Showing papers in "Physica A-statistical Mechanics and Its Applications in 1997"

Emergence of cooperation and organization in an evolutionary game

Abstract: A binary game is introduced and analysed. N players have to choose one of the two sides independently and those on the minority side win. Players use a finite set of ad hoc strategies to make their decision, based on the past record. The analysing power is limited and can adapt when necessary. Interesting cooperation and competition patterns of the society seem to arise and to be responsive to the payoff function.

Price variations in a stock market with many agents

Abstract: Large variations in stock prices happen with sufficient frequency to raise doubts about existing models, which all fail to account for non-Gaussian statistics. We construct simple models of a stock market, and argue that the large variations may be due to a crowd effect, where agents imitate each other's behavior. The variations over different time scales can be related to each other in a systematic way, similar to the Levy stable distribution proposed by Mandelbrot to describe real market indices. In the simplest least realistic case, exact results for the statistics of the variations are derived by mapping onto a model of diffusing and annihilating particles, which has been solved by quantum field theory methods. When the agents imitate each other and respond to recent market volatility, different scaling behavior is obtained. In this case, the statistics of price variations is consistent with empirical observations. The interplay between “rational” traders whose behavior is derived from fundamental analysis of the stock, including dividends, and “noise traders”, whose behavior is governed solely by studying the market dynamics and the behavior of other traders, is investigated. When the relative number of rational traders is small, “bubbles” often occur, where the market price moves outside the range justified by fundamental market analysis. When the number of rational traders is larger, the market price is generally locked within the price range they define.

Correlations in economic time series

Abstract: A financial index of the New York stock exchange, the SP here f× is called the crossover frequency. (iii) We confirm these results using the DFA (detrended fluctuation analysis) method (see Fig. 2b), which allows accurate estimates of exponents independent of local trends

New evidence for the power-law distribution of wealth

Abstract: We present a non-conventional approach for studying the distribution of wealth in society. We analyze data from the 1996 Forbes 400 list of the richest people in the US. Our results confirm that wealth is distributed according to a power law. The measured exponent of the power-law is 1.36. As theoretically predicted, this value is in close agreement with the exponent of the Levy distribution of stock market fluctuations.

Rational group decision making: A random field Ising model at T = 0

Abstract: A modified version of a finite random field Ising ferromagnetic model in an external magnetic field at zero temperature is presented to describe group decision making. Fields may have a non-zero average. A postulate of minimum inter-individual conflicts is assumed. Interactions then produce a group polarization along one very choice which is however randomly selected. A small external social pressure is shown to have a drastic effect on the polarization. Individual bias related to personal backgrounds, cultural values and past experiences are introduced via quenched local competing fields. They are shown to be instrumental in generating a larger spectrum of collective new choices beyond initial ones. In particular, compromise is found to results from the existence of individual competing bias. Conflict is shown to weaken group polarization. The model yields new psychosociological insights about consensus and compromise in groups.

Particle hopping models for two-lane traffic with two kinds of vehicles: Effects of lane-changing rules

Abstract: We develop particle-hopping models of two-lane traffic with two different types of vehicles (characterized by two different values of the maximum allowed speed Vmax) generalizing the Nagel-Schrecknnberg stochastic cellular-automata model for single-lane traffic with a single Vmax The simplest of the two models is symmetric with respect to the two lanes as well as with respect to the two types of vehicles In the asymmetric model, different rules govern the changing from the the “fast” lanes to the “slow” one and the reverse process Moreover, in the asymmetric model, the drivers of fast vehicles can anticipate, often well in advance, the possibility of getting trapped behind a slow vehicle and tend to avoid such possibilities

Large financial crashes

Abstract: We propose that large stock market crashes are analogous to critical points studied in statistical physics with log-periodic correction to scaling. We extend our previous renormalization group model of stock market prices prior to and after crashes (D. Sornette, A. Johansen, J.P. Bouchaud, J. Phys. I France 6 (1996) 167) by including the first non-linear correction. This predicts the existence of a log-frequency shift over time in the log-periodic oscillations prior to a crash. This is tested on the two largest historical crashes of the century, the October 1929 and October 1987 crashes, by fitting the stock market index over an interval of 8 yr prior to the crashes. The good quality of the fits, as well as the consistency of the parameter values obtained from the two crashes, promote the theory that crashes have their origin in the collective “crowd” behavior of many interacting agents.

