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Physical Review E

(Statistical, Nonlinear, and Soft Matter Physics)

July 2006

Volume 74, Number 1 , Articles (01xxxx)

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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
  • COMMENTS
  • ERRATA
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    Part 1 - Statistical, Soft Matter, and Biological Physics

    RAPID COMMUNICATIONS

    Statistical physics
    Rapid

    High-speed observation of the piston effect near the gas-liquid critical point
    Yuichi Miura, Shoichi Yoshihara, Mitsuru Ohnishi, Katsuya Honda, Masaaki Matsumoto, Jun Kawai, Masamichi Ishikawa, Hiroto Kobayashi, and Akira Onuki
    Published 10 July 2006 (4 pages)
    010101(R)  Full Text: PDF (127 kB)  | Buy Article
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    We investigated adiabatic changes in a near-critical fluid on acoustic time scales using an ultrasensitive interferometer. A sound emitted by very weak continuous heating caused a stepwise adiabatic change at its front with a density change of order 10–7  g/cm3 and a temperature change of order 10–5  K. Very small heat inputs at a heater produced short acoustic pulses with width of order 10  µs, which were broadened as they moved through the cell and interacted with the boundaries. The pulse broadening became enhanced near the critical point. We also examined theoretically how sounds are emitted from a heater and how applied heat is transformed into mechanical work. Our predictions agree well with our data.
    Rapid

    Coexistence diameter in two-dimensional colloid-polymer mixtures
    R. L. C. Vink and H. H. Wensink
    Published 13 July 2006 (4 pages)
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    We demonstrate that the law of the rectilinear coexistence diameter in two-dimensional mixtures of nonspherical colloids and nonadsorbing polymers is violated. Upon approach to the critical point, the diameter shows logarithmic singular behavior governed by a term t  ln  t, with t the relative distance from the critical point. No sign of a term t2beta could be detected, with beta the critical exponent of the order parameter, indicating a very weak or absent Yang-Yang anomaly. Our analysis thus reveals that nonspherical particle shape alone is not sufficient for the formation of a pronounced Yang-Yang anomaly in the critical behavior of fluids.
    Rapid

    Stochastic resonance due to internal noise in reaction kinetics
    Carlos Escudero
    Published 17 July 2006 (4 pages)
    010103(R)  Full Text: PDF (87 kB)  | Buy Article
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    We study a reaction model that presents stochastic resonance purely due to internal noise. This means that the only source of fluctuations comes from the discrete character of the reactants, and no more noises enter into the system. Our analysis reveals that the phenomenon is highly complex, and that is generated by the interplay of different stochasticity at the three fixed points of a bistable system.
    Rapid

    Equilibration through local information exchange in networks
    K. Y. Michael Wong and David Saad
    Published 17 July 2006 (4 pages)
    010104(R)  Full Text: PDF (243 kB)  | Buy Article
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    We study the equilibrium states of energy functions involving a large set of real variables, defined on the links of sparsely connected networks, and interacting at the network nodes, using the cavity and replica methods. When applied to the representative problem of network resource allocation, an efficient distributed algorithm is devised, with simulations showing full agreement with theory. Scaling properties with the network connectivity and the resource availability are found.
    Rapid

    Nonconcave entropies from generalized canonical ensembles
    Marius Costeniuc, Richard S. Ellis, and Hugo Touchette
    Published 31 July 2006 (4 pages)
    010105(R)  Full Text: PDF (211 kB)  | Buy Article
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    It is well known that the entropy of the microcanonical ensemble cannot be calculated as the Legendre transform of the canonical free energy when the entropy is nonconcave. To circumvent this problem, a generalization of the canonical ensemble that allows for the calculation of nonconcave entropies was recently proposed. Here, we study the mean-field Curie-Weiss-Potts spin model and show, by direct calculations, that the nonconcave entropy of this model can be obtained by using a specific instance of the generalized canonical ensemble known as the Gaussian ensemble.

    Granular materials
    Rapid

    Interstitial gas and density segregation of vertically vibrated granular media
    M. Klein, L. L. Tsai, M. S. Rosen, T. Pavlin, D. Candela, and R. L. Walsworth
    Published 18 July 2006 (4 pages)
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    We report experimental studies of the effect of interstitial gas on mass-density segregation in a vertically vibrated mixture of equal-sized bronze and glass spheres. Sufficiently strong vibration in the presence of interstitial gas induces vertical segregation into sharply separated bronze and glass layers. We find that the segregated steady state (i.e., bronze or glass layer on top) is a sensitive function of gas pressure and viscosity, as well as vibration frequency and amplitude. In particular, we identify distinct regimes of behavior that characterize the change from bronze-on-top to glass-on-top steady state.
    Rapid

    Simulation study of air-induced segregation of equal-sized bronze and glass particles
    C. Zeilstra, M. A. van der Hoef, and J. A. M. Kuipers
    Published 24 July 2006 (4 pages)
    010302(R)  Full Text: PDF (470 kB)  | Buy Article
    See Also: Publisher's Note
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    We have investigated the effect of air on the density segregation of fine, equal-sized bronze and glass particles under vertical sinusoidal vibrations by numerical simulation, using a hybrid granular dynamics-computational fluid dynamics model. We find both the bronze-on-top and the sandwich configurations as observed in previous experiments. The simulations allow us to give a detailed explanation of the phenomena. The key observation is the precise timing of the decompaction of the bed with the oscillating gas flow, which will cause the bronze to move to the top, due to the difference in acceleration from the air drag. For higher frequencies, the different inertia in collisions will cause the bronze clusters on top to sink through the bed, leading to a sandwich formation.

    Colloidal dispersions, suspensions, and aggregates
    Rapid

    Distribution of local fluxes in diluted porous media
    Ascânio D. Araújo, Wagner B. Bastos, José S. Andrade, Jr., and Hans J. Herrmann
    Published 17 July 2006 (4 pages)
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    We study the distributions of channel openings, local fluxes, and velocities in a two-dimensional random medium of nonoverlapping disks. We present theoretical arguments supported by numerical data of high precision and find scaling laws as functions of the porosity. For the channel openings we observe a crossover to a highly correlated regime at small porosities. The distribution of velocities through these channels scales with the square of the porosity. The fluxes turn out to be the convolution of velocity and channel width corrected by a geometrical factor. Furthermore, while the distribution of velocities follows a Gaussian form, the fluxes are distributed according to a stretched exponential with exponent 1/2. Finally, our scaling analysis allows us to express the tortuosity and pore shape factors from the Kozeny-Carman equation as direct average properties from microscopic quantities related to the geometry as well as the flow through the disordered porous medium.
    Rapid

    Screening in Yukawa fluid mixtures
    A. J. Archer, P. Hopkins, and R. Evans
    Published 18 July 2006 (4 pages)
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    The effective pair potential between mesoscopic charged particles in a neutralizing background medium takes a Yukawa form exp(–lambdar)/r with screening length lambda–1. We consider a dilute suspension of such Yukawa particles dispersed in a solvent with correlation length xi<lambda–1 and show that the Yukawa interaction is screened if the pair potentials between solvent particles exhibit Yukawa decay with the same screening length lambda–1. However, if the solvent pair potentials are shorter ranged than the solute Yukawa potentials, then the effective potential between pairs of solute particles is unscreened, i.e., the effective potential between the solute particles is equal to the bare potential at large particle separations.
    Rapid

    Columnar and lamellar phases in attractive colloidal systems
    A. de Candia, E. Del Gado, A. Fierro, N. Sator, M. Tarzia, and A. Coniglio
    Published 21 July 2006 (4 pages)
    010403(R)  Full Text: PDF (286 kB)  | Buy Article
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    In colloidal suspensions, at low volume fraction and temperature, dynamical arrest occurs via the growth of elongated structures that aggregate to form a connected network at gelation. Here we show that, in the region of parameter space where gelation occurs, the stable thermodynamical phase is a crystalline columnar one. Near and above the gelation threshold, the disordered spanning network slowly evolves and finally orders to form the crystalline structure. At higher volume fractions the stable phase is a lamellar one, which seems to have a still longer ordering time.
    Rapid

    Lack of long-range order in confined two-dimensional model colloidal crystals
    A. Ricci, P. Nielaba, S. Sengupta, and K. Binder
    Published 28 July 2006 (4 pages)
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    We investigate the nature of the ordered phase for a model of colloidal particles confined within a quasi-one-dimensional (Q1D) strip between two parallel boundaries, or walls, separated a distance D in two dimensions (2D). Using Monte Carlo simulations we find that at densities typical of the bulk 2D triangular solid the order in the D1D strip is determined by the nature of the boundaries. While the order is enhanced for a suitably corrugated boundary potential, for a uniformly repulsive smooth boundary potential ordering normal to the walls is enhanced ("layering"), but destroyed parallel to the wall.

