43,163 research outputs found
Nearly-logarithmic decay in the colloidal hard-sphere system
Nearly-logarithmic decay is identified in the data for the mean-squared
displacement of the colloidal hard-sphere system at the liquid-glass transition
[v. Megen et. al, Phys. Rev. E 58, 6073(1998)]. The solutions of mode-coupling
theory for the microscopic equations of motion fit the experimental data well.
Based on these equations, the nearly-logarithmic decay is explained as the
equivalent of a beta-peak phenomenon, a manifestation of the critical
relaxation when the coupling between of the probe variable and the density
fluctuations is strong. In an asymptotic expansion, a Cole-Cole formula
including corrections is derived from the microscopic equations of motion,
which describes the experimental data for three decades in time.Comment: 4 pages, 3 figure
Relaxation in a glassy binary mixture: Mode-coupling-like power laws, dynamic heterogeneity and a new non-Gaussian parameter
We examine the relaxation of the Kob-Andersen Lennard-Jones binary mixture
using Brownian dynamics computer simulations. We find that in accordance with
mode-coupling theory the self-diffusion coefficient and the relaxation time
show power-law dependence on temperature. However, different mode-coupling
temperatures and power laws can be obtained from the simulation data depending
on the range of temperatures chosen for the power-law fits. The temperature
that is commonly reported as this system's mode-coupling transition
temperature, in addition to being obtained from a power law fit, is a crossover
temperature at which there is a change in the dynamics from the high
temperature homogeneous, diffusive relaxation to a heterogeneous, hopping-like
motion. The hopping-like motion is evident in the probability distributions of
the logarithm of single-particle displacements: approaching the commonly
reported mode-coupling temperature these distributions start exhibiting two
peaks. Notably, the temperature at which the hopping-like motion appears for
the smaller particles is slightly higher than that at which the hopping-like
motion appears for the larger ones. We define and calculate a new non-Gaussian
parameter whose maximum occurs approximately at the time at which the two peaks
in the probability distribution of the logarithm of displacements are most
evident.Comment: Submitted for publication in Phys. Rev.
Mode-Coupling Theory as a Mean-Field Description of the Glass Transition
Mode-coupling theory (MCT) is conjectured to be a mean-field description of
dynamics of the structural glass transition and the replica theory to be its
thermodynamic counterpart. However, the relationship between the two theories
remains controversial and quantitative comparison is lacking. In this Letter,
we investigate MCT for monatomic hard sphere fluids at arbitrary dimensions
above three and compare the results with replica theory. We find grave
discrepancies between the predictions of two theories. While MCT describes the
nonergodic parameter quantitatively better than the replica theory in three
dimension, it predicts a completely different dimension dependence of the
dynamical transition point. We find it to be due to the pathological behavior
of the nonergodic parameters derived from MCT, which exhibit negative tails in
real space at high dimensions.Comment: 5 pages, to appear in Phys. Rev. Lett.: Typos have been correcte
A critical test of the mode-coupling theory of the glass transition
The mode-coupling theory of the glass transition predicts the time evolution
of the intermediate scattering functions in viscous liquids on the sole basis
of the structural information encoded in two-point density correlations. We
provide a critical test of this property and show that the theory fails to
describe the qualitatively distinct dynamical behavior obtained in two model
liquids characterized by very similar pair correlation functions. Because we
use `exact' static information provided by numerical simulations, our results
are a direct proof that some important information about the dynamics of
viscous liquids is not captured by pair correlations, and is thus not described
by the mode-coupling theory, even in the temperature regime where the theory is
usually applied.Comment: 7 pages, 5 figures
Multi-scale coarse-graining of diblock copolymer self-assembly: from monomers to ordered micelles
Starting from a microscopic lattice model, we investigate clustering,
micellization and micelle ordering in semi-dilute solutions of AB diblock
copolymers in a selective solvent. To bridge the gap in length scales, from
monomers to ordered micellar structures, we implement a two-step coarse
graining strategy, whereby the AB copolymers are mapped onto ``ultrasoft''
dumbells with monomer-averaged effective interactions between the centres of
mass of the blocks. Monte Carlo simulations of this coarse-grained model yield
clear-cut evidence for self-assembly into micelles with a mean aggregation
number n of roughly 100 beyond a critical concentration. At a slightly higher
concentration the micelles spontaneously undergo a disorder-order transition to
a cubic phase. We determine the effective potential between these micelles from
first principles.Comment: 4 pages, 4 figures, submitted to Phys. Rev. Lett
Connections of activated hopping processes with the breakdown of the Stokes-Einstein relation and with aspects of dynamical heterogeneities
We develop a new extended version of the mode-coupling theory (MCT) for glass
transition, which incorporates activated hopping processes via the dynamical
theory originally formulated to describe diffusion-jump processes in crystals.
