Showing papers in "Physica A-statistical Mechanics and Its Applications in 2002"

Multifractal Detrended Fluctuation Analysis of Nonstationary Time Series

Abstract: We develop a method for the multifractal characterization of nonstationary time series, which is based on a generalization of the detrended fluctuation analysis (DFA). We relate our multifractal DFA method to the standard partition function-based multifractal formalism, and prove that both approaches are equivalent for stationary signals with compact support. By analyzing several examples we show that the new method can reliably determine the multifractal scaling behavior of time series. By comparing the multifractal DFA results for original series with those for shuffled series we can distinguish multifractality due to long-range correlations from multifractality due to a broad probability density function. We also compare our results with the wavelet transform modulus maxima method, and show that the results are equivalent.

Evolution of the social network of scientific collaborations

Abstract: The co-authorship network of scientists represents a prototype of complex evolving networks. In addition, it o8ers one of the most extensive database to date on social networks. By mapping the electronic database containing all relevant journals in mathematics and neuro-science for an 8-year period (1991–98), we infer the dynamic and the structural mechanisms that govern the evolution and topology of this complex system. Three complementary approaches allow us to obtain a detailed characterization. First, empirical measurements allow us to uncover the topological measures that characterize the network at a given moment, as well as the time evolution of these quantities. The results indicate that the network is scale-free, and that the network evolution is governed by preferential attachment, a8ecting both internal and external links. However, in contrast with most model predictions the average degree increases in time, and the node separation decreases. Second, we propose a simple model that captures the network’s time evolution. In some limits the model can be solved analytically, predicting a two-regime scaling in agreement with the measurements. Third, numerical simulations are used to uncover the behavior of quantities that could not be predicted analytically. The combined numerical and analytical results underline the important role internal links play in determining the observed scaling behavior and network topology. The results and methodologies developed in the context of the co-authorship network could be useful for a systematic study of other complex evolving networks as well, such as the world wide web, Internet, or other social networks. c

Pinning control of scale-free dynamical networks

Abstract: Recently, it has been demonstrated that many large complex networks display a scale-free feature, that is, their connectivity distributions have the power-law form. In the present work, control of a scale-free dynamical network by applying local feedback injections to a fraction of network nodes is investigated. The specifically and randomly pinning schemes are considered. The specifically pinning of the most highly connected nodes is shown to require a significantly smaller number of local controllers as compared to the randomly pinning scheme. The method is applied to an array of Chua's oscillators as an example.

Simulation of evacuation processes using a bionics-inspired cellular automaton model for pedestrian dynamics

Abstract: We present simulations of evacuation processes using a recently introduced cellular automaton model for pedestrian dynamics. This model applies a bionics approach to describe the interaction between the pedestrians using ideas from chemotaxis. Here we study a rather simple situation, namely the evacuation from a large room with one or two doors. It is shown that the variation of the model parameters allows to describe different types of behaviour, from regular to panic. We find a non-monotonic dependence of the evacuation times on the coupling constants. These times depend on the strength of the herding behaviour, with minimal evacuation times for some intermediate values of the couplings, i.e., a proper combination of herding and use of knowledge about the shortest way to the exit.

Is the Boston subway a small-world network ?

Abstract: The mathematical study of the small-world concept has fostered quite some interest, showing that small-world features can be identified for some abstract classes of networks. However, passing to real complex systems, as for instance transportation networks, shows a number of new problems that make current analysis impossible. In this paper we show how a more refined kind of analysis, relying on transportation efficiency, can in fact be used to overcome such problems, and to give precious insights on the general characteristics of real transportation networks, eventually providing a picture where the small-world comes back as underlying construction principle.

Rough ideas on wetting

Abstract: After a brief presentation of the classical laws of wetting, we review different phenomenological descriptions of rough wetting, i.e., show how these classical laws must be modified on rough solids. This introduces the questions of hemi-wicking (can a film propagate inside the texture of a solid ?), rough films (is it possible for a liquid film to follow the roughness of a solid ?) and super-hydrophobicity (how can a solid be designed to become water repellent ?).

