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Physical Review E

(Statistical, Nonlinear, and Soft Matter Physics)

November 2009

Volume 80, Number 5 , partial issue

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Part 1 - Statistical, Soft Matter, and Biological Physics


Part 2 - Nonlinear and Plasma Physics, Fluid Dynamics, and Related Topics

 
 
  • RAPID COMMUNICATIONS
  • ARTICLES
  • BRIEF REPORTS
    		•
  • ARTICLES
  • BRIEF REPORTS
    		•

    Part 1 - Statistical, Soft Matter, and Biological Physics

    RAPID COMMUNICATIONS

    Statistical physics
    Rapid

    Avalanche dynamics in fluid imbibition near the depinning transition
    Marc Pradas, Juan M. López, and A. Hernández-Machado
    Published 4 November 2009 (4 pages)
    050101(R)  Full Text: PDF (2179 kB)  | Buy Article
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    We study avalanche dynamics and local activity of forced-flow imbibition fronts in disordered media. We focus on the front dynamics as the mean velocity of the interface [overline v] is decreased and the pinning state is approached. Scaling arguments allow us to obtain the statistics of avalanche sizes and durations, which become power-law distributed due to the existence of a critical point at [overline v]=0. Results are compared with phase-field numerical simulations.
    Rapid

    Loewner driving functions for off-critical percolation clusters
    Yoichiro Kondo, Namiko Mitarai, and Hiizu Nakanishi
    Published 4 November 2009 (4 pages)
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    We numerically study the Loewner driving function Ut of a site percolation cluster boundary on the triangular lattice for p<pc. It is found that Ut shows a drifted random walk with a finite crossover time. Within this crossover time, the averaged driving function <Ut> shows a scaling behavior −(pc−p)t(nu+1)/2nu with a superdiffusive fluctuation whereas, beyond the crossover time, the driving function Ut undergoes a normal diffusion with Hurst exponent 1/2 but with the drift velocity proportional to (pc−p)nu, where nu=4/3 is the critical exponent for two-dimensional percolation correlation length. The crossover time diverges as (pc−p)−2nu as p-->pc.
    Rapid

    Nature of the order-disorder transition in the Vicsek model for the collective motion of self-propelled particles
    Gabriel Baglietto and Ezequiel V. Albano
    Published 6 November 2009 (4 pages)
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    One of the most popular approaches to the study of the collective behavior of self-driven individuals is the well-known Vicsek model (VM) [T. Vicsek, A. Czirók, E. Ben-Jacob, I. Cohen, and O. Shochet, Phys. Rev. Lett. 75, 1226 (1995)]. In the VM one has that each individual tends to adopt the direction of motion of its neighbors with the perturbation of some noise. For low enough noise the individuals move in an ordered fashion with net transport of mass; however, when the noise is increased, one observes disordered motion in a gaslike scenario. The nature of the order-disorder transition, i.e., first-versus second-order, has originated an ongoing controversy. Here, we analyze the most used variants of the VM unambiguously establishing those that lead either to first- or second-order behavior. By requesting the invariance of the order of the transition upon rotation of the observational frame, we easily identify artifacts due to the interplay between finite-size and boundary conditions, which had erroneously led some authors to observe first-order transitionlike behavior.

    ARTICLES

    Statistical physics

    Finite-size analysis of a two-dimensional Ising model within a nonextensive approach
    N. Crokidakis, D. O. Soares-Pinto, M. S. Reis, A. M. Souza, R. S. Sarthour, and I. S. Oliveira
    Published 2 November 2009 (8 pages)
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    In this work we present a thorough analysis of the phase transitions that occur in a ferromagnetic two-dimensional Ising model, with only nearest-neighbors interactions, in the framework of the Tsallis nonextensive statistics. We performed Monte Carlo simulations on square lattices with linear sizes L ranging from 32 up to 512. The statistical weight of the Metropolis algorithm was changed according to the nonextensive statistics. Discontinuities in the m(T) curve are observed for q<=0.5. However, we have verified only one peak on the energy histograms at the critical temperatures, indicating the occurrence of continuous phase transitions. For the 0.5<q<=1.0 regime, we have found continuous phase transitions between the ordered and the disordered phases, and determined the critical exponents via finite-size scaling. We verified that the critical exponents alpha, beta, and gamma depend on the entropic index q in the range 0.5<q<=1.0 in the form alpha(q)=(10q2−33q+23)/20, beta(q)=(2q−1)/8, and gamma(q)=(q2−q+7)/4. On the other hand, the critical exponent nu does not depend on q. This suggests a violation of the scaling relations 2beta+gamma=dnu and alpha+2beta+gamma=2 and a nonuniversality of the critical exponents along the ferro-paramagnetic frontier.

