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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
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  • RAPID COMMUNICATIONS
  • ARTICLES
  • BRIEF REPORTS
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    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)
    050102(R)  Full Text: PDF (481 kB)  | Buy Article
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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.

    Semiclassical treatment of a Brownian ratchet using the quantum Smoluchowski equation
    Liam Cleary, William T. Coffey, Yuri P. Kalmykov, and Serguey V. Titov
    Published 9 November 2009 (14 pages)
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    Quantum effects in the noninertial Brownian motion of a particle in a one-dimensional ratchet potential are treated in the high temperature and weak bath-particle coupling limit by solving a quantum Smoluchowski equation for the time evolution of the Wigner function in configuration space. In particular, an analytical expression for the stationary average drift velocity for constant driving forces is presented including quantum corrections to any order in Planck's constant. The corresponding frequency response is determined using continued fractions in both the linear approximation holding for small ac driving amplitude and in the nonlinear regime for arbitrary driving amplitude exhibiting pronounced ac induced frequency dependence of the dc component of the average drift velocity. Moreover, Shapiro steps are apparent in the dc characteristics for strong ac driving just as in the dc current-voltage characteristics of a point Josephson junction.

    Fluctuation relations for diffusion that is thermally driven by a nonstationary bath
    Raphaël Chetrite
    Published 10 November 2009 (9 pages)
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    In the context of the Markovian dynamical evolution in a nonstationary thermal bath, we construct a family of fluctuation relations for the entropy production that are not verified by the work performed on the system. We exhibit fluctuation relations, which are global versions either of the generalized fluctuation-dissipation theorem around a nonequilibrium diffusion or of the usual fluctuation-dissipation theorem for energy resulting from a pulse of temperature.

    Avalanche dynamics of fiber bundle models
    R. C. Hidalgo, F. Kun, K. Kovács, and I. Pagonabarraga
    Published 10 November 2009 (8 pages)
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    We present a detailed analytical and numerical study of the avalanche distributions of the continuous damage fiber bundle model (CDFBM). Linearly elastic fibers undergo a series of partial failure events which give rise to a gradual degradation of their stiffness. We show that the model reproduces a wide range of mechanical behaviors. We find that macroscopic hardening and plastic responses are characterized by avalanche distributions, which exhibit an algebraic decay with exponents between 5/2 and 2 different from those observed in mean-field fiber bundle models. We also derive analytically the phase diagram of a family of CDFBM which covers a large variety of potential avalanche size distributions. Our results provide a unified view of the statistics of breaking avalanches in fiber bundle models.

    Escape dynamics of coupled particles in nonlinear, disordered lattices
    K. Manski and D. Hennig
    Published 10 November 2009 (12 pages)
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    We consider the deterministic escape dynamics of a lattice chain of harmonically coupled particles from a metastable state over a one-dimensional potential barrier. While the case of periodic lattices has already been elaborated, the aim of the present work is to explore the extension to nonperiodic, i.e., disordered, lattices. Each particle evolves in an individual local potential, which is characterized by a harmonic term and a nonlinear term. Two kinds of parametric disorder are considered. “Disorder in nonlinearity” is only caused by different nonlinear terms—“disorder in harmonicity” only by different harmonic terms. We assure that the two kinds of disorder, with their individual potential barriers uniformly distributed around a globally equal mean barrier height, exhibit a comparable strength of disorder. Starting with an initial completely delocalized state, we observe localization of energy and formation of breathers ensues. It is shown that increasing disorder in nonlinearity decreases the mean escape time opposite to increasing mean escape times resulting from increased disorder in harmonicity. Comparison with the mean escape time obtained for a third kind of parametric disorder characterized by overall equal barrier heights leads to the conclusion that indeed inhomogeneous barriers facilitate the speedy escape.

    Diffusion in the special theory of relativity
    Joachim Herrmann
    Published 11 November 2009 (9 pages)
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    The Markovian diffusion theory is generalized within the framework of the special theory of relativity. Since the velocity space in relativity is a hyperboloid, the mathematical stochastic calculus on Riemanian manifolds can be applied but adopted here to the velocity space. A generalized Langevin equation in the fiber space of position, velocity, and orthonormal velocity frames is defined from which the generalized relativistic Kramers equation in the phase space in external force fields is derived. The obtained diffusion equation is invariant under Lorentz transformations and its stationary solution is given by the Jüttner distribution. Besides, a nonstationary analytical solution is derived for the example of force-free relativistic diffusion.

    Ab initio method for locating characteristic potential-energy minima of liquids
    E. Holmström, N. Bock, Travis B. Peery, R. Lizárraga, G. De Lorenzi-Venneri, Eric D. Chisolm, and Duane C. Wallace
    Published 12 November 2009 (7 pages)
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    It is possible in principle to probe the many-atom potential surface using density functional theory (DFT). This will allow us to apply DFT to the Hamiltonian formulation of atomic motion in monatomic liquids by Wallace [Phys. Rev. E 56, 4179 (1997)]. For a monatomic system, analysis of the potential surface is facilitated by the random and symmetric classification of potential-energy valleys. Since the random valleys are numerically dominant and uniform in their macroscopic potential properties, only a few quenches are necessary to establish these properties. Here we describe an efficient technique for doing this. Quenches are done from easily generated “stochastic” configurations, in which the nuclei are distributed uniformly within a constraint limiting the closeness of approach. For metallic Na with atomic pair potential interactions, it is shown that quenches from stochastic configurations and quenches from equilibrium liquid molecular dynamics configurations produce statistically identical distributions of the structural potential energy. Again for metallic Na, it is shown that DFT quenches from stochastic configurations provide the parameters which calibrate the Hamiltonian. A statistical mechanical analysis shows how the underlying potential properties can be extracted from the distributions found in quenches from stochastic configurations.

