arXiv subjects

Sergey V. Buldyrev

Publications and source records attributed to Sergey V. Buldyrev.

At least 91 records · Page 5Linked to original sources

arXiv2005

Statistical Properties of Business Firms Structure and Growth

We analyze a database comprising quarterly sales of 55624 pharmaceutical products commercialized by 3939 pharmaceutical firms in the period 1992--2001. We study the probability density function (PDF) of growth in firms and product sales and find that the width of the PDF of growth decays with the sales as a power law with exponent $β= 0.20 \pm 0.01$. We also find that the average sales of products scales with the firm sales as a power law with exponent $α= 0.57 \pm 0.02$. And that the average number products of a firm scales with the firm sales as a power law with exponent $γ= 0.42 \pm 0.02$. We compare these findings with the predictions of models proposed till date on growth of business firms.

physics.soc-ph↗

arXiv2004

Liquid-Liquid Phase Transition for an Attractive Isotropic Potential with Wide Repulsive Range

Recent experimental and theoretical results have shown the existence of a liquid-liquid phase transition in isotropic systems, such as biological solutions and colloids, whose interaction can be represented via an effective potential with a repulsive soft-core and an attractive part. We investigate how the phase diagram of a schematic general isotropic system, interacting via a soft-core squared attractive potential, changes by varying the parameters of the potential. It has been shown that this potential has a phase diagram with a liquid-liquid phase transition in addition to the standard gas-liquid phase transition and that, for a short-range soft-core, the phase diagram resulting from molecular dynamics simulations can be interpreted through a modified van der Waals equation. Here we consider the case of soft-core ranges comparable with or larger than the hard-core diameter. Because an analysis using molecular dynamics simulations of such systems or potentials is too time-demanding, we adopt an integral equation approach in the hypernetted-chain approximation. Thus we can estimate how the temperature and density of both critical points depend on the potential's parameters for large soft-core ranges. The present results confirm and extend our previous analysis, showing that this potential has two fluid-fluid critical points that are well separated in temperature and in density only if there is a balance between the attractive and repulsive part of the potential. We find that for large soft-core ranges our results satisfy a simple relation between the potential's parameters.

cond-mat.soft↗

arXiv2004

Anomalous Transport in Complex Networks

To study transport properties of complex networks, we analyze the equivalent conductance $G$ between two arbitrarily chosen nodes of random scale-free networks with degree distribution $P(k)\sim k^{-λ}$ in which each link has the same unit resistance. We predict a broad range of values of $G$, with a power-law tail distribution $Φ_{\rm SF}(G)\sim G^{-g_G}$, where $g_G=2λ-1$, and confirm our predictions by simulations. The power-law tail in $Φ_{\rm SF}(G)$ leads to large values of $G$, thereby significantly improving the transport in scale-free networks, compared to Erdős-Rényi random graphs where the tail of the conductivity distribution decays exponentially. Based on a simple physical ``transport backbone'' picture we show that the conductances are well approximated by $ck_Ak_B/(k_A+k_B)$ for any pair of nodes $A$ and $B$ with degrees $k_A$ and $k_B$. Thus, a single parameter $c$ characterizes transport on scale-free networks.

cond-mat.other↗

arXiv2004

Static and Dynamic Anomalies in a Repulsive Spherical Ramp Liquid: Theory and Simulation

We compare theoretical and simulation results for static and dynamic properties for a model of particles interacting via a spherically symmetric repulsive ramp potential. The model displays anomalies similar to those found in liquid water, namely, expansion upon cooling and an increase of diffusivity upon compression. In particular, we calculate the phase diagram from the simulation and successfully compare it with the phase diagram obtained using the Rogers-Young (RY) closure for the Ornstein-Zernike equation. Both the theoretical and the numerical calculations confirm the presence of a line of isobaric density maxima, and lines of compressibility minima and maxima. Indirect evidence of a liquid-liquid critical point is found. Dynamic properties also show anomalies. Along constant temperature paths, as the density increases, the dynamics alternates several times between slowing down and speeding up, and we associate this behavior with the progressive structuring and de-structuring of the liquid. Finally we confirm that mode coupling theory successfully predicts the non-monotonic behavior of dynamics and the presence of multiple glass phases, providing strong evidence that structure (the only input of mode coupling theory) controls dynamics.