    Phase-space networks of geometrically frustrated systems
    Yilong Han (韩一龙)
    Published 5 November 2009 (5 pages)
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    We illustrate a network approach to the phase-space study by using two geometrical frustration models: antiferromagnet on triangular lattice and square ice. Their highly degenerated ground states are mapped as discrete networks such that the quantitative network analysis can be applied to phase-space studies. The resulting phase spaces share some comon features and establish a class of complex networks with unique Gaussian spectral densities. Although phase-space networks are heterogeneously connected, the systems are still ergodic due to the random Poisson processes. This network approach can be generalized to phase spaces of some other complex systems.

    Diffusion of finite-sized hard-core interacting particles in a one-dimensional box: Tagged particle dynamics
    L. Lizana and T. Ambjörnsson
    Published 5 November 2009 (16 pages)
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    We solve a nonequilibrium statistical-mechanics problem exactly, namely, the single-file dynamics of N hard-core interacting particles (the particles cannot pass each other) of size Delta diffusing in a one-dimensional system of finite length L with reflecting boundaries at the ends. We obtain an exact expression for the conditional probability density function rho[script T](y[script T],t|y[script T],0) that a tagged particle [script T] ([script T]=1,…,N) is at position y[script T] at time t given that it at time t=0 was at position y[script T],0. Using a Bethe ansatz we obtain the N-particle probability density function and, by integrating out the coordinates (and averaging over initial positions) of all particles but particle [script T], we arrive at an exact expression for rho[script T](y[script T],t|y[script T],0) in terms of Jacobi polynomials or hypergeometric functions. Going beyond previous studies, we consider the asymptotic limit of large N, maintaining L finite, using a nonstandard asymptotic technique. We derive an exact expression for rho[script T](y[script T],t|y[script T],0) for a tagged particle located roughly in the middle of the system, from which we find that there are three time regimes of interest for finite-sized systems: (A) for times much smaller than the collision time t<<taucoll=1/(rho2D), where rho=N/L is the particle concentration and D is the diffusion constant for each particle, the tagged particle undergoes a normal diffusion; (B) for times much larger than the collision time t>>taucoll but times smaller than the equilibrium time t<<taueq=L2/D, we find a single-file regime where rho[script T](y[script T],t|y[script T],0) is a Gaussian with a mean-square displacement scaling as t1/2; and (C) for times longer than the equilibrium time t>>taueq, rho[script T](y[script T],t|y[script T],0) approaches a polynomial-type equilibrium probability density function. Notably, only regimes (A) and (B) are found in the previously considered infinite systems.

    Social tolerance allows cooperation to prevail in an adaptive environment
    Xiaojie Chen, Feng Fu, and Long Wang
    Published 6 November 2009 (7 pages)
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    In real situations, individuals often have moderate tolerance toward ambient cooperative environment in which they tend to avoid unfavorable interactions and search for favorable ones. How such social tolerance affects the evolution of cooperation and the resulting cooperative networks remains to be answered. To address this issue, here we present an effective model of co-evolutionary prisoner's dilemma by introducing cooperative environment and social tolerance for networked players. An individual's level of cooperative environment characterizes the cooperativity and sustainability of its interaction environment centered on itself. In our model, for paired individuals we assume that the one in better cooperative environment has a certain tolerance threshold to the opponent. If the opponent's cooperative environment level is beyond the tolerance threshold, the one in better cooperative environment cuts unilaterally the link, and rewires to others. Otherwise, the link is not severed, and meanwhile an inhomogeneous strategy imitation process between them is considered. Moreover, a player's cooperative environment is adjusted in response to the strategy choices in the neighborhood. Interestingly, we find that there exists a moderate tolerance threshold warranting the best promotion of cooperation. We explain the nontrivial results by investigating the time ratio of strategy (network) updating during the whole process and properties in emerging networks. Furthermore, we investigate the effect of memory-dependent discounting of individuals' cooperative environment on the evolution of cooperation. We also demonstrate the robustness of our results by considering two other modified co-evolutionary rules. Our results highlight the importance of appropriate tolerance threshold for the evolution of cooperation during the entangled co-evolution of strategy and structure.

