arXiv subjects

H. Eugene Stanley

Publications and source records attributed to H. Eugene Stanley.

At least 217 records · Page 12Linked to original sources

arXiv2005

Structural Order in Glassy Water

We investigate structural order in glassy water by performing classical molecular dynamics simulations using the extended simple point charge (SPC/E) model of water. We perform isochoric cooling simulations across the glass transition temperature at different cooling rates and densities. We quantify structural order by orientational and translational order metrics. Upon cooling the liquid into the glassy state, both the orientational order parameter $Q$ and translational order parameter $τ$ increase. At T=0 K, the glasses fall on a line in the $Q$-$τ$ plane or {\it order map}. The position of this line depends only on density and coincides with the location in the order map of the inherent structures (IS) sampled upon cooling. We evaluate the energy of the IS, $e_{IS}(T)$, and find that both order parameters for the IS are proportional to $e_{IS}$. We also study the structural order during the transformation of low-density amorphous ice (LDA) to high-density amorphous ice (HDA) upon isothermal compression and are able to identify distinct regions in the order map corresponding to these glasses. Comparison of the order parameters for LDA and HDA with those obtained upon isochoric cooling indicates major structural differences between glasses obtained by cooling and glasses obtained by compression. These structural differences are only weakly reflected in the pair correlation function. We also characterize the evolution of structural order upon isobaric annealing, leading at high pressure to very-high density amorphous ice (VHDA).

cond-mat.soft↗

arXiv2005

Phase Diagram of Amorphous Solid Water: Low-Density, High-Density, and Very-High-Density Amorphous Ices

We describe the phase diagram of amorphous solid water by performing molecular dynamics simulations. Our simulations follow different paths in the phase diagram: isothermal compression/decompression, isochoric cooling/heating and isobaric cooling/heating. We are able to identify low-density amorphous (LDA), high-density amorphous (HDA), and very-high density amorphous (VHDA) ices. The density $ρ$ of these glasses at different pressure $P$ and temperature $T$ agree well with experimental values. We also study the radial distribution functions of glassy water. We obtain VHDA by isobaric heating of HDA, as in experiment. We also find that ``other forms'' of glassy water can be obtained upon isobaric heating of LDA, as well as amorphous ices formed during the transformation of LDA to HDA. We argue that these other forms of amorphous ices, as well as VHDA, are not altogether new glasses but rather are the result of aging induced by heating. Samples of HDA and VHDA with different densities are recovered at normal $P$, showing that there is a continuum of glasses. Furthermore, the two ranges of densities of recovered HDA and recovered VHDA overlap at ambient $P$. Our simulations are consistent with the possibility of HDA$\to$LDA and VHDA$\to$LDA transformations, reproducing the experimental findings. We do not observe a VHDA$\to$HDA transformation.

cond-mat.soft↗

arXiv2005

A Generalized Preferential Attachment Model for Complex Systems

Complex systems can be characterized by classes of equivalency of their elements defined according to system specific rules. We propose a generalized preferential attachment model to describe the class size distribution. The model postulates preferential growth of the existing classes and the steady influx of new classes. We investigate how the distribution depends on the initial conditions and changes from a pure exponential form for zero influx of new classes to a power law with an exponential cutoff form when the influx of new classes is substantial. We apply the model to study the growth dynamics of pharmaceutical industry.

physics.soc-ph↗

arXiv2005

Scaling Phenomena in the Growth Dynamics of Scientific Output

We analyze a set of three databases at different levels of aggregation (i) a database of approximately $10^6$ publications of 247 countries in the period between 1980--2001. (ii) A database of 508 academic institutions from European Union (EU) and 408 institutes from USA in the 11 year period between during 1991--2001. (iii) A database comprising of 2330 Flemish authors in the period 1980--2000. At all levels of aggregation we find that the mean annual growth rates of publications is independent of the number of publications of the various units involved. We also find that the standard deviation of the distribution of annual growth rates decays with the number of publications as a power law with exponent $\approx 0.3$. These findings are consistent with those of recent studies of systems such as the size of R&D funding budgets of countries, the research publication volumes of US universities, and the size of business firms.

physics.soc-ph↗

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

Levels of Complexity in Scale-Invariant Neural Signals

Many physical and physiological signals exhibit complex scale-invariant features characterized by $1/f$ scaling and long-range power-law correlations, suggesting a possibly common control mechanism. Specifically, it has been suggested that dynamical processes influenced by inputs and feedback on multiple time scales may be sufficient to give rise to $1/f$ scaling and scale invariance. Two examples of physiologic signals that are the output of hierarchical, multi-scale physiologic systems under neural control are the human heartbeat and human gait. Here we show that while both cardiac interbeat interval and gait interstride interval time series under healthy conditions have comparable $1/f$ scaling, they still may belong to different complexity classes. Our analysis of the magnitude series correlations and multifractal scaling exponents of the fluctuations in these two signals demonstrates that in contrast with the nonlinear multifractal behavior found in healthy heartbeat dynamics, gait time series exhibit less complex, close to monofractal behavior and a low degree of nonlinearity. These findings are of interest because they underscore the limitations of traditional two-point correlation methods in fully characterizing physiologic and physical dynamics. In addition, these results suggest that different mechanisms of control may be responsible for varying levels of complexity observed in physiological systems under neural regulation and in physical systems that possess similar $1/f$ scaling.

cond-mat.stat-mech↗

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↗

arXiv2004

Relation between the High Density Phase and the Very-High Density Phase of Amorphous Solid Water