    Hard versus soft dynamics for adsorption-desorption kinetics: Exact results in one-dimension
    S. J. Manzi, V. J. Huespe, R. E. Belardinelli, and V. D. Pereyra
    Published 12 November 2009 (15 pages)
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    The adsorption-desorption kinetics is discussed in the framework of the kinetic lattice-gas model. The master equation formalism has been introduced to describe the evolution of the system, where the transition probabilities are written as an expansion of the occupation configurations of all neighboring sites. Since the detailed balance principle determines half of the coefficients that arise from the expansion, it is necessary to introduce ad hoc, a dynamic scheme to get the rest of them. Three schemes of the so-called hard dynamics, in which the probability of transition from single site cannot be factored into a part which depends only on the interaction energy and one that only depends on the field energy, and five schemes of the so-called soft dynamics, in which this factorization is possible, were introduced for this purpose. It is observed that for the hard dynamic schemes, the equilibrium and nonequilibrium observables, such as adsorption isotherms, sticking coefficients, and thermal desorption spectra, have a normal or physical sustainable behavior. While for the soft dynamics schemes, with the exception of the transition state theory, the equilibrium and nonequilibrium observables have several problems. Some of them can be regarded as abnormal behavior.

    Multiplicative Lévy processes: Itô versus Stratonovich interpretation
    Tomasz Srokowski
    Published 12 November 2009 (8 pages)
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    Langevin equation with a multiplicative stochastic force is considered. That force is uncorrelated, it has the Lévy distribution and the power-law intensity. The Fokker-Planck equations, which correspond both to the Itô and Stratonovich interpretation, are presented. They are solved for the case without drift and for the harmonic oscillator potential. The variance is evaluated; it is always infinite for the Itô case whereas for the Stratonovich one it can be finite and rise with time slower that linearly, which indicates subdiffusion. Analytical results are compared with numerical simulations.

    Coagulation reactions in low dimensions: Revisiting subdiffusive A+A reactions in one dimension
    S. B. Yuste, J. J. Ruiz-Lorenzo, and Katja Lindenberg
    Published 13 November 2009 (11 pages)
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    We present a theory for the coagulation reaction A+A-->A for particles moving subdiffusively in one dimension. Our theory is tested against numerical simulations of the concentration of A particles as a function of time (“anomalous kinetics”) and of the interparticle distribution function as a function of interparticle distance and time. We find that the theory captures the correct behavior asymptotically and also at early times, and that it does so whether the particles are nearly diffusive or very subdiffusive. We find that, as in the normal diffusion problem, an interparticle gap responsible for the anomalous kinetics develops and grows with time. This corrects an earlier claim to the contrary on our part.

    Velocity and cluster distributions in a bottleneck system
    Vidar Frette and Per C. Hemmer
    Published 13 November 2009 (9 pages)
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    Velocity and cluster distributions for particles with unidirectional motion in one dimension are studied. The particles never pass each other, like cars on a narrow road that does not allow overtaking. As a result, particles cluster behind slow particles (queues are formed behind slow cars). Thus, the actual velocity of each particle is to a large extent determined by slow particles further ahead. Considering all possible permutations of N particles with initial velocities {vi}, the average number of particles with actual velocity vi is (N+1)/[i(i+1)] (in the sequence {vi}, the initial velocities are listed with monotonically increasing values). For i large and vi[proportional]i the average number of actual velocities is thus a power law in vi, even though the average cluster density is found to be independent of cluster size, L. On the other hand, the cluster density varies significantly with cluster velocity; we obtain [(N−i)!(N−L)!]/[N·N!(N−L−i+1)!]. The average velocity at a given position in the sequence of N particles, and the average global velocity are determined. Explicit results for several distributions of the initial velocities show that the global velocity depends sensitively on the form of this distribution.
    Physics Viewpoint

    Experimental realization of directed percolation criticality in turbulent liquid crystals
    Kazumasa A. Takeuchi, Masafumi Kuroda, Hugues Chaté, and Masaki Sano
    Published 16 November 2009 (12 pages)
    051116  Full Text: PDF (957 kB)  | Buy Article
    See accompanying Viewpoint Physics 2, 96 (2009)
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    This is a comprehensive report on the phase transition between two turbulent states of electroconvection in nematic liquid crystals, which was recently found by the authors to be in the directed percolation (DP) universality class [K. A. Takeuchi et al., Phys. Rev. Lett. 99, 234503 (2007)]. We further investigate both static and dynamic critical behaviors of this phase transition, measuring a total of 12 critical exponents, 5 scaling functions, and 8 scaling relations, all in full agreement with those characterizing the DP class in 2+1 dimensions. Developing an experimental technique to create a seed of topological-defect turbulence by pulse laser, we confirm in particular the rapidity symmetry, which is a basic but nontrivial consequence of the field-theoretic approach to DP. This provides a clear experimental realization of this outstanding truly out-of-equilibrium universality class, dominating most phase transitions into an absorbing state.

    Phase diagram and critical behavior of the square-lattice Ising model with competing nearest-neighbor and next-nearest-neighbor interactions
    Junqi Yin and D. P. Landau
    Published 17 November 2009 (8 pages)
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    Using the parallel tempering algorithm and graphics processing unit accelerated techniques, we have performed large-scale Monte Carlo simulations of the Ising model on a square lattice with antiferromagnetic (repulsive) nearest-neighbor and next-nearest-neighbor interactions of the same strength and subject to a uniform magnetic field. Both transitions from the (2×1) and row-shifted (2×2) ordered phases to the paramagnetic phase are continuous. From our data analysis, re-entrance behavior of the (2×1) critical line and a bicritical point which separates the two ordered phases at T=0 are confirmed. Based on the critical exponents we obtained along the phase boundary, Suzuki's weak universality seems to hold.