    Microcanonical finite-size scaling in second-order phase transitions with diverging specific heat
    L. A. Fernandez, A. Gordillo-Guerrero, V. Martin-Mayor, and J. J. Ruiz-Lorenzo
    Published 6 November 2009 (13 pages)
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    A microcanonical finite-size ansatz in terms of quantities measurable in a finite lattice allows extending phenomenological renormalization (the so-called quotients method) to the microcanonical ensemble. The ansatz is tested numerically in two models where the canonical specific heat diverges at criticality, thus implying Fisher renormalization of the critical exponents: the three-dimensional ferromagnetic Ising model and the two-dimensional four-state Potts model (where large logarithmic corrections are known to occur in the canonical ensemble). A recently proposed microcanonical cluster method allows simulating systems as large as L=1024 (Potts) or L=128 (Ising). The quotients method provides accurate determinations of the anomalous dimension, eta, and of the (Fisher-renormalized) thermal nu exponent. While in the Ising model the numerical agreement with our theoretical expectations is very good, in the Potts case, we need to carefully incorporate logarithmic corrections to the microcanonical ansatz in order to rationalize our data.

    Equilibrium and linear transport properties of fluids

    Asymptotic current-voltage relations for currents exceeding the diffusion limit
    Ehud Yariv
    Published 6 November 2009 (7 pages)
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    We consider the one-dimensional transport of ions into a perm-selective solid. Direct attempts to evaluate the current-voltage characteristics for currents exceeding the diffusion limit are frustrated by the appearance of nonconverging integrals. We describe how to overcome this obstacle using a regularization scheme.

    Granular materials

    Self-organized patterns in collections of chains
    T. Sykes and T. Mullin
    Published 3 November 2009 (4 pages)
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    Results are presented of an experimental investigation into patterned segregation in thin layers of poppy seeds and short lengths of metal chains subjected to vibration. Critical phenomena are uncovered and both continuous and discontinuous transitions are observed. A phase diagram for the behavior is mapped out and a tricritical point that separates hysteretic from continuous segregation is identified. Remarkable similarities are found between the observed behavior in this driven granular system and phase separation phenomena in mixtures where the dynamics of the constituent components are markedly different.

    Colloidal dispersions, suspensions, and aggregates

    Dynamics of colloids in a narrow channel driven by a nonuniform force
    D. V. Tkachenko, V. R. Misko, and F. M. Peeters
    Published 2 November 2009 (10 pages)
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    Using Brownian dynamics simulations, we investigate the dynamics of colloids confined in two-dimensional narrow channels driven by a nonuniform force Fdr(y). We considered linear-gradient, parabolic, and deltalike driving-force profiles. This driving force induces melting of the colloidal solid (i.e., shear-induced melting), and the colloidal motion experiences a transition from elastic to plastic regime with increasing Fdr. For intermediate Fdr (i.e., in the transition region) the response of the system, i.e., the distribution of the velocities of the colloidal chains upsiloni(y), in general does not coincide with the profile of the driving force Fdr(y), and depends on the magnitude of Fdr, the width of the channel, and the density of colloids. For example, we show that the onset of plasticity is first observed near the boundaries while the motion in the central region is elastic. This is explained by: (i) (in)commensurability between the chains due to the larger density of colloids near the boundaries, and (ii) the gradient in Fdr. Our study provides a deeper understanding of the dynamics of colloids in channels and could be accessed in experiments on colloids (or in dusty plasma) with, e.g., asymmetric channels or in the presence of a gradient potential field.

    Beyond diffusion-limited aggregation kinetics in microparticle suspensions
    Randall M. Erb, Melissa D. Krebs, Eben Alsberg, Bappaditya Samanta, Vincent M. Rotello, and Benjamin B. Yellen
    Published 2 November 2009 (7 pages)
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    Aggregation in nondiffusion limited colloidal particle suspensions follows a temporal power-law dependence that is consistent with classical diffusion limited cluster aggregation models; however, the dynamic scaling exponents observed in these systems are not adequately described by diffusion limited cluster aggregation models, which expect these scaling exponents to be constant over all experimental conditions. We show here that the dynamic scaling exponents for 10  µm particles increase with the particle concentration and the particle-particle free energy of interaction. We provide a semiquantitative explanation for the scaling behavior in terms of the long-ranged particle-particle interaction potential.

