arXiv subjects

H. Eugene Stanley

Publications and source records attributed to H. Eugene Stanley.

At least 307 records · Page 17Linked to original sources

arXiv1998

Fast and slow dynamics of hydrogen bonds in liquid water

We study hydrogen-bond dynamics in liquid water at low temperatures using molecular dynamics simulations. We find that bond lifetime (``fast dynamics'') has Arrhenius temperature dependence. We also calculate the bond correlation function and find that the correlation time (``slow dynamics'') shows power-law behavior. This power-law behavior, as well as the decay of the bond correlations, is consistent with the predictions of the mode-coupling theory. The correlation time at the lowest temperature studied shows deviation from power-law behavior that suggests continuity of dynamic functions between the liquid and glassy states of water at low pressure.

cond-mat↗

arXiv1998

Tracer Dispersion in Porous Media with Spatial Correlations

We analyze the transport properties of a neutral tracer in a carrier fluid flowing through percolation-like porous media with spatial correlations. We model convection in the mass transport process using the velocity field obtained by the numerical solution of the Navier-Stokes and continuity equations in the pore space. We show that the resulting statistical properties of the tracer can be approximated by a Levy walk model, which is a consequence of the broad distribution of velocities plus the existence of spatial correlations in the porous medium.

cond-mat.dis-nn↗

arXiv1998

Spontaneous Stratification in Granular Mixtures

Granular materials size segregate when exposed to external periodic perturbations such as vibrations. Moreover, mixtures of grains of different sizes spontaneously segregate in the absence of external perturbations: when a mixture is simply poured onto a pile, the large grains are more likely to be found near the base, while the small grains are more likely to be near the top. Here, we report a spontaneous phenomenon arising when we pour a mixture between two vertical plates: the mixture spontaneously stratifies into alternating layers of small and large grains whenever the large grains are rougher than the small grains. In contrast, we find only spontaneous segregation when the large grains are more rounded than the small grains. The stratification is related to the occurrence of avalanches; during each avalanche the grains comprising the avalanche spontaneously stratify into a pair of layers through a "kink" mechanism, with the small grains forming a sublayer underneath the layer of large grains.

cond-mat.stat-mech↗

arXiv1998

Dynamics of Granular Stratification

Spontaneous stratification in granular mixtures has been recently reported by H. A. Makse et al. [Nature 386, 379 (1997)]. Here we study experimentally the dynamical processes leading to spontaneous stratification. Using a high-speed video camera, we study a rapid flow regime where the rolling grains size segregate during the avalanche. We characterize the dynamical process of stratification by measuring all relevant quantities: the velocity of the rolling grains, the velocity of the kink, the wavelength of the layers, the rate of collision between rolling and static grains, and all the angles of repose characterizing the mixture. The wavelength of the layers behaves linearly with the thickness of the layer of rolling grains (i.e., with the flow rate), in agreement with theoretical predictions. The velocity profile of the grains in the rolling phase is a linear function of the position of the grains along the moving layer. We also find that the speed of the upward-moving kink has the same value as the mean speed of the downward-moving grains. We measure the shape and size of the kink, as well as the profiles of the rolling and static phases of grains, and find agreement with recent theoretical predictions.

cond-mat.stat-mech↗

arXiv1998

Modeling Urban Growth Patterns with Correlated Percolation

We propose and test a model that describes the morphology of cities, the scaling of the urban perimeter of individual cities, and the area distribution of systems of cities. The model is also consistent with observable urban growth dynamics, our results agreeing both qualitatively and quantitatively with urban data. The resulting growth morphology can be understood from interactions among the constituent units forming an urban region, and can be modeled using a correlated percolation model in the presence of a gradient.

cond-mat.dis-nn↗

arXiv1998

Mechanisms of Granular Spontaneous Stratification and Segregation in Two-Dimensional Silos