    Asymptotic shape of the region visited by an Eulerian walker
    Rajeev Kapri and Deepak Dhar
    Published 19 November 2009 (7 pages)
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    We study an Eulerian walker on a square lattice, starting from an initial randomly oriented background using Monte Carlo simulations. We present evidence that, for a large number of steps N, the asymptotic shape of the set of sites visited by the walker is a perfect circle. The radius of the circle increases as N1/3, for large N, and the width of the boundary region grows as Nalpha/3, with alpha=0.40±0.06. If we introduce stochasticity in the evolution rules, the mean-square displacement of the walker, <RN<sup>2</sup>>~N2nu, shows a crossover from the Eulerian (nu=1/3) to a simple random-walk (nu=1/2) behavior.

    Queueing process with excluded-volume effect
    Chikashi Arita
    Published 20 November 2009 (10 pages)
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    We introduce an extension of the M/M/1 queueing process with a spatial structure and excluded-volume effect. The rule of particle hopping is the same as for the totally asymmetric simple exclusion process (TASEP). A stationary-state solution is constructed in a slightly arranged matrix product form of the open TASEP. We obtain the critical line that separates the parameter space depending on whether the model has the stationary state. We calculate the average length of the model and the number of particles and show the monotonicity of the probability of the length in the stationary state. We also consider a generalization of the model with backward hopping of particles allowed and an alternate joined system of the M/M/1 queueing process and the open TASEP.

    Trapping in scale-free networks with hierarchical organization of modularity
    Zhongzhi Zhang, Yuan Lin, Shuyang Gao, Shuigeng Zhou, Jihong Guan, and Mo Li
    Published 20 November 2009 (8 pages)
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    A wide variety of real-life networks share two remarkable generic topological properties: scale-free behavior and modular organization, and it is natural and important to study how these two features affect the dynamical processes taking place on such networks. In this paper, we investigate a simple stochastic process—trapping problem, a random walk with a perfect trap fixed at a given location, performed on a family of hierarchical networks that exhibit simultaneously striking scale-free and modular structure. We focus on a particular case with the immobile trap positioned at the hub node having the largest degree. Using a method based on generating functions, we determine explicitly the mean first-passage time (MFPT) for the trapping problem, which is the mean of the node-to-trap first-passage time over the entire network. The exact expression for the MFPT is calculated through the recurrence relations derived from the special construction of the hierarchical networks. The obtained rigorous formula corroborated by extensive direct numerical calculations exhibits that the MFPT grows algebraically with the network order. Concretely, the MFPT increases as a power-law function of the number of nodes with the exponent much less than 1. We demonstrate that the hierarchical networks under consideration have more efficient structure for transport by diffusion in contrast with other analytically soluble media including some previously studied scale-free networks. We argue that the scale-free and modular topologies are responsible for the high efficiency of the trapping process on the hierarchical networks.

    Negative mobility induced by colored thermal fluctuations
    M. Kostur, J. Luczka, and P. Hänggi
    Published 20 November 2009 (7 pages)
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    Anomalous transport of non-Markovian thermal Brownian particle dynamics in spatially periodic symmetric systems that is driven by time-periodic symmetric driving and constant bias is investigated numerically. The Brownian dynamics is modeled by a generalized Langevin equation with exponentially correlated Gaussian thermal noise, obeying the fluctuation-dissipation theorem. We study the role of nonzero correlation time of thermal fluctuations for the occurrence of absolute negative (linear) mobility (ANM) near zero bias, negative-valued, nonlinear mobility (NNM), and negative differential mobility (NDM) at finite bias away from equilibrium. We detect that a nonzero thermal correlation time can either enhance or also diminish the value of ANM. Moreover, finite thermal noise correlation can induce NDM and NNM in regions of parameter space for which such ANM and NNM behaviors are distinctly absent for limiting white thermal noise. In parts of the parameter space, we find a complex structure of regions of linear and nonlinear negative mobility: islands and tongues which emerge and vanish under parameters manipulation. While certain such anomalous transport regimes fade away with increasing temperature some specific regions interestingly remain rather robust. Outside those regimes with anomalous mobility, the ac/dc driven transport is either normal or the driven Brownian particles are not transported at all.

    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.

    Boltzmann equation and hydrodynamic fluctuations
    Matteo Colangeli, Martin Kröger, and Hans Christian Öttinger
    Published 10 November 2009 (12 pages)
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    We apply the method of invariant manifolds to derive equations of generalized hydrodynamics from the linearized Boltzmann equation and determine exact transport coefficients, obeying Green-Kubo formulas. Numerical calculations are performed in the special case of Maxwell molecules. We investigate, through the comparison with experimental data and former approaches, the spectrum of density fluctuations and address the regime of finite Knudsen numbers and finite frequencies hydrodynamics.

    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.

    Theory of activated-rate processes under shear with application to shear-induced aggregation of colloids
    Alessio Zaccone, Hua Wu, Daniele Gentili, and Massimo Morbidelli
    Published 16 November 2009 (8 pages)
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    Using an approximation scheme within the convective diffusion (two-body Smoluchowski) equation framework, we unveil the shear-driven aggregation mechanism at the origin of structure formation in sheared colloidal systems. The theory, verified against numerics and experiments, explains the induction time followed by explosive (irreversible) rise of viscosity observed in charge-stabilized colloidal and protein systems under steady shear. The Arrhenius-type equation with shear derived here, extending Kramers' theory in the presence of shear, clearly demonstrates the important role of shear drive in activated-rate processes as they are encountered in soft condensed matter.

