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H. Eugene Stanley

Publications and source records attributed to H. Eugene Stanley.

At least 235 records · Page 13Linked to original sources
arXiv2003

Scale Invariance and Nonlinear Patterns of Human Activity

We investigate if known extrinsic and intrinsic factors fully account for the complex features observed in recordings of human activity as measured from forearm motion in subjects undergoing their regular daily routine. We demonstrate that the apparently random forearm motion possesses previously unrecognized dynamic patterns characterized by fractal and nonlinear dynamics. These patterns are unaffected by changes in the average activity level, and persist when the same subjects undergo time-isolation laboratory experiments designed to account for the circadian phase and to control the known extrinsic factors. We attribute these patterns to a novel intrinsic multi-scale dynamic regulation of human activity.

physics.bio-ph↗
arXiv2003

Multifractal Properties of Price Fluctuations of Stocks and Commodities

We analyze daily prices of 29 commodities and 2449 stocks, each over a period of $\approx 15$ years. We find that the price fluctuations for commodities have a significantly broader multifractal spectrum than for stocks. We also propose that multifractal properties of both stocks and commodities can be attributed mainly to the broad probability distribution of price fluctuations and secondarily to their temporal organization. Furthermore, we propose that, for commodities, stronger higher order correlations in price fluctuations result in broader multifractal spectra.

cond-mat.stat-mech↗
arXiv2003

Scale-Dependent Price Fluctuations for the Indian Stock Market

Classic studies of the probability density of price fluctuations $g$ for stocks and foreign exchanges of several highly developed economies have been interpreted using a {\it power-law} probability density function $P(g) \sim g^{-(α+1)}$ with exponent values $α> 2$, which are outside the Lévy-stable regime $0 < α< 2$. To test the universality of this relationship for less highly developed economies, we analyze daily returns for the period Nov. 1994--June 2002 for the 49 largest stocks of the National Stock Exchange which has the highest volume of trade in India. We find that $P(g)$ decays as an {\it exponential} function $P(g) \sim \exp(-βg)$ with a characteristic decay scales $β= 1.51 \pm 0.05$ for the negative tail and $β= 1.34 \pm 0.04$ for the positive tail, which is significantly different from that observed for developed economies. Thus we conclude that the Indian stock market may belong to a universality class that differs from those of developed countries analyzed previously.

cond-mat.stat-mech↗
arXiv2003

A possible mechanism for cold denaturation of proteins at high pressure

We study cold denaturation of proteins at high pressures. Using multicanonical Monte Carlo simulations of a model protein in a water bath, we investigate the effect of water density fluctuations on protein stability. We find that above the pressure where water freezes to the dense ice phase ($\approx2$ kbar), the mechanism for cold denaturation with decreasing temperature is the loss of local low-density water structure. We find our results in agreement with data of bovine pancreatic ribonuclease A.

cond-mat.soft↗
arXiv2003

A Potential Energy Landscape Study of the Amorphous-Amorphous Transformation in H$_2$O

We study the potential energy landscape explored during a compression-decompression cycle for the SPC/E (extended simple point charge) model of water. During the cycle, the system changes from low density amorphous ice (LDA) to high density amorphous ice (HDA). After the cycle, the system does not return to the same region of the landscape, supporting the interesting possibility that more than one significantly different configuration corresponds to LDA. We find that the regions of the landscape explored during this transition have properties remarkably different from those explored in thermal equilibrium in the liquid phase.

cond-mat.soft↗
arXiv2003

Quantification of Sleep Fragmentation Through the Analysis of Sleep-Stage Transitions

We introduce new quantitative approaches to study sleep-stage transitions with the goal of addressing the two following questions: (i) Can the new approaches provide more information on the structure of sleep-stage transitions? (ii) How does sleep fragmentation in patients with sleep apnea affect the structure of sleep-stage transitions? Our new results show that the distribution of sleep and wake duration have different functional forms, indicating fundamental differences in the dynamics between sleep and wake control. The difference remains even in the fragmented sleep of sleep apnea. The fragmentation of sleep in sleep apnea results in a shorter wake duration and interrupts the structure of sleep-stage transitions of sleep apnea subjects, causing the loss of certain particular transition paths.

cond-mat↗
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↗
arXiv2003

Information Entropy and Correlations in Prime Numbers

The difference between two consecutive prime numbers is called the distance between the primes. We study the statistical properties of the distances and their increments (the difference between two consecutive distances) for a sequence comprising the first $5\times 10^7$ prime numbers. We find that the histogram of the increments follows an exponential distribution with superposed periodic behavior of period three, similar to previously-reported period six oscillations for the distances.

cond-mat.stat-mech↗
arXiv2003

Relation between Magnitude Series Correlations and Multifractal Spectrum Width

We study the correlation properties of long-range correlated time series, $x_i$, with tunable correlation exponent and built-in multifractal properties. For the cases we investigate we find that the correlation exponent of the magnitude series, $|x_{i+1}-x_i|$, is a monotonically increasing function of the multifractal spectrum width of the original series.

cond-mat↗
arXiv2002

Intra-molecular coupling as a mechanism for a liquid-liquid phase transition

We study a model for water with a tunable intra-molecular interaction $J_σ$, using mean field theory and off-lattice Monte Carlo simulations. For all $J_σ\geq 0$, the model displays a temperature of maximum density.For a finite intra-molecular interaction $J_σ> 0$,our calculations support the presence of a liquid-liquid phase transition with a possible liquid-liquid critical point for water, likely pre-empted by inevitable freezing. For J=0 the liquid-liquid critical point disappears at T=0.