Evaluating scaled windowed variance methods for estimating the Hurst coefficient of time series

Abstract: Three-scaled windowed variance methods (standard, linear regression detrended, and brdge detrended) for estimating the Hurst coefficient (H) are evaluated. The Hurst coefficient, with 0 < H < 1, characterizes self-similar decay in the time-series autocorrelation function. The scaled windowed variance methods estimate H for fractional Brownian motion (fBm) signals which are cumulative sums of fractional Gaussian noise (fGn) signals. For all three methods both the bias and standard deviation of estimates are less than 0.05 for series having N ≥ 2(9) points. Estimates for short series (N < 2(8)) are unreliable. To have a 0.95 probability of distinguishing between two signals with true H differing by 0.1, more than 2(15) points are needed. All three methods proved more reliable (based on bias and variance of estimates) than Hurst's rescaled range analysis, periodogram analysis, and autocorrelation analysis, and as reliable as dispersional analysis. The latter methods can only be applied to fGn or differences of fBm, while the scaled windowed variance methods must be applied to fBm or cumulative sums of fGn.

Volatility distribution in the S&P500 stock index

Abstract: 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 ≌ 0.9 .

Realistic multi-lane traffic rules for cellular automata

Abstract: A set of lane changing rules for cellular automata simulating multi-lane traffic is proposed. It reproduces qualitatively that the passing lane becomes more crowded than the one for slower cars if the flux is high enough, which is true for motorways in countries like Germany where passing should be done on a specified lane as a rule. The rules have two parameters allowing to adjust the inversion point of the lane-usage distribution and to calibrate the model.

Coherent and random sequences in financial fluctuations

Abstract: The detrended fluctuation analysis (DFA) is used to sort out temporal correlations in financial data. Its usefulness for the investigations of long-range power-law correlations in economic sequences is shown. Our findings of persistent and antipersistent sequences are suprisingly similar to those for DNA sequences which appeared as a mosaic of coding and non-coding patches.

A simulation technique for many spheres in quasi-static motion under frame-invariant pair drag and Brownian forces

Abstract: We report on details of a simulation technique for particles under quasi-static motion determined by a balance of conservative and dissipative interactions acting at the pair level. We develop frame-invariant and linear viscous interactions between pairs of translating and rotating spheres in a form suitable for computation. We report an o(N) method for generating Brownian forces correlated with a pair resistance tensor and show how explicit finite difference schemes lead naturally to an algorithm with Brownian motion and an estimate of the Brownian stress. We justify the algorithm by appeal to the second-order Langevin equation. We discuss the choice of time step and imposition of boundary conditions. We assess a model of this kind as an approximation for colloid spheres concentrated in a fluid medium under shear flow. It is noted that the algorithm is also that required for simulation, in the diffusive limit, of a technique known as dissipative particle dynamics. We report on structural effects in Brownian sphere colloids and their sensitivity to the model details. We argue that the approximation has heuristic value in the study of the rheology in concentrated colloid systems. Its predictions for the rheology of suspensions are in semi-quantitative agreement with experiment.

Pattern analysis with two-dimensional spectral localisation: Applications of two-dimensional S transforms

Abstract: An image is a function, f(x, y) , of the independent space variables x and y . The global Fourier spectrum of the image is a complex function F(k x , k y ) of the wave numbers k x and k y . The global spectrum may be viewed as a construct of the spectra of an arbitrary number of segments of f(x, y) , leading to the concept of a local spectrum at every point of f(x, y) . The two-dimensional S transform is introduced here as a method of computation of the local spectrum at every point of an image. In addition to the variables x and y , the 2-D S transform retains the variables k x and k y , being a complex function of four variables. Visualisation of a function of four variables is difficult. We skirt around this by removing one degree of freedom, through examination of ‘slices’. Each slice of the 2-D S transform would then be a complex function of three variables, with separate amplitude and phase components. By ranging through judiciously chosen slice locations the entire S transform can be examined. Images with strictly periodic patterns are best analysed with a global Fourier spectrum. On the other hand, the 2-D S transform would be more useful in spectral characterisation of aperiodic or random patterns.

Analyzing exact fractal time series: evaluating dispersional analysis and rescaled range methods

Abstract: Precise reference signals are required to evaluate methods for characterizing a fractal time series. Here we use fGp (fractional Gaussian process) to generate exact fractional Gaussian noise (fGn) reference signals for one-dimensional time series. The average autocorrelation of multiple realizations of fGn converges to the theoretically expected autocorrelation. Two methods commonly used to generate fractal time series, an approximate spectral synthesis (SSM) method and the successive random addition (SRA) method, do not give the correct correlation structures and should be abandoned. Time series from fGp were used to test how well several versions of rescaled range analysis (R/S) and dispersional analysis (Disp) estimate the Hurst coefficient (0 0.9. R/S-detrended overestimates H for time series with H 0.7. Estimates of H(Ĥ) from all versions of Disp usually have lower bias and variance than those from R/S. All versions of dispersional analysis, Disp, now tested on fGp, are better than we previously thought and are recommended for evaluating time series as long-memory processes.