cond-mat.stat-mech↗

arXiv2004

Folding Trp-cage to NMR resolution native structure using a coarse-grained model

We develop a coarse-grained protein model with a simplified amino acid interaction potential. We perform discrete molecular dynamics folding simulations of a small 20 residue protein - Trp-cage - from a fully extended conformation. We demonstrate the ability of the Trp-cage model to consistently reach conformations within 2angstrom backbone root-mean-square distance (RMSD) from the corresponding NMR structures. The minimum RMSD of Trp-cage conformations in the simulation can be smaller than 1.00angstrom. Our findings suggest that, at least for the case of Trp-cage, a detailed all-atom protein model with a physical molecular mechanics force field is not necessary to reach the native state of a protein. Our results also suggest that the success folding Trp-cage in our simulations and in the reported all-atom molecular mechanics simulations studies may be mainly due to the special stabilizing features specific to this miniprotein.

physics.bio-ph↗

arXiv2004

Effect of Disorder Strength on Optimal Paths in Complex Networks

We study the transition between the strong and weak disorder regimes in the scaling properties of the average optimal path $\ell_{\rm opt}$ in a disordered Erdős-Rényi (ER) random network and scale-free (SF) network. Each link $i$ is associated with a weight $τ_i\equiv\exp(a r_i)$, where $r_i$ is a random number taken from a uniform distribution between 0 and 1 and the parameter $a$ controls the strength of the disorder. We find that for any finite $a$, there is a crossover network size $N^*(a)$ at which the transition occurs. For $N \ll N^*(a)$ the scaling behavior of $\ell_{\rm opt}$ is in the strong disorder regime, with $\ell_{\rm opt} \sim N^{1/3}$ for ER networks and for SF networks with $λ\ge 4$, and $\ell_{\rm opt} \sim N^{(λ-3)/(λ-1)}$ for SF networks with $3 < λ< 4$. For $N \gg N^*(a)$ the scaling behavior is in the weak disorder regime, with $\ell_{\rm opt}\sim\ln N$ for ER networks and SF networks with $λ> 3$. In order to study the transition we propose a measure which indicates how close or far the disordered network is from the limit of strong disorder. We propose a scaling ansatz for this measure and demonstrate its validity. We proceed to derive the scaling relation between $N^*(a)$ and $a$. We find that $N^*(a)\sim a^3$ for ER networks and for SF networks with $λ\ge 4$, and $N^*(a)\sim a^{(λ-1)/(λ-3)}$ for SF networks with $3 < λ< 4$.

cond-mat.dis-nn↗

arXiv2003

Optimal Paths in Disordered Complex Networks

We study the optimal distance in networks, $\ell_{\scriptsize opt}$, defined as the length of the path minimizing the total weight, in the presence of disorder. Disorder is introduced by assigning random weights to the links or nodes. For strong disorder, where the maximal weight along the path dominates the sum, we find that $\ell_{\scriptsize opt}\sim N^{1/3}$ in both Erdős-Rényi (ER) and Watts-Strogatz (WS) networks. For scale free (SF) networks, with degree distribution $P(k) \sim k^{-λ}$, we find that $\ell_{\scriptsize opt}$ scales as $N^{(λ- 3)/(λ- 1)}$ for $3<λ<4$ and as $N^{1/3}$ for $λ\geq 4$. Thus, for these networks, the small-world nature is destroyed. For $2 < λ< 3$, our numerical results suggest that $\ell_{\scriptsize opt}$ scales as $\ln^{λ-1}N$. We also find numerically that for weak disorder $\ell_{\scriptsize opt}\sim\ln N$ for both the ER and WS models as well as for SF networks.

cond-mat.soft↗

arXiv2003

A System with Multiple Liquid-Liquid Critical Points

We study a three-dimensional system of particles interacting via spherically-symmetric pair potentials consisting of several discontinuous steps. We show that at certain values of the parameters desribing the potential, the system has three first-order phase transitions between fluids of different densities ending in three critical points.