    Structure and rheology of SiO2 nanoparticle suspensions under very high shear rates
    J. Chevalier, O. Tillement, and F. Ayela
    Published 6 November 2009 (7 pages)
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    High shear rate experiments have been performed with capillary microviscometers onto SiO2 nanoparticles dispersed in alcohol (so-called nanofluids). The aim of these experiments was to investigate the processes of aggregation and dislocation of the nanoparticles in a shear flow under perikinetic and orthokinetic conditions. Shear rates as high as 2×105  s−1 were obtained in pressure-driven microchannels laminar flows. All the nanofluids under test have displayed a Newtonian behavior but with a strong enhanced viscosity, that is, the consequence of an effective volume concentration higher than the real one. It was possible to determine the average size of the aggregates and to find a correlation between their structure and the range of the hydrodynamic Peclet number at which experiments were performed. These results display a strong evidence of the role of aggregates and support the recent conclusions about the controversy of the thermal properties of nanofluids.

    Structured and complex fluids

    Density nonlinearities in field theories for a toy model of fluctuating nonlinear hydrodynamics of supercooled liquids
    Joonhyun Yeo
    Published 3 November 2009 (11 pages)
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    We study a zero-dimensional version of the fluctuating nonlinear hydrodynamics (FNH) of supercooled liquids originally investigated by Das and Mazenko (DM) [Shankar P. Das and Gene F. Mazenko Phys. Rev. A 34, 2265 (1986)]. The time-dependent density-like and momentum-like variables are introduced with no spatial degrees of freedom in this toy model. The structure of nonlinearities takes the similar form to the original FNH, which allows one to study in a simpler setting the issues raised recently regarding the field theoretical approaches to glass forming liquids. We study the effects of density nonlinearities on the time evolution of correlation and response functions by developing field theoretic formulations in two different ways: first by following the original prescription of DM and then by constructing a dynamical action which possesses a linear time-reversal symmetry as proposed recently. We show explicitly that, at the one-loop order of the perturbation theory, the DM-type field theory does not support a sharp ergodic-nonergodic transition, while the other admits one. The simple nature of the toy model in the DM formulation allows us to develop numerical solutions to a complete set of coupled dynamical equations for the correlation and response functions at the one-loop order.

    Dipolar particles in an external field: Molecular dynamics simulation and mean field theory
    Ran Jia and Reinhard Hentschke
    Published 5 November 2009 (9 pages)
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    Using molecular dynamics computer simulation we compute gas-liquid phase coexistence curves for the Stockmayer fluid in an external electric field. We observe a field-induced shift of the critical temperature DeltaTc. The sign of DeltaTc depends on whether the potential or the surface charge density is held constant assuming that the dielectric material fills the space between capacitor plates. Our own as well as previous literature data for DeltaTc are compared to and interpreted in terms of a simple mean field theory. Despite considerable errors in the simulation results, we find consistency between the simulation results obtained by different groups including our own and the mean field description. The latter ties the sign of DeltaTc to the outside constraints via the electric field dependence of the orientation part of the mean field free energy.

    Films, interfaces, and crystal growth

    Weakly faceted cellular patterns versus growth-induced plastic deformation in thin-sample directional solidification of monoclinic biphenyl
    Tamás Börzsönyi, Silvère Akamatsu, and Gabriel Faivre
    Published 2 November 2009 (11 pages)
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    We present an experimental study of thin-sample directional solidification (T-DS) in impure biphenyl. The platelike growth shape of the monoclinic biphenyl crystals includes two low-mobility (001) facets and four high-mobility {110} facets. Upon T-DS, biphenyl plates oriented with (001) facets parallel to the sample plane can exhibit either a strong growth-induced plastic deformation (GID), or deformation-free weakly faceted (WF) growth patterns. We determine the respective conditions of appearance of these phenomena. GID is shown to be a long-range thermal-stress effect, which disappears when the growth front has a cellular structure. An early triggering of the cellular instability allowed us to avoid GID and study the dynamics of WF patterns as a function of the orientation of the crystal.

