arXiv subjects

S. V. Buldyrev

Publications and source records attributed to S. V. Buldyrev.

47 records · Page 3Linked to original sources

arXiv2000

Hierarchical organization of cities and nations

Universality in the behavior of complex systems often reveals itself in the form of scale-invariant distributions that are essentially independent of the details of the microscopic dynamics. A representative paradigm of complex behavior in nature is cooperative evolution. The interaction of individuals gives rise to a wide variety of collective phenomena that strongly differ from individual dynamics---such as demographic evolution, cultural and technological development, and economic activity. A striking example of such cooperative phenomena is the formation of urban aggregates which, in turn, can be considered to cooperate in giving rise to nations. We find that population and area distributions of nations follow an inverse power-law behavior, as is known for cities. The exponents, however, are radically different in the two cases ($μ\approx 1$ for nations, $μ\approx 2$ for cities). We interpret these findings by developing growth models for cities and for nations related to basic properties of partition of the plane. These models allow one to understand the empirical findings without resort to the introduction of complex socio-economic factors.

cond-mat.stat-mech↗

arXiv2000

Multifractal Properties of the Random Resistor Network

We study the multifractal spectrum of the current in the two-dimensional random resistor network at the percolation threshold. We consider two ways of applying the voltage difference: (i) two parallel bars, and (ii) two points. Our numerical results suggest that in the infinite system limit, the probability distribution behaves for small current i as P(i) ~ 1/i. As a consequence, the moments of i of order q less than q_c=0 do not exist and all current of value below the most probable one have the fractal dimension of the backbone. The backbone can thus be described in terms of only (i) blobs of fractal dimension d_B and (ii) high current carrying bonds of fractal dimension going from $1/ν$ to d_B.

cond-mat.stat-mech↗

arXiv1999

Applications of the Stell-Hemmer Potential to Understanding Second Critical Points in Real Systems

We consider the novel properties of the Stell-Hemmer core-softened potentials. First we explore how the theoretically predicted second critical point for these potentials is related to the occurrence of the experimentally observed solid-solid isostructural critical point. We then discuss how this class of potentials can generate anomalies analogous to those found experimentally in liquid water.

cond-mat.soft↗

arXiv1999

Quasicrystals in a Monodisperse System

We investigate the formation of a two-dimensional quasicrystal in a monodisperse system, using molecular dynamics simulations of hard sphere particles interacting via a two-dimensional square-well potential. We find that more than one stable crystalline phase can form for certain values of the square-well parameters. Quenching the liquid phase at a very low temperature, we obtain an amorphous phase. By heating this amorphous phase, we obtain a quasicrystalline structure with five-fold symmetry. From estimations of the Helmholtz potentials of the stable crystalline phases and of the quasicrystal, we conclude that the observed quasicrystal phase can be the stable phase in a specific range of temperatures.

cond-mat.soft↗

arXiv1999

Scaling for the Percolation Backbone

We study the backbone connecting two given sites of a two-dimensional lattice separated by an arbitrary distance $r$ in a system of size $L$. We find a scaling form for the average backbone mass: $ \sim L^{d_B}G(r/L)$, where $G$ can be well approximated by a power law for $0\le x\le 1$: $G(x)\sim x^ψ$ with $ψ=0.37\pm 0.02$. This result implies that $ \sim L^{d_B-ψ}r^ψ$ for the entire range $0<r<L$. We also propose a scaling form for the probability distribution $P(M_B)$ of backbone mass for a given $r$. For $r\approx L, P(M_B)$ is peaked around $L^{d_B}$, whereas for $r\ll L, P(M_B)$ decreases as a power law, $M_B^{-τ_B}$, with $τ_B\simeq 1.20\pm 0.03$. The exponents $ψ$ and $τ_B$ satisfy the relation $ψ=d_B(τ_B-1)$, and $ψ$ is the codimension of the backbone, $ψ=d-d_B$.

cond-mat.stat-mech↗

arXiv1997

Power Law Scaling for a System of Interacting Units with Complex Internal Structure