    Triangular tessellation scheme for the adsorption free energy at the liquid-liquid interface: Towards nonconvex patterned colloids
    Joost de Graaf, Marjolein Dijkstra, and René van Roij
    Published 17 November 2009 (19 pages)
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    We present a numerical technique, namely, triangular tessellation, to calculate the free energy associated with the adsorption of a colloidal particle at a flat interface. The theory and numerical scheme presented here are sufficiently general to handle nonconvex patchy colloids with arbitrary surface patterns characterized by a wetting angle, e.g., amphiphilicity. We ignore interfacial deformation due to capillary, electrostatic, or gravitational forces, but the method can be extended to take such effects into account. It is verified that the numerical method presented is accurate and sufficiently stable to be applied to more general situations than presented in this paper. The merits of the tessellation method prove to outweigh those of traditionally used semianalytic approaches, especially when it comes to generality and applicability.

    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.

    Growth and melting of droplets in cold vapors
    Jean-Marc L'Hermite
    Published 13 November 2009 (14 pages)
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    A model has been developed to investigate the growth of droplets in a supersaturated cold vapor taking into account their possible solid-liquid phase transition. It is shown that the solid-liquid phase transition is nontrivially coupled, through the energy released in attachment, to the nucleation process. The model is based on the one developed by J. Feder, K. C. Russell, J. Lothe, and G. M. Pound [Adv. Phys. 15, 111 (1966)], where the nucleation process is described as a thermal diffusion motion in a two-dimensional field of force given by the derivatives of a free-energy surface. The additional dimension accounts for droplets internal energy. The solid-liquid phase transition is introduced through a bimodal internal energy distribution in a Gaussian approximation derived from small clusters physics. The coupling between nucleation and melting results in specific nonequilibrium thermodynamical properties, exemplified in the case of water droplets. Analyzing the free-energy landscapes gives an insight into the nucleation dynamics. This landscape can be complex but generally exhibits two paths: the first one can generally be ascribed to the solid state, while the other to the liquid state. Especially at high supersaturation, the growth in the liquid state is often favored, which is not unexpected since in a supersaturated vapor the droplets can stand higher internal energy than at equilibrium. From a given critical temperature that is noticeably lower than the bulk melting temperature, nucleation may end in very large liquid droplets. These features can be qualitatively generalized to systems other than water.

    Liquid crystals

    Quenched random disorder and x-ray scattering in smectic elastomers
    L. T. Witkowski and E. M. Terentjev
    Published 10 November 2009 (8 pages)
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    In this work we examine layer fluctuations in a smectic elastomer with quenched random disorder induced by crosslinks. The system is analyzed in a continuum model and crosslinks are introduced as a random field in a macroscopic picture. In the case of small deformations and replica symmetry the intensity profile for x-ray scattering along the layer normal was determined for layer displacements smaller than the layer separation. In this regime it is predicted that for large enough crosslink densities the first-order diffraction pattern of the solid assumes a characteristic squared-Lorentzian form, showing a decay of short-range order over a length scale of 20 nm. Crosslinks are observed to disorder the system by decreasing the correlation length, which we show not to be a consequence of the random field. The coupling to random crosslinks is predicted to retard the decrease in the correlation length and hence found to stabilize the one-dimensional periodic layer structure against thermal fluctuations. The dependence of the correlation length on the crosslink density leads us to propose an estimate for the percolation limit of a smectic elastomer network.

    Dielectrophoretic and electrophoretic force analysis of colloidal fullerenes in a nematic liquid-crystal medium
    Anoop Kumar Srivastava, Miyoung Kim, Sung Min Kim, Mi-Kyung Kim, Kyu Lee, Young Hee Lee, Myong-Hoon Lee, and Seung Hee Lee
    Published 16 November 2009 (6 pages)
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    This research focuses on the electrokinetic motion of fullerenes suspended in liquid crystal host medium, which are investigated in the homogeneously aligned nematic liquid crystal cells driven by in-plane field. We investigated the effect of electrophoretic and dielectrophoretic forces and related parameters of the colloidal fullerenes in liquid crystals. The electrophoretic mobility, zeta potential, and critical voltage have been evaluated. Fullerenes suspended in liquid crystal medium migrated toward the positive electrode, but were pulled back in the opposite direction when the polarity was reversed especially at low frequency range (<5  Hz). At higher electric field and higher frequency ranges, the net displacement of fullerenes has been observed. We demonstrate that the dielectrophoretic force dominated the motion in the colloidal fullerenes by a proper analysis of different electrophoretic parameters. In addition, the electrodynamics of fullerenes was explained by applying the theory of the dielectrophoresis and Schwarz's formula. We propose a model to estimate the density of fullerenes suspended in liquid crystal medium.

    Extrinsic curvature, geometric optics, and lamellar order on curved substrates
    Randall D. Kamien, David R. Nelson, Christian D. Santangelo, and Vincenzo Vitelli
    Published 18 November 2009 (12 pages)
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    When thermal energies are weak, two-dimensional lamellar structures confined on a curved substrate display complex patterns arising from the competition between layer bending and compression in the presence of geometric constraints. We present broad design principles to engineer the geometry of the underlying substrate so that a desired lamellar pattern can be obtained by self-assembly. Two distinct physical effects are identified as key factors that contribute to the interaction between the shape of the underlying surface and the resulting lamellar morphology. The first is a local ordering field for the direction of each individual layer, which tends to minimize its curvature with respect to the three-dimensional embedding. The second is a nonlocal effect controlled by the intrinsic geometry of the surface that forces the normals to the (nearly incompressible) layers to lie on geodesics, leading to caustic formation as in optics. As a result, different surface morphologies with predominantly positive or negative Gaussian curvature can act as converging or diverging lenses, respectively. By combining these ingredients, as one would with different optical elements, complex lamellar morphologies can be obtained. This smectic optometry enables the manipulation of lamellar configurations for the design of materials.

    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.

