662 research outputs found
The Glass Transition in Driven Granular Fluids: A Mode-Coupling Approach
We consider the stationary state of a fluid comprised of inelastic hard
spheres or disks under the influence of a random, momentum-conserving external
force. Starting from the microscopic description of the dynamics, we derive a
nonlinear equation of motion for the coherent scattering function in two and
three space dimensions. A glass transition is observed for all coefficients of
restitution, epsilon, at a critical packing fraction, phi_c(epsilon), below
random close packing. The divergence of timescales at the glass-transition
implies a dependence on compression rate upon further increase of the density -
similar to the cooling rate dependence of a thermal glass. The critical
dynamics for coherent motion as well as tagged particle dynamics is analyzed
and shown to be non-universal with exponents depending on space dimension and
degree of dissipation.Comment: 16 pages, 9 figure
Bond formation and slow heterogeneous dynamics in adhesive spheres with long--ranged repulsion: Quantitative test of Mode Coupling Theory
A colloidal system of spheres interacting with both a deep and narrow
attractive potential and a shallow long-ranged barrier exhibits a prepeak in
the static structure factor. This peak can be related to an additional
mesoscopic length scale of clusters and/or voids in the system. Simulation
studies of this system have revealed that it vitrifies upon increasing the
attraction into a gel-like solid at intermediate densities. The dynamics at the
mesoscopic length scale corresponding to the prepeak represents the slowest
mode in the system. Using mode coupling theory with all input directly taken
from simulations, we reveal the mechanism for glassy arrest in the system at
40% packing fraction. The effects of the low-q peak and of polydispersity are
considered in detail. We demonstrate that the local formation of physical bonds
is the process whose slowing down causes arrest.
It remains largely unaffected by the large-scale heterogeneities, and sets
the clock for the slow cluster mode. Results from mode-coupling theory without
adjustable parameters agree semi-quantitatively with the local density
correlators but overestimate the lifetime of the mesoscopic structure (voids).Comment: 10 pages, 8 figure
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
The Cole-Cole Law for Critical Dynamics in Glass-Forming Liquids
Within the mode-coupling theory (MCT) for glassy dynamics, the asymptotic
low-frequency expansions for the dynamical susceptibilities at critical points
are compared to the expansions for the dynamic moduli; this shows that the
convergence properties of the two expansions can be quite different. In some
parameter regions, the leading-order expansion formula for the modulus
describes the solutions of the MCT equations of motion outside the transient
regime successfully; at the same time, the leading- and next-to-leading order
expansion formulas for the susceptibility fail. In these cases, one can derive
a Cole-Cole law for the susceptibilities; and this law accounts for the
dynamics for frequencies below the band of microscopic excitations and above
the high-frequency part of the alpha-peak. It is shown that this scenario
explains the optical-Kerr-effect data measured for salol and benzophenone
(BZP). For BZP it is inferred that the depolarized light-scattering spectra
exhibit a wing for the alpha-peak within the Gigahertz band. This wing results
from the crossover of the von Schweidler-law part of the alpha-peak to the
high-frequency part of the Cole-Cole peak; and this crossover can be described
quantitatively by the leading-order formulas of MCT for the modulus.Comment: 15 pages, 9 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
The Effects of Name Agreement on Dual-Task Picture Naming
The understanding of the relationship between attention and normal language processing can provide insight into the underpinnings of language disorders. Dual-task experiments can be used to understand the allocation of attention during different stages of word production. The central bottleneck model posits that while the central (response selection) stage of any cognitive task is being carried out, the same stage of any other task cannot be simultaneously carried out. The central bottleneck model permits the testing of specific hypotheses about the attentional requirements of particular elements of competing tasks. One purpose of the current study was to determine if the process of lemma selection can be said to require central attention. A secondary aim of this study was to determine whether name agreement is a variable that can be used to index lemma selection. A preliminary study was conducted to construct a set of pictures with high and low name agreement that were balanced on important confounding variables. The main experiment was a dual-task experiment involving tone identification and picture naming. Name agreement effects were examined in the dual-task experiment. The effects were investigated in relation to the central bottleneck model, word production models, and the semantic picture-word interference effect. Low name agreement due to multiple correct names was employed. Tone identification was the primary task, while picture naming was the secondary task. Average picture naming reaction times were significantly longer for low than for high name agreement condition across levels of stimulus onset asynchrony. The results are consistent with a locus of the name agreement effect at the central, response selection stage of the central bottleneck model
Pressure and Motion of Dry Sand -- Translation of Hagen's Paper from 1852
In a remarkable paper from 1852, Gotthilf Heinrich Ludwig Hagen measured and
explained two fundamental aspects of granular matter: The first effect is the
saturation of pressure with depth in a static granular system confined by silo
walls -- generally known as the Janssen effect. The second part of his paper
describes the dynamics observed during the flow out of the container -- today
often called the Beverloo law -- and forms the foundation of the hourglass
theory. The following is a translation of the original German paper from 1852.Comment: 4 pages, accepted for publication in Granular Matter, original
article (German) can be found under http://www.phy.duke.edu/~msperl/Janssen
The Jamming Transition in Granular Systems
Recent simulations have predicted that near jamming for collections of
spherical particles, there will be a discontinuous increase in the mean contact
number, Z, at a critical volume fraction, phi_c. Above phi_c, Z and the
pressure, P are predicted to increase as power laws in phi-phi_c. In
experiments using photoelastic disks we corroborate a rapid increase in Z at
phi_c and power-law behavior above phi_c for Z and P. Specifically we find
power-law increase as a function of phi-phi_c for Z-Z_c with an exponent beta
around 0.5, and for P with an exponent psi around 1.1. These exponents are in
good agreement with simulations. We also find reasonable agreement with a
recent mean-field theory for frictionless particles.Comment: 4 pages, 4 figures, 2 pages supplement; minor changes and
clarifications, 2 addtl. refs., accepted for publication in Phys. Rev. Let
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