29 research outputs found
Morphology transition at depinning in a solvable model of interface growth in a random medium
We propose a simple, exactly solvable, model of interface growth in a random
medium that is a variant of the zero-temperature random-field Ising model on
the Cayley tree. This model is shown to have a phase diagram (critical
depinning field versus disorder strength) qualitatively similar to that
obtained numerically on the cubic lattice. We then introduce a specifically
tailored random graph that allows an exact asymptotic analysis of the height
and width of the interface. We characterize the change of morphology of the
interface as a function of the disorder strength, a change that is found to
take place at a multicritical point along the depinning-transition line.Comment: 7 pages, 6 figure
Hysteresis and avalanches in the T=0 random-field Ising model with 2-spin-flip dynamics
We study the non-equilibrium behavior of the three-dimensional Gaussian
random-field Ising model at T=0 in the presence of a uniform external field
using a 2-spin-flip dynamics. The deterministic, history-dependent evolution of
the system is compared with the one obtained with the standard 1-spin-flip
dynamics used in previous studies of the model. The change in the dynamics
yields a significant suppression of coercivity, but the distribution of
avalanches (in number and size) stays remarkably similar, except for the
largest ones that are responsible for the jump in the saturation magnetization
curve at low disorder in the thermodynamic limit. By performing a finite-size
scaling study, we find strong evidence that the change in the dynamics does not
modify the universality class of the disorder-induced phase transition.Comment: 9 pages, 10 figure
Information-theoretic analysis of the directional influence between cellular processes
Inferring the directionality of interactions between cellular processes is a
major challenge in systems biology. Time-lagged correlations allow to
discriminate between alternative models, but they still rely on assumed
underlying interactions. Here, we use the transfer entropy (TE), an
information-theoretic quantity that quantifies the directional influence
between fluctuating variables in a model-free way. We present a theoretical
approach to compute the transfer entropy, even when the noise has an extrinsic
component or in the presence of feedback. We re-analyze the experimental data
from Kiviet et al. (2014) where fluctuations in gene expression of metabolic
enzymes and growth rate have been measured in single cells of E. coli. We
confirm the formerly detected modes between growth and gene expression, while
prescribing more stringent conditions on the structure of noise sources. We
furthermore point out practical requirements in terms of length of time series
and sampling time which must be satisfied in order to infer optimally transfer
entropy from times series of fluctuations.Comment: 24 pages, 7 figure
The magnetization-driven random field Ising model at T=0
We study the hysteretic evolution of the random field Ising model (RFIM) at
T=0 when the magnetization M is controlled externally and the magnetic field H
becomes the output variable. The dynamics is a simple modification of the
single-spin-flip dynamics used in the H-driven situation and consists in
flipping successively the spins with the largest local field. This allows to
perform a detailed comparison between the microscopic trajectories followed by
the system with the two protocols. Simulations are performed on random graphs
with connectivity z=4 (Bethe lattice) and on the 3-D cubic lattice. The same
internal energy U(M)is found with the two protocols when there is no
macroscopic avalanche and it does not depend on whether the microscopic states
are stable or not. On the Bethe lattice, the energy inside the macroscopic
avalanche also coincides with the one that is computed analytically with the
H-driven algorithm along the unstable branch of the hysteresis loop. The output
field, defined here as dU/dM, exhibits very large fluctuations with the
magnetization and is not self-averaging. Relation to the experimental situation
is discussed.Comment: 11 pages, 13 figure
Influence of the driving mechanism on the response of systems with athermal dynamics: the example of the random-field Ising model
We investigate the influence of the driving mechanism on the hysteretic
response of systems with athermal dynamics. In the framework of local-mean
field theory at finite temperature (but neglecting thermallly activated
processes), we compare the rate-independent hysteresis loops obtained in the
random field Ising model (RFIM) when controlling either the external magnetic
field or the extensive magnetization . Two distinct behaviors are
observed, depending on disorder strength. At large disorder, the -driven and
-driven protocols yield identical hysteresis loops in the thermodynamic
limit. At low disorder, when the -driven magnetization curve is
discontinuous (due to the presence of a macroscopic avalanche), the -driven
loop is re-entrant while the induced field exhibits strong intermittent
fluctuations and is only weakly self-averaging. The relevance of these results
to the experimental observations in ferromagnetic materials, shape memory
alloys, and other disordered systems is discussed.Comment: 11 pages, 11 figure
Hierarchical Reference Theory of critical fluids in disordered porous media
We consider the equilibrium behavior of fluids imbibed in disordered
mesoporous media, including their gas-liquid critical point when present. Our
starting points are on the one hand a description of the fluid/solid-matrix
system as a quenched-annealed mixture and on the other hand the Hierarchical
Reference Theory (HRT) developed by A. Parola and L. Reatto to cope with
density fluctuations on all length scales. The formalism combines liquid-state
statistical mechanics and the theory of systems in the presence of quenched
disorder. A straightforward implementation of the HRT to the quenched-annealed
mixture is shown to lead to unsatisfactory results, while indicating that the
critical behavior of the system is in the same universality class as that of
the random-field Ising model. After a detour via the field-theoretical
renormalization group approach of the latter model, we finally lay out the
foundations for a proper HRT of fluids in a disordered porous material.Comment: 23 pages. Article for Luciano Reatto's festschrif
UNE APPROCHE THERMODYNAMIQUEMENT COHERENTE POUR LES MODELES DE SPINS CLASSIQUES TRIDIMENSIONNELS
LIMOGES-ENSCI (870852305) / SudocORSAY-PARIS 11-BU Sciences (914712101) / SudocSudocFranceF
Condensation capillaire et transitions hors d' équilibre dans les milieux poreux désordonnées (l' exemple des aérogels de silice)
PARIS-BIUSJ-Thèses (751052125) / SudocPARIS-BIUSJ-Physique recherche (751052113) / SudocSudocFranceF