19,773 research outputs found
Dynamics of Shear-Transformation Zones in Amorphous Plasticity: Formulation in Terms of an Effective Disorder Temperature
This investigation extends earlier studies of a shear-transformation-zone
(STZ) theory of plastic deformation in amorphous solids. My main purpose here
is to explore the possibility that the configurational degrees of freedom of
such systems fall out of thermodynamic equilibrium with the heat bath during
persistent mechanical deformation, and that the resulting state of
configurational disorder may be characterized by an effective temperature. The
further assumption that the population of STZ's equilibrates with the effective
temperature allows the theory to be compared directly with experimentally
measured properties of metallic glasses, including their calorimetric behavior.
The coupling between the effective temperature and mechanical deformation
suggests an explanation of shear-banding instabilities.Comment: 29 pages, 11 figure
Glassy dynamics in granular compaction
Two models are presented to study the influence of slow dynamics on granular
compaction. It is found in both cases that high values of packing fraction are
achieved only by the slow relaxation of cooperative structures. Ongoing work to
study the full implications of these results is discussed.Comment: 12 pages, 9 figures; accepted in J. Phys: Condensed Matter,
proceedings of the Trieste workshop on 'Unifying concepts in glass physics
On random graphs and the statistical mechanics of granular matter
The dynamics of spins on a random graph with ferromagnetic three-spin
interactions is used to model the compaction of granular matter under a series
of taps. Taps are modelled as the random flipping of a small fraction of the
spins followed by a quench at zero temperature. We find that the density
approached during a logarithmically slow compaction
- the random-close-packing density - corresponds to a dynamical phase
transition. We discuss the the role of cascades of successive spin-flips in
this model and link them with density-noise power fluctuations observed in
recent experiments.Comment: minor changes, to appear in EP
Athermal Shear-Transformation-Zone Theory of Amorphous Plastic Deformation I: Basic Principles
We develop an athermal version of the shear-transformation-zone (STZ) theory
of amorphous plasticity in materials where thermal activation of irreversible
molecular rearrangements is negligible or nonexistent. In many respects, this
theory has broader applicability and yet is simpler than its thermal
predecessors. For example, it needs no special effort to assure consistency
with the laws of thermodynamics, and the interpretation of yielding as an
exchange of dynamic stability between jammed and flowing states is clearer than
before. The athermal theory presented here incorporates an explicit
distribution of STZ transition thresholds. Although this theory contains no
conventional thermal fluctuations, the concept of an effective temperature is
essential for understanding how the STZ density is related to the state of
disorder of the system.Comment: 7 pages, 2 figures; first of a two-part serie
Competition and cooperation:aspects of dynamics in sandpiles
In this article, we review some of our approaches to granular dynamics, now
well known to consist of both fast and slow relaxational processes. In the
first case, grains typically compete with each other, while in the second, they
cooperate. A typical result of {\it cooperation} is the formation of stable
bridges, signatures of spatiotemporal inhomogeneities; we review their
geometrical characteristics and compare theoretical results with those of
independent simulations. {\it Cooperative} excitations due to local density
fluctuations are also responsible for relaxation at the angle of repose; the
{\it competition} between these fluctuations and external driving forces, can,
on the other hand, result in a (rare) collapse of the sandpile to the
horizontal. Both these features are present in a theory reviewed here. An arena
where the effects of cooperation versus competition are felt most keenly is
granular compaction; we review here a random graph model, where three-spin
interactions are used to model compaction under tapping. The compaction curve
shows distinct regions where 'fast' and 'slow' dynamics apply, separated by
what we have called the {\it single-particle relaxation threshold}. In the
final section of this paper, we explore the effect of shape -- jagged vs.
regular -- on the compaction of packings near their jamming limit. One of our
major results is an entropic landscape that, while microscopically rough,
manifests {\it Edwards' flatness} at a macroscopic level. Another major result
is that of surface intermittency under low-intensity shaking.Comment: 36 pages, 23 figures, minor correction
Smoothing of sandpile surfaces after intermittent and continuous avalanches: three models in search of an experiment
We present and analyse in this paper three models of coupled continuum
equations all united by a common theme: the intuitive notion that sandpile
surfaces are left smoother by the propagation of avalanches across them. Two of
these concern smoothing at the `bare' interface, appropriate to intermittent
avalanche flow, while one of them models smoothing at the effective surface
defined by a cloud of flowing grains across the `bare' interface, which is
appropriate to the regime where avalanches flow continuously across the
sandpile.Comment: 17 pages and 26 figures. Submitted to Physical Review
Shaking a Box of Sand
We present a simple model of a vibrated box of sand, and discuss its dynamics
in terms of two parameters reflecting static and dynamic disorder respectively.
The fluidised, intermediate and frozen (`glassy') dynamical regimes are
extensively probed by analysing the response of the packing fraction to steady,
as well as cyclic, shaking, and indicators of the onset of a `glass transition'
are analysed. In the `glassy' regime, our model is exactly solvable, and allows
for the qualitative description of ageing phenomena in terms of two
characteristic lengths; predictions are also made about the influence of grain
shape anisotropy on ageing behaviour.Comment: Revised version. To appear in Europhysics Letter
Statistical properties of determinantal point processes in high-dimensional Euclidean spaces
The goal of this paper is to quantitatively describe some statistical
properties of higher-dimensional determinantal point processes with a primary
focus on the nearest-neighbor distribution functions. Toward this end, we
express these functions as determinants of matrices and then
extrapolate to . This formulation allows for a quick and accurate
numerical evaluation of these quantities for point processes in Euclidean
spaces of dimension . We also implement an algorithm due to Hough \emph{et.
al.} \cite{hough2006dpa} for generating configurations of determinantal point
processes in arbitrary Euclidean spaces, and we utilize this algorithm in
conjunction with the aforementioned numerical results to characterize the
statistical properties of what we call the Fermi-sphere point process for to 4. This homogeneous, isotropic determinantal point process, discussed
also in a companion paper \cite{ToScZa08}, is the high-dimensional
generalization of the distribution of eigenvalues on the unit circle of a
random matrix from the circular unitary ensemble (CUE). In addition to the
nearest-neighbor probability distribution, we are able to calculate Voronoi
cells and nearest-neighbor extrema statistics for the Fermi-sphere point
process and discuss these as the dimension is varied. The results in this
paper accompany and complement analytical properties of higher-dimensional
determinantal point processes developed in \cite{ToScZa08}.Comment: 42 pages, 17 figure
Entanglement Generation of Nearly-Random Operators
We study the entanglement generation of operators whose statistical
properties approach those of random matrices but are restricted in some way.
These include interpolating ensemble matrices, where the interval of the
independent random parameters are restricted, pseudo-random operators, where
there are far fewer random parameters than required for random matrices, and
quantum chaotic evolution. Restricting randomness in different ways allows us
to probe connections between entanglement and randomness. We comment on which
properties affect entanglement generation and discuss ways of efficiently
producing random states on a quantum computer.Comment: 5 pages, 3 figures, partially supersedes quant-ph/040505
A two-species continuum model for aeolian sand ripples
We formulate a continuum model for aeolian sand ripples consisting of two
species of grains: a lower layer of relatively immobile clusters, with an upper
layer of highly mobile grains moving on top. We predict analytically the ripple
wavelength, initial ripple growth rate and threshold saltation flux for ripple
formation. Numerical simulations show the evolution of realistic ripple
profiles from initial surface roughness via ripple growth and merger.Comment: 9 pages, 3 figure
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