    Films, interfaces, and crystal growth
    Rapid

    Possible explanation of the Lambda-shape anomaly in polymer surface diffusion
    Debashish Mukherji and Martin H. Müser
    Published 18 July 2006 (4 pages)
    010601(R)  Full Text: PDF (107 kB)  | Buy Article
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    We suggest an explanation for the anomalous behavior of the polymer surface-diffusion coefficient D reported by Zhao and Granick [J. Am. Chem. Soc. 126, 6242 (2004)]: D first increased with increasing polymer surface concentration Gamma, then suddenly dropped at a threshold value Gamma*. Our molecular dynamics simulations show the same behavior. We find that polymers form single-layered pancake structures for Gamma<Gamma*, while double layers form for Gamma>Gamma*. The double-layer structures allow the polymers to better adapt to the substrate corrugation. This increases barriers for lateral diffusion and is thus consistent with small values of D at larger Gamma.
    Rapid

    Observation of a low-viscosity interface between immiscible polymer layers
    Xuesong Hu, Zhang Jiang, Suresh Narayanan, Xuesong Jiao, Alec R. Sandy, Sunil K. Sinha, Laurence B. Lurio, and Jyotsana Lal
    Published 19 July 2006 (4 pages)
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    X-ray photon correlation spectroscopy was employed in a surface standing wave geometry in order to resolve the thermally driven in-plane dynamics at both the surface/vacuum (top) and polymer/polymer (bottom) interfaces of a thin polystyrene (PS) film on top of Poly(4-bromo styrene) (PBrS) and supported on a Si substrate. The top vacuum interface shows two relaxation modes: one fast and one slow, while the buried polymer-polymer interface shows a single slow mode. The slow mode of the top interface is similar in magnitude and wave vector dependence to the single mode of the buried interface. The dynamics are consistent with a low-viscosity mixed layer between the PS and PBrS and coupling of the capillary wave fluctuations between this layer and the PS.

    Polymers
    Rapid

    Density functional theory for flexible and semiflexible polymers of infinite length
    Clifford E. Woodward and Jan Forsman
    Published 18 July 2006 (4 pages)
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    We develop a density functional theory for infinitely long flexible and semiflexible polymers, as an appropriate simplification of the corresponding treatment of finite chains. We demonstrate that very long chains sometimes are required to reproduce even qualitatively correct limiting behaviors.

    Biological physics
    Rapid

    Dynamic buckling of morphoelastic filaments
    Raymond E. Goldstein and Alain Goriely
    Published 11 July 2006 (4 pages)
    010901(R)  Full Text: PDF (250 kB)  | Buy Article
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    The equilibrium shapes of biological structures as diverse as plant tendrils and bacterial filaments can be altered by externally imposed stresses of sufficient duration. We study the simplest model for this morphoelasticity—a filament whose intrinsic curvatures relax to the local curvatures—and illustrate its properties in the context of dynamic Euler buckling and writhing. When a thrust or twist is ramped in time the effective elastic properties of the filament depend on the load rate. Slow ramps interrupted by removal of the external forces can leave in equilibrium any of a whole continuum of buckled shapes. Morphoelastic relaxation can also allow a filament to bypass a bifurcation.
    Rapid

    Generalized Haldane equation and fluctuation theorem in the steady-state cycle kinetics of single enzymes
    Hong Qian and X. Sunney Xie
    Published 12 July 2006 (4 pages)
    010902(R)  Full Text: PDF (96 kB)  | Buy Article
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    Enyzme kinetics are cyclic. We study a Markov renewal process model of single-enzyme turnover in nonequilibrium steady state (NESS) with sustained concentrations for substrates and products. We show that the forward and backward cycle times have identical nonexponential distributions: Theta+(t)=Theta–(t). This equation generalizes the Haldane relation in reversible enzyme kinetics. In terms of the probabilities for the forward (p+) and backward (p–) cycles, kBT  ln(p+/p–) is shown to be the chemical driving force of the NESS, Deltaµ. More interestingly, the moment generating function of the stochastic number of substrate cycle nu(t), <e–lambdanu(t)>, follows the fluctuation theorem in the form of Kurchan-Lebowitz-Spohn-type symmetry. When lambda=Deltaµ/kBT, we obtain the Jarzynski-Hatano-Sasa-type equality <e–nu(t)Deltaµ/kBT> [equivalent] 1 for all t, where nuDeltaµ is the fluctuating chemical work done for sustaining the NESS. This theory suggests possible methods to experimentally determine the nonequilibrium driving force in situ from turnover data via single-molecule enzymology.
    Rapid

    Characteristic length scale of electric transport properties of genomes
    C. T. Shih
    Published 25 July 2006 (4 pages)
    010903(R)  Full Text: PDF (262 kB)  | Buy Article
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    A tight-binding model together with a statistical method are used to investigate the relation between the sequence-dependent electric transport properties and the sequences of protein-coding regions of complete genomes. A correlation parameter Omega is defined to analyze the relation. For some particular propagation length wmax, the transport behaviors of the coding and noncoding sequences are very different and the correlation reaches its maximal value Omegamax. wmax and Omegamax are characteristic values for each species. A possible reason for the difference between the features of transport properties in the coding and noncoding regions is the mechanism of DNA damage repair processes together with natural selection.

    ARTICLES

    Statistical physics

    Freezing transition of the directed polymer in a 1+d random medium: Location of the critical temperature and unusual critical properties
    Cécile Monthus and Thomas Garel
    Published 5 July 2006 (11 pages)
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    In dimension d>=3, the directed polymer in a random medium undergoes a phase transition between a free phase at high temperature and a low-temperature disorder-dominated phase. For the latter phase, Fisher and Huse have proposed a droplet theory based on the scaling of the free-energy fluctuations DeltaF(l)~ltheta at scale l. On the other hand, in related growth models belonging to the Kardar-Parisi-Zhang universality class, Forrest and Tang have found that the height-height correlation function is logarithmic at the transition. For the directed polymer model at criticality, this translates into logarithmic free-energy fluctuations DeltaFTc(l)~(ln  l)sigma with sigma=1/2. In this paper, we propose a droplet scaling analysis exactly at criticality based on this logarithmic scaling. Our main conclusion is that the typical correlation length xi(T) of the low-temperature phase diverges as ln  xi(T)~[–ln(Tc–T)]1/sigma~[–ln(Tc–T)]2, instead of the usual power law xi(T)~(Tc–T)–nu. Furthermore, the logarithmic dependence of DeltaFTc(l) leads to the conclusion that the critical temperature Tc actually coincides with the explicit upper bound T2 derived by Derrida and co-workers, where T2 corresponds to the temperature below which the ratio [overline Z[sub L][sup 2]]/([overline Z[sub L]])2 diverges exponentially in L. Finally, since the Fisher-Huse droplet theory was initially introduced for the spin-glass phase, we briefly mention the similarities with and differences from the directed polymer model. If one speculates that the free energy of droplet excitations for spin glasses is also logarithmic at Tc, one obtains a logarithmic decay for the mean square correlation function at criticality, [overline C[sup 2](r)]~1/(ln  r)sigma, instead of the usual power law 1/rd–2+eta.