Transient gelation by spinodal decomposition in colloid-polymer mixtures

Abstract: We have investigated with small angle light scattering and optical microscopy transient gelation phenomena which occur in phase-separating colloid-polymer mixtures. The scattering intensity distribution shows a peak at non-zero wave vector and satisfies the asymptotic q−4 Porod behaviour. Consistent with these observations, optical micrographs show an alternating pattern of dark and bright domains. These findings suggest that the polymer-induced depletion forces lead to the formation of a bicontinuous network of colloid-rich and colloid-poor domains, via a spinodal decomposition process. This bicontinuous network rapidly attains a gel-like character as indicated by the arrest of speckle fluctuations. The occurrence of the gel is ascribed to polymer-induced aggregation between the colloids in the colloid-rich phase. Due to the reversible nature of the aggregation the network restructures and eventually the gel collapses, as is manifested by the rapid separation of the colloid-rich phase from the colloid-poor phase.

Hydrophobic hydration, hydrophobic forces and protein folding

Abstract: There is no general agreement about the molecular mechanism of hydrophobic hydration. The preferred models all consider only the state of single water molecules immediately adjacent to the hydrophobic solute to which they cannot hydrogen bond. Because, fortuitously, all experiments, until recently, have been done at room temperature, the large decrease in entropy accompanying hydrophobic hydration has been taken to mean that the phenomenon is “entropy driven” when common sense says that the effect of losing a whole hydrogen bond is a large increase in enthalpy. At higher temperatures, enthalpy does become positive, further confusing interpretation. When the cooperativity of water-water hydrogen bonding is taken into account, many of the conceptual difficulties of the nature of hydrophobic hydration, the magnitude of the hydrophobic force and its role in protein folding disappear. 1. (1) It accounts for the long-range over which the hydrophobic force can sometimes (but not always) act. 2. (2) It suggests that an appreciable population of water molecules close to a hydrophobic surface, out-of-equilibrium with more distant populations compensate for their excess enthalpy by expanding and decreasing their local chemical potential. This explains the thermodynamics findings for transfer of hydrocarbons from the vapour phase to water as a function of temperature. 3. (3) It offers a resolution of the current uncertainty as to whether the hydrophobic interaction stabilises or destabilises the folded conformation of proteins. The belief that it is destabilising is based on extensive calorimetric measurements of transfer of amino acids from the vapour phase to water as a model for the transfer of amino acids from the central core of a protein to contact with water. It is suggested that this is an inappropriate model. 4. (4) It is shown that the true hydrophobic interaction which drives protein folding is not due to oil/water incompatibility as has always been assumed, but is due to oil/low-density water incompatibility. Low-density water, which has stronger hydrogen bonds and lower intrinsic entropy than normal water has been shown to form outside double layers of polyelectrolytes. This low-density water can overlap adjacent nonpolar amino acids, inducing a powerful driving force for their sequestration out of contact with low-density water. 5. (5) It offers mechanisms for the effects of ions of the Hofmeister series and of compensatory solutes in the stabilisation and destabilisation of folded proteins and other structures. 6. (6) Other biological structures such as micelles, lipid bilayers, polysaccharides and polynucleotides also have both hydrophobic and charged groups to generate the extreme oil/low-density water incompatibility which promotes structures of singular stability. and order.

Negative thermal expansion in the Gaussian core model

Abstract: The pressure equation of state of the classical many-body system with Gaussian pair interactions has been examined over a wide density range. Both analytical and simulational methods have been involved. A simply-connected region of negative thermal expansion has emerged from the study. It includes portions of the BCC crystal and fluid sections of the equilibrium phase diagram.

Stock market dynamics and turbulence: parallel analysis of fluctuation phenomena

Abstract: We report analogies and differences between the fluctuations in an economic index and the fluctuations in velocity of a fluid in a fully turbulent state. Specifically, we systematically compare (i) the statistical properties of the S&P 500 cash index recorded during the period January 84–December 89 with (ii) the statistical properties of the velocity of turbulent air measured in the atmospheric surface layer about 6 m above a wheat canopy in the Connecticut Agricultural Research Station. We find non-Gaussian statistics, and intermittency, for both processes (i) and (ii) but the deviation from a Gaussian probability density function are different for stock market dynamics and turbulence.

