1,125 research outputs found
Asymptotic analysis of mode-coupling theory of active nonlinear microrheology
We discuss a schematic model of mode-coupling theory for force-driven active
nonlinear microrheology, where a single probe particle is pulled by a constant
external force through a dense host medium. The model exhibits both a glass
transition for the host, and a force-induced delocalization transition, where
an initially localized probe inside the glassy host attains a nonvanishing
steady-state velocity by locally melting the glass. Asymptotic expressions for
the transient density correlation functions of the schematic model are derived,
valid close to the transition points. There appear several nontrivial time
scales relevant for the decay laws of the correlators. For the nonlinear
friction coeffcient of the probe, the asymptotic expressions cause various
regimes of power-law variation with the external force, and two-parameter
scaling laws.Comment: 17 pages, 12 figure
Emergence of Long-range Correlations and Rigidity at the Dynamic Glass Transition
At the microscopic level, equilibrium liquid's translational symmetry is
spontaneously broken at the so-called dynamic glass transition predicted by the
mean-field replica approach. We show that this fact implies the emergence of
Goldstone modes and long-range density correlations. We derive and evaluate a
new statistical mechanical expression for the glass shear modulus.Comment: 4 page
Glass Transition of the Monodisperse Gaussian Core Model
We numerically study dynamical properties of the one-component Gaussian Core
Model in the supercooled states. We find that nucleation is suppressed as
density increases. Concomitantly the system exhibits glassy slow dynamics
characterized by the two-step and stretched exponential relaxation of the
density correlation as well as drastic increase of the relaxation time. It is
found that violation of the Stokes-Einstein relation is weaker and the
non-Gaussian parameter is smaller than typical model glass formers, implying
weaker dynamic heterogeneities. Besides, agreement of simulation data with the
prediction of mode-coupling theory is exceptionally good, indicating that the
nature of slow dynamics of this ultra-soft particle fluid is mean-field-like.
This fact may be understood as the consequences of multiple overlaps of the
constituent particles at high densities.Comment: 5 pages, 4 figure
Critical Decay at Higher-Order Glass-Transition Singularities
Within the mode-coupling theory for the evolution of structural relaxation in
glass-forming systems, it is shown that the correlation functions for density
fluctuations for states at A_3- and A_4-glass-transition singularities can be
presented as an asymptotic series in increasing inverse powers of the logarithm
of the time t: , where
with p_n denoting some polynomial and x=ln (t/t_0). The results are
demonstrated for schematic models describing the system by solely one or two
correlators and also for a colloid model with a square-well-interaction
potential.Comment: 26 pages, 7 figures, Proceedings of "Structural Arrest Transitions in
Colloidal Systems with Short-Range Attractions", Messina, Italy, December
2003 (submitted
Evidence of a higher-order singularity in dense short-ranged attractive colloids
We study a model in which particles interact through a hard-core repulsion
complemented by a short-ranged attractive potential, of the kind found in
colloidal suspensions. Combining theoretical and numerical work we locate the
line of higher-order glass transition singularities and its end-point -- named
-- on the fluid-glass line. Close to the point, we detect
logarithmic decay of density correlations and sub linear power-law increase of
the mean square displacement, for time intervals up to four order of
magnitudes. We establish the presence of the singularity by studying how
the range of the potential affects the time-window where anomalous dynamics is
observed.Comment: 4 pages, 4 figures, REVTE
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
Tests of mode coupling theory in a simple model for two-component miscible polymer blends
We present molecular dynamics simulations on the structural relaxation of a
simple bead-spring model for polymer blends. The introduction of a different
monomer size induces a large time scale separation for the dynamics of the two
components. Simulation results for a large set of observables probing density
correlations, Rouse modes, and orientations of bond and chain end-to-end
vectors, are analyzed within the framework of the Mode Coupling Theory (MCT).
An unusually large value of the exponent parameter is obtained. This feature
suggests the possibility of an underlying higher-order MCT scenario for dynamic
arrest.Comment: Revised version. Additional figures and citation
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