5,678 research outputs found
On-off intermittency over an extended range of control parameter
We propose a simple phenomenological model exhibiting on-off intermittency
over an extended range of control parameter. We find that the distribution of
the 'off' periods has as a power-law tail with an exponent varying continuously
between -1 and -2, at odds with standard on-off intermittency which occurs at a
specific value of the control parameter, and leads to the exponent -3/2. This
non-trivial behavior results from the competition between a strong slowing down
of the dynamics at small values of the observable, and a systematic drift
toward large values.Comment: 4 pages, 3 figure
Optimization to low temperature activity in psychrophilic enzymes
Psychrophiles, i.e., organisms thriving permanently at near-zero temperatures, synthesize cold-active enzymes to sustain their cell cycle. These enzymes are already used in many biotechnological applications requiring high activity at mild temperatures or fast heat-inactivation rate. Most psychrophilic enzymes optimize a high activity at low temperature at the expense of substrate affinity, therefore reducing the free energy barrier of the transition state. Furthermore, a weak temperature dependence of activity ensures moderate reduction of the catalytic activity in the cold. In these naturally evolved enzymes, the optimization to low temperature activity is reached via destabilization of the structures bearing the active site or by destabilization of the whole molecule. This involves a reduction in the number and strength of all types of weak interactions or the disappearance of stability factors, resulting in improved dynamics of active site residues in the cold. Considering the subtle structural adjustments required for low temperature activity, directed evolution appears to be the most suitable methodology to engineer cold activity in biological catalysts
Geometric origin of scaling in large traffic networks
Large scale traffic networks are an indispensable part of contemporary human
mobility and international trade. Networks of airport travel or cargo ships
movements are invaluable for the understanding of human mobility
patterns\cite{Guimera2005}, epidemic spreading\cite{Colizza2006}, global
trade\cite{Imo2006} and spread of invasive species\cite{Ruiz2000}. Universal
features of such networks are necessary ingredients of their description and
can point to important mechanisms of their formation. Different
studies\cite{Barthelemy2010} point to the universal character of some of the
exponents measured in such networks. Here we show that exponents which relate
i) the strength of nodes to their degree and ii) weights of links to degrees of
nodes that they connect have a geometric origin. We present a simple robust
model which exhibits the observed power laws and relates exponents to the
dimensionality of 2D space in which traffic networks are embedded. The model is
studied both analytically and in simulations and the conditions which result
with previously reported exponents are clearly explained. We show that the
relation between weight strength and degree is , the relation
between distance strength and degree is and the relation
between weight of link and degrees of linked nodes is
on the plane 2D surface. We further analyse the
influence of spherical geometry, relevant for the whole planet, on exact values
of these exponents. Our model predicts that these exponents should be found in
future studies of port networks and impose constraints on more refined models
of port networks.Comment: 17 pages, 5 figures, 1 tabl
Noise-enhanced trapping in chaotic scattering
We show that noise enhances the trapping of trajectories in scattering
systems. In fully chaotic systems, the decay rate can decrease with increasing
noise due to a generic mismatch between the noiseless escape rate and the value
predicted by the Liouville measure of the exit set. In Hamiltonian systems with
mixed phase space we show that noise leads to a slower algebraic decay due to
trajectories performing a random walk inside Kolmogorov-Arnold-Moser islands.
We argue that these noise-enhanced trapping mechanisms exist in most scattering
systems and are likely to be dominant for small noise intensities, which is
confirmed through a detailed investigation in the Henon map. Our results can be
tested in fluid experiments, affect the fractal Weyl's law of quantum systems,
and modify the estimations of chemical reaction rates based on phase-space
transition state theory.Comment: 5 pages, 5 figure
Critical percolation of free product of groups
In this article we study percolation on the Cayley graph of a free product of
groups.
The critical probability of a free product of groups
is found as a solution of an equation involving only the expected subcritical
cluster size of factor groups . For finite groups these
equations are polynomial and can be explicitly written down. The expected
subcritical cluster size of the free product is also found in terms of the
subcritical cluster sizes of the factors. In particular, we prove that
for the Cayley graph of the modular group (with the
standard generators) is , the unique root of the polynomial
in the interval .
