Showing papers in "Physica A-statistical Mechanics and Its Applications in 1996"

Two lane traffic simulations using cellular automata

Abstract: We examine a simple two-lane cellular automaton based upon the single-lane CA introduced by Nagel and Schreckenberg. We point out important parameters defining the shape of the fundamental diagram. Moreover we investigate the importance of stochastic elements with respect to real life traffic.

Generalized simulated annealing

Abstract: We discuss and illustrate a new stochastic algorithm (generalized simulated annealing) for computationally finding the global minimum of a given (not necessarily convex) energy/cost function defined in a continuous D-dimensional space. This algorithm recovers, as particular cases, the so-called classical (“Boltzmann machine”) and fast (“Cauchy machine”) simulated annealings, and turns out to be quicker than both.

Mode-coupling approximations, glass theory and disordered systems

Abstract: We discuss the general link between mode-coupling like equations (which serve as the basis of some recent theories of supercooled liquids) and the dynamical equations governing mean-field spin-glass models, or the dynamics of a particle in a random potential. The physical consequences of this interrelation are underlined. It suggests to extend the mode-coupling approximation to temperatures well below the freezing temperature, in which aging effects become important. In this regime we suggest some new experiments in order to test a non-trivial prediction of the Mode-Coupling picture, which is a generalized relation between the short (β) and long (α) time regimes.

Criticality in the hard-sphere ionic fluid

Abstract: A physically based mean-field theory of criticality and phase separation in the restricted primitive model of an electrolyte (hard spheres of diameter a carrying charges ± q) is developed on the basis of the Debye-Huckel (DH) approach. Simple DH theory yields a critical point at T ∗ ≡ k B Ta/q 2 = 1 16 , which is only about 15% above the best recent simulation estimates ( T c,sim ∗ = 0.052–0.056 ) but a critical density ( ϱ c ∗ ≡ ϱ c a 3 = 1 64 π ⋍ 0.005 that is much too small ( ϱ c,sim ∗ = 0.023–0.035 ). Allowing for hard-core exclusion effects reduces these values slightly. However, correction of the DH linearization of the Poisson-Boltzmann equation by including pairing of + and − charges improves ϱ c ∗ significantly. Bjerrum's theory of the (required) association constant is revisited critically; Ebeling's reformulation is strongly endorsed but makes negligible numerical difference at criticality and below. The nature and size of the associated, dipolar ion pairs is examined quantitatively and their solvation free-energy in the residual fluid of free ions is calculated on the basis of DH theory. This contribution to the total free energy proves crucial and leads to a rather satisfactory description of the critical region. The temperature variation of the vapor pressure and of the density of neural dipolar pairs correlates fairly well with Gillan's numerical cluster analysis. Possible improvements to allow for larger ion clusters and to better represent the denser ionic liquid below criticality are discussed. Finally, the replacement of the DH approximation for the ionic free energy by the mean spherical approximation is studied. Reasonable critical densities are generated but the MSA critical temperatures are all 40–50% too high; in addition, the predicted density of neutral clusters seems much too low near criticality and, along with the vapor pressure, appears to decrease too rapidly by an exponential factor below Tc.

Anomalous fluctuations in the dynamics of complex systems: from DNA and physiology to econophysics

Abstract: We discuss examples of complex systems composed of many interacting subsystems. We focus on those systems displaying nontrivial long-range correlations. These include the one-dimensional sequence of base pairs in DNA, the sequence of flight times of the large seabird Wandering Albatross, and the annual fluctuations in the growth rate of business firms. We review formal analogies in the models that describe the observed long-range correlations, and conclude by discussing the possibility that behavior of large numbers of humans (as measured, e.g., by economic indices) might conform to analogs of the scaling laws that have proved useful in describing systems composed of large numbers of inanimate objects.