    Logarithmic corrections in the free energy of monomer-dimer model on plane lattices with free boundaries
    Yong Kong
    Published 6 July 2006 (8 pages)
    011102  Full Text: PDF (551 kB)  | Buy Article
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    Using exact computations we study the classical hard-core monomer-dimer models on m×n plane lattice strips with free boundaries. For an arbitrary number v of monomers (or vacancies), we found a logarithmic correction term in the finite-size correction of the free energy per lattice site. The coefficient of the logarithmic correction term depends on the number of monomers present (v) and the parity of the width n of the lattice strip: the coefficient equals to v when n is odd, and v/2 when n is even. The results are generalizations of the previous results for a single monomer in an otherwise fully packed lattice of dimers. We also study the finite-size correction in the low dimer density limit, where the number of dimers d is fixed. In this case the coefficient of the logarithmic correction term equals to d, for both odd and even n.

    Sol-gel transition in a source-enhanced coagulating system
    A. A. Lushnikov
    Published 10 July 2006 (9 pages)
    011103  Full Text: PDF (149 kB)  | Buy Article
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    This paper considers the time evolution of disperse systems in which binary coagulation and a source of fresh particles govern the temporal changes to the particle mass spectra. The source is assumed to produce fresh particles at a constant rate. The Smoluchowski equation describing the time evolution of the particle mass spectrum is solved exactly for the coagulation kernel proportional to the product of masses of two coalescing particles. It is shown that after a critical time tc a gel forms in the system and the sol spectrum becomes an algebraic function of the particle mass at t=tc. It begins to shrink after the critical time due to the mass loss supporting the growth of the gel mass. The pre- and post-critical behavior of the mass spectrum and its integral characteristics (total particle number and mass concentrations) are investigated for the source productivity I(g) dropping down algebraically with the particle mass g as I(g)[proportional]g–gamma. The critical particle mass spectrum is proved to be a universal function of g (it drops down as g–5/2) if the third moment of I(g) is finite (gamma>4). Otherwise (3<gamma<=4) this and other critical exponents begin to depend on alpha. Still the mass spectrum remains self-similar, i.e., it depends on a combination of g and t. At smaller gamma the gelation process is shown to begin at t=0. All critical characteristics of the particle mass spectrum are determined for this case.

    Global phase diagram and six-state clock universality behavior in the triangular antiferromagnetic Ising model with anisotropic next-nearest-neighbor coupling: Level-spectroscopy approach
    Hiromi Otsuka, Yutaka Okabe, and Kiyohide Nomura
    Published 11 July 2006 (7 pages)
    011104  Full Text: PDF (150 kB)  | Buy Article
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    We investigate the triangular-lattice antiferromagnetic Ising model with a spatially anisotropic next-nearest-neighbor ferromagnetic coupling, which was first discussed by Kitatani and Oguchi. By employing the effective geometric factor, we analyze the scaling dimensions of the operators around the Berezinskii-Kosterlitz-Thouless (BKT) transition lines, and determine the global phase diagram. Our numerical data exhibit that two types of BKT-transition lines separate the intermediate critical region from the ordered and disordered phases, and they do not merge into a single curve in the antiferromagnetic region. We also estimate the central charge and perform some consistency checks among scaling dimensions in order to provide the evidence of the six-state clock universality. Further, we provide an analysis of the shapes of boundaries based on the crossover argument.

    Fractional translational diffusion of a Brownian particle in a double well potential
    Yuri P. Kalmykov, William T. Coffey, and Serguey V. Titov
    Published 11 July 2006 (7 pages)
    011105  Full Text: PDF (149 kB)  | Buy Article
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    The fractional translational diffusion of a particle in a double-well potential (excluding inertial effects) is considered. The position correlation function and its spectrum are evaluated using a fractional probability density diffusion equation (based on the diffusion limit of a fractal time random walk). Exact and approximate solutions for the dynamic susceptibility describing the position response to a small external field are obtained. The exact solution is given by matrix continued fractions while the approximate solution relies on the exponential separation of the time scales of the fast "intrawell" and low overbarrier relaxation processes associated with the bistable potential. It is shown that knowledge of the characteristic relaxation times for normal diffusion allows one to predict accurately the anomalous relaxation behavior of the system for all relevant time scales.

    Phase transitions in systems possessing shock solutions
    Maryam Arabsalmani and Amir Aghamohammadi
    Published 14 July 2006 (9 pages)
    011107  Full Text: PDF (147 kB)  | Buy Article
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    Recently it has been shown that there are three families of stochastic one-dimensional nonequilibrium lattice models for which the single-shock measures form an invariant subspace of the states of these models. Here, both the stationary states and dynamics of single-shocks on a one-dimensional lattice are studied. This is done for both an infinite lattice and a finite lattice with boundaries. It is seen that these models possess both static and dynamical phase transitions. The static phase transition is the well-known low-high density phase transition for the asymmetric simple exclusion process. The branching-coalescing random walk and asymmetric Kawasaki-Glauber process models also show the same phase transition. Double-shocks on a one-dimensional lattice are also investigated. It is shown that at the stationary state the contribution of double-shocks with higher width becomes small, and the main contribution comes from thin double-shocks.

    Continuous phase transitions with a convex dip in the microcanonical entropy
    Hans Behringer and Michel Pleimling
    Published 17 July 2006 (8 pages)
    011108  Full Text: PDF (135 kB)  | Buy Article
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    The appearance of a convex dip in the microcanonical entropy of finite systems usually signals a first order transition. However, a convex dip also shows up in some systems with a continuous transition as, for example, in the Baxter-Wu model and in the four-state Potts model in two dimensions. We demonstrate that the appearance of a convex dip in those cases can be traced back to a finite-size effect. The properties of the dip are markedly different from those associated with a first order transition and can be understood within a microcanonical finite-size scaling theory for continuous phase transitions. Results obtained from numerical simulations corroborate the predictions of the scaling theory.

    Velocity and diffusion coefficient of A+A<-->A reaction fronts in one dimension
    Niraj Kumar and Goutam Tripathy
    Published 17 July 2006 (5 pages)
    011109  Full Text: PDF (119 kB)  | Buy Article
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    We study front propagation in the reversible reaction-diffusion system A+A<-->A on a one-dimensional lattice. Extending the idea of leading particle in studying the motion of the front we write a master equation in the stochastically moving frame attached to this particle. This approach provides a systematic way to improve on estimates of front speed obtained earlier. We also find that the leading particle performs a correlated random walk and this correlation needs to be taken into account to get the correct the value of the front diffusion coefficient.

    Dynamic phase transition in the kinetic spin-3/2 Blume-Capel model under a time-dependent oscillating external field
    Mustafa Keskin, Osman Canko, and Bayram Deviren
    Published 17 July 2006 (10 pages)
    011110  Full Text: PDF (344 kB)  | Buy Article
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    We present a study, within a mean-field approach, of the stationary states of the kinetic spin-3/2 Blume-Capel model in the presence of a time-dependent oscillating external magnetic field. We use the Glauber-type stochastic dynamics to describe the time evolution of the system. We have found that the behavior of the system strongly depends on the crystal-field interaction. We can identify two types of solutions: a symmetric one where the magnetization (m) of the system oscillates in time around zero, which corresponds to a paramagnetic phase (P), and an antisymmetric one where m oscillates in time around a finite value different from zero, namely ±3/2 and ±1/2 that corresponds to the ferromagnetic-3/2 (F3/2) and the ferromagnetic-1/2 (F1/2) phases, respectively. There are coexistence regions of the phase space where the F3/2, F1/2 (F3/2+F1/2), F3/2, P (F3/2+P), F1/2, P (F1/2+P), and F3/2, F1/2, P (F3/2+F1/2+P) phases coexist, hence the system exhibits seven different phases. We obtain the dynamic phase transition points and find six fundamental phase diagrams which exhibit one or three dynamic tricritical points. We have also calculated the Liapunov exponent to verify the stability of the solutions and the dynamic phase transition points.