It has been suggested that high-density amorphous (HDA) ice is a structurally arrested form of high-density liquid (HDL) water, while low-density amorphous (LDA) ice is a structurally arrested form of low-density liquid (LDL) water. Recent experiments and simulations have been interpreted to support the possibility of a second "distinct" high-density structural state, named very high-density amorphous (VHDA) ice, questioning the LDL-HDL hypothesis. We test this interpretation using extensive computer simulations, and find that VHDA is a more stable form of HDA and that in fact VHDA should be considered as the amorphous ice of the quenched HDL.

cond-mat.soft↗

arXiv2004

Cooling rate, heating rate and aging effects in glassy water

We report a molecular dynamics simulation study of the properties of the potential energy landscape sampled by a system of water molecules during the process of generating a glass by cooling, and during the process of regenerating the equilibrium liquid by heating the glass. We study the dependence of these processes on the cooling/heating rates as well as on the role of aging (the time elapsed in the glass state). We compare the properties of the potential energy landscape sampled during these processes with the corresponding properties sampled in the liquid equilibrium state to elucidate under which conditions glass configurations can be associated with equilibrium liquid configurations.

cond-mat.soft↗

arXiv2004

The Glass Transition Temperature of Water: A Simulation Study

We report a computer simulation study of the glass transition for water. To mimic the difference between standard and hyperquenched glass, we generate glassy configurations with different cooling rates and calculate the $T$ dependence of the specific heat on heating. The absence of crystallization phenomena allows us, for properly annealed samples, to detect in the specific heat the simultaneous presence of a weak pre-peak (``shadow transition''), and an intense glass transition peak at higher temperature. We discuss the implications for the currently debated value of the glass transition temperature of water. We also compare our simulation results with the Tool-Narayanaswamy-Moynihan phenomenological model.

cond-mat.soft↗

arXiv2004

On the Origin of Power-Law Fluctuations in Stock Prices

We respond to the issues discussed by Farmer and Lillo (FL) related to our proposed approach to understanding the origin of power-law distributions in stock price fluctuations. First, we extend our previous analysis to 1000 US stocks and perform a new estimation of market impact that accounts for splitting of large orders and potential autocorrelations in the trade flow. Our new analysis shows clearly that price impact and volume are related by a square-root functional form of market impact for large volumes, in contrast to the claim of FL that this relationship increases as a power law with a smaller exponent. Since large orders are usually executed by splitting into smaller size trades, procedures used by FL give a downward bias for this power law exponent. Second, FL analyze 3 stocks traded on the London Stock Exchange, and solely on this basis they claim that the distribution of transaction volumes do not have a power-law tail for the London Stock Exchange. We perform new empirical analysis on transaction data for the 262 largest stocks listed in the London Stock Exchange, and find that the distribution of volume decays as a power-law with an exponent $\approx 3/2$ -- in sharp contrast to FL's claim that the distribution of transaction volume does not have a power-law tail. Our exponent estimate of $\approx 3/2$ is consistent with our previous results from the New York and Paris Stock Exchanges. We conclude that the available empirical evidence is consistent with our hypothesis on the origin of power-law fluctuations in stock prices.

cond-mat.dis-nn↗

arXiv2003

Minimal Brownian Ratchet: An Exactly Solvable Model

We develop an exactly-solvable three-state discrete-time minimal Brownian ratchet (MBR), where the transition probabilities between states are asymmetric. By solving the master equations we obtain the steady-state probabilities. Generally the steady-state solution does not display detailed balance, giving rise to an induced directional motion in the MBR. For a reduced two-dimensional parameter space we find the null-curve on which the net current vanishes and detailed balance holds. A system on this curve is said to be balanced. On the null-curve, an additional source of external random noise is introduced to show that a directional motion can be induced under the zero overall driving force. We also indicate the off-balance behavior with biased random noise.

cond-mat.stat-mech↗

arXiv2003

Universal Mechanisms in the Growth of Voluntary Organizations

We analyze the growth statistics of Swedish trade unions and find a universal functional form for the probability distribution of growth rates of union size, and a power law dependence of the standard deviation of this distribution on the number of members of the union. We also find that the typical size and the typical number of local chapters scales as a power law of the union size. Intriguingly, our results are similar to results reported for other human organizations of a quite different nature. Our findings are consistent with the possibility that universal mechanisms may exist governing the growth patterns of human organizations.

nlin.AO↗

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

Heuristic Segmentation of a Nonstationary Time Series

Many phenomena, both natural and human-influenced, give rise to signals whose statistical properties change under time translation, i.e., are nonstationary. For some practical purposes, a nonstationary time series can be seen as a concatenation of stationary segments. Using a segmentation algorithm, it has been reported that for heart beat data and Internet traffic fluctuations--the distribution of durations of these stationary segments decays with a power law tail. A potential technical difficulty that has not been thoroughly investigated is that a nonstationary time series with a (scale-free) power law distribution of stationary segments is harder to segment than other nonstationary time series because of the wider range of possible segment sizes. Here, we investigate the validity of a heuristic segmentation algorithm recently proposed by Bernaola-Galvan et al. by systematically analyzing surrogate time series with different statistical properties. We find that if a given nonstationary time series has stationary periods whose size is distributed as a power law, the algorithm can split the time series into a set of stationary segments with the correct statistical properties. We also find that the estimated power law exponent of the distribution of stationary-segment sizes is affected by (i) the minimum segment size, and (ii) the ratio of the standard deviation of the mean values of the segments, and the standard deviation of the fluctuations within a segment. Furthermore, we determine that the performance of the algorithm is generally not affected by uncorrelated noise spikes or by weak long-range temporal correlations of the fluctuations within segments.

cond-mat.stat-mech↗