Discrete Painlevé equations: coalescences, limits and degeneracies

Abstract: Starting from the standard form of the five discrete Painleve equations we show how one can obtain (through appropriate limits) a host of new equations which are also the discrete analogues of the continuous Painleve equations A particularly interesting technique is the one based on the assumption that some simplification takes place in the autonomous form of the mapping following which the deautonomization leads to a new n -dependence and introduces more new discrete Painleve equations

Aggregating pattern dynamics in a chemotaxis model including growth

Abstract: A population model including diffusion, chemotaxis and growth is studied. Assuming that the diffusion rate and the chemotactic rate are both very small compared with the growth rate, we derive a new equation to describe the time-evolution of the aggregating region of biological individuals and show the conditions for the existence and stability of radially symmetric equilibrium solutions of the equation, which indicate the aggregation of individuals.

On the Cole-Cole relaxation function and related Mittag-Leffler distribution

Abstract: In the framework of the one-dimensional fractal time random walk (FTRW) relaxation model, we rigorously show that the frequency domain response takes, in both nonbiased and biased walks, the only possible Cole-Cole form. The underlying reason for this is the specific form of the relaxation function (the survival probability of a relaxing system) determined in this model by the Mittag-Leffler distribution. We provide also analytical formulas for the propagators of the nonbiased and biased FTRWs.

Critical behaviors and 1/Φ noise in information traffic

Abstract: We observe 1/Φ-type noise in packet density fluctuations and round trip time sequences of packets in Internet computer network traffic. The method of IDL (interval distribution of level set) is applied to analyze the 1/Φ-type power-spectra. A simple dynamic phase transition model, the contact process, is introduced to explain the intermittent packet density fluctuation.

Analysis of daily temperature fluctuations

Abstract: We study daily temperature fluctuations over more than 50 yr in two places on the globe that are separated by more than 3000 km. We analyze the temperature fluctuations ΔT i with respect to the mean noon temperature 〈 T i 〉 averaged, for each day of the year, over the whole year, ΔT i = T i − 〈 T i 〉. We find that the ΔT i are correlated and can be characterized for up to at least 10 3 days by a power law correlation with an exponent α ≅ 0.65.

A 3 sx 3 matrix spectral problem for AKNS hierarchy and its binary nonlinearization

Abstract: A 3 × 3 matrix spectral problem for AKNS soliton hierarchy is introduced and the corresponding Bargmann symmetry constraint involving Lax pairs and adjoint Lax pairs is discussed. An explicit new Poisson algebra is proposed and thus the Liouville integrability is established for the nonlinearized spatial system ind a hierarchy of nonlinearized temporal systems under the control of the nonlinearized spatial system. The obtained nonlinearized Lax systems, in which the nonlinearized spatial system is intimately related to stationary AKNS flows, lead to a sort of new involutive solutions to each AKNS soliton equation. Therefore, the binary nonlinearization theory is successfully extended to a case of 3 × 3 matrix spectral problem for AKNS hierarchy.

Phase diagram of the two-dimensional complex Ginzburg-Landau equation

Abstract: After a brief introduction to the complex Ginzburgh-Landau equation, some of its important features in two space dimensions are reviewed. A comprehensive study of the various phases observed numerically in large systems over the whole parameter space is then presented. The nature of the transitions between these phases is investigated and some theoretical problems linked to the phase diagram are discussed.

Counterion condensation theory constructed from different models

Abstract: The primitive model and the line of charges model for ionized polymers both predict the emergence of a condensed counterion layer at a critical polymer charge density, but the two models describe the condensed layer in different ways. The Zimm-Le Bret and Ramanathan distributions for the condensed layer in the primitive model are reviewed. The extended Debye-Huckel theory of the line of charges model is recast in a more general form in an attempt to make its underlying assumptions transparent. We show that the counterion-polyion potential of mean force at great distances behaves differently for the two models.

Derivation and empirical validation of a refined traffic flow model

Abstract: The gas-kinetic foundation of fluid-dynamic traffic equations suggested in previous papers (D. Helbing, Physica A 219 (1995) 375 and 391) is further refined by applying the theory of dense gases and granular materials to the Boltzmann-like traffic model by Paveri-Fontana. It is shown that, despite the phenomenologically similar behaviour or ordinary and granular fluids, the relations for these cannot directly be transferred to vehicular traffic. The dissipative and anisotropic interactions of vehicles as well as their velocity-dependent space requirements lead to a considerably different structure of the macroscopic traffic equations, also in comparison with the previously suggested traffic flow models. As a consequence. the instability mechanisms of emergent density waves are different. Crucial assumptions are validated by empirical traffic data and essential results are illustrated by figures.