    Generic multifractality in exponentials of long memory processes
    A. Saichev and D. Sornette
    Published 18 July 2006 (11 pages)
    011111  Full Text: PDF (638 kB)  | Buy Article
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    We find that multifractal scaling is a robust property of a large class of continuous stochastic processes, constructed as exponentials of long-memory processes. The long memory is characterized by a power law kernel with tail exponent phi+1/2, where phi>0. This generalizes previous studies performed only with phi=0 (with a truncation at an integral scale) by showing that multifractality holds over a remarkably large range of dimensionless scales for phi>0. The intermittency multifractal coefficient can be tuned continuously as a function of the deviation phi from 1/2 and of another parameter sigma2 embodying information on the short-range amplitude of the memory kernel, the ultraviolet cutoff ("viscous") scale, and the variance of the white-noise innovations. In these processes, both a viscous scale and an integral scale naturally appear, bracketing the "inertial" scaling regime. We exhibit a surprisingly good collapse of the multifractal spectra zeta(q) on a universal scaling function, which enables us to derive high-order multifractal exponents from the small-order values and also obtain a given multifractal spectrum zeta(q) by different combinations of phi and sigma2.

    Dynamics of the Bose-Einstein condensation: Analogy with the collapse dynamics of a classical self-gravitating Brownian gas
    Julien Sopik, Clément Sire, and Pierre-Henri Chavanis
    Published 18 July 2006 (15 pages)
    011112  Full Text: PDF (228 kB)  | Buy Article
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    We consider the dynamics of a gas of free bosons within a semiclassical Fokker-Planck equation for which we give a physical justification. In this context, we find a striking similarity between the Bose-Einstein condensation in the canonical ensemble, and the gravitational collapse of a gas of classical self-gravitating Brownian particles. The paper is mainly devoted to the complete study of the Bose-Einstein "collapse" within this model. We find that at the Bose-Einstein condensation temperature Tc, the chemical potential µ(t) vanishes exponentially with a universal rate that we compute exactly. Below Tc, we show analytically that sqrt( mu(t)) vanishes linearly in a finite time tcoll. After tcoll, the mass of the condensate grows linearly with time and saturates exponentially to its equilibrium value for large time. We also give analytical results for the density scaling functions, for the corrections to scaling, and for the exponential relaxation time. Finally, we find that the equilibration time (above Tc) and the collapse time tcoll (below Tc) both behave like –Tc<sup>-3</sup>  ln|T–Tc|, near Tc.

    Nonequilibrium thermodynamics of glasses
    Hans Christian Öttinger
    Published 21 July 2006 (25 pages)
    011113  Full Text: PDF (347 kB)  | Buy Article
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    We consider the nonequilibrium thermodynamics of glasses from various perspectives. For the commonly used equilibriumlike approach based on Gibbs' fundamental form with an additional pair of conjugate variables, we discuss possible choices of the independent out-of-equilibrium variable and we illustrate some implications by concrete results for a well-known exactly solvable lattice model. The choice of variables is further illuminated from the complementary atomistic perspective offered by the inherent-structure formalism. A general formalism of nonequilibrium thermodynamics is employed (i) to derive the standard equilibriumlike approach, (ii) to formulate two self-contained levels to describe glassy dynamics and thermodynamics, and (iii) to offer guidance for future simulations of glasses. The thermodynamic approach suggests to introduce four-point correlation functions associated with structural rearrangements after imposed deformations, which might offer a possibility to detect a growing length scale at the glass transition without employing any dynamic information.

    Chaotic noisy transport of electron pairs in a superconducting junction device: Thermal-inertia ratchets
    Jing-hui Li
    Published 24 July 2006 (4 pages)
    011114  Full Text: PDF (109 kB)  | Buy Article
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    Chaotic noisy transport of electron pairs in a superconducting junction device (thermal-inertia ratchets) is investigated. The study shows that when the temperature is low enough, the transport of the electron pairs can be mainly chaotic; when the temperature is high enough, it can be mainly stochastic. By controlling the temperature and the amplitude of the input ac signal, the current of electron pairs can be reversed.

    Exactly solvable interacting spin-ice vertex model
    Anderson A. Ferreira and Francisco C. Alcaraz
    Published 24 July 2006 (14 pages)
    011115  Full Text: PDF (251 kB)  | Buy Article
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    A special family of solvable five-vertex model is introduced on a square lattice. In addition to the usual nearest-neighbor interactions, the vertices defining the model also interact along one of the diagonals of the lattice. This family of models includes in a special limit the standard six-vertex model. The exact solution of these models is an application of the matrix product ansatz introduced recently and applied successfully in the solution of quantum chains. The phase diagram and the free energy of the models are calculated in the thermodynamic limit. The models exhibit massless phases, and our analytical and numerical analyses indicate that such phases are governed by a conformal field theory with central charge c=1 and continuously varying critical exponents.

    Bulk and surface transitions in asymmetric simple exclusion process: Impact on boundary layers
    Sutapa Mukherji and Vivek Mishra
    Published 24 July 2006 (11 pages)
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    In this paper, we study the boundary-induced phase transitions in a particle nonconserving asymmetric simple exclusion process with open boundaries. Using a boundary layer analysis on the mean field version of the model, we show that the key signatures of various bulk phase transitions are present in the boundary layers of the density profiles. In addition, we also find surface transitions in the low- and high-density phases. The surface transition in the low-density phase provides a complete description of the nonequilibrium critical point found in this system.

    Generic features of the wealth distribution in ideal-gas-like markets
    P. K. Mohanty
    Published 26 July 2006 (4 pages)
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    We provide an exact solution to the ideal-gas-like models studied in econophysics to understand the microscopic origin of Pareto law. In these classes of models the key ingredient necessary for having a self-organized scale-free steady-state distribution is the trading or collision rule where agents or particles save a definite fraction of their wealth or energy and invest the rest for trading. Using a Gibbs ensemble approach we could obtain the exact distribution of wealth in this model. Moreover we show that in this model (a) good savers are always rich and (b) every agent poor or rich invests the same amount for trading. Nonlinear trading rules could alter the generic scenario observed here.

    Transport coefficients of a quantum system interacting with a squeezed heat bath
    Sh. A. Kalandarov, Z. Kanokov, G. G. Adamian, and N. V. Antonenko
    Published 26 July 2006 (11 pages)
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    The analytical expressions for the time-dependent friction and diffusion coefficients are presented for the case of coupling in coordinates between the collective subsystem and a squeezed heat bath. The effects of initial phase-sensitive and -insensitive correlations of the heat bath on the diffusion coefficients, fluctuations, and decoherence are studied. The interplay between friction and decoherence is discussed.

    Density of Yang-Lee zeros for the Ising ferromagnet
    Seung-Yeon Kim
    Published 26 July 2006 (7 pages)
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    The densities of Yang-Lee zeros for the Ising ferromagnet on the L×L square lattice are evaluated from the exact grand partition functions (L=3~16). The properties of the density of Yang-Lee zeros are discussed as a function of temperature T and system size L. The three different classes of phase transitions for the Ising ferromagnet—first-order phase transition, second-order phase transition, and Yang-Lee edge singularity—are clearly distinguished by estimating the magnetic scaling exponent yh from the densities of zeros for finite-size systems. The divergence of the density of zeros at Yang-Lee edge in high temperatures (Yang-Lee edge singularity), which has been detected only by the series expansion until now for the square-lattice Ising ferromagnet, is obtained from the finite-size data. The identification of the orders of phase transitions in small systems is also discussed using the density of Yang-Lee zeros.

