1,012 research outputs found
Work probability distribution and tossing a biased coin
We show that the rare events present in dissipated work that enters Jarzynski
equality, when mapped appropriately to the phenomenon of large deviations found
in a biased coin toss, are enough to yield a quantitative work probability
distribution for Jarzynski equality. This allows us to propose a recipe for
constructing work probability distribution independent of the details of any
relevant system. The underlying framework, developed herein, is expected to be
of use in modelling other physical phenomena where rare events play an
important role.Comment: 6 pages, 4 figures
A Spatio-Temporal Model Reveals Self-Limiting FcɛRI Cross-Linking by Multivalent Antigens
Aggregation of cell surface receptor proteins by multivalent antigens is an essential early step for immune cell signalling. A number of experimental and modelling studies in the past have investigated multivalent ligand-mediated aggregation of IgE receptors (FcɛRI) in the plasma membrane of mast cells. However, understanding of the mechanisms of FcɛRI aggregation remains incomplete. Experimental reports indicate that FcɛRI forms relatively small and finite-sized clusters when stimulated by a multivalent ligand. By contrast, modelling studies have shown that receptor cross-linking by a trivalent ligand may lead to the formation of large receptor superaggregates that may potentially give rise to hyperactive cellular responses. In this work, we have developed a Brownian dynamics-based spatio-temporal model to analyse FcɛRI aggregation by a trivalent antigen. Unlike the existing models, which implemented non-spatial simulation approaches, our model explicitly accounts for the coarse-grained site-specific features of the multivalent species (molecules and complexes). The model incorporates membrane diffusion, steric collisions and sub-nanometre-scale site-specific interaction of the time-evolving species of arbitrary structures. Using the model, we investigated temporal evolution of the species and their diffusivities. Consistent with a recent experimental report, our model predicted sharp decay in species mobility in the plasma membrane in response receptor cross-linking by a multivalent antigen. We show that, due to such decay in the species mobility, post-stimulation receptor aggregation may become self-limiting. Our analysis reveals a potential regulatory mechanism suppressing hyperactivation of immune cells in response to multivalent antigens
Ising models on power-law random graphs
We study a ferromagnetic Ising model on random graphs with a power-law degree
distribution and compute the thermodynamic limit of the pressure when the mean
degree is finite (degree exponent ), for which the random graph has a
tree-like structure. For this, we adapt and simplify an analysis by Dembo and
Montanari, which assumes finite variance degrees (). We further
identify the thermodynamic limits of various physical quantities, such as the
magnetization and the internal energy
Dynamic Phase Transitions in Cell Spreading
We monitored isotropic spreading of mouse embryonic fibroblasts on
fibronectin-coated substrates. Cell adhesion area versus time was measured via
total internal reflection fluorescence microscopy. Spreading proceeds in
well-defined phases. We found a power-law area growth with distinct exponents
a_i in three sequential phases, which we denote basal (a_1=0.4+-0.2), continous
(a_2=1.6+-0.9) and contractile (a_3=0.3+-0.2) spreading. High resolution
differential interference contrast microscopy was used to characterize local
membrane dynamics at the spreading front. Fourier power spectra of membrane
velocity reveal the sudden development of periodic membrane retractions at the
transition from continous to contractile spreading. We propose that the
classification of cell spreading into phases with distinct functional
characteristics and protein activity patterns serves as a paradigm for a
general program of a phase classification of cellular phenotype. Biological
variability is drastically reduced when only the corresponding phases are used
for comparison across species/different cell lines.Comment: 4 pages, 5 figure
A numerical approach to copolymers at selective interfaces
We consider a model of a random copolymer at a selective interface which
undergoes a localization/delocalization transition. In spite of the several
rigorous results available for this model, the theoretical characterization of
the phase transition has remained elusive and there is still no agreement about
several important issues, for example the behavior of the polymer near the
phase transition line. From a rigorous viewpoint non coinciding upper and lower
bounds on the critical line are known.
In this paper we combine numerical computations with rigorous arguments to
get to a better understanding of the phase diagram. Our main results include:
- Various numerical observations that suggest that the critical line lies
strictly in between the two bounds.
- A rigorous statistical test based on concentration inequalities and
super-additivity, for determining whether a given point of the phase diagram is
in the localized phase. This is applied in particular to show that, with a very
low level of error, the lower bound does not coincide with the critical line.