cond-mat.stat-mech↗
arXiv2002

Fractal Dimension of 3-Blocks in 4d, 5d, and 6d Percolation Systems

Using Monte Carlo simulations we study the distributions of the 3-block mass $N_3$ in 4d, 5d, and 6d percolation systems. Because the probability of creating large 3-blocks in these dimensions is very small, we use a ``go with the winners'' method of statistical enhancement to simulate configurations having probability as small as $10^{-30}$. In earlier work, the fractal dimensions of 3-blocks, $d_3$, in 2d and 3d were found to be $1.20\pm 0.1$ and $1.15\pm 0.1$, respectively, consistent with the possibility that the fractal dimension might be the same in all dimensions. We find that the fractal dimension of 3-blocks decreases rapidly in higher dimensions, and estimate $d_3=0.7\pm 0.2$ (4d) and $0.5\pm 0.2$ (5d). At the upper critical dimension of percolation, $d_c=6$, our simulations are consistent with $d_3=0$ with logarithmic corrections to power-law scaling.

cond-mat.dis-nn↗
arXiv2002

Discrepancy between Monte-Carlo Results and Analytic Values for the Average Excluded Volume of Rectangular Prisms

We perform Monte Carlo simulations to determine the average excluded volume of randomly oriented rectangular prisms, randomly oriented ellipsoids and randomly oriented capped cylinders in 3-D. There is agreement between the analytically obtained and the results of simulations for randomly oriented ellipsoids and randomly oriented capped cylinders. However, we find that the for randomly oriented prisms obtained from the simulations differs from the analytically obtained results. In particular, for cubes, the percentage difference is 3.92, far exceeding the bounds of statistical error in our simulation.{\bf Added in Revision 2: We recently found the cause of the discrepancy between the simulation result and the analytic value of the excluded volume to be the effect of an error in our simulation code. Upon rectification of the simulation code, the simulation yields $ 11.00 \pm 0.002 $ as the excluded volume of a pair of randomly oriented cubes of unit volume. The simulation also yields results as predicted by the analytic formula for all other cases of rectangular prisms that we study.}

cond-mat.dis-nn↗
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

The Approximate Invariance of the Average Number of Connections for the Continuum Percolation of Squares at Criticality

We perform Monte Carlo simulations to determine the average excluded area $ $ of randomly oriented squares, randomly oriented widthless sticks and aligned squares in two dimensions. We find significant differences between our results for randomly oriented squares and previous analytical results for the same. The sources of these differences are explained. Using our results for $ $ and Monte Carlo simulation results for the percolation threshold, we estimate the mean number of connections per object $B_c$ at the percolation threshold for squares in 2-D. We study systems of squares that are allowed random orientations within a specified angular interval. Our simulations show that the variation in $B_c$ is within 1.6% when the angular interval is varied from 0 to $π/2$.

cond-mat.dis-nn↗
arXiv2002

Effect of nonstationarities on detrended fluctuation analysis

Detrended fluctuation analysis (DFA) is a scaling analysis method used to quantify long-range power-law correlations in signals. Many physical and biological signals are ``noisy'', heterogeneous and exhibit different types of nonstationarities, which can affect the correlation properties of these signals. We systematically study the effects of three types of nonstationarities often encountered in real data. Specifically, we consider nonstationary sequences formed in three ways: (i) stitching together segments of data obtained from discontinuous experimental recordings, or removing some noisy and unreliable parts from continuous recordings and stitching together the remaining parts -- a ``cutting'' procedure commonly used in preparing data prior to signal analysis; (ii) adding to a signal with known correlations a tunable concentration of random outliers or spikes with different amplitude, and (iii) generating a signal comprised of segments with different properties -- e.g. different standard deviations or different correlation exponents. We compare the difference between the scaling results obtained for stationary correlated signals and correlated signals with these three types of nonstationarities.

physics.data-an↗
arXiv2002

The continuum percolation threshold for interpenetrating squares and cubes

Monte Carlo simulations are performed to determine the critical percolation threshold for interpenetrating square objects in two dimensions and cubic objects in three dimensions. Simulations are performed for two cases: (i) objects whose edges are aligned parallel to one another and (ii) randomly oriented objects. For squares whose edges are aligned, the critical area fraction at the percolation threshold phi_c=0.6666 +/- 0.0004, while for randomly oriented squares phi_c=0.6254 +/- 0.0002, 6% smaller. For cubes whose edges are aligned, the critical volume fraction at the percolation threshold phi_c=0.2773 +/- 0.0002, while for randomly oriented cubes phi_c=0.2236 +/- 0.0002, 24% smaller.

cond-mat.stat-mech↗
arXiv2002

Fractal Behavior of the Shortest Path Between Two Lines in Percolation Systems

Using Monte-Carlo simulations, we determine the scaling form for the probability distribution of the shortest path, $\ell$, between two lines in a 3-dimensional percolation system at criticality; the two lines can have arbitrary positions, orientations and lengths. We find that the probability distributions can exhibit up to four distinct power law regimes (separated by cross-over regimes) with exponents depending on the relative orientations of the lines. We explain this rich fractal behavior with scaling arguments.

cond-mat.stat-mech↗