Scaling in currency exchange

Abstract: We study the scaling behavior in currency exchange rates. Our results suggest that they satisfy scaling with an exponent close to 0.5, but that it differs qualitatively from that of a simple random walk. Indeed price variations cannot be considered as independent variables and subtle correlations are present. Furthermore, we introduce a novel statistical analysis for economic data which makes the physical properties of a signal more evident and eliminates the systematic effects of time periodicity.

Scaling behavior in economics: The problem of quantifying company growth

Abstract: Inspired by work of both Widom and Mandelbrot, we analyze the Computstat database comprising all publicly traded United States manufacturing companies in the years 1974–1993. We find that the distribution of company size remains stable for the 20 years we study, i.e., the mean value and standard deviation remain approximately constant. We study the distribution of sizes of the “new” companies in each year and find it to be well approximated by a log- normal. We find (i) the distribution of the logarithm of the growth rates, for a fixed growth period of T years, and for companies with approximately the same size S displays an exponential “tent-shaped” form rather than the bell-shaped Gaussian, one would expect for a log-normal distribution, and (ii) the fluctuations in the growth rates — measured by the width of this distribution σT — decrease with company size and increase with time T. We find that for annual growth rates (T = 1), σT ∼ S−β, and that the exponent β takes the same value, within the error bars, for several measures of the size of a company. In particular, we obtain β = 0.20 ± 0.03 for sales, β = 0.18 ± 0.03 for number of employees, β = 0.18±0.03 for assets, β = 0.18 ± 0.03 for cost of goods sold, and β = 0.20 ± 0.03 for propert, plant, and equipment. We propose models that may lead to some insight into these phenomena. First, we study a model in which the growth rate of a company is affected by a tendency to retain an “optimal” size. That model leads to an exponential distribution of the logarithm of growth rate in agreement with the empirical results. Then, we study a hierarchical tree-like model of a company that enables us to relate β to parameters of a company structure. We find that β = −1n Π/1nz, where z defines the mean branching ratio of the hierarchical tree and Π is the probability that the lower levels follow the policy of higher levels in the hierarchy. We also study the output distribution of growth rates of this hierarchical model. We find that the distribution is consistent with the exponential form found empirically. We also discuss the time dependence of the shape of the distribution of the growth rates.

Compaction of granular mixtures: a free volume model

Abstract: We describe compaction, induced by weak tapping of a powder, as a process where a grain can jump into a hole, only if the hole is large enough. The distribution of hole sizes is taken to be the Poisson type, with a certain characteristic free volume. For macrodisperse powders, this leads to a classical logarithmic law of compaction, already derived by Knight et al. Here we focus our attention on the case of mixtures, between two populations: large grains (L) and small grains (S) with very different sizes, so that the (S) grains may fill the interstices of the (L) grains. Geometrically, these mixtures can exist as “gravels” (where the intersices are not completely filled) or “puddings” (where the L grains are not tighlty packed). Dynamically, we expect a cross over curve between L-type compaction and S-type compaction, which is different from the geometrical boundary. This implies that, for certain material ratios ρ = L/S, the plot of density versus number of tappings should show two distinct branches.

On the validity of hydrodynamics in plane Poiseuille flows

Abstract: Microscopic simulations of plane Poiseuille flow for a dilute gas are presented. Although the flow is laminar (Reynolds number ≈10) and sub-sonic, the temperature and pressure profiles measured in the simulations differ qualitatively from the hydrodynamic predictions. The results are in agreement with a recent theoretical analysis based on the asymptotic solution of the BGK model of the Boltzmann equation.

Protein adsorption on tethered polymer layers: effect of polymer chain architecture and composition

Abstract: The ability of tethered polymer layers to modify the adsorption behavior of simple model proteins is studied using single-chain mean-field theory. Several different polymer molecular structures are considered. It is found that branched polymer chains are much more effective in preventing protein adsorption than linear flexible chains. Diblock copolymers formed by a flexible and a rigid block show similar steric repulsion than fully flexible chains of the same number of monomers. However, the distribution of free ends is very different for the two types of molecules. Polymers with the two ends tethered at surfaces are more efficient than chains with one end on the surface with the same molecular weight to prevent protein adsorption. Mixtures of polymer chains at the surface show an ability to prevent protein adsorption that is different from a linear combination of the pure component polymer layers. The effect of attractive interactions between the protein and the segments of the tethered polymer chains is studied. The effective interaction between the protein and the polymer layer shows an attractive part for proteins that are at the tip of the polymer layer in qualitative agreement with recent experimental observations.

