427 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.
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.
Phase transitions in a disordered system in and out of equilibrium
The equilibrium and non--equilibrium disorder induced phase transitions are
compared in the random-field Ising model (RFIM). We identify in the
demagnetized state (DS) the correct non-equilibrium hysteretic counterpart of
the T=0 ground state (GS), and present evidence of universality. Numerical
simulations in d=3 indicate that exponents and scaling functions coincide,
while the location of the critical point differs, as corroborated by exact
results for the Bethe lattice. These results are of relevance for optimization,
and for the generic question of universality in the presence of disorder.Comment: Accepted for publication in Phys. Rev. Let
Ground-States of Two Directed Polymers
Joint ground states of two directed polymers in a random medium are
investigated. Using exact min-cost flow optimization the true two-line
ground-state is compared with the single line ground state plus its first
excited state. It is found that these two-line configurations are (for almost
all disorder configurations) distinct implying that the true two-line
ground-state is non-separable, even with 'worst-possible' initial conditions.
The effective interaction energy between the two lines scales with the system
size with the scaling exponents 0.39 and 0.21 in 2D and 3D, respectively.Comment: 19 pages RevTeX, figures include
Ground state optimization and hysteretic demagnetization: the random-field Ising model
We compare the ground state of the random-field Ising model with Gaussian
distributed random fields, with its non-equilibrium hysteretic counterpart, the
demagnetized state. This is a low energy state obtained by a sequence of slow
magnetic field oscillations with decreasing amplitude. The main concern is how
optimized the demagnetized state is with respect to the best-possible ground
state. Exact results for the energy in d=1 show that in a paramagnet, with
finite spin-spin correlations, there is a significant difference in the
energies if the disorder is not so strong that the states are trivially almost
alike. We use numerical simulations to better characterize the difference
between the ground state and the demagnetized state. For d>=3 the random-field
Ising model displays a disorder induced phase transition between a paramagnetic
and a ferromagnetic state. The locations of the critical points R_c(DS),
R_c(GS) differ for the demagnetized state and ground state. Consequently, it is
in this regime that the optimization of the demagnetized stat is the worst
whereas both deep in the paramagnetic regime and in the ferromagnetic one the
states resemble each other to a great extent. We argue based on the numerics
that in d=3 the scaling at the transition is the same in the demagnetized and
ground states. This claim is corroborated by the exact solution of the model on
the Bethe lattice, where the R_c's are also different.Comment: 13 figs. Submitted to Phys. Rev.
How important tasks are performed: peer review
The advancement of various fields of science depends on the actions of individual scientists via the peer review process. The referees' work patterns and stochastic nature of decision making both relate to the particular features of refereeing and to the universal aspects of human behavior. Here, we show that the time a referee takes to write a report on a scientific manuscript depends on the final verdict. The data is compared to a model, where the review takes place in an ongoing competition of completing an important composite task with a large number of concurrent ones - a Deadline -effect. In peer review human decision making and task completion combine both long-range predictability and stochastic variation due to a large degree of ever-changing external âfrictionâ.Peer reviewe
Ground states versus low-temperature equilibria in random field Ising chains
We discuss with the aid of random walk arguments and exact numerical
computations the magnetization properties of one-dimensional random field
chains. The ground state structure is explained in terms of absorbing and
non-absorbing random walk excursions. At low temperatures, the magnetization
profiles follow those of the ground states except at regions where a local
random field fluctuation makes thermal excitations feasible. This follows also
from the non-absorbing random walks, and implies that the magnetization length
scale is a product of these two scales. It is not simply given by the
Imry-Ma-like ground state domain size nor by the scale of the thermal
excitations.Comment: 7 pages LaTeX, 8 eps-figures include
Kinetic Roughening in Slow Combustion of Paper
Results of experiments on the dynamics and kinetic roughening of
one-dimensional slow-combustion fronts in three grades of paper are reported.
Extensive averaging of the data allows a detailed analysis of the spatial and
temporal development of the interface fluctuations. The asymptotic scaling
properties, on long length and time scales, are well described by the
Kardar-Parisi-Zhang (KPZ) equation with short-range, uncorrelated noise. To
obtain a more detailed picture of the strong-coupling fixed point,
characteristic of the KPZ universality class, universal amplitude ratios, and
the universal coupling constant are computed from the data and found to be in
good agreement with theory. Below the spatial and temporal scales at which a
cross-over takes place to the standard KPZ behavior, the fronts display higher
apparent exponents and apparent multiscaling. In this regime the interface
velocities are spatially and temporally correlated, and the distribution of the
magnitudes of the effective noise has a power-law tail. The relation of the
observed short-range behavior and the noise as determined from the local
velocity fluctuations is discussed.Comment: RevTeX v3.1, 13 pages, 12 Postscript figures (uses epsf.sty), 3
tables; submitted to Phys. Rev.
Comment on: `Pipe Network Model for Scaling of Dynamic Interfaces in Porous Media'
We argue that a proposed exponent identity [Phys. Rev. Lett 85, 1238 (2000)]
for interface roughening in spontaneous imbibition is wrong. It rests on the
assumption that the fluctuations are controlled by a single time scale, but
liquid conservation imposes two distinct time scales.Comment: 1 page, to appear in Phys. Rev. Let
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