Waiting-times and returns in high-frequency financial data: an empirical study

Abstract: In financial markets, not only prices and returns can be considered as random variables, but also the waiting time between two transactions varies randomly. In the following, we analyse the statistical properties of General Electric stock prices, traded at NYSE, in October 1999. These properties are critically revised in the framework of theoretical predictions based on a continuous-time random walk model.

An introduction to statistical finance

Abstract: We summarize recent research in a rapid growing field, that of statistical finance, also called ‘econophysics’. There are three main themes in this activity: (i) empirical studies and the discovery of interesting universal features in the statistical texture of financial time series, (ii) the use of these empirical results to devise better models of risk and derivative pricing, of direct interest for the financial industry, and (iii) the study of ‘agent-based models’ in order to unveil the basic mechanisms that are responsible for the statistical ‘anomalies’ observed in financial time series. We give a brief overview of some of the results in these three directions.

Estimating long-range dependence: finite sample properties and confidence intervals

Abstract: A major issue in financial economics is the behavior of asset returns over long horizons. Various estimators of long-range dependence have been proposed. Even though some have known asymptotic properties, it is important to test their accuracy by using simulated series of different lengths. We test R/S analysis, Detrended Fluctuation Analysis and periodogram regression methods on samples drawn from Gaussian white noise. The DFA statistics turns out to be the unanimous winner. Unfortunately, no asymptotic distribution theory has been derived for this statistics so far. We were able, however, to construct empirical (i.e. approximate) confidence intervals for all three methods. The obtained values differ largely from heuristic values proposed by some authors for the R/S statistics and are very close to asymptotic values for the periodogram regression method.

Some applications of persistent random walks and the telegrapher's equation

Abstract: A persistent random walk can be regarded as a multidimensional Markov process. The bias-free telegraphers equation is ∂ 2 p ∂t 2 + 1 T ∂p ∂t =v 2 ∇ 2 p . It can be regarded as interpolating between the wave equation (T→∞) and the diffusion equation (T→0). Previously, it has found application in thermodynamics (cf. the review in Rev. Mod. Phys. 61 (1989) 41; 62 (1990) 375). More recent applications are reviewed in the present article.

Ferromagnetic phase transition in Barabási-Albert networks

Abstract: Ising spins put onto a Barabasi–Albert scale-free network show an effective phase transition from ferromagnetism to paramagnetism upon heating, with an effective critical temperature increasing as the logarithm of the system size. Starting with all spins up and upon equilibration pinning the few most-connected spins down nucleates the phase with most of the spins down.

Effective Markovian approximation for non-Gaussian noises: a path integral approach

Abstract: We have analyzed diffusion in a double well potential driven by a colored non-Gaussian noise. Using a path-integral approach we have obtained a consistent Markovian approximation to the initially non-Markovian problem. Such an approximation allows us to get analytical expressions for the “mean-first-passage-time” that has been tested against extensive numerical simulations.

Multifractal Hurst analysis of crude oil prices

Abstract: Daily records of international crude oil prices are studied using multifractal analysis methods. Rescaled range Hurst analysis provides evidence that the crude oil market is a persistent process with long-run memory effects. On the other hand, height–height correlation analysis reveals evidence of multifractal structures in the sense that the crude oil dynamics displays mixing of (rough) Hurst exponents. The existence of two characteristic time scales in the order of weeks and quarters is discovered and the corresponding prices dynamics are extracted using moving-average-based filtering. These results seem to demonstrate that the crude oil market is consistent with the random-walk assumption only at time scales of the order of days to weeks. A plausible oil price formation mechanism is discussed in terms of the market dynamics at three different time scales.

Traffic flow: a statistical physics point of view

Abstract: The investigation of traffic flow problems has a long tradition and various methods and approaches have been applied. In this review we focus on statistical mechanics and nonequilibrium aspects. It is shown that many properties of traffic flow can be modelled successfully by using rather simple cellular automaton models. Analytical methods for the investigation of discrete models are presented in some detail. Apart from highway traffic, also the modelling of city traffic and pedestrian dynamics will be discussed.