In the case when groups can be "well approximated" by a sequence of
quotient groups, we show that the critical probabilities of the free product of
these approximations converge to the critical probability of
and the speed of convergence is exponential. Thus for residually finite groups,
for example, one can restrict oneself to the case when each free factor is
finite.
We show that the critical point, introduced by Schonmann,
of the free product is just the minimum of for the factors
Probability distribution of residence times of grains in models of ricepiles
We study the probability distribution of residence time of a grain at a site,
and its total residence time inside a pile, in different ricepile models. The
tails of these distributions are dominated by the grains that get deeply buried
in the pile. We show that, for a pile of size , the probabilities that the
residence time at a site or the total residence time is greater than , both
decay as for where
is an exponent , and values of and in the two
cases are different. In the Oslo ricepile model we find that the probability
that the residence time at a site being greater than or equal to ,
is a non-monotonic function of for a fixed and does not obey simple
scaling. For model in dimensions, we show that the probability of minimum
slope configuration in the steady state, for large , varies as where is a constant, and hence .Comment: 13 pages, 23 figures, Submitted to Phys. Rev.
Edgeworth expansions for slow-fast systems with finite time scale separation
We derive Edgeworth expansions that describe corrections to the Gaussian limiting behaviour of slow-fast systems. The Edgeworth expansion is achieved using a semi-group formalism for the transfer operator, where a Duhamel-Dyson series is used to asymptotically determine the corrections at any desired order of the time scale parameter ε. The corrections involve integrals over higher-order auto-correlation functions. We develop a diagrammatic representation of the series to control the combinatorial wealth of the asymptotic expansion in ε and provide explicit expressions for the first two orders. At a formal level, the expressions derived are valid in the case when the fast dynamics is stochastic as well as when the fast dynamics is entirely deterministic. We corroborate our analytical results with numerical simulations and show that our method provides an improvement on the classical homogenization limit which is restricted to the limit of infinite time scale separation
Computing the entropy of user navigation in the web
Navigation through the web, colloquially known as "surfing", is one of the main activities of users during web interaction. When users follow a navigation trail they often tend to get disoriented in terms of the goals of their original query and thus the discovery of typical user trails could be useful in providing navigation assistance. Herein, we give a theoretical underpinning of user navigation in terms of the entropy of an underlying Markov chain modelling the web topology. We present a novel method for online incremental computation of the entropy and a large deviation result regarding the length of a trail to realize the said entropy. We provide an error analysis for our estimation of the entropy in terms of the divergence between the empirical and actual probabilities. We then indicate applications of our algorithm in the area of web data mining. Finally, we present an extension of our technique to higher-order Markov chains by a suitable reduction of a higher-order Markov chain model to a first-order one
A Random Walk to a Non-Ergodic Equilibrium Concept
Random walk models, such as the trap model, continuous time random walks, and
comb models exhibit weak ergodicity breaking, when the average waiting time is
infinite. The open question is: what statistical mechanical theory replaces the
canonical Boltzmann-Gibbs theory for such systems? In this manuscript a
non-ergodic equilibrium concept is investigated, for a continuous time random
walk model in a potential field. In particular we show that in the non-ergodic
phase the distribution of the occupation time of the particle on a given
lattice point, approaches U or W shaped distributions related to the arcsin
law. We show that when conditions of detailed balance are applied, these
distributions depend on the partition function of the problem, thus
establishing a relation between the non-ergodic dynamics and canonical
statistical mechanics. In the ergodic phase the distribution function of the
occupation times approaches a delta function centered on the value predicted
based on standard Boltzmann-Gibbs statistics. Relation of our work with single
molecule experiments is briefly discussed.Comment: 14 pages, 6 figure
Equilibrium of anchored interfaces with quenched disordered growth
The roughening behavior of a one-dimensional interface fluctuating under
quenched disorder growth is examined while keeping an anchored boundary. The
latter introduces detailed balance conditions which allows for a thorough
analysis of equilibrium aspects at both macroscopic and microscopic scales. It
is found that the interface roughens linearly with the substrate size only in
the vicinity of special disorder realizations. Otherwise, it remains stiff and
tilted.Comment: 6 pages, 3 postscript figure
- …