cond-mat.soft↗

arXiv2002

Connection between Adam-Gibbs Theory and Spatially Heterogeneous Dynamics

We investigate the spatially heterogeneous dynamics in the SPC/E model of water by using molecular dynamics simulations. We relate the average mass $n^*$ of mobile particle clusters to the diffusion constant and the configurational entropy. Hence, $n^*$ can be interpreted as the mass of the ``cooperatively rearranging regions'' that form the basis of the Adam-Gibbs theory of the dynamics of supercooled liquids. Finally, we examine the time and temperature dependence of these transient clusters.

cond-mat.soft↗

arXiv2002

Transitions between Inherent Structures in Water

The energy landscape approach has been useful to help understand the dynamic properties of supercooled liquids and the connection between these properties and thermodynamics. The analysis in numerical models of the inherent structure (IS) trajectories -- the set of local minima visited by the liquid -- offers the possibility of filtering out the vibrational component of the motion of the system on the potential energy surface and thereby resolving the slow structural component more efficiently. Here we report an analysis of an IS trajectory for a widely-studied water model, focusing on the changes in hydrogen bond connectivity that give rise to many IS separated by relatively small energy barriers. We find that while the system \emph{travels} through these IS, the structure of the bond network continuously modifies, exchanging linear bonds for bifurcated bonds and usually reversing the exchange to return to nearly the same initial configuration. For the 216 molecule system we investigate, the time scale of these transitions is as small as the simulation time scale ($\approx 1$ fs). Hence for water, the transitions between each of these IS is relatively small and eventual relaxation of the system occurs only by many of these transitions. We find that during IS changes, the molecules with the greatest displacements move in small ``clusters'' of 1-10 molecules with displacements of $\approx 0.02-0.2$ nm, not unlike simpler liquids. However, for water these clusters appear to be somewhat more branched than the linear ``string-like'' clusters formed in a supercooled Lennar d-Jones system found by Glotzer and her collaborators.

cond-mat.soft↗

arXiv2001

Glassy behavior of a homopolymer from molecular dynamics simulations

We study at- and out-of-equilibrium dynamics of a single homopolymer chain at low temperature using molecular dynamics simulations. The main quantities of interest are the average root mean square displacement of the monomers below the theta point, and the structure factor, as a function of time. The observation of these quantities show a close resemblance to those measured in structural glasses and suggest that the polymer chain in its low temperature phase is in a glassy phase, with its dynamics dominated by traps. In equilibrium, at low temperature, we observe the trapping of the monomers and a slowing down of the overall motion of the polymer as well as non-exponential relaxation of the structure factor. In out-of-equilibrium, at low temperatures, we compute the two-time quantities and observe breaking of ergodicity in a range of waiting times, with the onset of aging.

cond-mat.soft↗

arXiv2001

Scaling in the growth of geographically subdivided populations: invariant patterns from a continent-wide biological survey

We consider statistical patterns of variation in growth rates for over 400 species of breeding birds across North America surveyed from 1966 to 1998. We report two results. First, the standard deviation of population growth rates decays as a power-law function of total population size with an exponent $β= 0.36\pm0.02$. Second, the number of subpopulations, measured as the number of survey locations with non-zero counts, scales to the 3/4-power of total number of birds counted in a given species. We show how these patterns may be related, and discuss a simple stochastic growth model for a geographically subdivided population that formalizes the relationship. We also examine reasons that may explain why some species deviate from these scaling-laws.

cond-mat.stat-mech↗

arXiv2001

Generic mechanism for generating a liquid-liquid phase transition

Recent experimental results indicate that phosphorus, a single-component system, can have two liquid phases: a high-density liquid (HDL) and a low-density liquid (LDL) phase. A first-order transition between two liquids of different densities is consistent with experimental data for a variety of materials, including single-component systems such as water, silica and carbon. Molecular dynamics simulations of very specific models for supercooled water, liquid carbon and supercooled silica, predict a LDL-HDL critical point, but a coherent and general interpretation of the LDL-HDL transition is lacking. Here we show that the presence of a LDL and a HDL can be directly related to an interaction potential with an attractive part and two characteristic short-range repulsive distances. This kind of interaction is common to other single-component materials in the liquid state (in particular liquid metals), and such potentials are often used to decribe systems that exhibit a density anomaly. However, our results show that the LDL and HDL phases can occur in systems with no density anomaly. Our results therefore present an experimental challenge to uncover a liquid-liquid transition in systems like liquid metals, regardless of the presence of the density anomaly.