    Aging dynamics in the polymer glass of poly(2-chlorostyrene): Dielectric susceptibility and volume
    Koji Fukao and Daisuke Tahara
    Published 10 November 2009 (11 pages)
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    Aging dynamics was investigated in the glassy states of poly(2-chlorostyrene) by measuring the complex electrical capacitance during aging below the glass transition temperature. The variations with time and temperature of the ac dielectric susceptibility and volume could be determined by simply measuring the variation in the complex electrical capacitance. Isothermal aging at a given temperature for several hours after an intermittent stop in constant-rate cooling is stored in the deviations of both the real and imaginary parts of the complex ac dielectric susceptibility and volume. During cooling after isothermal aging, the deviation of the ac dielectric susceptibility from the reference value decreases and almost vanishes at room temperature. By contrast, the deviation in volume induced during isothermal aging remains almost constant during cooling. The simultaneous measurement of ac dielectric susceptibility and volume clearly revealed that the ac dielectric susceptibility exhibits a full rejuvenation effect, whereas the volume does not show any rejuvenation effects. We discuss a plausible model that can reproduce the present experimental results.

    Ordering of a lamella-forming fluid near an interface
    Andrew B. Croll, An-Chang Shi, and Kari Dalnoki-Veress
    Published 11 November 2009 (5 pages)
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    By using wedged thin films, we have measured the effect of interfaces on the ordering of an anisotropic fluid in real space. Symmetric diblock copolymers can form an ordered lamellar fluid, and the preference of the substrate for one of the blocks can induce order well into the disordered bulk phase. The induced order decays away from the substrate with a length scale that diverges at the bulk ordering transition. Ordering and disordering kinetics are found to differ: all layers relax identically upon disordering, whereas the formation of lamellae is found to vary with the distance from the substrate and can be understood from the time-dependent Ginzburg-Landau theory.

    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.

    Model for amorphous aggregation processes
    Samuel D. Stranks, Heath Ecroyd, Steven Van Sluyter, Elizabeth J. Waters, John A. Carver, and Lorenz von Smekal
    Published 9 November 2009 (13 pages)
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    The amorphous aggregation of proteins is associated with many phenomena, ranging from the formation of protein wine haze to the development of cataract in the eye lens and the precipitation of recombinant proteins during their expression and purification. While much literature exists describing models for linear protein aggregation, such as amyloid fibril formation, there are few reports of models which address amorphous aggregation. Here, we propose a model to describe the amorphous aggregation of proteins which is also more widely applicable to other situations where a similar process occurs, such as in the formation of colloids and nanoclusters. As first applications of the model, we have tested it against experimental turbidimetry data of three proteins relevant to the wine industry and biochemistry, namely, thaumatin, a thaumatinlike protein, and alpha-lactalbumin. The model is very robust and describes amorphous experimental data to a high degree of accuracy. Details about the aggregation process, such as shape parameters of the aggregates and rate constants, can also be extracted.

    Formation and growth of lipofuscin in the retinal pigment epithelium cells
    K. I. Mazzitello, C. M. Arizmendi, F. Family, and H. E. Grossniklaus
    Published 12 November 2009 (7 pages)
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    The kinetics of lipofuscin growth in diseased retinal pigment epithelium cells is investigated using Monte Carlo simulations and scaling theory on a cluster aggregation model. The model captures the essential physics of lipofuscin growth in the cells. A remarkable feature is that small particles may be removed from the cells while the larger ones become fixed and grow by aggregation. Model simulations are compared to the number of lipofuscin granules in eyes with early age-related degeneration.

    Detection of protein secondary structures via the discrete wavelet transform
    Jesús Pando, Luke Sands, and Sean E. Shaheen
    Published 16 November 2009 (10 pages)
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    We subject the primary sequence of proteins gathered from the Structural Classification of Proteins (SCOP) database to a discrete wavelet transform (DWT) analysis to search for predictors of secondary structures. We use proteins with both alpha helices and beta sheets (the A/B, A+B databases from SCOP). The amino acids composing the protein are converted to their hydrophobicity values using three hydrophobicity scales. Results prove to be independent of the scale used. Using a DWT multiresolution decomposition, each protein is coarse grained, in effect, creating snapshots of each protein at multiple scales. For each protein, a control data set is formed by generating random realizations that remove the positional informational in the sequence but still contain the same amino acid frequencies. Regions of salient hydrophobicity in the protein sequence are identified by comparing the transforms of the original sequence with those of the control set, at each resolution. We find significant matching between regions of salient hydrophobicity and the locations of secondary structure along the amino acid chains. We calculate the sensitivity, specificity, and Matthews correlation to quantify the agreement between the wavelet detected structures and the real protein. In addition we are able to distinguish between the morphologically different subsets, A/B and A+B. We also construct a correlation function based on the DWT that correlates quasilocalized structures at lengths in wavelet space. Through a similar comparison to the control data sets, features in this space-scale correlation are identified that show correspondence to the typical lengths of the secondary structures.

    Growing heterogeneous tumors in silico
    Jana Gevertz and S. Torquato
    Published 16 November 2009 (12 pages)
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    An in silico tool that can be utilized in the clinic to predict neoplastic progression and propose individualized treatment strategies is the holy grail of computational tumor modeling. Building such a tool requires the development and successful integration of a number of biophysical and mathematical models. In this paper, we work toward this long-term goal by formulating a cellular automaton model of tumor growth that accounts for several different inter-tumor processes and host-tumor interactions. In particular, the algorithm couples the remodeling of the microvasculature with the evolution of the tumor mass and considers the impact that organ-imposed physical confinement and environmental heterogeneity have on tumor size and shape. Furthermore, the algorithm is able to account for cell-level heterogeneity, allowing us to explore the likelihood that different advantageous and deleterious mutations survive in the tumor cell population. This computational tool we have built has a number of applications in its current form in both predicting tumor growth and predicting response to treatment. Moreover, the latent power of our algorithm is that it also suggests other tumor-related processes that need to be accounted for and calls for the conduction of new experiments to validate the model's predictions.