Deformed exponentials and logarithms in generalized thermostatistics

Abstract: Criteria are given that κ -deformed logarithmic and exponential functions should satisfy. With a pair of such functions one can associate another function, called the deduced logarithmic function. It is shown that generalized thermostatistics can be formulated in terms of κ -deformed exponential functions together with the associated deduced logarithmic functions.

A Stochastic Model of Human Gait Dynamics

Abstract: We present a stochastic model of gait rhythm dynamics, based on transitions between different “neural centers”, that reproduces distinctive statistical properties of normal human walking. By tuning one model parameter, the transition (hopping) range, the model can describe alterations in gait dynamics from childhood to adulthood—including a decrease in the correlation and volatility exponents with maturation. The model also generates time series with multifractal spectra whose broadness depends only on this parameter. Moreover, we find that the volatility exponent increases monotonically as a function of the width of the multifractal spectrum, suggesting the possibility of a change in multifractality with maturation.

Oscillatory finite-time singularities in finance, population and rupture

Abstract: We present a simple two-dimensional dynamical system where two nonlinear terms, exerting respectively positive feedback and reversal, compete to create a singularity in finite time decorated by accelerating oscillations. The power law singularity results from the increasing growth rate. The oscillations result from the restoring mechanism. As a function of the order of the nonlinearity of the growth rate and of the restoring term, a rich variety of behavior is documented analytically and numerically. The dynamical behavior is traced back fundamentally to the self-similar spiral structure of trajectories in phase space unfolding around an unstable spiral point at the origin. The interplay between the restoring mechanism and the nonlinear growth rate leads to approximately log-periodic oscillations with remarkable scaling properties. Three domains of applications are discussed: (1) the stock market with a competition between nonlinear trend-followers and nonlinear value investors; (2) the world human population with a competition between a population-dependent growth rate and a nonlinear dependence on a finite carrying capacity; (3) the failure of a material subjected to a time-varying stress with a competition between positive geometrical feedback on the damage variable and nonlinear healing.

Clogging transition of pedestrian flow in T-shaped channel

Abstract: Pedestrian flow is investigated under the open boundaries in a T-shaped channel where the branch flow joins the main flow at the junction. The pedestrian merging flow is simulated by the use of the lattice-gas model of biased random walkers. When the main flow rate increases under the constant value of branch flow rate, the clogging transitions occur at the main flow or branch flow or both flows. It is shown that the dynamical phase transitions depend on both inlet densities. The four distinct phases are found. The phase diagram is presented for the distinct phases. The scaling of saturated flow rate and transition point is shown. The flow rate exhibits the universal scaling form.

Nanobubbles: the big picture

Abstract: Nanobubbles, whose existence on hydrophobic surfaces immersed in water has previously been inferred from measurements of long-ranged attractions between such surfaces, are directly imaged by tapping mode atomic force microscopy. It is found that the nanobubbles cover the surfaces in an irregular, interconnected or close-packed network whose morphology is dependent on pH and whose lifetimes are at least of the order of hours. Their height is of the order of 30 nm and their radius of curvature is of the order of 100– 300 nm . It appears that the nanobubbles form from a solution supersaturated with air. A thermodynamic and statistical mechanical analysis of the homogeneous nucleation of liquid droplets from a supersaturated vapour shows that although a single droplet can be in equilibrium with a finite volume of gas, for a gas reservoir the equilibrium state is represented by a single macroscopic droplet, which grows by collisions and by Ostwald ripening. It is concluded that the electric double-layer repulsion between neighbouring nanobubbles on the hydrophobic surface plays a role in their stabilisation.

Dynamics of price and trading volume in a spin model of stock markets with heterogeneous agents

Abstract: The dynamics of a stock market with heterogeneous agents is discussed in the framework of a recently proposed spin model for the emergence of bubbles and crashes. We relate the log-returns of stock prices to magnetization in the model and find that it is closely related to trading volume as observed in real markets. The cumulative distribution of log-returns exhibits scaling with exponents steeper than 2 and scaling is observed in the distribution of transition times between bull and bear markets.

