11,343 research outputs found
Anomalous diffusion and stretched exponentials in heterogeneous glass-forming liquids: Low-temperature behavior
We propose a model of a heterogeneous glass forming liquid and compute the
low-temperature behavior of a tagged molecule moving within it. This model
exhibits stretched-exponential decay of the wavenumber-dependent, self
intermediate scattering function in the limit of long times. At temperatures
close to the glass transition, where the heterogeneities are much larger in
extent than the molecular spacing, the time dependence of the scattering
function crosses over from stretched-exponential decay with an index at
large wave numbers to normal, diffusive behavior with at small
wavenumbers. There is a clear separation between early-stage, cage-breaking
relaxation and late-stage relaxation. The spatial
representation of the scattering function exhibits an anomalously broad
exponential (non-Gaussian) tail for sufficiently large values of the molecular
displacement at all finite times.Comment: 9 pages, 6 figure
Dynamics of Large-Scale Plastic Deformation and the Necking Instability in Amorphous Solids
We use the shear transformation zone (STZ) theory of dynamic plasticity to
study the necking instability in a two-dimensional strip of amorphous solid.
Our Eulerian description of large-scale deformation allows us to follow the
instability far into the nonlinear regime. We find a strong rate dependence;
the higher the applied strain rate, the further the strip extends before the
onset of instability. The material hardens outside the necking region, but the
description of plastic flow within the neck is distinctly different from that
of conventional time-independent theories of plasticity.Comment: 4 pages, 3 figures (eps), revtex4, added references, changed and
added content, resubmitted to PR
Direct Identification of the Glass Transition: Growing Length Scale and the Onset of Plasticity
Understanding the mechanical properties of glasses remains elusive since the
glass transition itself is not fully understood, even in well studied examples
of glass formers in two dimensions. In this context we demonstrate here: (i) a
direct evidence for a diverging length scale at the glass transition (ii) an
identification of the glass transition with the disappearance of fluid-like
regions and (iii) the appearance in the glass state of fluid-like regions when
mechanical strain is applied.
These fluid-like regions are associated with the onset of plasticity in the
amorphous solid. The relaxation times which diverge upon the approach to the
glass transition are related quantitatively.Comment: 5 pages, 5 figs.; 2 figs. omitted, new fig., quasi-crystal discussion
omitted, new material on relaxation time
Shear flow of angular grains: acoustic effects and non-monotonic rate dependence of volume
Naturally-occurring granular materials often consist of angular particles
whose shape and frictional characteristics may have important implications on
macroscopic flow rheology. In this paper, we provide a theoretical account for
the peculiar phenomenon of auto-acoustic compaction -- non-monotonic variation
of shear band volume with shear rate in angular particles -- recently observed
in experiments. Our approach is based on the notion that the volume of a
granular material is determined by an effective-disorder temperature known as
the compactivity. Noise sources in a driven granular material couple its
various degrees of freedom and the environment, causing the flow of entropy
between them. The grain-scale dynamics is described by the
shear-transformation-zone (STZ) theory of granular flow, which accounts for
irreversible plastic deformation in terms of localized flow defects whose
density is governed by the state of configurational disorder. To model the
effects of grain shape and frictional characteristics, we propose an Ising-like
internal variable to account for nearest-neighbor grain interlocking and
geometric frustration, and interpret the effect of friction as an acoustic
noise strength. We show quantitative agreement between experimental
measurements and theoretical predictions, and propose additional experiments
that provide stringent tests on the new theoretical elements.Comment: 12 pages, 3 figure
Stick-slip instabilities in sheared granular flow: the role of friction and acoustic vibrations
We propose a theory of shear flow in dense granular materials. A key
ingredient of the theory is an effective temperature that determines how the
material responds to external driving forces such as shear stresses and
vibrations. We show that, within our model, friction between grains produces
stick-slip behavior at intermediate shear rates, even if the material is
rate-strengthening at larger rates. In addition, externally generated acoustic
vibrations alter the stick-slip amplitude, or suppress stick-slip altogether,
depending on the pressure and shear rate. We construct a phase diagram that
indicates the parameter regimes for which stick-slip occurs in the presence and
absence of acoustic vibrations of a fixed amplitude and frequency. These