    Enhanced low-Reynolds-number propulsion in heterogeneous viscous environments
    A. M. Leshansky
    Published 18 November 2009 (13 pages)
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    It has been known for some time that some microorganisms can swim faster in high-viscosity gel-forming polymer solutions. These gel-like media come to mimic highly viscous heterogeneous environment that these microorganisms encounter in-vivo. The qualitative explanation of this phenomena first offered by Berg and Turner [Nature (London) 278, 349 (1979)], suggests that propulsion enhancement is a result of flagellum pushing on quasi-rigid loose polymer network formed in some polymer solutions. Inspired by these observations, inertia-less propulsion in a heterogeneous viscous medium composed of sparse array of stationary obstacles embedded into a incompressible Newtonian liquid is considered. It is demonstrated that for prescribed propulsion gaits, including propagating surface distortions and rotating helical filament, the propulsion speed is enhanced when compared to swimming in purely viscous solvent. It is also shown that the locomotion in heterogenous viscous media is characterized by improved hydrodynamic efficiency. The results of the rigorous numerical simulation of the rotating helical filament propelled through a random sparse array of stationary obstructions are in close agreement with predictions of the proposed resistive force theory based on effective media approximation.

    Statistical physics of cerebral embolization leading to stroke
    J. P. Hague and E. M. L. Chung
    Published 18 November 2009 (9 pages)
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    We discuss the physics of embolic stroke using a minimal model of emboli moving through the cerebral arteries. Our model of the blood flow network consists of a bifurcating tree into which we introduce particles (emboli) that halt flow on reaching a node of similar size. Flow is weighted away from blocked arteries inducing an effective interaction between emboli. We justify the form of the flow weighting using a steady flow (Poiseuille) analysis and a more complicated nonlinear analysis. We discuss free flowing and heavily congested limits and examine the transition from free flow to congestion using numerics. The correlation time is found to increase significantly at a critical value and a finite-size scaling is carried out. An order parameter for nonequilibrium critical behavior is identified as the overlap of blockages' flow shadows. Our work shows embolic stroke to be a feature of the cerebral blood flow network on the verge of a phase transition.

    Arterial wall tethering as a distant boundary condition
    S. Hodis and M. Zamir
    Published 18 November 2009 (7 pages)
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    A standing difficulty in the problem of blood vessel tethering has been that only one of the two required boundary conditions can be fully specified, namely, that at the inner (endothelial) wall surface. The other, at the outer layer of the vessel wall, is not known except in the limiting case where the wall is fully tethered such that its outer layer is prevented from any displacement. In all other cases, where the wall is either free or partially tethered, a direct boundary condition is not available. We present a method of determining this missing boundary condition by considering the limiting case of a semi-infinite wall. The result makes it possible to define the degree of tethering imposed by surrounding tissue more accurately in terms of the displacement of the outer layer of the vessel wall, rather than in terms of equivalent added mass which has been done in the past. This new approach makes it possible for the first time to describe the effect of partial tethering in its full range, from zero to full tethering. The results indicate that high tethering leads to high stresses and low displacements within the vessel wall, while low tethering leads to low stresses and high displacements. Since both extremes would be damaging to wall tissue, particularly elastin, this suggest that moderate tethering would be optimum in the physiological setting.

    Response of a Hodgkin-Huxley neuron to a high-frequency input
    L. S. Borkowski
    Published 19 November 2009 (6 pages)
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    We study the response of a Hodgkin-Huxley neuron stimulated by a periodic sequence of conductance pulses arriving through the synapse in the high-frequency regime. In addition to the usual excitation threshold there is a smooth crossover from the firing to the silent regime for increasing pulse amplitude gsyn. The amplitude of the voltage spikes decreases approximately linearly with gsyn. In some regions of parameter space the response is irregular, probably chaotic. In the chaotic regime between the mode-locked regions 3:1 and 2:1 near the lower excitation threshold, the output interspike interval histogram (ISIH) undergoes a sharp transition. If the driving period is below the critical value, Ti<T*, the output histogram contains only odd multiples of Ti. For Ti>T* even multiples of Ti also appear in the histogram, starting from the largest values. Near T* the ISIH scales logarithmically on both sides of the transition. The coefficient of variation of ISIH has a cusp singularity at T*. The average response period has a maximum slightly above T*. Near the excitation threshold in the chaotic regime the average firing rate rises sublinearly from frequencies of order 1 Hz.

    Cluster approximations for infection dynamics on random networks
    G. Rozhnova and A. Nunes
    Published 20 November 2009 (12 pages)
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    In this paper, we consider a simple stochastic epidemic model on large regular random graphs and the stochastic process that corresponds to this dynamics in the standard pair approximation. Using the fact that the nodes of a pair are unlikely to share neighbors, we derive the master equation for this process and obtain from the system size expansion the power spectrum of the fluctuations in the quasistationary state. We show that whenever the pair approximation deterministic equations give an accurate description of the behavior of the system in the thermodynamic limit, the power spectrum of the fluctuations measured in long simulations is well approximated by the analytical power spectrum. If this assumption breaks down, then the cluster approximation must be carried out beyond the level of pairs. We construct an uncorrelated triplet approximation that captures the behavior of the system in a region of parameter space where the pair approximation fails to give a good quantitative or even qualitative agreement. For these parameter values, the power spectrum of the fluctuations in finite systems can be computed analytically from the master equation of the corresponding stochastic process.

