544 research outputs found
Energy landscapes, lowest gaps, and susceptibility of elastic manifolds at zero temperature
We study the effect of an external field on (1+1) and (2+1) dimensional
elastic manifolds, at zero temperature and with random bond disorder. Due to
the glassy energy landscape the configuration of a manifold changes often in
abrupt, ``first order'' -type of large jumps when the field is applied. First
the scaling behavior of the energy gap between the global energy minimum and
the next lowest minimum of the manifold is considered, by employing exact
ground state calculations and an extreme statistics argument. The scaling has a
logarithmic prefactor originating from the number of the minima in the
landscape, and reads ,
where is the roughness exponent and is the energy fluctuation
exponent of the manifold, is the linear size of the manifold, and is
the system height. The gap scaling is extended to the case of a finite external
field and yields for the susceptibility of the manifolds . We also present a mean field argument
for the finite size scaling of the first jump field, .
The implications to wetting in random systems, to finite-temperature behavior
and the relation to Kardar-Parisi-Zhang non-equilibrium surface growth are
discussed.Comment: 20 pages, 22 figures, accepted for publication in Eur. Phys. J.
Dynamic hysteresis in cyclic deformation of crystalline solids
The hysteresis or internal friction in the deformation of crystalline solids
stressed cyclically is studied from the viewpoint of collective dislocation
dynamics. Stress-controlled simulations of a dislocation dynamics model at
various loading frequencies and amplitudes are performed to study the stress -
strain rate hysteresis. The hysteresis loop areas exhibit a maximum at a
characteristic frequency and a power law frequency dependence in the low
frequency limit, with the power law exponent exhibiting two regimes,
corresponding to the jammed and the yielding/moving phases of the system,
respectively. The first of these phases exhibits non-trivial critical-like
viscoelastic dynamics, crossing over to intermittent viscoplastic deformation
for higher stress amplitudes.Comment: 5 pages, 4 figures, to appear in Physical Review Letter
A periodic elastic medium in which periodicity is relevant
We analyze, in both (1+1)- and (2+1)- dimensions, a periodic elastic medium
in which the periodicity is such that at long distances the behavior is always
in the random-substrate universality class. This contrasts with the models with
an additive periodic potential in which, according to the field theoretic
analysis of Bouchaud and Georges and more recently of Emig and Nattermann, the
random manifold class dominates at long distances in (1+1)- and
(2+1)-dimensions. The models we use are random-bond Ising interfaces in
hypercubic lattices. The exchange constants are random in a slab of size
and these coupling constants are periodically repeated
along either {10} or {11} (in (1+1)-dimensions) and {100} or {111} (in
(2+1)-dimensions). Exact ground-state calculations confirm scaling arguments
which predict that the surface roughness behaves as: and , with in
-dimensions and; and , with in -dimensions.Comment: Submitted to Phys. Rev.
Intermittence and roughening of periodic elastic media
We analyze intermittence and roughening of an elastic interface or domain
wall pinned in a periodic potential, in the presence of random-bond disorder in
(1+1) and (2+1) dimensions. Though the ensemble average behavior is smooth, the
typical behavior of a large sample is intermittent, and does not self-average
to a smooth behavior. Instead, large fluctuations occur in the mean location of
the interface and the onset of interface roughening is via an extensive
fluctuation which leads to a jump in the roughness of order , the
period of the potential. Analytical arguments based on extreme statistics are
given for the number of the minima of the periodicity visited by the interface
and for the roughening cross-over, which is confirmed by extensive exact ground
state calculations.Comment: Accepted for publication in Phys. Rev.
Power spectra of self-organized critical sandpiles
We analyze the power spectra of avalanches in two classes of self-organized
critical sandpile models, the Bak-Tang-Wiesenfeld model and the Manna model. We
show that these decay with a power law, where the exponent value
is significantly smaller than 2 and equals the scaling exponent
relating the avalanche size to its duration. We discuss the basic ingredients
behind this result, such as the scaling of the average avalanche shape.Comment: 7 pages, 3 figures, submitted to JSTA
Effect of Disorder and Notches on Crack Roughness
We analyze the effect of disorder and notches on crack roughness in two
dimensions. Our simulation results based on large system sizes and extensive
statistical sampling indicate that the crack surface exhibits a universal local
roughness of and is independent of the initial notch size
and disorder in breaking thresholds. The global roughness exponent scales as
and is also independent of material disorder. Furthermore, we
note that the statistical distribution of crack profile height fluctuations is
also independent of material disorder and is described by a Gaussian
distribution, albeit deviations are observed in the tails.Comment: 6 pages, 6 figure
Network inference using asynchronously updated kinetic Ising Model
Network structures are reconstructed from dynamical data by respectively
naive mean field (nMF) and Thouless-Anderson-Palmer (TAP) approximations. For
TAP approximation, we use two methods to reconstruct the network: a) iteration
method; b) casting the inference formula to a set of cubic equations and
solving it directly. We investigate inference of the asymmetric Sherrington-
Kirkpatrick (S-K) model using asynchronous update. The solutions of the sets
cubic equation depend of temperature T in the S-K model, and a critical
temperature Tc is found around 2.1. For T < Tc, the solutions of the cubic
equation sets are composed of 1 real root and two conjugate complex roots while
for T > Tc there are three real roots. The iteration method is convergent only
if the cubic equations have three real solutions. The two methods give same
results when the iteration method is convergent. Compared to nMF, TAP is
somewhat better at low temperatures, but approaches the same performance as
temperature increase. Both methods behave better for longer data length, but
for improvement arises, TAP is well pronounced.Comment: 6 pages, 4 figure
Collective roughening of elastic lines with hard core interaction in a disordered environment
We investigate by exact optimization methods the roughening of two and
three-dimensional systems of elastic lines with point disorder and hard-core
repulsion with open boundary conditions. In 2d we find logarithmic behavior
whereas in 3d simple random walk-like behavior. The line 'forests' become
asymptotically completely entangled as the system height is increased at fixed
line density due to increasing line wandering
Scaling of interfaces in brittle fracture and perfect plasticity
The roughness properties of two-dimensional fracture surfaces as created by
the slow failure of random fuse networks are considered and compared to yield
surfaces of perfect plasticity with similar disorder. By studying systems up to
a linear size L=350 it is found that in the cases studied the fracture surfaces
exhibit self-affine scaling with a roughness exponent close to 2/3, which is
asymptotically exactly true for plasticity though finite-size effects are
evident for both. The overlap of yield or minimum energy and fracture surfaces
with exactly the same disorder configuration is shown to be a decreasing
function of the system size and to be of a rather large magnitude for all cases
studied. The typical ``overlap cluster'' length between pairs of such
interfaces converges to a constant with increasing.Comment: Accepted for publication in Phys. Rev.
Particle Survival and Polydispersity in Aggregation
We study the probability, , of a cluster to remain intact in
one-dimensional cluster-cluster aggregation when the cluster diffusion
coefficient scales with size as . exhibits a
stretched exponential decay for and the power-laws for
, and for . A random walk picture
explains the discontinuous and non-monotonic behavior of the exponent. The
decay of determines the polydispersity exponent, , which
describes the size distribution for small clusters. Surprisingly,
is a constant for .Comment: submitted to Europhysics Letter
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