cond-mat.stat-mech↗

arXiv2000

Thermodynamically Important Contacts in Folding of Model Proteins

We introduce a quantity, the entropic susceptibility, that measures the thermodynamic importance-for the folding transition-of the contacts between amino acids in model proteins. Using this quantity, we find that only one equilibrium run of a computer simulation of a model protein is sufficient to select a subset of contacts that give rise to the peak in the specific heat observed at the folding transition. To illustrate the method, we identify thermodynamically important contacts in a model 46-mer. We show that only about 50% of all contacts present in the protein native state are responsible for the sharp peak in the specific heat at the folding transition temperature, while the remaining 50% of contacts do not affect the specific heat.

cond-mat.stat-mech↗

arXiv2000

Flow Between Two Sites on a Percolation Cluster

We study the flow of fluid in porous media in dimensions $d=2$ and 3. The medium is modeled by bond percolation on a lattice of $L^d$ sites, while the flow front is modeled by tracer particles driven by a pressure difference between two fixed sites (``wells'') separated by Euclidean distance $r$. We investigate the distribution function of the shortest path connecting the two sites, and propose a scaling {\it Ansatz} that accounts for the dependence of this distribution (i) on the size of the system, $L$, and (ii) on the bond occupancy probability, $p$. We confirm by extensive simulations that the {\it Ansatz} holds for $d=2$ and 3, and calculate the relevant scaling parameters. We also study two dynamical quantities: the minimal traveling time of a tracer particle between the wells and the length of the path corresponding to the minimal traveling time ``fastest path'', which is not identical to the shortest path. A scaling {\it Ansatz} for these dynamical quantities also includes the effect of finite system size $L$ and off-critical bond occupation probability $p$. We find that the scaling form for the distribution functions for these dynamical quantities for $d=2$ and 3 is similar to that for the shortest path but with different critical exponents. The scaling form is represented as the product of a power law and three exponential cutoff functions. We summarize our results in a table which contains estimates for all parameters which characterize the scaling form for the shortest path and the minimal traveling time in 2 and 3 dimensions; these parameters are the fractal dimension, the power law exponent, and the constants and exponents that characterize the exponential cutoff functions.

cond-mat.stat-mech↗

arXiv1999

Dependence of Conductance on Percolation Backbone Mass

On two-dimensional percolation clusters at the percolation threshold, we study $<σ(M_B,r)>$, the average conductance of the backbone, defined by two points separated by Euclidean distance $r$, of mass $M_B$. We find that with increasing $M_B$ and for fixed r, $<σ(M_B,r)>$ asymptotically {\it decreases} to a constant, in contrast with the behavior of homogeneous sytems and non-random fractals (such as the Sierpinski gasket) in which conductance increases with increasing $M_B$. We explain this behavior by studying the distribution of shortest paths between the two points on clusters with a given $M_B$. We also study the dependence of conductance on $M_B$ slightly above the percolation threshold.

cond-mat.stat-mech↗

arXiv1999

Scaling of the distribution of shortest paths in percolation

We present a scaling hypothesis for the distribution function of the shortest paths connecting any two points on a percolating cluster which accounts for {\it (i)} the effect of the finite size of the system, and {\it (ii)} the dependence of this distribution on the site occupancy probability $p$. We test the hypothesis for the case of two-dimensional percolation.

cond-mat.stat-mech↗

arXiv1999

Traveling time and traveling length for flow in porous media

We study traveling time and traveling length for tracer dispersion in porous media. We model porous media by two-dimensional bond percolation, and we model flow by tracer particles driven by a pressure difference between two points separated by Euclidean distance $r$. We find that the minimal traveling time $t_{min}$ scales as $t_{min} \sim r^{1.40}$, which is different from the scaling of the most probable traveling time, ${\tilde t} \sim r^{1.64}$. We also calculate the length of the path corresponding to the minimal traveling time and find $\ell_{min} \sim r^{1.13}$ and that the most probable traveling length scales as ${\tilde \ell} \sim r^{1.21}$. We present the relevant distribution functions and scaling relations.

cond-mat.stat-mech↗