We study the dynamics of a system composed of interacting units each with a complex internal structure comprising many subunits. We consider the case in which each subunit grows in a multiplicative manner. We propose a model for such systems in which the interaction among the units is treated in a mean field approximation and the interaction among subunits is nonlinear. To test the model, we identify a large data base spanning 20 years, and find that the model correctly predicts a variety of empirical results.

cond-mat.stat-mech↗

arXiv1997

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 $S$ displays an exponential form, and (ii) the fluctuations in the growth rates -- measured by the width of this distribution $σ_1$ -- scale as a power law with $S$, $σ_1\sim S^{-β}$. We find that the exponent $β$ takes the same value, within the error bars, for several measures of the size of a company. In particular, we obtain: $β=0.20\pm0.03$ for sales, $β=0.18\pm0.03$ for number of employees, $β=0.18\pm0.03$ for assets, $β=0.18\pm0.03$ for cost of goods sold, and $β=0.20\pm0.03$ for property, plant, & equipment.

cond-mat.stat-mech↗

arXiv1997

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 $β$, which describes the dependence of the standard deviation of the distribution of growth rates on size. We find that $β= -\ln Π/ \ln z$, where $z$ defines the mean branching ratio of the hierarchical tree and $Π$ 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.

cond-mat.stat-mech↗

arXiv1996

Avalanches in the lung: A statistical mechanical model

We study a statistical mechanical model for the dynamics of lung inflation which incorporates recent experimental observations on the opening of individual airways by a cascade or avalanche mechanism. Using an exact mapping of the avalanche problem onto percolation on a Cayley tree, we analytically derive the exponents describing the size distribution of the first avalanches and test the analytical solution by numerical simulations. We find that the tree-like structure of the airways together with the simplest assumptions concerning opening threshold pressures of each airway, is sufficient to explain the existence of power-law distributions observed experimentally.

cond-mat↗

arXiv1994

Avalanches and the Directed Percolation Depinning Model: Experiments, Simulations and Theory

We study the recently-introduced directed percolation depinning (DPD) model for interface roughening with quenched disorder for which the interface becomes pinned by a directed percolation (DP) cluster for $d = 1$, or a directed surface (DS) for $d > 1$. The mapping to DP enables us to predict some of the critical exponents of the growth process. For the case of $(1+1)$ dimensions, the theory predicts that the roughness exponent $α$ is given by $α= ν_{\perp} / ν_{\parallel}$, where $ν_{\perp}$ and $ν_{\parallel}$ are the exponents governing the divergence of perpendicular and parallel correlation lengths of the DP incipient infinite cluster. The theory also predicts that the dynamical exponent $z$ equals the exponent $d_{\rm min}$ characterizing the scaling of the shortest path on a isotropic percolation cluster. The exponent $α$ decreases monotonically with $d$ but does not seem to approach zero for any dimension calculated ($d \le 6$), suggesting that the DPD model has no upper critical dimension for the static exponents. On the other hand, $z$ appears to approach $2$ as $d \rightarrow 6$, as expected by the result $z = d_{\rm min}$, suggesting that $d_c = 6$ for the dynamics. We also perform a set of imbibition experiments, in both $(1+1)$ and $(2+1)$ dimensions, that can be used to test the DPD model. We find good agreement between experimental, theoretical and numerical approaches. Further, we study the properties of avalanches in the context of the DPD model. We relate the scaling properties of the avalanches in the DPD model to the scaling properties for the self-organized depinning (SOD) model, a variant of the DPD model. We calculate the exponent characterizing the avalanches distribution $τ_{\rm aval}$ for $d = 1$ to $d = 6$, and compare our results with recent theoretical

cond-mat↗

arXiv1994

Dynamics of Surface Roughening with Quenched Disorder

We study the dynamical exponent $z$ for the directed percolation depinning (DPD) class of models for surface roughening in the presence of quenched disorder. We argue that $z$ for $(d+1)$ dimensions is equal to the exponent $d_{\rm min}$ characterizing the shortest path between two sites in an isotropic percolation cluster in $d$ dimensions. To test the argument, we perform simulations and calculate $z$ for DPD, and $d_{\rm min}$ for percolation, from $d = 1$ to $d = 6$.

cond-mat↗