Spontaneous stratification of granular mixtures has been reported by Makse et al. [Nature 386, 379 (1997)] when a mixture of grains differing in size and shape is poured in a quasi-two-dimensional heap. We study this phenomenon using two different approaches. First, we introduce a cellular automaton model that illustrates clearly the physical mechanism; the model displays stratification whenever the large grains are rougher than the small grains, in agreement with the experiments. Moreover, the dynamics are close to those of the experiments, where the layers are built through a ``kink'' at which the rolling grains are stopped. Second, we develop a continuum approach, based on a recently introduced set of coupled equations for surface flows of granular mixtures that allows us to make quantitative predictions for relevant quantities. We study the continuum model in two limit regimes: the large flux or thick flow regime, where the percolation effect (i.e., segregation of the rolling grains in the flow) is important, and the small flux or thin flow regime, where all the rolling grains are in contact with the surface of the sandpile. We find that the wavelength of the layers behaves linearly with the flux of grains. We obtain analytical predictions for the shape of the kink giving rise to stratification as well as the profile of the rolling and static species when segregation of the species is observed.

cond-mat.stat-mech↗

arXiv1998

Possible Stratification Mechanism in Granular Mixtures

We propose a mechanism to explain what occurs when a mixture of grains of different sizes and different shapes (i.e. different repose angles) is poured into a quasi-two-dimensional cell. Specifically, we develop a model that displays spontaneous stratification of the large and small grains in alternating layers. We find that the key requirement for stratification is a difference in the repose angles of the two pure species, a prediction confirmed by experimental findings. We also identify a kink mechanism that appears to describe essential aspects of the dynamics of stratification.

cond-mat.stat-mech↗

arXiv1998

Filling a silo with a mixture of grains: Friction-induced segregation

We study the filling process of a two-dimensional silo with inelastic particles by simulation of a granular media lattice gas (GMLG) model. We calculate the surface shape and flow profiles for a monodisperse system and we introduce a novel generalization of the GMLG model for a binary mixture of particles of different friction properties where, for the first time, we measure the segregation process on the surface. The results are in good agreement with a recent theory, and we explain the observed small deviations by the nonuniform velocity profile.

cond-mat.dis-nn↗

arXiv1998

Universality in sandpiles

We perform extensive numerical simulations of different versions of the sandpile model. We find that previous claims about universality classes are unfounded, since the method previously employed to analyze the data suffered a systematic bias. We identify the correct scaling behavior and conclude that sandpiles with stochastic and deterministic toppling rules belong to the same universality class.

cond-mat.stat-mech↗

arXiv1998

Liquid State Anomalies for the Stell-Hemmer Core-Softened Potential

We study the Stell-Hemmer potential using both analytic (exact $1d$ and approximate $2d$) solutions and numerical $2d$ simulations. We observe in the liquid phase an anomalous decrease in specific volume and isothermal compressibility upon heating, and an anomalous increase in the diffusion coefficient with pressure. We relate the anomalies to the existence of two different local structures in the liquid phase. Our results are consistent with the possibility of a low temperature/high pressure liquid-liquid phase transition.

cond-mat.soft↗

arXiv1998

Modeling of Financial Data: Comparison of the Truncated Lévy Flight and the ARCH(1) and GARCH(1,1) processes

We compare our results on empirical analysis of financial data with simulations of two stochastic models of the dynamics of stock market prices. The two models are (i) the truncated Lévy flight recently introduced by us and (ii) the ARCH(1) and GARCH(1,1) processes. We find that the TLF well describes the scaling and its breakdown observed in empirical data, while it is not able to properly describe the fluctuations of volatility empirically detected. The ARCH(1) and GARCH(1,1) models are able to describe the probability density function of price changes at a given time horizon, but both fail to describe the scaling properties of the PDFs for short time horizons.

cond-mat.stat-mech↗

arXiv1998

Universal features in the growth dynamics of complex organizations

We analyze the fluctuations in the gross domestic product (GDP) of 152 countries for the period 1950--1992. We find that (i) the distribution of annual growth rates for countries of a given GDP decays with ``fatter'' tails than for a Gaussian, and (ii) the width of the distribution scales as a power law of GDP with a scaling exponent $β\approx 0.15$. Both findings are in surprising agreement with results on firm growth. These results are consistent with the hypothesis that the evolution of organizations with complex structure is governed by similar growth mechanisms.

cond-mat.stat-mech↗

arXiv1998

Dynamics of a ferromagnetic domain wall: avalanches, depinning transition and the Barkhausen effect

