a microscopic theory for the glass transition
in systems with trivial static correlations. As an example we have chosen N
infinitely thin hard rods with length L, fixed with their centers on a periodic
lattice with lattice constant a. Starting from the N-rod Smoluchowski equation
we derive a coupled set of equations for fluctuations of reduced k-rod
densities. We approximate the influence of the surrounding rods onto the
dynamics of a pair of rods by introduction of an effective rotational diffusion
tensor D and in this way we obtain a self-consistent equation for D. This
equation exhibits a feedback mechanism leading to a slowing down of the
relaxation. It involves as an input the Laplace transform v_0(l/r) at z=0,
l=L/a, of a torque-torque correlator of an isolated pair of rods with distance
R=ar. Our equation predicts the existence of a continuous ergodicity-breaking
transition at a critical length l_c=L_c/a. To estimate the critical length we
perform an approximate analytical calculation of v_0(l/r) based on a
variational approach and obtain l_c^{var}=5.68, 4.84 and 3.96 for an sc, bcc
and fcc lattice. We also evaluate v_0(l/r) numerically exactly from a two-rod
simulation. The latter calculation leads to l_c^{num}=3.45, 2.78 and 2.20 for
the corresponding lattices. Close to l_c the rotational diffusion constant
decreases as D(l) ~ (l_c - l)^\gamma with \gamma=1 and a diverging time scale
t_\epsilon ~ |l_c - l|^{-\delta}, \delta=2, appears. On this time scale the t-
and l-dependence of the 1-rod density is determined by a master function
depending only on t/t_\epsilon. In contrast to present microscopic theories our
approach predicts a glass transition despite the absence of any static
correlations.Comment: 22 pages, 7 figures (minor revisions in the text, corrected figures
Stochastic model for the dynamics of interacting Brownian particles
Using the scheme of mesoscopic nonequilibrium thermodynamics, we construct
the one- and two- particle Fokker-Planck equations for a system of interacting
Brownian particles. By means of these equations we derive the corresponding
balance equations. We obtain expressions for the heat flux and the pressure
tensor which enable one to describe the kinetic and potential energy
interchange of the particles with the heat bath. Through the momentum balance
we analyze in particular the diffusion regime to obtain the collective
diffusion coefficient in terms of the hydrodynamic and the effective forces
acting on the Brownian particles.Comment: latex fil
Mechanical Responses and Stress Fluctuations of a Supercooled Liquid in a Sheared Non-Equilibrium State
A steady shear flow can drive supercooled liquids into a non-equilibrium
state. Using molecular dynamics simulations under steady shear flow
superimposed with oscillatory shear strain for a probe, non-equilibrium
mechanical responses are studied for a model supercooled liquid composed of
binary soft spheres. We found that even in the strongly sheared situation, the
supercooled liquid exhibits surprisingly isotropic responses to oscillating
shear strains applied in three different components of the strain tensor. Based
on this isotropic feature, we successfully constructed a simple two-mode
Maxwell model that can capture the key features of the storage and loss moduli,
even for highly non-equilibrium state. Furthermore, we examined the correlation
functions of the shear stress fluctuations, which also exhibit isotropic
relaxation behaviors in the sheared non-equilibrium situation. In contrast to
the isotropic features, the supercooled liquid additionally demonstrates
anisotropies in both its responses and its correlations to the shear stress
fluctuations. Using the constitutive equation (a two-mode Maxwell model), we
demonstrated that the anisotropic responses are caused by the coupling between
the oscillating strain and the driving shear flow. We measured the magnitude of
this violation in terms of the effective temperature. It was demonstrated that
the effective temperature is notably different between different components,
which indicates that a simple scalar mapping, such as the concept of an
effective temperature, oversimplifies the true nature of supercooled liquids
under shear flow. An understanding of the mechanism of isotropies and
anisotropies in the responses and fluctuations will lead to a better
appreciation of these violations of the FDT, as well as certain consequent
modifications to the concept of an effective temperature.Comment: 15pages, 17figure
Dynamics in Colloidal Liquids near a Crossing of Glass- and Gel-Transition Lines
Within the mode-coupling theory for ideal glass-transitions, the mean-squared
displacement and the correlation function for density fluctuations are
evaluated for a colloidal liquid of particles interacting with a square-well
potential for states near the crossing of the line for transitions to a gel
with the line for transitions to a glass. It is demonstrated how the dynamics
is ruled by the interplay of the mechanisms of arrest due to hard-core
repulsion and due to attraction-induced bond formation as well as by a nearby
higher-order glass-transition singularity. Application of the universal
relaxation laws for the slow dynamics near glass-transition singularities
explains the qualitative features of the calculated time dependence of the
mean-squared displacement, which are in accord with the findings obtained in
molecular-dynamics simulation studies by Zaccarelli et. al [Phys. Rev. E 66,
041402 (2002)]. Correlation functions found by photon-correlation spectroscopy
in a micellar system by Mallamace et. al [Phys. Rev. Lett. 84, 5431 2000)] can
be interpreted qualitatively as a crossover from gel to glass dynamics.Comment: 13 pages, 12 figure
Approach to equilibrium for a class of random quantum models of infinite range
We consider random generalizations of a quantum model of infinite range
introduced by Emch and Radin. The generalization allows a neat extension from
the class of absolutely summable lattice potentials to the optimal class
of square summable potentials first considered by Khanin and Sinai and
generalised by van Enter and van Hemmen. The approach to equilibrium in the
case of a Gaussian distribution is proved to be faster than for a Bernoulli
distribution for both short-range and long-range lattice potentials. While
exponential decay to equilibrium is excluded in the nonrandom case, it is
proved to occur for both short and long range potentials for Gaussian
distributions, and for potentials of class in the Bernoulli case. Open
problems are discussed.Comment: 10 pages, no figures. This last version, to appear in J. Stat. Phys.,
corrects some minor errors and includes additional references and comments on
the relation to experiment
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