The dynamical-theory approach adapted here to glass-forming liquids treats
hopping as arising from vibrational fluctuations in quasi-arrested state where
particles are trapped inside their cages, and the hopping rate is formulated in
terms of the Debye-Waller factors characterizing the structure of the
quasi-arrested state. The resulting expression for the hopping rate takes an
activated form, and the barrier height for the hopping is ``self-generated'' in
the sense that it is present only in those states where the dynamics exhibits a
well defined plateau. It is discussed how such a hopping rate can be
incorporated into MCT so that the sharp nonergodic transition predicted by the
idealized version of the theory is replaced by a rapid but smooth crossover. We
then show that the developed theory accounts for the breakdown of the
Stokes-Einstein relation observed in a variety of fragile glass formers. It is
also demonstrated that characteristic features of dynamical heterogeneities
revealed by recent computer simulations are reproduced by the theory. More
specifically, a substantial increase of the non-Gaussian parameter, double-peak
structure in the probability distribution of particle displacements, and the
presence of a growing dynamic length scale are predicted by the extended MCT
developed here, which the idealized version of the theory failed to reproduce.
These results of the theory are demonstrated for a model of the Lennard-Jones
system, and are compared with related computer-simulation results and
experimental data.Comment: 13 pages, 5 figure
Fluids confined in wedges and by edges: Virial series for the line-thermodynamic properties of hard spheres
This work is devoted to analyze the relation between the thermodynamic properties of a confined fluid and the shape of its confining vessel. Recently, new insights in this topic were found through the study of cluster integrals for inhomogeneous fluids that revealed the dependence on the vessel shape of the low density behavior of the system. Here, the statistical mechanics and thermodynamics of fluids confined in wedges or by edges is revisited, focusing on their cluster integrals. In particular, the well known hard sphere fluid, which was not studied in this framework so far, is analyzed under confinement and its thermodynamic properties are analytically studied up to order two in the density. Furthermore, the analysis is extended to the confinement produced by a corrugated wall. These results rely on the obtained analytic expression for the second cluster integral of the confined hard sphere system as a function of the opening dihedral angle 0 < β < 2Ď€. It enables a unified approach to both wedges and edges.Fil: Urrutia, Ignacio. ComisiĂłn Nacional de EnergĂa AtĂłmica. Centro AtĂłmico Constituyentes; Argentina. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas; Argentin
Slow Dynamics of the High Density Gaussian Core Model
We numerically study crystal nucleation and glassy slow dynamics of the
one-component Gaussian core model (GCM) at high densities. The nucleation rate
at a fixed supersaturation is found to decrease as the density increases. At
very high densities, the nucleation is not observed at all in the time window
accessed by long molecular dynamics (MD) simulation. Concomitantly, the system
exhibits typical slow dynamics of the supercooled fluids near the glass
transition point. We compare the simulation results of the supercooled GCM with
the predictions of mode-coupling theory (MCT) and find that the agreement
between them is better than any other model glassformers studied numerically in
the past. Furthermore, we find that a violation of the Stokes-Einstein relation
is weaker and the non-Gaussian parameter is smaller than canonical
glassformers. Analysis of the probability distribution of the particle
displacement clearly reveals that the hopping effect is strongly suppressed in
the high density GCM. We conclude from these observations that the GCM is more
amenable to the mean-field picture of the glass transition than other models.
This is attributed to the long-ranged nature of the interaction potential of
the GCM in the high density regime. Finally, the intermediate scattering
function at small wavevectors is found to decay much faster than its self part,
indicating that dynamics of the large-scale density fluctuations decouples with
the shorter-ranged caging motion.Comment: 15 pages, 13 figure
Spatial correlations in sheared isothermal liquids : From elastic particles to granular particles
Spatial correlations for sheared isothermal elastic liquids and granular
liquids are theoretically investigated. Using the generalized fluctuating
hydrodynamics, correlation functions for both the microscopic scale and the
macroscopic scale are obtained. The existence of the long-range correlation
functions obeying power laws has been confirmed. The validity of our
theoretical predictions have been verified from the molecular dynamics
simulation.Comment: 34 pages, 12 figure
Experimental Comparisons of Derivative Free Optimization Algorithms
In this paper, the performances of the quasi-Newton BFGS algorithm, the
NEWUOA derivative free optimizer, the Covariance Matrix Adaptation Evolution
Strategy (CMA-ES), the Differential Evolution (DE) algorithm and Particle Swarm
Optimizers (PSO) are compared experimentally on benchmark functions reflecting
important challenges encountered in real-world optimization problems.
Dependence of the performances in the conditioning of the problem and
rotational invariance of the algorithms are in particular investigated.Comment: 8th International Symposium on Experimental Algorithms, Dortmund :
Germany (2009
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