    Polymers

    Experimental observation of effects of seeds on polymer crystallization
    Peng-Wei Zhu, Andy Phillips, Graham Edward, and Lance Nichols
    Published 3 November 2009 (9 pages)
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    The effects of two seeds on the melt crystallization of isotactic polypropylene were experimentally investigated. The seed, which has the flat surface full of a nonuniform size distribution, has provided a right surface pattern to activate effectively the heterogeneous nucleation. In contrast, the seed, which has the curved surface full of a uniform size distribution, has failed to induce the heterogeneous nucleation. The results from the present work have also shown that the seed with strong nucleating ability leads to the formation of large crystals but the seed without nucleating ability does not influence much the crystal size.

    Biological physics

    Charge transport in DNA molecules: Cooperative interplay between the disordered base-pair channel and the ordered backbone
    Wei Zhang, Rong Yang, and Sergio E. Ulloa
    Published 4 November 2009 (7 pages)
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    Charge transport in DNA molecules has raised considerable interest because of its importance in biological processes and potential applications in nanoscale devices. A DNA molecule can be viewed as a quasi-one-dimensional system composed of stacked base pairs (AT, CG) together with backbones of sugar phosphates. Motivated by recent experimental observations on the importance of the backbone integrity, we investigate the interplay between charge transport through the ordered backbone and disordered base stacks with random sequences. By analytical and numerical calculations, we find that the coupling between the backbone and base-pair channels plays an important role in charge transport. The backbone can generate effective hopping constants well beyond the adjacent base pairs, enhancing charge transport through the base-pair channel. The corresponding enhancement of the localization length is nearly independent of the length of the DNA and increases with increasing coupling between backbone and base pair. Our model can explain qualitatively several experimental observations.

    Generating variable birdsong syllable sequences with branching chain networks in avian premotor nucleus HVC
    Dezhe Z. Jin
    Published 5 November 2009 (13 pages)
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    Songs of songbird species such as Bengalese finch consist of sequences of syllables. While syllables are temporally stereotypical, syllable sequences can vary and follow complex, probabilistic transition rules. Recent experiments and computational models suggest that a syllable is encoded in a chain network of projection neurons in premotor nucleus HVC (proper name). Precisely timed spikes propagate along the chain, driving vocalization of the syllable through downstream nuclei. However, the neural basis of the probabilistic transitions between the syllables is not understood. Here we propose that variable syllable sequences are generated through spike propagations in a network in HVC in which the syllable-encoding chain networks are connected into a branching chain pattern. The neurons mutually inhibit each other through the inhibitory HVC interneurons, and are driven by external inputs from nuclei upstream of HVC. At a branching point that connects the final group of a chain to the first groups of several chains, the spike activity selects one branch to continue the propagation. The selection is probabilistic, and is due to the winner-take-all mechanism mediated by the inhibition and noise. The transitions between the chains are Markovian. If the same syllable can be driven by multiple chains, the generated syllable sequences are statistically described by partially observable Markov models. We suggest that the syntax of birdsong syllable sequences is embedded in the connection patterns of HVC projection neurons.

    Order-disorder effects in structure and color relation of photonic-crystal-type nanostructures in butterfly wing scales
    Géza I. Márk, Zofia Vértesy, Krisztián Kertész, Zsolt Bálint, and László P. Biró
    Published 5 November 2009 (11 pages)
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    In order to study local and global order in butterfly wing scales possessing structural colors, we have developed a direct space algorithm, based on averaging the local environment of the repetitive units building up the structure. The method provides the statistical distribution of the local environments, including the histogram of the nearest-neighbor distance and the number of nearest neighbors. We have analyzed how the different kinds of randomness present in the direct space structure influence the reciprocal space structure. It was found that the Fourier method is useful in the case of a structure randomly deviating from an ordered lattice. The direct space averaging method remains applicable even for structures lacking long-range order. Based on the first Born approximation, a link is established between the reciprocal space image and the optical reflectance spectrum. Results calculated within this framework agree well with measured reflectance spectra because of the small width and moderate refractive index contrast of butterfly scales. By the analysis of the wing scales of Cyanophrys remus and Albulina metallica butterflies, we tested the methods for structures having long-range order, medium-range order, and short-range order.