Chemomodulation of cellular movement, collective formation of vortices by swarming bacteria, and colonial development

Abstract: Bacterial colonies have developed sophisticated modes of cooperative behavior which enable them to respond to adverse growth conditions. It has been shown that such behavior can be manifested in formation of complex colonial patterns. Certain Bacillus species exhibit collective migration, “turbulent like” flow and emergence of whirlpools during colonial development. Here we present experimental observations of collective behavior and a generic model to explain such behavior. The model incorporates self-propelled and interacting “particles” (swarmers). We show that velocity interaction between the particles can lead to a synchronized movement. To explain vortices formation, we propose a plausible mechanism involving a special chemotactic response (rotational chemotaxis) which is based on speed modulations according to the concentration of a chemoattractant. This mechanism differs from that exhibited by swimming bacteria. We show that the chemomodulation of swarmers' speed together with the velocity interactions impose a torque on the collective motion and can lead to formation of vortices. The inclusion of both attractive and repulsive rotational chemotaxis in the model captures the salient features of the observed growth patterns.

On the angles of dry granular heaps

Abstract: We perform careful experiments in a turnable cell to determine the angle of repose and various other angles of dry granular materials. We study the dependence of the angle on the presence of walls and find an exponential decay on the distance between the walls. Modification of the granular fabric close to the surface changes the static angle of repose and the effect can still be noted after several inclinations of the cell indicating the existence of a memory effect. The dynamic angle of repose is particularly small after the first inclination of the cell. When part of the heap is removed through an outlet, three different angles are obtained showing the effect of fabric and heap preparation on the dynamic angle.

Phase separation morphology of spin-coated polymer blend thin films

Abstract: We present the results of a study of the morphology of phase separation in thin films of two different polymer blend systems: polystyrene/polyisoprene and polystyrene/poly(methyl methacrylate). For each blend system, the two polymer components are dissolved in a common solvent. Spin coating of the ternary solutions (polymer blend/solvent) is used to confine the blends to a thin film geometry and to produce phase separation because of rapid evaporation of the solvent (solvent quench). As a quantitative measure of the phase separation morphology the average domain area of the minority component is measured as a function of the polystyrene mass fraction. For both blend systems we identify a small range of composition corresponding to a large increase in the average domain area. We show that the strong dependence of the average domain area on spin speed allows control over the quench time of the polymer blend thin films.

Electrode effects in dielectric spectroscopy of colloidal suspensions

Abstract: We present a simple model to account for electrode polarization in colloidal suspensions. Apart from correctly predicting the ω −3 2 dependence for the dielectric permittivity at low frequencies ω, the model provides an explicit dependence of the effect on electrode spacing. The predictions are tested for the sodium bis(2-ethylhexyl) sulfosuccinate (AOT) water-in-oil microemulsion with iso-octane as continuous phase. In particular, the dependence of electrode polarization effects on electrode spacing has been measured and is found to be in accordance with the model prediction. Methods to reduce or account for electrode polarization are briefly discussed.

Phase separation in dilute solutions of poly (N-isopropylacrylamide)

Abstract: The appearance of spherical particles resulting from phase separation in dilute solutions of poly(N-isopropylacrylamide) has been observed by dynamic light scattering (DLS). The particles have a relatively narrow size distribution. The size of particles increases with increasing concentration of polymer, and decreasing heating speed. Electron microscopy confirms the existence of spherical particles with size and polydispersity in agreement with DLS.

An improved cellular automaton model for traffic flow simulation

Abstract: Starting from a basic cellular automaton model (CA) for traffic flow on a freeway we study various modifications to its update procedure aiming at a quantitative improvement of the fundamental diagram obtained. The investigation results in the suggestion of an improved automaton, showing qualitative and quantitative coincidence of maximum flux with values taken from real traffic measurements.

Non-equilibrium behaviour of colloid-polymer mixtures

Abstract: Moderate concentrations of a small non-adsorbing polymer cause a suspension of colloidal particles to phase-separate into coexisting colloidal fluid and crystal via the ‘depletion’ mechanism. At higher polymer concentrations, crystallization is suppressed, and a variety of non-equilibrium aggregation behaviour is observed. We report the results of small-angle laser light scattering studies of aggregation in a model system - colloidal PMMA + polystyrene. In all cases, ‘rings’ in the small-angle scattering are observed. The different temporal behaviour of these small-angle scattering rings allowed us to classify the non-equilibrium region into three regimes, ‘nucleation-like’, ‘spinodal-like’ and ‘transient gelation’. It is suggested that non-equilibrium behaviour is ‘switched on’ by a hidden, metastable gas-liquid binodal. Different regimes of aggregation behaviour are controlled by the nucleation-spinodal cross-over and the transient percolation lines within this binodal.