Fragmentation versus stability in bimodal coalitions

Abstract: Competing bimodal coalitions among a group of actors are discussed. First, a model from political sciences is revisited. Most of the model statements are found not to be contained in the model. Second, a new coalition model is built. It accounts for local versus global alignment with respect to the joining of a coalition. The existence of two competing world coalitions is found to yield one unique stable distribution of actors. On the opposite a unique world leadership allows the emergence of unstable relationships. In parallel to regular actors which have a clear coalition choice, “neutral”, “frustrated” and “risky” actors are produced. The cold war organisation after world war II is shown to be rather stable. The emergence of a fragmentation process from eastern group disappearance is explained as well as continuing western group stability. Some hints are obtained about possible policies to stabilize world nation relationships. European construction is analyzed with respect to European stability. Chinese stability is also discussed.

Semiclassical theory of shot noise in mesoscopic conductors

Abstract: A semiclassical theory is developed for time-dependent current fluctuations in mesoscopic conductors. The theory is based on the Boltzmann-Langevin equation for a degenerate electron gas. The low-frequency shot-noise power is related to classical transmission probabilities at the Fermi level. For a disordered conductor with impurity scattering, it is shown how the shot noise crosses over from zero in the ballistic regime to one-third of the Poisson noise in the diffusive regime. In a conductor consisting of n tunnel barriers in series, the shot noise approaches one-third of the Poisson noise as n goes to infinity, independent of the transparency of the barriers. The analysis confirms that phase coherence is not required for the occurrence of the one-third suppression of the shot noise. The effects of electron heating and inelastic scattering are calculated, by inserting charge-conserving electron reservoirs between segments of the conductor.

“Self-organized” formulation of standard percolation phenomena

Abstract: We consider standard percolation processes such as epidemic processes with or without immunization. We show that their dynamics can be formulated so that they mimic self-organized critical phenomena: the wetting probability p needs not to be fine tuned to its critical value p c in order to arrive at criticality, but it rather emerges as a singularity in some time-dependent distribution. On the one hand, this casts doubts on the significance of self-organized as opposed to ordinary criticality. On the other hand, it suggests very efficient algorithms where percolation problems are studied at several values of p in a single run. As an example, we apply such an algorithm to directed percolation in 2 + 1 dimensions, where it allows a very precise determination of critical behavior.

Force, torque, and absorbed energy for a body of arbitrary shape and constitution in an electromagnetic radiation field

Abstract: The force and torque exerted on a body of arbitrary shape and constitution by a stationary radiation field are in principle given by integrals of Minkowski's stress tensor over a surface surrounding the body. Similarly the absorbed energy is given by an integral of the Poynting vector. These integrals are notoriously difficult to evaluate, and so far only spherical bodies have been considered. It is shown here that the integrals may be cast into a simpler form by use of Debye potentials. General expressions for the integrals are derived as sums of bilinear expressions in the coefficients of the expansion of the incident and scattered waves in terms of vector spherical waves. The expressions are simplified for small particles, such as atoms, for which the electric dipole approximation may be used. It is shown that the calculation is also relevant for bodies with nonlinear electromagnetic response.

Avoided critical behavior in a uniformly frustrated system

Abstract: We study the effects of weak long-ranged antiferromagnetic interactions of strength Q on a spin model with predominant short-ranged ferromagnetic interactions. In three dimensions, this model exhibits an avoided critical point in the sense that the critical temperature Tc(Q = 0) is strictly greater than limQ→0Tc(Q). The behavior of this system at temperatures less than Tc(Q = 0) is controlled by the proximity to the avoided critical point. We also quantize the model in a novel way to study the interplay between charge-density wave and superconducting order.