    Scaling and self-organized criticality in proteins: Lysozyme c
    J. C. Phillips
    Published 20 November 2009 (8 pages)
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    Proteins appear to be the most dramatic natural example of self-organized criticality (SOC), a concept that explains many otherwise apparently unlikely phenomena. Protein functionality is often dominated by long-range hydro(phobic/philic) interactions, which both drive protein compaction and mediate protein-protein interactions. In contrast to previous reductionist short-range hydrophobicity scales, the holistic Moret-Zebende hydrophobicity scale [Phys. Rev. E 75, 011920 (2007)] represents a hydroanalytic tool that bioinformatically quantifies SOC in a way fully compatible with evolution. Hydroprofiling identifies chemical trends in the activities and substrate binding abilities of model enzymes and antibiotic animal lysozymes c, as well as defensins, which have been the subject of tens of thousands of experimental studies. The analysis is simple and easily performed and immediately yields insights not obtainable by traditional methods based on short-range real-space interactions, as described either by classical force fields used in molecular-dynamics simulations, or hydrophobicity scales based on transference energies from water to organic solvents or solvent-accessible areas.

    Phase statistics approach to human ventricular fibrillation
    Ming-Chya Wu, Eiichi Watanabe, Zbigniew R. Struzik, Chin-Kun Hu, and Yoshiharu Yamamoto
    Published 20 November 2009 (9 pages)
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    Ventricular fibrillation (VF) is known to be the most dangerous cardiac arrhythmia, frequently leading to sudden cardiac death (SCD). During VF, cardiac output drops to nil and, unless the fibrillation is promptly halted, death usually ensues within minutes. While delivering life saving electrical shocks is a method of preventing SCD, it has been recognized that some, though not many, VF episodes are self-terminating, and understanding the mechanism of spontaneous defibrillation might provide newer therapeutic options for treatment of this otherwise fatal arrhythmia. Using the phase statistics approach, recently developed to study financial and physiological time series, here, we reveal the timing characteristics of transient features of ventricular tachyarrhythmia (mostly VF) electrocardiogram (ECG) and find that there are three distinct types of probability density function (PDF) of phase distributions: uniform (UF), concave (CC), and convex (CV). Our data show that VF patients with UF or CC types of PDF have approximately the same probability of survival and nonsurvival, while VF patients with CV type PDF have zero probability of survival, implying that their VF episodes are never self-terminating. Our results suggest that detailed phase statistics of human ECG data may be a key to understanding the mechanism of spontaneous defibrillation of fatal VF.

    BRIEF REPORTS

    Colloidal dispersions, suspensions, and aggregates

    Dynamical regimes of a paramagnetic particle circulating a magnetic bubble domain
    Pietro Tierno, Tom H. Johansen, and Francesc Sagués
    Published 17 November 2009 (4 pages)
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    We study the dynamics of a single paramagnetic colloidal particle dispersed in water and circulating around a cylindrical magnetic domain (“magnetic bubble”) when driven by an external rotating magnetic field. We record the particle trajectories and measure its angular displacement by changing the strength, frequency, and ellipticity of the applied magnetic field and show that this simple system exhibits several interesting phenomena, from synchronous-asynchronous rotations, to localized oscillations. We complement the experimental results with numerical simulations which explore the dynamical regimes of the rotating particle.

    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.

    Adsorption of Ar on planar surfaces studied with a density functional theory
    Salvador A. Sartarelli and Leszek Szybisz
    Published 19 November 2009 (4 pages)
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    The adsorption of Ar on planar structureless substrates of alkali metals, alkaline-earth metal Mg, CO2, and Au was analyzed by applying a density functional formalism which includes a recently proposed effective attractive pair potential conditioned to Ar. It is shown that this approach reproduces the experimental surface tension of the liquid-vapor interface over the entire bulk coexistence curve for temperatures T spanning from the triple point Tt up to the critical point Tc. The wetting properties were studied over the entire range temperatures Tt<-->Tc. It was found that Ar wets all the investigated surfaces. The adsorption isotherms for alkali metals exhibit first-order phase transitions. Prewetting lines were resolved even for the less attractive surfaces. In the cases of Mg, CO2, and Au a continuous growth for T>=Tt was obtained. A comparison with experimental data and other microscopic calculations is reported.

    Polymers

    Bending affects entropy of semiflexible polymers: Application to protein-DNA complexes
    Shay M. Rappaport and Yitzhak Rabin
    Published 12 November 2009 (4 pages)
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    We discuss a class of generalized wormlike chain models of polymers with spontaneous curvature and show that the density of states and consequently the entropy of such natively bent polymers are higher than that of straight ones. This effect changes the classical Langmuir binding isotherm by giving rise to enhanced binding of DNA-bending proteins.

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

    RAPID COMMUNICATIONS

    Interdisciplinary physics
    Rapid

    Measurement of the temperature profile of an exothermic autocatalytic reaction front
    J. Martin, N. Rakotomalala, L. Talon, and D. Salin
    Published 19 November 2009 (4 pages)
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    Autocatalytic reactions may propagate as solitary waves, namely, at a constant front velocity and with a stationary concentration profile, resulting from a balance between molecular diffusion and chemical reaction. When the reaction is exothermic, a thermal wave is linked to the chemical front. As the thermal diffusivity is nearly two orders of magnitude larger than the molecular one, the temperature profile spreads over length scales (mm) two orders of magnitude larger than the concentration one. Using an infrared camera, we measure the temperature profiles for a chlorite-tetrathionate autocatalytic reaction. The profiles are compared quantitatively to lattice Bhatnagar-Gross-Krook (BGK) numerical simulations. Our analysis also accounts for the lack of observation of the thermal wave for the iodate arsenous acid reaction.

    Fluid dynamics
    Rapid

    Reconnecting flux-rope dynamo
    Andrew W. Baggaley, Carlo F. Barenghi, Anvar Shukurov, and Kandaswamy Subramanian
    Published 18 November 2009 (4 pages)
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    We develop a model of the fluctuation dynamo in which the magnetic field is confined to thin flux ropes advected by a multiscale model of turbulence. Magnetic dissipation occurs only via reconnection of the flux ropes. This model can be viewed as an implementation of the asymptotic limit Rm-->[infinity] for a continuous magnetic field, where magnetic dissipation is strongly localized to small regions of strong-field gradients. We investigate the kinetic-energy release into heat mediated by the dynamo action, both in our model and by solving the induction equation with the same flow. We find that a flux-rope dynamo is an order of magnitude more efficient at converting mechanical energy into heat. The probability density of the magnetic energy release in reconnections has a power-law form with the slope −3, consistent with the solar corona heating by nanoflares.