    Effect of intrinsic curvature on semiflexible polymers
    Surya K. Ghosh, Kulveer Singh, and Anirban Sain
    Published 5 November 2009 (4 pages)
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    Recently many important biopolymers have been found to possess intrinsic curvature. Tubulin protofilaments in animal cells, FtsZ filaments in bacteria and double stranded DNA are examples. We examine how intrinsic curvature influences the conformational statistics of such polymers. We give exact results for the tangent-tangent spatial correlation function C(r)=<t-hat(s).t-hat(s+r)>, both in two and three dimensions. Contrary to expectation, C(r) does not show any oscillatory behavior, rather decays exponentially and the effective persistence length has strong length dependence for short polymers. We also compute the distribution function P(R) of the end to end distance R and show how curved chains can be distinguished from wormlike chains using loop formation probability.

    Theory of a reconstructive structural transformation in capsids of icosahedral viruses
    S. B. Rochal and V. L. Lorman
    Published 6 November 2009 (6 pages)
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    A theory of a reconstructive structural transformation in icosahedral capsid shells is developed for a whole family of virulent human viruses. It is shown that the reversible rearrangement of proteins during the virus maturation transformation is driven by the variation in the wave number l associated with the protein density distribution function. The collective displacement field of protein centers from their positions in the initial (procapsid) and the final (capsid) two-dimensional icosahderal structures is derived. The amplitude of the displacement field is shown to be small and it minimizes the calculated free energy of the transformation. The theory allows us to propose a continuous thermodynamical mechanism of the reconstructive procapsid-to-capsid transformation. In the frame of the density-wave approach, we also propose to take an equivalent plane-wave vector as a common structural feature for different icosahedral capsid shells formed by the same proteins. Using these characteristics, we explain the relation between the radii of the procapsid and capsid shells and generalize it to the case of the viral capsid polymorphism.

    Dynamical activities of primary somatosensory cortices studied by magnetoencephalography
    Kuniharu Kishida
    Published 6 November 2009 (13 pages)
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    A blind identification method of transfer functions in feedback systems is introduced for examination of dynamical activities of cortices by magnetoencephalography study. Somatosensory activities are examined in 5 Hz periodical median nerve stimulus. In the present paper, we will try two careful preprocessing procedures for the identification method to obtain impulse responses between primary somatosensory cortices. Time series data of the somatosensory evoked field are obtained by using a blind source separation of the T/k type (fractional) decorrelation method. Time series data of current dipoles of primary somatosensory cortices are transformed from the time series data of the somatosensory evoked field by the inverse problem. Fluctuations of current dipoles of them are obtained after elimination of deterministic periodical evoked waveforms. An identification method based on feedback system theory is used for estimation of transfer functions in a feedback model from obtained fluctuations of currents dipoles of primary somatosensory cortices. Dynamical activities between them are presented by Bode diagrams of transfer functions and their impulse responses: the time delay of about 30 ms via corpus callosum is found in the impulse response of identified transfer function.

    BRIEF REPORTS

    Films, interfaces, and crystal growth

    Nanostructure instability induced by anisotropic epitaxial stresses
    Jérôme Colin, Jean Grilhé, and Pierre Müller
    Published 5 November 2009 (4 pages)
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    The morphological evolution of an initially straight stripe assimilated to a straight line of infinite length lying on a semi-infinite substrate has been investigated in the linear regime when the mass transport mechanism is the diffusion of adatoms along stripe edges and when the heteroepitaxy between the line and the substrate is taken to be anisotropic. It is found that contrary to the isotropic case where serpentine-like morphology is favored, antiphase fluctuations grows faster than in-phase ones for selected values of epitaxial stress components such that a pinched shape preferentially emerges.

    Part 2 - Nonlinear and Plasma Physics, Fluid Dynamics, and Related Topics

    ARTICLES

    Interdisciplinary physics

    Phase transitions in traffic flow on multilane roads
    Boris S. Kerner and Sergey L. Klenov
    Published 4 November 2009 (20 pages)
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    Based on empirical and numerical analyses of vehicular traffic, the physics of spatiotemporal phase transitions in traffic flow on multilane roads is revealed. The complex dynamics of moving jams observed in single vehicle data measured by video cameras on American highways is explained by the nucleation-interruption effect in synchronized flow, i.e., the spontaneous nucleation of a narrow moving jam with the subsequent jam dissolution. We find that (i) lane changing, vehicle merging from on-ramps, and vehicle leaving to off-ramps result in different traffic phases—free flow, synchronized flow, and wide moving jams—occurring and coexisting in different road lanes as well as in diverse phase transitions between the traffic phases; (ii) in synchronized flow, the phase transitions are responsible for a non-regular moving jam dynamics that explains measured single vehicle data: moving jams emerge and dissolve randomly at various road locations in different lanes; (iii) the phase transitions result also in diverse expanded general congested patterns occurring at closely located bottlenecks.