We study the dynamics of a ferromagnetic domain wall driven by an external magnetic field through a disordered medium. The avalanche-like motion of the domain walls between pinned configurations produces a noise known as the Barkhausen effect. We discuss experimental results on soft ferromagnetic materials, with reference to the domain structure and the sample geometry, and report Barkhausen noise measurements on Fe$_{21}$Co$_{64}$B$_{15}$ amorphous alloy. We construct an equation of motion for a flexible domain wall, which displays a depinning transition as the field is increased. The long-range dipolar interactions are shown to set the upper critical dimension to $d_c=3$, which implies that mean-field exponents (with possible logarithmic correction) are expected to describe the Barkhausen effect. We introduce a mean-field infinite-range model and show that it is equivalent to a previously introduced single-degree-of-freedom model, known to reproduce several experimental results. We numerically simulate the equation in $d=3$, confirming the theoretical predictions. We compute the avalanche distributions as a function of the field driving rate and the intensity of the demagnetizing field. The scaling exponents change linearly with the driving rate, while the cutoff of the distribution is determined by the demagnetizing field, in remarkable agreement with experiments.

cond-mat.stat-mech↗

arXiv1997

Stochastic Feedback and the Regulation of Biological Rhythms

We propose a general approach to the question of how biological rhythms spontaneously self-regulate, based on the concept of ``stochastic feedback''. We illustrate this approach by considering the neuroautonomic regulation of the heart rate. The model generates complex dynamics and successfully accounts for key characteristics of cardiac variability, including the $1/f$ power spectrum, the functional form and scaling of the distribution of variations, and correlations in the Fourier phases. Our results suggest that in healthy systems the control mechanisms operate to drive the system away from extreme values while not allowing it to settle down to a constant output.

cond-mat.stat-mech↗

arXiv1997

Dynamics of a ferromagnetic domain wall and the Barkhausen effect

We derive an equation of motion for the the dynamics of a ferromagnetic domain wall driven by an external magnetic field through a disordered medium and we study the associated depinning transition. The long-range dipolar interactions set the upper critical dimension to be $d_c=3$, so we suggest that mean-field exponents describe the Barkhausen effect for three-dimensional soft ferromagnetic materials. We analyze the scaling of the Barkhausen jumps as a function of the field driving rate and the intensity of the demagnetizing field, and find results in quantitative agreement with experiments on crystalline and amorphous soft ferromagnetic alloys.

cond-mat.mtrl-sci↗

arXiv1997

Volatility distribution in the S&P500 Stock Index

We study the volatility of the S&P500 stock index from 1984 to 1996 and find that the volatility distribution can be very well described by a log-normal function. Further, using detrended fluctuation analysis we show that the volatility is power-law correlated with Hurst exponent $α\cong0.9$.

cond-mat.stat-mech↗

arXiv1997

Correlations in Economic Time Series

The correlation function of a financial index of the New York stock exchange, the S&P 500, is analyzed at 1 min intervals over the 13-year period, Jan 84 -- Dec 96. We quantify the correlations of the absolute values of the index increment. We find that these correlations can be described by two different power laws with a crossover time t_\times\approx 600 min. Detrended fluctuation analysis gives exponents $α_1=0.66$ and $α_2=0.93$ for $t t_\times$ respectively. Power spectrum analysis gives corresponding exponents $β_1=0.31$ and $β_2=0.90$ for $f>f_\times$ and $f< f_\times$ respectively.

cond-mat.stat-mech↗

arXiv1997

Dispersity-Driven Melting Transition in Two Dimensional Solids

We perform extensive simulations of $10^4$ Lennard-Jones particles to study the effect of particle size dispersity on the thermodynamic stability of two-dimensional solids. We find a novel phase diagram in the dispersity-density parameter space. We observe that for large values of the density there is a threshold value of the size dispersity above which the solid melts to a liquid along a line of first order phase transitions. For smaller values of density, our results are consistent with the presence of an intermediate hexatic phase. Further, these findings support the possibility of a multicritical point in the dispersity-density parameter space.

cond-mat.mtrl-sci↗