    Nonanalytic microscopic phase transitions and temperature oscillations in the microcanonical ensemble: An exactly solvable one-dimensional model for evaporation
    Stefan Hilbert and Jörn Dunkel
    Published 26 July 2006 (7 pages)
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    We calculate exactly both the microcanonical and canonical thermodynamic functions (TDFs) for a one-dimensional model system with piecewise constant Lennard-Jones type pair interactions. In the case of an isolated N-particle system, the microcanonical TDFs exhibit (N–1) singular (nonanalytic) microscopic phase transitions of the formal order N/2, separating N energetically different evaporation (dissociation) states. In a suitably designed evaporation experiment, these types of phase transitions should manifest themselves in the form of pressure and temperature oscillations, indicating cooling by evaporation. In the presence of a heat bath (thermostat), such oscillations are absent, but the canonical heat capacity shows a characteristic peak, indicating the temperature-induced dissociation of the one-dimensional chain. The distribution of complex zeros of the canonical partition may be used to identify different degrees of dissociation in the canonical ensemble.

    Kardar-Parisi-Zhang interfaces bounded by long-ranged potentials
    Omar Al Hammal, Francisco de los Santos, Miguel A. Muñoz, and Margarida M. Telo da Gama
    Published 26 July 2006 (11 pages)
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    We study unbinding transitions of a nonequilibrium Kardar-Parisi-Zhang interface in the presence of long-ranged substrates. Both attractive and repulsive substrates, as well as positive and negative Kardar-Parisi-Zhang nonlinearities, are considered, leading to four different physical situations. A detailed comparison with equilibrium wetting transitions as well as with nonequilibrium unbinding transitions in systems with short-ranged forces is presented, yielding a comprehensive picture of unbinding transitions and of their classification into universality classes. These nonequilibrium transitions may play a crucial role in the dynamics of the wetting or growth of systems with intrinsic anisotropies.

    Ising model on two connected Barabasi-Albert networks
    Krzysztof Suchecki and Janusz A. Holyst
    Published 26 July 2006 (5 pages)
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    We investigate analytically the behavior of the Ising model on two connected Barabasi-Albert networks. Depending on relative ordering of both networks there are two possible phases corresponding to parallel or antiparallel alignment of spins in both networks. A difference between critical temperatures of both phases disappears in the limit of vanishing inter-network coupling for identical networks. The analytic predictions are confirmed by numerical simulations.

    Directed percolation with incubation times
    Andrea Jiménez-Dalmaroni
    Published 26 July 2006 (16 pages)
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    We introduce a model for directed percolation with a long-range temporal diffusion, while the spatial diffusion is kept short ranged. In an interpretation of directed percolation as an epidemic process, this non-Markovian modification can be understood as incubation times, which are distributed accordingly to a Lévy distribution. We argue that the best approach to find the effective action for this problem is through a generalization of the Cardy-Sugar method, adding the non-Markovian features into the geometrical properties of the lattice. We formulate a field theory for this problem and renormalize it up to one loop in a perturbative expansion. We solve the various technical difficulties that the integrations possess by means of an asymptotic analysis of the divergences. We show the absence of field renormalization at one-loop order, and we argue that this would be the case to all orders in perturbation theory. Consequently, in addition to the characteristic scaling relations of directed percolation, we find a scaling relation valid for the critical exponents of this theory. In this universality class, the critical exponents vary continuously with the Lévy parameter.

    Moment ratios for the pair-contact process with diffusion
    Marcelo M. de Oliveira and Ronald Dickman
    Published 31 July 2006 (6 pages)
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    We study the continuous absorbing-state phase transition in the one-dimensional pair contact process with diffusion (PCPD). In previous studies [Dickman and de Menezes, Phys. Rev. E 66, 045101(R) (2002)], the critical point moment ratios of the order parameter showed anomalous behavior, growing with system size rather than taking universal values, as expected. Using the quasistationary simulation method we determine the moments of the order parameter up to fourth order at the critical point, in systems of up to 40 960 sites. Due to strong finite-size effects, the ratios converge only for large system sizes. Moment ratios and associated order-parameter histograms are compared with those of directed percolation. We also report an improved estimate [pc=0.077  092(1)] for the location of the critical point in the nondiffusive pair contact process.

    Phase transitions and superuniversality in the dynamics of a self-driven particle
    R. Grima
    Published 31 July 2006 (6 pages)
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    We study an active random walker model in which a particle's motion is determined by a self-generated field. The field encodes information about the particle's path history. This leads to either self-attractive or self-repelling behavior. For self-repelling behavior, we find a phase transition in the dynamics: when the coupling between the field and the walker exceeds a critical value, the particle's behavior changes from renormalized diffusion to one characterized by a diverging diffusion coefficient. The dynamical behavior for all cases is surprisingly independent of dimension and of the noise amplitude.

    Upper and lower bounds of stochastic resonance and noise-induced synchronization in a bistable oscillator
    Agnessa Kovaleva
    Published 31 July 2006 (5 pages)
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    This paper discusses concepts of stochastic resonance and noise-induced synchronization in a bistable oscillator subject to both periodic signal and noise. We demonstrate that stochastic resonance is not directly correlated with the matching of the signal frequency and the switching rate. The phenomena of stochastic resonance and noise-induced synchronization are the limiting cases of noise-induced transitions, and the spectral response heavily depends on the input signal-to-noise ratio. The lower and upper bounds of noise intensity allowing synchronization are found as functions of the system's parameters.

    Monte Carlo results for continuum percolation in low and high dimensions
    N. Wagner, I. Balberg, and D. Klein
    Published 31 July 2006 (9 pages)
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    We report on Monte Carlo simulations of continuum percolation thresholds, by implementing highly efficient algorithms for very large samples. Our work, which includes percolation of hyperspheres, hypercubes, and boxes, in various dimensions, sizes, and shapes, has confirmed the expected dependence of the threshold on Vex, the total excluded volume, and on Bc, the average number of bonds per site. We have further confirmed that Vex=Bc, and that Bc is dependent on the objects shape, for which we offer a possible explanation. In particular we find that, counterintuitively, one can have Bc<1, as we have found for hyperspheres of dimension >=12. From our many results for differently sized hyperspheres, we were also able to derive the correlation length exponent nu solely from the behavior of the thresholds using finite-size scaling.

    Equilibrium and linear transport properties of fluids

    Bridge functions near the liquid-vapor coexistence curve in binary Lennard-Jones mixtures
    Tapas R. Kunor and Srabani Taraphder
    Published 25 July 2006 (8 pages)
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    We have carried out extensive NPT molecular-dynamics simulation studies of binary Lennard-Jones mixtures to calculate directly the bridge function at state points lying in a very narrow single fluid phase region between the vapor-liquid and solid-liquid coexistence lines [Lamm and Hall, Fluid Phase Equilib. 182, 37 (2001); 194–197, 197 (2002)]. By varying the density close to the liquid-vapor coexistence line, significant deviations are observed at intermediate distances between the simulated bridge function and two widely used approximate closures in the integral equation theory of liquids, viz. the hybrid mean spherical approximation and the Duh-Henderson closures. The overall qualitative agreement remains the same with small variation in temperature that brings the system closer to either the liquid-vapor or liquid-solid coexistence curve. We also report a comparison of the direct and indirect correlation functions obtained from our simulation studies as well as from the integral equation theory of liquids. Our results emphasize the need for developing new closures applicable to binary fluid mixtures over a wide range of thermodynamic parameters.