    Boolean networks with reliable dynamics
    Tiago P. Peixoto and Barbara Drossel
    Published 6 November 2009 (10 pages)
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    We investigated the properties of Boolean networks that follow a given reliable trajectory in state space. A reliable trajectory is defined as a sequence of states, which is independent of the order in which the nodes are updated. We explored numerically the topology, the update functions, and the state space structure of these networks, which we constructed using a minimum number of links and the simplest update functions. We found that the clustering coefficient is larger than in random networks and that the probability distribution of three-node motifs is similar to that found in gene regulation networks. Among the update functions, only a subset of all possible functions occurs, and they can be classified according to their probability. More homogeneous functions occur more often, leading to a dominance of canalyzing functions. Finally, we studied the entire state space of the networks. We observed that with increasing systems size, fixed points become more dominant, moving the networks close to the frozen phase.

    Chaos and pattern formation

    Principal bifurcations and symmetries in the emergence of reaction-diffusion-advection patterns on finite domains
    Arik Yochelis and Moshe Sheintuch
    Published 2 November 2009 (7 pages)
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    Pattern formation mechanisms of a reaction-diffusion-advection system, with one diffusivity, differential advection, and (Robin) boundary conditions of Danckwerts type, are being studied. Pattern selection requires mapping the domains of coexistence and stability of propagating or stationary nonuniform solutions, which for the general case of far from instability onsets, is conducted using spatial dynamics and numerical continuations. The selection is determined by the boundary conditions which either preserve or destroy the translational symmetry of the model. Accordingly, we explain the criterion and the properties of stationary periodic states if the system is bounded and show that propagation of nonlinear waves (including solitary) against the advective flow corresponds to coexisting family that emerges nonlinearly from a distinct oscillatory Hopf instability. Consequently, the resulting pattern selection is qualitatively different from the symmetric finite wavenumber Turing or Hopf instabilities.

    Asymptotic-boundary-layer method for unstable trajectories: Semiclassical expansions for individual scar wave functions
    A. Vagov, H. Schomerus, and V. V. Zalipaev
    Published 3 November 2009 (8 pages)
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    We extend the asymptotic boundary layer (ABL) method, originally developed for stable resonator modes, to the description of individual wave functions localized around unstable periodic orbits. The formalism applies to the description of scar states in fully or partially chaotic quantum systems, and also allows for the presence of smooth and sharp potentials, as well as magnetic fields. We argue that the separatrix wave function provides the largest contribution to the scars on a single wave function. This agrees with earlier results on the wave-function asymptotics and on the quantization condition of the scar states. Predictions of the ABL formalism are compared with the exact numerical solution for a strip resonator with a parabolic confinement potential and a magnetic field.

    Fluid dynamics

    Mass transport subject to time-dependent flow with nonuniform sorption in porous media
    Marie-Christine Néel, Andrea Zoia, and Maminirina Joelson
    Published 4 November 2009 (13 pages)
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    We address the description of solutes flow with trapping processes in porous media. Starting from a small-scale model for tracer particle trajectories, we derive the corresponding governing equations for the concentration of the mobile and immobile phases within a fractal mobile-immobile model approach. We show that this formulation is fairly general and can easily take into account nonconstant coefficients and in particular space-dependent sorption rates. The transport equations are solved numerically and a comparison with Monte Carlo particle-tracking simulations of spatial contaminant profiles and breakthrough curves is proposed, so as to illustrate the obtained results.

    Large deviation theory for coin tossing and turbulence
    Sagar Chakraborty, Arnab Saha, and Jayanta K. Bhattacharjee
    Published 6 November 2009 (5 pages)
    056302  Full Text: PDF (88 kB)  | Buy Article
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    Large deviations play a significant role in many branches of nonequilibrium statistical physics. They are difficult to handle because their effects, though small, are not amenable to perturbation theory. Even the Gaussian model, which is the usual initial step for most perturbation theories, fails to be a starting point while discussing intermittency in fluid turbulence, where large deviations dominate. Our contention is: in the large deviation theory, the central role is played by the distribution associated with the tossing of a coin and the simple coin toss is the “Gaussian model” of problems where rare events play significant role. We illustrate this by applying it to calculate the multifractal exponents of the order structure factors in fully developed turbulence.

