arXiv subjects

H. Eugene Stanley

Publications and source records attributed to H. Eugene Stanley.

At least 289 records · Page 16Linked to original sources

arXiv1999

Entropy and dynamic properties of water below the homogeneous nucleation temperature

Controversy exists regarding the possible existence of a transition between the liquid and glassy states of water. Here we use experimental measurements of the entropy, specific heat, and enthalpy of both liquid and glassy water to construct thermodynamically-plausible forms of the entropy in the difficult-to-probe region between 150 K and 236 K. We assume there is no discontinuity in the entropy of the liquid in this temperature range, and use the Adam-Gibbs theory -- which relates configurational entropy to dynamic behavior -- to predict that dynamic quantities such as the diffusion constant and the viscosity pass through an inflection where the liquid behavior changes from that of an extremely ``fragile'' liquid to that of a ``strong'' liquid.

cond-mat↗

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

Configurational Entropy and Diffusivity of Supercooled Water

We calculate the configurational entropy S_conf for the SPC/E model of water for state points covering a large region of the (T,rho) plane. We find that (i) the (T,rho) dependence of S_conf correlates with the diffusion constant and (ii) that the line of maxima in S_conf tracks the line of density maxima. Our simulation data indicate that the dynamics are strongly influenced by S_conf even above the mode-coupling temperature T_MCT(rho).

cond-mat.soft↗

arXiv1999

Dynamics of simulated water under pressure

We present molecular dynamics simulations of the SPC/E model of water to probe the dynamic properties at temperatures from 350 K down to 190 K and pressures from 2.5GPa (25kbar) down to -300MPa (-3kbar). We compare our results with those obtained experimentally, both of which show a diffusivity maximum as a function of pressure. We find that our simulation results are consistent with the predictions of the mode-coupling theory (MCT) for the dynamics of weakly supercooled liquids -- strongly supporting the hypothesis that the apparent divergences of {\it dynamic} properties observed experimentally may be independent of a possible thermodynamic singularity at low temperature. The dramatic change in water's dynamic and structural properties as a function of pressure allows us to confirm the predictions of MCT over a much broader range of the von Schweidler exponent values than has been studied for simple atomic liquids. We also show how structural changes are reflected in the wave-vector dependence of dynamic properties of the liquid along a path of nearly constant diffusivity. For temperatures below the crossover temperature of MCT (where the predictions of MCT are expected to fail), we find tentative evidence for a crossover of the temperature dependence of the diffusivity from power-law to Arrhenius behavior, with an activation energy typical of a strong liquid.

cond-mat↗

arXiv1999

Instantaneous Normal Mode Analysis of Supercooled Water

We use the instantaneous normal mode approach to provide a description of the local curvature of the potential energy surface of a model for water. We focus on the region of the phase diagram in which the dynamics may be described by the mode-coupling theory. We find, surprisingly, that the diffusion constant depends mainly on the fraction of directions in configuration space connecting different local minima, supporting the conjecture that the dynamics are controlled by the geometric properties of configuration space. Furthermore, we find an unexpected relation between the number of basins accessed in equilibrium and the connectivity between them.

cond-mat↗

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↗

arXiv1999

Water-like anomalies for core-softened models of fluids: One dimension

We use a one-dimensional (1d) core-softened potential to develop a physical picture for some of the anomalies present in liquid water. The core-softened potential mimics the effect of hydrogen bonding. The interest in the 1d system stems from the facts that closed-form results are possible and that the qualitative behavior in 1d is reproduced in the liquid phase for higher dimensions. We discuss the relation between the shape of the potential and the density anomaly, and we study the entropy anomaly resulting from the density anomaly. We find that certain forms of the two-step square well potential lead to the existence at T=0 of a low-density phase favored at low pressures and of a high-density phase favored at high pressures, and to the appearance of a point $C'$ at a positive pressure, which is the analog of the T=0 ``critical point'' in the $1d$ Ising model. The existence of point $C'$ leads to anomalous behavior of the isothermal compressibility $K_T$ and the isobaric specific heat $C_P$.