    Long-time behavior of the velocity autocorrelation function at low densities and near the critical point of simple fluids
    R. F. A. Dib, F. Ould-Kaddour, and D. Levesque
    Published 31 July 2006 (6 pages)
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    Numerous theoretical and numerical works have been devoted to the study of the algebraic decrease at large times of the velocity autocorrelation function of particles in a fluid. The derivation of this behavior, the so-called long-time tail, generally based on linearized hydrodynamics, makes no reference to any specific characteristic of the particle interactions. However, in the literature doubts have been expressed about the possibility that by numerical simulations the long-time tail can be observed in the whole fluid phase domain of systems in which the particles interact by soft-core and attractive pair potentials. In this work, extensive and accurate molecular-dynamics simulations establish that the predicted long-time tail of the velocity autocorrelation function exists in a low-density fluid of particles interacting by a soft-repulsive potential and near the liquid-gas critical point of a Lennard-Jones system. These results contribute to the confirmation that the algebraic decay of the velocity autocorrelation function is universal in these fluid systems.

    Granular materials

    Pattern formation during air injection into granular materials confined in a circular Hele-Shaw cell
    Ø. Johnsen, R. Toussaint, K. J. Måløy, and E. G. Flekkøy
    Published 11 July 2006 (13 pages)
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    We investigate the dynamics of granular materials confined in a radial Hele-Shaw cell, during central air injection. The behavior of this granular system, driven by its interstitial fluid, is studied both experimentally and numerically. This allows us to explore the associated pattern formation process, characterize its features and dynamics. We classify different hydrodynamic regimes as function of the injection pressure. The numerical model takes into account the interactions between the granular material and the interstitial fluid, as well as the solid-solid interactions between the grains and the confining plates. Numerical and experimental results are comparable, both to reproduce the hydrodynamical regimes experimentally observed, as well as the dynamical features associated to fingering and compacting.

    Statistical description of sediment transport experiments
    Christophe Ancey, Tobias Böhm, Magali Jodeau, and Philippe Frey
    Published 18 July 2006 (14 pages)
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    A longstanding problem in the study of sediment transport in gravel-bed rivers is related to the physical mechanisms governing bed resistance and particle motion. To study this problem, we investigated the motion of coarse spherical glass beads entrained by a steady shallow turbulent water flow down a steep two-dimensional channel with a mobile bed. This experimental facility is the simplest representation of sediment transport on the laboratory scale, with the tremendous advantages that boundary conditions are perfectly controlled and a wealth of information can be obtained using imaging techniques. Flows were filmed from the side by a high-speed camera. Using image processing software made it possible to determine the flow characteristics such as particle trajectories, their state of motion (rest, rolling, or saltating motion), and flow depth. In accordance with earlier investigations, we observed that over short time periods, sediment transport appeared as a very intermittent process. To interpret these results, we revisited Einstein's theory on sediment and derived the statistical properties (probability distribution and autocorrelation function) of the key variables such as the solid discharge and the number of moving particles. Analyzing the autocorrelation functions and the probability distributions of our measurements revealed the existence of long-range correlations. For instance, whereas theory predicts a Binomial distribution for the number of moving particles, experiments demonstrated that a negative binomial distribution best fit our data, which emphasized the crucial role played by wide fluctuations. These frequent wide fluctuations stemmed particle entrainment and motion being collective phenomena rather than individual processes, contrary to what is assumed in most theoretical models.

    Front propagation sustained by additive noise
    M. G. Clerc, C. Falcón, and E. Tirapegui
    Published 21 July 2006 (15 pages)
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    The effect of noise in a motionless front between a periodic spatial state and an homogeneous one is studied. Numerical simulations show that noise induces front propagation. From the subcritical Swift-Hohenberg equation with noise, we deduce an adequate equation for the envelope and the core of the front. The equation of the core of the front is characterized by an asymmetrical periodic potential plus additive noise. The conversion of random fluctuations into direct motion of the core of the front is responsible of the propagation. We obtain an analytical expression for the velocity of the front, which is in good agreement with numerical simulations.

    Fluidization of a vertically vibrated two-dimensional hard sphere packing: A granular meltdown
    Andreas Götzendorfer, Chi-Hwang Tai, Christof A. Kruelle, Ingo Rehberg, and Shu-San Hsiau
    Published 21 July 2006 (9 pages)
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    We report measurements of the fluidization process in vertically vibrated two-dimensional granular packings. An initially close packed granular bed is exposed to sinusoidal container oscillations with gradually increasing amplitude. At first the particles close to the free surface become mobile. When a critical value of the forcing strength is reached the remaining crystal suddenly breaks up and the bed fluidizes completely. This transition leads to discontinuous changes in the density distribution and in the root mean square displacement of the individual particles. Likewise the vertical center of mass coordinate increases by leaps and bounds at the transition. It turns out that the maximum container velocity v0 is the crucial driving parameter determining the state of a fully fluidized system. For particles of various sizes the transition to full fluidization occurs at the same value of v0<sup>2</sup>/gd, where d is the particle diameter and g is the gravitational acceleration. A discontinuous fluidization transition is only observed when the particles are highly elastic.

    Collapse of periodic orbits in a driven inelastic particle system
    Jonathan J. Wylie and Qiang Zhang
    Published 21 July 2006 (10 pages)
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    The dynamical behavior of a one-dimensional inelastic particle system with particles of unequal mass traveling between two walls is investigated. The system is driven by adding energy at one of the walls while the other wall is stationary and does not add energy. By deriving analytic solutions for the periodic orbits of this system, we show that there are a countable infinity of critical mass ratios at which the particle dynamics become highly degenerate in the following sense. As the mass ratio passes through these critical points, large numbers of stable periodic orbits can collapse onto a single trivial orbit. We show that the widely studied equal-mass systems represent one of these critical points and are therefore such a degenerate case. We also show that in the elastic limit the number of orbits that collapse onto the single trivial orbit can become arbitrarily large.

    Flux through a hole from a shaken granular medium
    K. Chen, M. B. Stone, R. Barry, M. Lohr, W. McConville, K. Klein, B. L. Sheu, A. J. Morss, T. Scheidemantel, and P. Schiffer
    Published 25 July 2006 (4 pages)
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    We have measured the flux of grains from a hole in the bottom of a shaken container of grains. We find that the peak velocity of the vibration, vmax, controls the flux, i.e., the flux is nearly independent of the frequency and acceleration amplitude for a given value of vmax. The flux decreases with increasing peak velocity and then becomes almost constant for the largest values of vmax. The data at low peak velocity can be quantitatively described by a simple model, but the crossover to nearly constant flux at larger peak velocity suggests a regime in which the granular density near the container bottom is independent of the energy input to the system.

    Mechanisms in the size segregation of a binary granular mixture
    Matthias Schröter, Stephan Ulrich, Jennifer Kreft, Jack B. Swift, and Harry L. Swinney
    Published 26 July 2006 (14 pages)
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    A granular mixture of particles of two sizes that is shaken vertically will in most cases segregate. If the larger particles accumulate at the top of the sample, this is called the Brazil-nut effect (BNE); if they accumulate at the bottom, it is called the reverse Brazil-nut effect (RBNE). While this process is of great industrial importance in the handling of bulk solids, it is not well understood. In recent years ten different mechanisms have been suggested to explain when each type of segregation is observed. However, the dependence of the mechanisms on driving conditions and material parameters and hence their relative importance is largely unknown. In this paper we present experiments and simulations where both types of particles are made from the same material and shaken under low air pressure, which reduces the number of mechanisms to be considered to seven. We observe both BNE and RBNE by varying systematically the driving frequency and amplitude, diameter ratio, ratio of total volume of small to large particles, and overall sample volume. All our results can be explained by a combination of three mechanisms: a geometrical mechanism called void filling, transport of particles in sidewall-driven convection rolls, and thermal diffusion, a mechanism predicted by kinetic theory.

    Colloidal dispersions, suspensions, and aggregates

    Relaxation of jammed colloidal suspensions after shear cessation
    Francesca Ianni, David Lasne, Régis Sarcia, and Pascal Hébraud
    Published 20 July 2006 (6 pages)
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    The dynamics of heterogeneities in a shear thickening, concentrated colloidal suspension is investigated through speckle visibility spectroscopy, a dynamic light scattering technique recently introduced [P. K. Dixon and D. J. Durian, Phys. Rev. Lett. 90, 184302 (2003)]. Formation of shear-induced heterogeneities is observed in the jamming regime, and their relaxation after shear cessation is monitored as a function of the applied shear stress. The relaxation time of these heterogeneities increases when a higher stress is applied.