    Plasma physics

    Lower hybrid drift instability in a neutral sheet with O+ ions
    Feng Huang, Yinhua Chen, Hai-Ou Peng, Ju-Gao Zheng, Gui-Fen Shi, Zu-Quan Hu, and M. Y. Yu
    Published 3 November 2009 (5 pages)
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    The electromagnetic lower-hybrid drift instability (LHDI) in the intermediate-wavelength regime kysqrt( rho[sub i] rho[sub e])~1, where ky and rhoe,i are the wave vector and the electron and ion gyroradii, respectively, in a thin plasma sheet containing electrons and H+ and O+ ions is examined using kinetic theory. It is shown that the growth rate of the LHDI first decreases and then increases with increase in the O+ content and temperature, with a minimum at a moderate level of the latter. The results can be relevant to understanding magnetic reconnection in the presence of LHDI.

    Modeling of population kinetics of plasmas that are not in local thermodynamic equilibrium, using a versatile collisional-radiative model based on analytical rates
    R. Florido, R. Rodríguez, J. M. Gil, J. G. Rubiano, P. Martel, E. Mínguez, and R. C. Mancini
    Published 4 November 2009 (18 pages)
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    We discuss the modeling of population kinetics of nonequilibrium steady-state plasmas using a collisional-radiative model and code based on analytical rates (ABAKO). ABAKO can be applied to low-to-high Z ions for a wide range of laboratory plasma conditions: coronal, local thermodynamic equilibrium or nonlocal thermodynamic equilibrium, and optically thin or thick plasmas. ABAKO combines a set of analytical approximations to atomic rates, which yield substantial savings in computer running time, still comparing well with more elaborate codes and experimental data. A simple approximation to calculate the electron capture cross section in terms of the collisional excitation cross section has been adapted to work in a detailed-configuration-accounting approach, thus allowing autoionizing states to be explicitly included in the kinetics in a fast and efficient way. Radiation transport effects in the atomic kinetics due to line trapping in the plasma are taken into account via geometry-dependent escape factors. Since the kinetics problem often involves very large sparse matrices, an iterative method is used to perform the matrix inversion. In order to illustrate the capabilities of the model, we present a number of results which show that the ABAKO compares well with customized models and simulations of ion population distribution. The utility of ABAKO for plasma spectroscopic applications is also outlined.

    Analytical expressions of the front shape of non-quasi-neutral plasma expansions with anisotropic electron pressures
    Yongsheng Huang, Yijin Shi, Yuanjie Bi, Xiaojiao Duan, Naiyan Wang, Xiuzhang Tang, and Zhe Gao
    Published 6 November 2009 (5 pages)
    056403  Full Text: PDF (242 kB)  | Buy Article
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    An analytical expression is proposed to describe the front shape of a non-quasi-neutral plasma expansion with anisotropic electron pressures. It is of significance in the study of ultrashort plasma expansions generated from laser-foil interactions and anisotropic astroplasma expansions in space science. It is found that the plasma front shape depends on the relationship between the ratio of the longitudinal and the transverse temperature of hot electrons kappa2 and the electron-ion mass ratio µ. For kappa2[is-an-element-of](µ,1], the ion front is a part of an ellipse and the major axis is in the lower-temperature axis. For kappa2<=µ, the ion front is composed by a part of a hyperbolic and a small pointed projection at the center. In the strongly anisotropic region, there is an ultrashort anomalous plasma emission of tens of femtoseconds at the angle of near 90°. The ion-velocity distribution and angular-energy distribution at the ion front have also been given. Particularly, anomalous positron emissions exist in the electron-positron plasma anisotropic expansion.

    BRIEF REPORTS

    Interdisciplinary physics

    Distribution for the number of coauthors
    Jiann-wien Hsu and Ding-wei Huang
    Published 4 November 2009 (4 pages)
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    We study the coauthorship distribution by analyzing the number of coauthors on each paper published in Physical Review Letters and Physical Review for the last decade. We propose that the structure of the distribution can be understood as the result of a two-parameter Poisson process. We develop a dynamic model of dual mechanisms to simulate the personal and group collaborations. In this model, the single-author papers are portrayed as a leftover from the collaboration process. We also comment on the huge collaborations involving hundreds of coauthors.