cond-mat.soft↗

arXiv1999

Scale-invariant Truncated Lévy Process

We develop a scale-invariant truncated Lévy (STL) process to describe physical systems characterized by correlated stochastic variables. The STL process exhibits Lévy stability for the probability density, and hence shows scaling properties (as observed in empirical data); it has the advantage that all moments are finite (and so accounts for the empirical scaling of the moments). To test the potential utility of the STL process, we analyze financial data.

cond-mat.stat-mech↗

arXiv1999

Ivory Tower Universities and Competitive Business Firms

There is nowadays considerable interest on ways to quantify the dynamics of research activities, in part due to recent changes in research and development (R&D) funding. Here, we seek to quantify and analyze university research activities, and compare their growth dynamics with those of business firms. Specifically, we analyze five distinct databases, the largest of which is a National Science Foundation database of the R&D expenditures for science and engineering of 719 United States (US) universities for the 17-year period 1979--1995. We find that the distribution of growth rates displays a ``universal'' form that does not depend on the size of the university or on the measure of size used, and that the width of this distribution decays with size as a power law. Our findings are quantitatively similar to those independently uncovered for business firms, and consistent with the hypothesis that the growth dynamics of complex organizations may be governed by universal mechanisms.

cond-mat.stat-mech↗

arXiv1999

Multifractality in Human Heartbeat Dynamics

Recent evidence suggests that physiological signals under healthy conditions may have a fractal temporal structure. We investigate the possibility that time series generated by certain physiological control systems may be members of a special class of complex processes, termed multifractal, which require a large number of exponents to characterize their scaling properties. We report on evidence for multifractality in a biological dynamical system --- the healthy human heartbeat. Further, we show that the multifractal character and nonlinear properties of the healthy heart rate are encoded in the Fourier phases. We uncover a loss of multifractality for a life-threatening condition, congestive heart failure.

cond-mat.stat-mech↗

arXiv1999

Scaling of the distribution of fluctuations of financial market indices

We study the distribution of fluctuations over a time scale $Δt$ (i.e., the returns) of the S&P 500 index by analyzing three distinct databases. Database (i) contains approximately 1 million records sampled at 1 min intervals for the 13-year period 1984-1996, database (ii) contains 8686 daily records for the 35-year period 1962-1996, and database (iii) contains 852 monthly records for the 71-year period 1926-1996. We compute the probability distributions of returns over a time scale $Δt$, where $Δt$ varies approximately over a factor of 10^4 - from 1 min up to more than 1 month. We find that the distributions for $Δt \leq$ 4 days (1560 mins) are consistent with a power-law asymptotic behavior, characterized by an exponent $α\approx 3$, well outside the stable Lévy regime $0 < α< 2$. To test the robustness of the S&P result, we perform a parallel analysis on two other financial market indices. Database (iv) contains 3560 daily records of the NIKKEI index for the 14-year period 1984-97, and database (v) contains 4649 daily records of the Hang-Seng index for the 18-year period 1980-97. We find estimates of $α$ consistent with those describing the distribution of S&P 500 daily-returns. One possible reason for the scaling of these distributions is the long persistence of the autocorrelation function of the volatility. For time scales longer than $(Δt)_{\times} \approx 4$ days, our results are consistent with slow convergence to Gaussian behavior.

cond-mat.stat-mech↗

arXiv1999

The statistical properties of the volatility of price fluctuations

We study the statistical properties of volatility---a measure of how much the market is likely to fluctuate. We estimate the volatility by the local average of the absolute price changes. We analyze (a) the S&P 500 stock index for the 13-year period Jan 1984 to Dec 1996 and (b) the market capitalizations of the largest 500 companies registered in the Trades and Quotes data base, documenting all trades for all the securities listed in the three major stock exchanges in the US for the 2-year period Jan 1994 to Dec 1995. For the S&P 500 index, the probability density function of the volatility can be fit with a log-normal form in the center. However, the asymptotic behavior is better described by a power-law distribution characterized by an exponent 1 + μ\approx 4. For individual companies, we find a power law asymptotic behavior of the probability distribution of volatility with exponent 1 + μ\approx 4, similar to the S&P 500 index. In addition, we find that the volatility distribution scales for a range of time intervals. Further, we study the correlation function of the volatility and find power law decay with long persistence for the S&P 500 index and the individual companies with a crossover at approximately 1.5 days. To quantify the power-law correlations, we apply power spectrum analysis and a recently-developed modified root-mean-square analysis, termed detrended fluctuation analysis (DFA). For the S&P 500 index, DFA estimates for the exponents characterizing the power law correlations are α_1=0.66 for short time scales (within \approx 1.5 days) and α_2=0.93 for longer time scales (up to a year). For individual companies, we find α_1=0.60 and α_2=0.74, respectively. The power spectrum gives consistent estimates of the two power-law exponents.