    Formalism for calculation of polymer-solvent-mediated potential
    Shiqi Zhou
    Published 20 July 2006 (11 pages)
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    A simple theoretical approach is proposed for calculation of a solvent-mediated potential (SMP) between two colloid particles immersed in a polymer solvent bath in which the polymer is modeled as a chain with intramolecular degrees of freedom. The present recipe is only concerned with the estimation of the density profile of a polymer site around a single solute colloid particle instead of two solute colloid particles separated by a varying distance as done in existing calculational methods for polymer-SMP. Therefore the present recipe is far simpler for numerical implementation than the existing methods. The resultant predictions for the polymer-SMP and polymer solvent-mediated mean force (polymer-SMMF) are in very good agreement with available simulation data. With the present recipe, change tendencies of the contact value and second virial coefficiency of the SMP as a function of size ratio between the colloid particle and polymer site, the number of sites per chain, and the polymer concentration are investigated in detail. The metastable critical polymer concentration as a function of size ratio and the number of sites per chain is also reported for the first time. To yield the numerical solution of the present recipe at less than 1  min on a personal computer, a rapid and accurate algorithm for the numerical solution of the classical density functional theory is proposed to supply rapid and accurate estimation of the density profile of the polymer site as an input into the present formalism.

    Cooperative behavior and pattern formation in mixtures of driven and nondriven colloidal assemblies
    C. Reichhardt and C. J. Olson Reichhardt
    Published 24 July 2006 (5 pages)
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    We simulate a disordered assembly of particles interacting through a repulsive Yukawa potential with a small fraction of the particles coupled to an external drive. Distortions in the arrangement of the nondriven particles produce a dynamically induced effective attraction between the driven particles, giving rise to intermittent one-dimensional stringlike structures. The velocity of a moving string increases with the number of driven particles in the string. We identify the average stable string length as a function of driving force, background particle density, and particle charge. This model represents a type of collective transport system composed of interacting particles moving through deformable disorder.

    Dynamic scaling in entangled mean-field gelation polymers
    Chinmay Das, Daniel J. Read, Mark A. Kelmanson, and Tom C. B. McLeish
    Published 27 July 2006 (11 pages)
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    We present a simple reaction kinetics model to describe the polymer synthesis used by Lusignan et al. [Phys. Rev. E 60, 5657 (1999)] to produce randomly branched polymers in the vulcanization class. Numerical solution of the rate equations gives probabilities for different connections in the final product, which we use to generate a numerical ensemble of representative molecules. All structural quantities probed in the experiments are in quantitative agreement with our results for the entire range of molecular weights considered. However, with detailed topological information available in our calculations, our estimate of the "rheologically relevant" linear segment length is smaller than that estimated from the experimental results. We use a numerical method based on a tube model of polymer melts to calculate the rheological properties of such molecules. Results are in good agreement with experiment, except that in the case of the largest molecular weight samples our estimate of the zero-shear viscosity is significantly lower than the experimental findings. Using acid concentration as an indicator for closeness to the gelation transition, we show that the high-molecular-weight polymers considered are at the limit of mean-field behavior—which possibly is the reason for this disagreement. For a truly mean-field gelation class of model polymers, we numerically calculate the rheological properties for a range of segment lengths. Our calculations show that the tube theory with dynamical dilation predicts that, very close to the gelation limit, the contribution to viscosity for this class of polymers is dominated by the contribution from constraint-release Rouse motion and the final viscosity exponent approaches a Rouse-like value.

    Structured and complex fluids

    Nonlinear electrochemical relaxation around conductors
    Kevin T. Chu and Martin Z. Bazant
    Published 6 July 2006 (25 pages)
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    We analyze the simplest problem of electrochemical relaxation in more than one dimension—the response of an uncharged, ideally polarizable metallic sphere (or cylinder) in a symmetric, binary electrolyte to a uniform electric field. In order to go beyond the circuit approximation for thin double layers, our analysis is based on the Poisson-Nernst-Planck (PNP) equations of dilute solution theory. Unlike most previous studies, however, we focus on the nonlinear regime, where the applied voltage across the conductor is larger than the thermal voltage. In such strong electric fields, the classical model predicts that the double layer adsorbs enough ions to produce bulk concentration gradients and surface conduction. Our analysis begins with a general derivation of surface conservation laws in the thin double-layer limit, which provide effective boundary conditions on the quasineutral bulk. We solve the resulting nonlinear partial differential equations numerically for strong fields and also perform a time-dependent asymptotic analysis for weaker fields, where bulk diffusion and surface conduction arise as first-order corrections. We also derive various dimensionless parameters comparing surface to bulk transport processes, which generalize the Bikerman-Dukhin number. Our results have basic relevance for double-layer charging dynamics and nonlinear electrokinetics in the ubiquitous PNP approximation.

    Dynamics of ternary mixtures with photosensitive chemical reactions: Creating three-dimensionally ordered blends
    Olga Kuksenok, Rui D. M. Travasso, and Anna C. Balazs
    Published 11 July 2006 (13 pages)
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    Using computer simulations, we establish an approach for creating defect-free, periodically ordered polymeric materials. The system involves ABC ternary mixtures where the A and B components undergo a reversible photochemical reaction. In addition, all three components are mutually immiscible and undergo phase separation. Through the simulations, we model the effects of illuminating a three-dimensional (3D) sample with spatially and temporally dependent light irradiation. Experimentally, this situation can be achieved by utilizing both a uniform background light and a spatially localized, higher intensity light, and then rastering a higher-intensity light over the 3D sample. We first focus on the case where the higher-intensity light is held stationary and focused in a distinct region within the system. The C component is seen to displace the A and B within this region and replicate the pattern formed by the higher-intensity light. In effect, one can write a pattern of C onto the AB binary system by focusing the higher-intensity light in the desired arrangement. We isolate the conditions that are necessary for producing clearly written patterns of C (i.e., for obtaining sharp interfaces between the C and A/B domains). We next consider the effect of rastering a higher-intensity light over this sample and find that this light "combs out" defects in the AB blend as it moves through the system. The resulting material displays a defect-free structure that encompasses both a periodic ordering of the A and B domains and a well-defined motif of C. In this manner, one can create hierarchically patterned materials that exhibit periodicity over two distinct length scales. The approach is fully reversible, noninvasive, and points to a novel means of patterning with homopolymers, which normally do not self-assemble into periodic structures.

    Cole-Cole law for critical dynamics in glass-forming liquids
    Matthias Sperl
    Published 13 July 2006 (15 pages)
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    Within the mode-coupling theory (MCT) for glassy dynamics, the asymptotic low-frequency expansions for the dynamical susceptibilities at critical points are compared to the expansions for the dynamic moduli; this shows that the convergence properties of the two expansions can be quite different. In some parameter regions, the leading-order expansion formula for the modulus describes the solutions of the MCT equations of motion outside the transient regime successfully; at the same time, the leading- and next-to-leading-order expansion formulas for the susceptibility fail. In these cases, one can derive a Cole-Cole law for the susceptibilities; and this law accounts for the dynamics for frequencies below the band of microscopic excitations and above the high-frequency part of the alpha peak. It is shown that this scenario explains the optical-Kerr-effect data measured for salol and benzophenone (BZP). For BZP it is inferred that the depolarized light-scattering spectra exhibit a wing for the alpha peak within the Gigahertz band. This wing results from the crossover of the von Schweidler law part of the alpha peak to the high-frequency part of the Cole-Cole peak; and this crossover can be described quantitatively by the leading-order formulas of MCT for the modulus.