Aggregation, gelation and phase separation of heat denatured globular proteins

Abstract: β -lactoglobulin is a globular protein which aggregates after a heat-induced denaturation. It may be considered as a good model system to investigate the processes of aggregation, gelation and phase separation which play a major role in the chemical physics of complex systems. We present here the main results of an extensive study of the denaturation of this protein in various experimental conditions: pH, ionic strength, concentration, temperature, and presence or not of polyoside. The structure and distribution of β -lactoglobulin aggregates were characterized by dynamic and static light scattering, small angle neutron scattering and size exclusion chromatography. Microscopy was used to study the effect of phase separation on the morphology. The competition between phase separation and aggregation/gelation process is discussed.

Statistical Physics for cosmic structures

Abstract: Ideas of Statistical Physics are very relevant for cosmic structures especially considering that the field is undergoing a period of exceptional development with many new data appearing on a monthly basis. In the past years we have focused mostly on galaxy distributions and their statistical properties. This led to an interesting debate which will be resolved by the next generation of data in a couple of years. In addition, here we discuss the statistical properties of the fluctuations of the cosmic microwave background which are small in amplitude but complex in structure. We finally discuss the connection between these observations and the Harrison–Zeldovich spectrum and its further implications on the theories of structure formation and the cosmological N -body simulations.

Pattern formation and jamming transition in pedestrian counter flow

Abstract: Pattern formation is investigated in the pedestrian counter flow within a channel where there are two types of walkers going to the right and to the left. The lattice gas model of biased random walkers is extended to take into account following the front persons with the same direction (model A). According as the walkers go ahead, the pedestrian segregate into the two kinds of segments: the one is the group of the right walkers and the other is the group of left walkers. Walkers form in line and the two types of walkers file alternately. With increasing density, the filing appears distinctly. When the density is higher than the critical value, all walkers are hard to go ahead and the jamming transition occurs. Model B is also presented to take into account avoiding the front persons with the opposite direction. The pattern formation and jamming transition are compared with those of model A.

Lévy flight random searches in biological phenomena

Abstract: There has been growing interest in the study of Levy flights observed in the movements of biological organisms performing random walks while searching for other organisms. Here, we approach the problem of what is the best statistical strategy for optimizing the encounter rate between “searcher” and “target” organisms—either of the same or of different species—in terms of a limiting generalized searcher–target model (e.g., predator-prey, mating partner, pollinator–flower). In this context, we discuss known results showing that for fixed targets an inverse square density distribution of step lengths can optimize the encounter rate. For moving targets, we review how the encounter rate depends on whether organisms move in Levy or Brownian random walks. We discuss recent findings indicating that Levy walks confer a significant advantage for increasing encounter rates only when the searcher is larger or moves rapidly relative to the target, and when the target density is low.

Quantum market games

Abstract: We propose a quantum-like description of markets and economics. The approach has roots in the recently developed quantum game theory.

Precursors of primary nucleation induced by flow in isotactic polypropylene

Abstract: Small-angle X-ray scattering (SAXS) patterns of the sheared isotactic polypropylene (i-PP) melt at 175°C, above the nominal melting point of 162°C, showed development of oriented structures or aggregates of polymer molecules that did not disappear even after a long time relaxation (up to 2 h ). However, the corresponding wide-angle X-ray diffraction (WAXD) patterns did not show any visible Bragg reflections, suggesting that the induced structures are probably non-crystalline. The results suggest that metastable aggregates of polymer molecules are generated in the melt by assembly of bundle of oriented chain segments (especially in long chains). We speculate that the oriented aggregates of chain segments are precursors of primary nuclei. The spatial arrangement of these precursors showed a layer-like superstructure, evident by the appearance of the meridional maxima in SAXS. The spacing between the ‘layers’ was estimated to be 430 A . A microstructural model of the orientation-induced precursors for primary nucleation is presented. An Avrami model was used to fit the evolution of the oriented structures in i-PP melt, which provided insights into the early stages of polymer crystallization.