results connect the microscopic physics to macroscopic dynamics, and thus
produce useful information about a variety of granular phenomena including
rupture and slip along earthquake faults, the remote triggering of
instabilities, and the control of friction in material processing.Comment: 12 pages, 8 figure
Nonequilibrium Thermodynamics of Amorphous Materials III: Shear-Transformation-Zone Plasticity
We use the internal-variable, effective-temperature thermodynamics developed
in two preceding papers to reformulate the shear-transformation-zone (STZ)
theory of amorphous plasticity. As required by the preceding analysis, we make
explicit approximations for the energy and entropy of the STZ internal degrees
of freedom. We then show that the second law of thermodynamics constrains the
STZ transition rates to have an Eyring form as a function of the effective
temperature. Finally, we derive an equation of motion for the effective
temperature for the case of STZ dynamics.Comment: 8 pages. Third of a three-part serie
Steady-State Cracks in Viscoelastic Lattice Models II
We present the analytic solution of the Mode III steady-state crack in a
square lattice with piecewise linear springs and Kelvin viscosity. We show how
the results simplify in the limit of large width. We relate our results to a
model where the continuum limit is taken only along the crack direction. We
present results for small velocity, and for large viscosity, and discuss the
structure of the critical bifurcation for small velocity. We compute the size
of the process zone wherein standard continuum elasticity theory breaks down.Comment: 17 pages, 3 figure
Rate dependent shear bands in a shear transformation zone model of amorphous solids
We use Shear Transformation Zone (STZ) theory to develop a deformation map
for amorphous solids as a function of the imposed shear rate and initial
material preparation. The STZ formulation incorporates recent simulation
results [Haxton and Liu, PRL 99 195701 (2007)] showing that the steady state
effective temperature is rate dependent. The resulting model predicts a wide
range of deformation behavior as a function of the initial conditions,
including homogeneous deformation, broad shear bands, extremely thin shear
bands, and the onset of material failure. In particular, the STZ model predicts
homogeneous deformation for shorter quench times and lower strain rates, and
inhomogeneous deformation for longer quench times and higher strain rates. The
location of the transition between homogeneous and inhomogeneous flow on the
deformation map is determined in part by the steady state effective
temperature, which is likely material dependent. This model also suggests that
material failure occurs due to a runaway feedback between shear heating and the
local disorder, and provides an explanation for the thickness of shear bands
near the onset of material failure. We find that this model, which resolves
dynamics within a sheared material interface, predicts that the stress weakens
with strain much more rapidly than a similar model which uses a single state
variable to specify internal dynamics on the interface.Comment: 10 pages, 13 figures, corrected typos, added section on rate
strengthening vs. rate weakening material
Langevin Equation for the Density of a System of Interacting Langevin Processes
We present a simple derivation of the stochastic equation obeyed by the
density function for a system of Langevin processes interacting via a pairwise
potential. The resulting equation is considerably different from the
phenomenological equations usually used to describe the dynamics of non
conserved (Model A) and conserved (Model B) particle systems. The major feature
is that the spatial white noise for this system appears not additively but
multiplicatively. This simply expresses the fact that the density cannot
fluctuate in regions devoid of particles. The steady state for the density
function may however still be recovered formally as a functional integral over
the coursed grained free energy of the system as in Models A and B.Comment: 6 pages, latex, no figure
Metastability in Two Dimensions and the Effective Potential
We study analytically and numerically the decay of a metastable phase in
(2+1)-dimensional classical scalar field theory coupled to a heat bath, which
is equivalent to two-dimensional Euclidean quantum field theory at zero
temperature. By a numerical simulation we obtain the nucleation barrier as a
function of the parameters of the potential, and compare it to the theoretical
prediction from the bounce (critical bubble) calculation. We find the
nucleation barrier to be accurately predicted by theory using the bounce
configuration obtained from the tree-level (``classical'') effective action.
Within the range of parameters probed, we found that using the bounce derived
from the one-loop effective action requires an unnaturally large prefactor to
match the lattice results. Deviations from the tree-level prediction are seen
in the regime where loop corrections would be expected to become important.Comment: 13pp, LaTex with Postscript figs, CLNS 93/1202, DART-HEP-93/0
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