cond-mat.stat-mech↗

arXiv1999

Universal and non-universal properties of cross-correlations in financial time series

We use methods of random matrix theory to analyze the cross-correlation matrix C of price changes of the largest 1000 US stocks for the 2-year period 1994-95. We find that the statistics of most of the eigenvalues in the spectrum of C agree with the predictions of random matrix theory, but there are deviations for a few of the largest eigenvalues. We find that C has the universal properties of the Gaussian orthogonal ensemble of random matrices. Furthermore, we analyze the eigenvectors of C through their inverse participation ratio and find eigenvectors with large inverse participation ratios at both edges of the eigenvalue spectrum--a situation reminiscent of results in localization theory.

cond-mat.stat-mech↗

arXiv1999

Avalanches in Breakdown and Fracture Processes

We investigate the breakdown of disordered networks under the action of an increasing external---mechanical or electrical---force. We perform a mean-field analysis and estimate scaling exponents for the approach to the instability. By simulating two-dimensional models of electric breakdown and fracture we observe that the breakdown is preceded by avalanche events. The avalanches can be described by scaling laws, and the estimated values of the exponents are consistent with those found in mean-field theory. The breakdown point is characterized by a discontinuity in the macroscopic properties of the material, such as conductivity or elasticity, indicative of a first order transition. The scaling laws suggest an analogy with the behavior expected in spinodal nucleation.

cond-mat.stat-mech↗

arXiv1999

Slow dynamics of water under pressure

We perform lengthy molecular dynamics simulations of the SPC/E model of water to investigate the dynamics under pressure at many temperatures and compare with experimental measurements. We calculate the isochrones of the diffusion constant $D$ and observe power-law behavior of $D$ on lowering temperature with an apparent singularity at a temperature $T_c(P)$, as observed for water. Additional calculations show that the dynamics of the SPC/E model are consistent with slowing down due to the transient caging of molecules, as described by the mode-coupling theory (MCT). This supports the hypothesis that the apparent divergences of dynamic quantities along $T_c(P)$ in water may be associated with ``slowing down'' as described by MCT.

cond-mat↗

arXiv1998

Identifying the protein folding nucleus using molecular dynamics

Molecular dynamics simulations of folding in an off-lattice protein model reveal a nucleation scenario, in which a few well-defined contacts are formed with high probability in the transition state ensemble of conformations. Their appearance determines folding cooperativity and drives the model protein into its folded conformation.

cond-mat.stat-mech↗

arXiv1998

Discrete molecular dynamics studies of the folding of a protein-like model

Background: Many attempts have been made to resolve in time the folding of model proteins in computer simulations. Different computational approaches have emerged. Some of these approaches suffer from the insensitivity to the geometrical properties of the proteins (lattice models), while others are computationally heavy (traditional MD). Results: We use a recently-proposed approach of Zhou and Karplus to study the folding of the protein model based on the discrete time molecular dynamics algorithm. We show that this algorithm resolves with respect to time the folding --- unfolding transition. In addition, we demonstrate the ability to study the coreof the model protein. Conclusion: The algorithm along with the model of inter-residue interactions can serve as a tool to study the thermodynamics and kinetics of protein models.

cond-mat.stat-mech↗

arXiv1998

Structural evidence for the continuity of liquid and glassy water

An open question is whether the liquid and glassy phases of water are thermodynamically distinct or continuous. Here we address this question using molecular dynamics simulations in comparison with neutron scattering experiments to study the effect of temperature and pressure on the local structure of liquid water. From both simulations and experiments, we find that the liquid structure at high pressure is nearly independent of temperature, and remarkably similar to the known structure of the high-density amorphous ice (HDA). Further at low pressure, the liquid structure appears to approach the experimentally-measured structure of low-density amorphous ice (LDA) as temperature decreases. These results are consistent with continuity between the liquid and glassy phases of H$_2$O.

cond-mat↗