A discussion on embedding the Black-Scholes option pricing model in a quantum physics setting

Abstract: In this paper we consider the implications of embedding the Black–Scholes option pricing model within a quantum physical setting. The option price is considered to be a state function and a potential function is found which allows the option price to satisfy the Schrodinger differential equation. Once this arbitrage-free potential function is obtained, we argue for the construction of a so-called ‘arbitrage’ potential function. This functional is instrumental in determining the existence of a ‘financial’ state function. We show the existence of an arbitrage-free price when the potential function converges to one. The existence of arbitrage hinges on the non-zero value of the Planck constant. This constant is then linked to a parameter which regulates the probability of occurence of strategy paths. We call this parameter the ‘belief’ parameter. We argue that it is the belief parameter which may indeed proxy arbitrage. The outcome of this paper shows that the Black–Scholes model can be captured within a quantum physical setting and that the advantages of doing so may indeed provide for a first step to include arbitrage in a natural way in an otherwise arbitrage free model.

Growing random networks with fitness

Abstract: Three models of growing random networks with fitness-dependent growth rates are analysed using the rate equations for the distribution of their connectivities. In the first model (A), a network is built by connecting incoming nodes to nodes of connectivity k and random additive fitness η , with rate ( k −1)+ η . For η >0 we find the connectivity distribution is power law with exponent γ =〈 η 〉+2. In the second model (B), the network is built by connecting nodes to nodes of connectivity k , random additive fitness η and random multiplicative fitness ζ with rate ζ ( k −1)+ η . This model also has a power law connectivity distribution, but with an exponent which depends on the multiplicative fitness at each node. In the third model (C), a directed graph is considered and is built by the addition of nodes and the creation of links. A node with fitness ( α , β ), i incoming links and j outgoing links gains a new incoming link with rate α ( i +1), and a new outgoing link with rate β ( j +1). The distributions of the number of incoming and outgoing links both scale as power laws, with inverse logarithmic corrections.

Models for a liquid-liquid phase transition

Abstract: We use molecular dynamics simulations to study two- and three-dimensional models with the isotropic double-step poten tial which inadditionto the hard core has a repulsive soft core of larger radius. Our results indicate that the presence of two characteristic repulsive distances (hard core and soft core) is su8cient to explain liquid anomalies and a liquid–liquid phase transition, but these two phenomena may occur independently. Thus liquid–liquid transitions may exist in systems like liquid metals, regardless of the presence of the density anomaly. For 2D, we propose a model with a speci;c set of hard core and soft core parameters, that qualitatively reproduces the phase diagram and anomalies of liquid water. We identify two solid phases: a square crystal (high density phase), and a triangular crystal (low density phase) and discuss the relationbetweenthe an omalies of liquid an d the polymorphism of the solid. Similarly to real water, our 2D system may have the second critical point in the metastable liquid phase beyond the freezing line. In 3D, we ;nd several sets of parameters for which two >uid–>uid phase transition lines exist: the ;rst line between gas and liquid and the second line between high-density liquid (HDL) and low-density liquid (LDL). In all cases, the LDL phase shows no density anomaly in 3D. We relate the absence of the density anomaly with the positive slope of the LDL–HDL phase transition line. c

The variance of firm growth rates: the ‘scaling’ puzzle

Abstract: Recent evidence suggests that a power-law relationship exists between a firm's size and the variance of its growth rate. The flatness of the relation is regarded as puzzling, in that it suggests that large firms are not much more stable than small firms. It has been suggested that the power-law nature of the relationship reflects the presence of some form of correlation of growth rates across the firm's constituent businesses. Here, it is shown that a model of independent businesses which allows for the fact that these businesses vary in size, as modelled by a simple ‘partitions of integers’ model, provides a good representation of what is observed empirically.