- An analysis of the precise asymptotic behavior of the partition function in
the delocalized phase, with particular attention to the effect of rare atypical
stretches in the disorder sequence and on whether or not in the delocalized
regime the polymer path has a Brownian scaling.
- A new proof of the lower bound on the critical line. This proof relies on a
characterization of the localized regime which is more appealing for
interpreting the numerical data.Comment: accepted for publication on J. Stat. Phy
Condensation of Silica Nanoparticles on a Phospholipid Membrane
The structure of the transient layer at the interface between air and the
aqueous solution of silica nanoparticles with the size distribution of
particles that has been determined from small-angle scattering has been studied
by the X-ray reflectometry method. The reconstructed depth profile of the
polarizability of the substance indicates the presence of a structure
consisting of several layers of nanoparticles with the thickness that is more
than twice as large as the thickness of the previously described structure. The
adsorption of 1,2-distearoyl-sn-glycero-3-phosphocholine molecules at the
hydrosol/air interface is accompanied by the condensation of anion silica
nanoparticles at the interface. This phenomenon can be qualitatively explained
by the formation of the positive surface potential due to the penetration and
accumulation of Na+ cations in the phospholipid membrane.Comment: 7 pages, 5 figure
The Non--Ergodicity Threshold: Time Scale for Magnetic Reversal
We prove the existence of a non-ergodicity threshold for an anisotropic
classical Heisenberg model with all-to-all couplings. Below the threshold, the
energy surface is disconnected in two components with positive and negative
magnetizations respectively. Above, in a fully chaotic regime, magnetization
changes sign in a stochastic way and its behavior can be fully characterized by
an average magnetization reversal time. We show that statistical mechanics
predicts a phase--transition at an energy higher than the non-ergodicity
threshold. We assess the dynamical relevance of the latter for finite systems
through numerical simulations and analytical calculations. In particular, the
time scale for magnetic reversal diverges as a power law at the ergodicity
threshold with a size-dependent exponent, which could be a signature of the
phenomenon.Comment: 4 pages 4 figure
Quantum properties of classical Fisher information
The Fisher information of a quantum observable is shown to be proportional to
both (i) the difference of a quantum and a classical variance, thus providing a
measure of nonclassicality; and (ii) the rate of entropy increase under
Gaussian diffusion, thus providing a measure of robustness. The joint
nonclassicality of position and momentum observables is shown to be
complementary to their joint robustness in an exact sense.Comment: 16 page
Ensemble Inequivalence in Mean-field Models of Magnetism
Mean-field models, while they can be cast into an {\it extensive}
thermodynamic formalism, are inherently {\it non additive}. This is the basic
feature which leads to {\it ensemble inequivalence} in these models. In this
paper we study the global phase diagram of the infinite range
Blume-Emery-Griffiths model both in the {\it canonical} and in the {\it
microcanonical} ensembles. The microcanonical solution is obtained both by
direct state counting and by the application of large deviation theory. The
canonical phase diagram has first order and continuous transition lines
separated by a tricritical point. We find that below the tricritical point,
when the canonical transition is first order, the phase diagrams of the two
ensembles disagree. In this region the microcanonical ensemble exhibits energy
ranges with negative specific heat and temperature jumps at transition
energies. These two features are discussed in a general context and the
appropriate Maxwell constructions are introduced. Some preliminary extensions
of these results to weakly decaying nonintegrable interactions are presented.Comment: Chapter of the forthcoming "Lecture Notes in Physics" volume:
``Dynamics and Thermodynamics of Systems with Long Range Interactions'', T.
Dauxois, S. Ruffo, E. Arimondo, M. Wilkens Eds., Lecture Notes in Physics
Vol. 602, Springer (2002). (see http://link.springer.de/series/lnpp/
The maximum of the local time of a diffusion process in a drifted Brownian potential
We consider a one-dimensional diffusion process in a
-drifted Brownian potential for . We are interested
in the maximum of its local time, and study its almost sure asymptotic
behaviour, which is proved to be different from the behaviour of the maximum
local time of the transient random walk in random environment. We also obtain
the convergence in law of the maximum local time of under the annealed law
after suitable renormalization when . Moreover, we characterize
all the upper and lower classes for the hitting times of , in the sense of
Paul L\'evy, and provide laws of the iterated logarithm for the diffusion
itself. To this aim, we use annealed technics.Comment: 38 pages, new version, merged with hal-00013040 (arXiv:math/0511053),
with some additional result
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