    Plasma physics
    Rapid

    Numerical simulation of harmonic generation by relativistic laser interaction with a grating
    X. Lavocat-Dubuis and J.-P. Matte
    Published 10 November 2009 (4 pages)
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    The interaction of a femtosecond relativistic intensity laser pulse with a grating of subwavelength periodicity was simulated numerically. Strong coherent emission at the wavelength of the grating period and its harmonics was seen, nearly parallel to the target surface, due to relativistic electron bunches emanating from each protuberance. Normal and oblique incidence (30°) gave rise to trains of attosecond pulses and an efficiency greater than 10−4 was obtained for the 24th harmonic (lambda~=16.7  nm). Similarity theory gives optimum conditions for harmonic emission.
    Rapid

    Characterization of two distinct, simultaneous hot electron beams in intense laser-solid interactions
    B. I. Cho, J. Osterholz, A. C. Bernstein, G. M. Dyer, A. Karmakar, A. Pukhov, and T. Ditmire
    Published 11 November 2009 (4 pages)
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    The transport of energetic electron beams generated from aluminum foils irradiated by ultraintense laser pulses has been studied by imaging coherent transition radiation from the rear side of the target. Two distinct beams of MeV electrons are emitted from the target rear side at the same time. This measurement indicates that two different mechanisms, namely resonance absorption and j×B heating, accelerate the electrons at the targets front side and drive them to different directions, with different temperatures. This interpretation is consistent with 3D-particle-in-cell simulations.

    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.

    Diffusion of scientific credits and the ranking of scientists
    Filippo Radicchi, Santo Fortunato, Benjamin Markines, and Alessandro Vespignani
    Published 11 November 2009 (10 pages)
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    Recently, the abundance of digital data is enabling the implementation of graph-based ranking algorithms that provide system level analysis for ranking publications and authors. Here, we take advantage of the entire Physical Review publication archive (1893–2006) to construct authors' networks where weighted edges, as measured from opportunely normalized citation counts, define a proxy for the mechanism of scientific credit transfer. On this network, we define a ranking method based on a diffusion algorithm that mimics the spreading of scientific credits on the network. We compare the results obtained with our algorithm with those obtained by local measures such as the citation count and provide a statistical analysis of the assignment of major career awards in the area of physics. A website where the algorithm is made available to perform customized rank analysis can be found at the address http://www.physauthorsrank.org.

    Phase diagrams for three-strategy evolutionary prisoner's dilemma games on regular graphs
    Attila Szolnoki, Matjaž Perc, and György Szabó
    Published 12 November 2009 (7 pages)
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    Evolutionary prisoner's dilemma games are studied with players located on square lattice and random regular graph defining four neighbors for each one. The players follow one of the three strategies: tit-for-tat, unconditional cooperation, and defection. The simplified payoff matrix is characterized by two parameters: the temptation b to choose defection and the cost c of inspection reducing the income of tit-for-tat. The strategy imitation from one of the neighbors is controlled by pairwise comparison at a fixed level of noise. Using Monte Carlo simulations and the extended versions of pair approximation we have evaluated the b-c phase diagrams indicating a rich plethora of phase transitions between stationary coexistence, absorbing, and oscillatory states, including continuous and discontinuous phase transitions. By reasonable costs the tit-for-tat strategy prevents extinction of cooperators across the whole span of b determining the prisoner's dilemma game, irrespective of the connectivity structure. We also demonstrate that the system can exhibit a repetitive succession of oscillatory and stationary states upon changing a single payoff value, which highlights the remarkable sensitivity of cyclical interactions on the parameters that define the strength of dominance.

    Coevolution of Glauber-like Ising dynamics and topology
    Salvatore Mandrà, Santo Fortunato, and Claudio Castellano
    Published 13 November 2009 (4 pages)
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    We study the coevolution of a generalized Glauber dynamics for Ising spins with tunable threshold and of the graph topology where the dynamics takes place. This simple coevolution dynamics generates a rich phase diagram in the space of the two parameters of the model, the threshold and the rewiring probability. The diagram displays phase transitions of different types: spin ordering, percolation, and connectedness. At variance with traditional coevolution models, in which all spins of each connected component of the graph have equal value in the stationary state, we find that, for suitable choices of the parameters, the system may converge to a state in which spins of opposite sign coexist in the same component organized in compact clusters of like-signed spins. Mean field calculations enable one to estimate some features of the phase diagram.

    Revising the simple measures of assortativity in complex networks
    Xiao-Ke Xu, Jie Zhang, Junfeng Sun, and Michael Small
    Published 17 November 2009 (7 pages)
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    We find that traditional statistics for measuring degree mixing are strongly affected by superrich nodes. To counteract and measure the effect of superrich nodes, we propose a paradigm to quantify the mixing pattern of a real network in which different mixing patterns may appear among low-degree nodes and among high-degree nodes. This paradigm and the simple revised measure uncover the true complex degree mixing patterns of complex networks with superrich nodes. The alternate method indicates that some networks show a false disassortative mixing induced by superrich nodes and have no tendency to be genuinely disassortative. Our results also show that the previously observed fragility of scale-free networks is actually greatly exacerbated by the presence of even a very small number of superrich nodes.

    Language structure in the n-object naming game
    Adam Lipowski and Dorota Lipowska
    Published 19 November 2009 (8 pages)
    056107  Full Text: PDF (244 kB)  | Buy Article