Fluid-fluid phase separation in colloid-polymer mixtures studied with small angle light scattering and light microscopy

Abstract: Mixtures of colloidal silica spheres and polydimethylsiloxane in cyclohexane with a colloid-polymer size ratio of about one were found to phase separate into two fluid phases, one which is colloid-rich and one which is colloid-poor. In this work the phase separation kinetics of this fluid-fluid phase separation is studied for different compositions of the colloid-polymer mixtures, and at several degrees of supersaturation, with small angle light scattering and with light microscopy. The small angle light scattering curve exhibits a peak that grows in intensity and that shifts to smaller wave vector with time. The characteristic length scale that is obtained from the scattering peak is of the order of a few μm, in agreement with observations by light microscopy. The domain size increases with time as t 1 3 , which might be an indication of coarsening by diffusion and coalescence, like in the case of binary liquid mixtures and polymer blends. For sufficiently low degrees of supersaturation the angular scattering intensity curves satisfy dynamical scaling behavior.

The ground state energy of the Edwards-Anderson Ising spin glass with a hybrid genetic algorithm

Abstract: Ground states of three-dimensional Edwards-Anderson ±J Ising spin glasses were calculated with a hybrid of genetic algorithm and local optimization. The algorithm was fast and reliable enough to allow extensive calculations for systems of linear size between 3 and 14 and determination of the average ground state energies with small errors. A linear dependence on 1/volume approximates the data very accurately in the whole range. The −1.7863 ± 0.0004 value for the ground state energy per spin of the infinite system was determined with extrapolation. The main source of uncertainty is that the functional form of the small but significant deviation from the linear 1/volume dependence is unknown.

The green wave model of two-dimensional traffic: Transitions in the flow properties and in the geometry of the traffic jam

Abstract: We carried out computer simulations to study the green wave model (GWM), the parallel updating version of the two-dimensional traffic model of Biham et al. The better convergence properties of the GWM together with a multi-spin coding technique enabled us to extrapolate to the infinite system size which indicates a nonzero density transition from the free flow to the congested state (jamming transition). In spite of the sudden change in the symmetry of the correlation function at the transition point, finite size scaling and temporal scaling seems to hold, at least above the threshold density. There is a second transition point at a density deep in the congested phase where the geometry of the cluster of jammed cars changes from linear to branched: Just at this transition point this cluster has fractal geometry with dimension 1.58. The jamming transition is also described within the mean field approach.

Noise-induced spatial patterns

Abstract: By modifying the spatial coupling a la Swift-Hohenberg in the model introduced in Phys. Rev. Lett. 73 (1994) 3395, we obtain a system that displays noise-induced spatial patterns. We present a mean field theory of this phenomenon and verify some of its predictions by numerical simulations.

Effect of particle size distribution on crystallisation and the glass transition of hard sphere colloids

Abstract: Phase behaviour, crystallisation kinetics and particle dynamics are compared for two colloidal suspensions of hard spherical particles with different particle size distributions; one is narrow and roughly symmetrical and the other is broader and skewed towards smaller particles. Both suspensions exhibit the equilibrium phase behaviour expected for a system of identical hard spheres and they show a glass transition, indicated by the cessation of homogeneous nucleation and the partial arrest of concentration fluctuations, at approximately the same volume fraction, Φg ≈ 0.58. Interestingly, compared to the suspension with the narrower size distribution, crystallisation rates are significantly slower in the more polydisperse suspension. In its colloidal glass state no crystal growth occurs on secondary nuclei, such as the shear-aligned crystals that can be induced in both suspensions by regular rocking.

Pattern formation during mixing and segregation of flowing granular materials

Abstract: Powder mixing plays an important role in a number of industries ranging from pharmaceuticals and food to ceramics and mining. Avalanches provide a mechanism for the stretching and folding needed to mix granular solids. However, unlike fluids, when particles dissimilar in size, density, or shape flow, they can spontaneously demix or segregate. Using magnetic resonance imaging, we track the transport of granular solids in a slowly rotating tube both with and without segregation effects. Compared with experiments in a 2-dimensional rotating disk partially filled with colored particles, the mixing kinematics and the granular pattern formation in a tube are changed by an axial flow instability. From simple physical principles we argue how size and density segregation mechanisms can be made to cancel, allowing good mixing of dissimilar particles, and we show experiments verifying this. Further experiments isolate the axial transport in the slowly rotating tube. Axial transport can appear faster with segregation than without.

