411 research outputs found
Dynamics of Surface Roughening with Quenched Disorder
We study the dynamical exponent for the directed percolation depinning
(DPD) class of models for surface roughening in the presence of quenched
disorder. We argue that for dimensions is equal to the exponent
characterizing the shortest path between two sites in an
isotropic percolation cluster in dimensions. To test the argument, we
perform simulations and calculate for DPD, and for
percolation, from to .Comment: RevTex manuscript 3 pages + 6 figures (obtained upon request via
email [email protected]
Worldwide spreading of economic crisis
We model the spreading of a crisis by constructing a global economic network
and applying the Susceptible-Infected-Recovered (SIR) epidemic model with a
variable probability of infection. The probability of infection depends on the
strength of economic relations between the pair of countries, and the strength
of the target country. It is expected that a crisis which originates in a large
country, such as the USA, has the potential to spread globally, like the recent
crisis. Surprisingly we show that also countries with much lower GDP, such as
Belgium, are able to initiate a global crisis. Using the {\it k}-shell
decomposition method to quantify the spreading power (of a node), we obtain a
measure of ``centrality'' as a spreader of each country in the economic
network. We thus rank the different countries according to the shell they
belong to, and find the 12 most central countries. These countries are the most
likely to spread a crisis globally. Of these 12 only six are large economies,
while the other six are medium/small ones, a result that could not have been
otherwise anticipated. Furthermore, we use our model to predict the crisis
spreading potential of countries belonging to different shells according to the
crisis magnitude.Comment: 13 pages, 4 figures and Supplementary Materia
Directed Polymer -- Directed Percolation Transition
We study the relation between the directed polymer and the directed
percolation models, for the case of a disordered energy landscape where the
energies are taken from bimodal distribution. We find that at the critical
concentration of the directed percolation, the directed polymer undergoes a
transition from the directed polymer universality class to the directed
percolation universality class. We also find that directed percolation clusters
affect the characterisrics of the directed polymer below the critical
concentration.Comment: LaTeX 2e; 12 pages, 5 figures; in press, will be published in
Europhys. Let
Optimization of Network Robustness to Waves of Targeted and Random Attack
We study the robustness of complex networks to multiple waves of simultaneous
(i) targeted attacks in which the highest degree nodes are removed and (ii)
random attacks (or failures) in which fractions and respectively of
the nodes are removed until the network collapses. We find that the network
design which optimizes network robustness has a bimodal degree distribution,
with a fraction of the nodes having degree k_2= (\kav - 1 +r)/r and the
remainder of the nodes having degree , where \kav is the average
degree of all the nodes. We find that the optimal value of is of the order
of for
Financial factor influence on scaling and memory of trading volume in stock market
We study the daily trading volume volatility of 17,197 stocks in the U.S.
stock markets during the period 1989--2008 and analyze the time return
intervals between volume volatilities above a given threshold q. For
different thresholds q, the probability density function P_q(\tau) scales with
mean interval as P_q(\tau)=^{-1}f(\tau/) and the tails of
the scaling function can be well approximated by a power-law f(x)~x^{-\gamma}.
We also study the relation between the form of the distribution function
P_q(\tau) and several financial factors: stock lifetime, market capitalization,
volume, and trading value. We find a systematic tendency of P_q(\tau)
associated with these factors, suggesting a multi-scaling feature in the volume
return intervals. We analyze the conditional probability P_q(\tau|\tau_0) for
following a certain interval \tau_0, and find that P_q(\tau|\tau_0)
depends on \tau_0 such that immediately following a short/long return interval
a second short/long return interval tends to occur. We also find indications
that there is a long-term correlation in the daily volume volatility. We
compare our results to those found earlier for price volatility.Comment: 17 pages, 6 figure
Traveling length and minimal traveling time for flow through percolation networks with long-range spatial correlations
We study the distributions of traveling length l and minimal traveling time t
through two-dimensional percolation porous media characterized by long-range
spatial correlations. We model the dynamics of fluid displacement by the
convective movement of tracer particles driven by a pressure difference between
two fixed sites (''wells'') separated by Euclidean distance r. For strongly
correlated pore networks at criticality, we find that the probability
distribution functions P(l) and P(t) follow the same scaling Ansatz originally
proposed for the uncorrelated case, but with quite different scaling exponents.
We relate these changes in dynamical behavior to the main morphological
difference between correlated and uncorrelated clusters, namely, the
compactness of their backbones. Our simulations reveal that the dynamical
scaling exponents for correlated geometries take values intermediate between
the uncorrelated and homogeneous limiting cases
Scaling behavior in economics: II. Modeling of company growth
In the preceding paper we presented empirical results describing the growth
of publicly-traded United States manufacturing firms within the years
1974--1993. Our results suggest that the data can be described by a scaling
approach. Here, we propose models that may lead to some insight into these
phenomena. First, we study a model in which the growth rate of a company is
affected by a tendency to retain an ``optimal'' size. That model leads to an
exponential distribution of the logarithm of the growth rate in agreement with
the empirical results. Then, we study a hierarchical tree-like model of a
company that enables us to relate the two parameters of the model to the
exponent , which describes the dependence of the standard deviation of
the distribution of growth rates on size. We find that , where defines the mean branching ratio of the hierarchical tree and
is the probability that the lower levels follow the policy of higher
levels in the hierarchy. We also study the distribution of growth rates of this
hierarchical model. We find that the distribution is consistent with the
exponential form found empirically.Comment: 19 pages LateX, RevTeX 3, 6 figures, to appear J. Phys. I France
(April 1997
Scaling behavior in economics: I. Empirical results for company growth
We address the question of the growth of firm size. To this end, we analyze
the Compustat data base comprising all publicly-traded United States
manufacturing firms within the years 1974-1993. We find that the distribution
of firm sizes remains stable for the 20 years we study, i.e., the mean value
and standard deviation remain approximately constant. We study the distribution
of sizes of the ``new'' companies in each year and find it to be well
approximated by a log-normal. We find (i) the distribution of the logarithm of
the growth rates, for a fixed growth period of one year, and for companies with
approximately the same size displays an exponential form, and (ii) the
fluctuations in the growth rates -- measured by the width of this distribution
-- scale as a power law with , . We find
that the exponent takes the same value, within the error bars, for
several measures of the size of a company. In particular, we obtain:
for sales, for number of employees,
for assets, for cost of goods sold, and
for property, plant, & equipment.Comment: 16 pages LateX, RevTeX 3, 10 figures, to appear J. Phys. I France
(April 1997
Diffusion and Trapping on a one-dimensional lattice
The properties of a particle diffusing on a one-dimensional lattice where at
each site a random barrier and a random trap act simultaneously on the particle
are investigated by numerical and analytical techniques. The combined effect of
disorder and traps yields a decreasing survival probability with broad
distribution (log-normal). Exact enumerations, effective-medium approximation
and spectral analysis are employed. This one-dimensional model shows rather
rich behaviours which were previously believed to exist only in higher
dimensionality. The possibility of a trapping-dominated super universal class
is suggested.Comment: 20 pages, Revtex 3.0, 13 figures in compressed format using uufiles
command, to appear in Phys. Rev. E, for an hard copy or problems e-mail to:
[email protected]
- …