Temporal dynamics in perturbation theory

Abstract: Perturbation theory can be reformulated as dynamical theory. Then a sequence of perturbative approximations is bijective to a trajectory of dynamical system with discrete time, called the approximation cascade. Here we concentrate our attention on the stability conditions permitting to control the convergence of approximation sequences. We show that several types of mapping multipliers and Lyapunov exponents can be introduced and, respectively, several types of conditions controlling local stability can be formulated. The ideas are illustrated by calculating the energy levels of an anharmonic oscillator.

Hard ellipsoid rod-plate mixtures: Onsager theory and computer simulations

Abstract: The liquid crystal phase transitions for a classical fluid mixture of hard ellipsoids with aspect ratios 10 : 1 and 1 : 10, and equal volume, have been studied at two compositions using Onsager theories and by computer simulation. The original Onsager from of the Helmholtz free energy contains the second virial coefficient, but the effect of higher virial coefficients may be taken into account indirectly by resummation theories such as the y -expansion theory of Barboy and Gelbart or by renormalised two-particle theories such as that due to Parsons. A comparison of order parameters and equation of state data calculated by computer simulation and by Onsager, y -expansion-Onsager and Parsons theories shows good qualitative agreement. The resummation of higher virial coefficients is seen to offer improved quantitative agreement with simulation at the level of the second virial coefficient. The predicted phase diagram at this level of approximation is symmetric about the equal mixture of prolate and oblate ellipsoids as a result of the prolate-oblate symmetry of the excluded volume. The direct inclusion of higher virial coefficients has not been attempted but it is anticipated that this would give an asymmetric phase diagram.

Rheology and shape transitions of vesicles under capillary flow

Abstract: We present an analytical description of the rheology and shape of axisymmetric vesicles flowing down narrow capillaries. The vesicle surface is described by the Helfrich bending energy. We find that the rheological properties of the vesicle are independent of the Helfrich bending energy. The classical Bretherton theory for tense drops can be applied provided we replace the drop tension with a “dynamical tension” discussed in the text. Darcy's Law is obeyed with an effective permeability which depends on the filling fraction and the dimensions of the vesicle and the pore. For vesicles with tension, there are two rheological regimes. At low applied pressure heads, the vesicle moves very slowly and violates Darcy's Law. With increasing-pressure gradient, there is a singular point beyond which the rear of the vesicle becomes tensionless and Darcy's Law is obeyed. This singular point marks a whole sequence of shapes transitions of the vesicle, starting from a sphero-cylinder and ending in a Bell shape, similar to those reported for red blood cells in the physiological literature.

Late-stage coarsening of adlayers by dynamic cluster coalescence

Abstract: We consider the late stages of adlayer coarsening when this process is dominated by cluster diffusion and coalescence. The growth rate of the average cluster size can be directly related to the cluster diffusion coefficient of individual clusters. The distribution of cluster sizes and the spatial correlations between clusters are examined as a function of coverage and cluster diffusion rate using Monte Carlo simulations. We also show how the Smoluchowski equation can give an approximate closed-form solution for the cluster size distribution during coarsening by coalescence. The coarsening of adlayers by cluster coalescence in a model that includes local inter-cluster interactions is also examined.

Escaping orbits in trace maps

Abstract: We study the finitely-generated group A of invertible polynomial mappings from C 3 to itself (or R 3 to itself) which preserve the Fricke-Vogt invariant I(x, y, z) = x2 + y2 + z2 − 2xyz − 1. Using properties of suitably-chosen generators, we give a necessary condition and sufficient conditions for infinite order elements of A to have an unbounded orbit escaping to infinity in forward or backward time. Our main motivation for this study is that A includes the so-called trace maps derived from transfer matrix approaches to various physical processes displaying non-periodicity in space or time. As shown previously, characterising escaping orbits leads to various conclusions for the physical model and vice versa (e.g. electronic properties of ID quasicrystals). Our results generalize in a simple constructive way those previously proved for Fibonacci-type trace maps.