    Observations of coarsening of air voids in a polymer–highly-soluble crystalline matrix during dissolution
    Eleni Karakosta, Paul M. Jenneson, Richard P. Sear, and Peter J. McDonald
    Published 17 July 2006 (7 pages)
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    A combination of magnetic resonance imaging and x-ray microcomputed tomography has been used to visualize the development of the internal micro-structure within compressed tablets made from a combination of insoluble particles (Eudragit, a polymer) and soluble particles (diltiazem hydrochloride, a drug), during dissolution in water. Air voids in the tablet are seen to coarsen. The size distribution of the air voids is well fitted by a log-normal distribution with a mean size that grows linearly with time. There is evidence for both diffusion of voids and sudden collapse of individual voids, presumably as they coalesce. The behavior of the voids is studied and compared with models of coarsening; the implications for tablet dissolution are considered.

    Morphologies and flow patterns in quenching of lamellar systems with shear
    Aiguo Xu, G. Gonnella, and A. Lamura
    Published 24 July 2006 (11 pages)
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    We study the behavior of a fluid quenched from the disordered into the lamellar phase under the action of a shear flow. The dynamics of the system is described by Navier-Stokes and convection-diffusion equations with the pressure tensor and the chemical potential derived by the Brazovskii free energy. Our simulations are based on a mixed numerical method with the lattice Boltzmann equation and a finite difference scheme for Navier-Stokes and order parameter equations, respectively. We focus on cases where banded flows are observed with two different slopes for the component of velocity in the direction of the applied flow. Close to the walls the system reaches a lamellar order with very few defects, and the slope of the horizontal velocity is higher than the imposed shear rate. In the middle of the system the local shear rate is lower than the imposed one, and the system looks like a mixture of tilted lamellae, droplets, and small elongated domains. We refer to this as a region with a shear-induced structures (SIS) configuration. The local behavior of the stress shows that the system with the coexisting lamellar and SIS regions is in mechanical equilibrium. This phenomenon occurs, at fixed viscosity, for shear rates under a certain threshold; when the imposed shear rate is sufficiently large, lamellar order develops in the whole system. Effects of different viscosities have been also considered. The SIS region is observed only at low enough viscosity. We compare the above scenario with the usual one of shear banding. In particular, we do not find evidence for a plateau of the stress at varying imposed shear rates in the region with banded flow. We interpret our results as due to a tendency of the lamellar system to oppose the presence of the applied flow.

    Transitions among crystal, glass, and liquid in a binary mixture with changing particle-size ratio and temperature
    Toshiyuki Hamanaka and Akira Onuki
    Published 25 July 2006 (7 pages)
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    Using molecular dynamics simulation we examine changeovers among crystal, glass, and liquid at high density in a two dimensional binary mixture. We change the ratio between the diameters of the two components and the temperature. The transitions from crystal to glass or liquid occur with proliferation of defects. We visualize the defects in terms of a disorder variable Dj(t) representing a deviation from the hexagonal order for particle j. The defect structures are heterogeneous and are particularly extended in polycrystal states. They look similar at the crystal-glass crossover and at the melting. Taking the average of Dj(t) over the particles, we define a disorder parameter D(t), which measures the degree of overall disorder. The relaxation of D(t) after quenching becomes slow at low temperature in the presence of size dispersity. Its steady state average is small in crystal and large in glass and liquid. We also find that grain boundaries tend to be pinned with increasing size dispersity in polycrystal states.

    Effects of quenching rate and viscosity on spinodal decomposition
    P. Poesio, G. Cominardi, A. M. Lezzi, R. Mauri, and G. P. Beretta
    Published 25 July 2006 (13 pages)
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    Spinodal decomposition of deeply quenched mixtures is studied experimentally, with particular emphasis on the domain growth rate during the late stage of coarsening. We provide some experimental evidence that at high Péclet number, the process is isotropic and the domain growth is linear in time, even at finite quenching rates. In fact, the quenching rate appears to influence the magnitude of the growth rate, but not its scaling law. In the second part of the work we analyze the effect of viscosity on the growth rate. As predicted by the diffuse interface model, we do not find any effect of viscosity on the growth rate of the nucleating drops, although, as expected, the viscosity of the continuous phase does influence the settling speed and thus the total separation time.

    Films, interfaces, and crystal growth

    Renormalization-group theory for the phase-field crystal equation
    Badrinarayan P. Athreya, Nigel Goldenfeld, and Jonathan A. Dantzig
    Published 17 July 2006 (13 pages)
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    We derive a set of rotationally covariant amplitude equations for use in multiscale simulation of the two-dimensional phase-field crystal model by a variety of renormalization-group (RG) methods. We show that the presence of a conservation law introduces an ambiguity in operator ordering in the RG procedure, which we show how to resolve. We compare our analysis with standard multiple-scale techniques, where identical results can be obtained with greater labor, by going to sixth order in perturbation theory, and by assuming the correct scaling of space and time.

    Effects of island disaggregation in growth models
    K. Mazzitello, C. M. Aldao, and H. O. Mártin
    Published 18 July 2006 (7 pages)
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    We introduced two point island models with island disaggregation. In the first one, particles can detach from islands with an odd number of particles and from those with two particles. In the second model, particles can detach from all islands with more than two particles. The scaling exponents are analytically obtained and verified with Monte Carlo simulations. Specially, the power-law scalings of the island and monomer densities are analyzed. Comparison with other models indicates that the models introduced here present different scaling behaviors.

    Surface and interfacial dynamics of polymeric bilayer films
    Zhang Jiang, Hyunjung Kim, Simon G. J. Mochrie, L. B. Lurio, and Sunil K. Sinha
    Published 19 July 2006 (9 pages)
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    The theory for surface dynamics of the thermally excited fluctuations on a homogenous single-layer film of arbitrary depth is generalized to describe surface and interfacial dynamics of polymeric liquid bilayer films in terms of susceptibilities, power spectra, and characteristic relaxation time constants. The effects on surface dynamics originating from viscosity inhomogeneities close to the surface and interfacial regions are investigated by the bilayer theory and compared with the surface dynamics of homogeneous single-layer films under nonslip and slip boundary conditions. Our bilayer theory can also be extended to study interfacial dynamics of more generalized multilayer systems. The effects of viscoelasticity and van der Waals interactions on surface and interfacial dynamics are also briefly discussed.

    Universal and nonuniversal features in the crossover from linear to nonlinear interface growth
    T. J. Oliveira, K. Dechoum, J. A. Redinz, and F. D. A. Aarão Reis
    Published 31 July 2006 (6 pages)
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    We study a restricted solid-on-solid model involving deposition and evaporation with probabilities p and 1–p, respectively, in one-dimensional substrates. It presents a crossover from Edwards-Wilkinson (EW) to Kardar-Parisi-Zhang (KPZ) scaling for p[approximate]0.5. The associated KPZ equation is analytically derived, exhibiting a coefficient lambda of the nonlinear term proportional to q[equivalent]p–1/2, which is confirmed numerically by calculation of tilt-dependent growth velocities for several values of p. This linear lambda–q relation contrasts to the apparently universal parabolic law obtained in competitive models mixing EW and KPZ components. The regions where the interface roughness shows pure EW and KPZ scaling are identified for 0.55<=p<=0.8, which provides numerical estimates of the crossover times tc. They scale as tc~lambda–phi with phi=4.1±0.1, which is in excellent agreement with the theoretically predicted universal value phi=4 and improves previous numerical estimates, which suggested phi[approximate]3.

    Liquid crystals

    Investigations of nanoscale helical pitch in smectic-C<sub>alpha</sub><sup>*</sup> and smectic-C* phases of a chiral smectic liquid crystal using differential optical reflectivity measurements
    V. P. Panov, B. K. McCoy, Z. Q. Liu, J. K. Vij, J. W. Goodby, and C. C. Huang
    Published 6 July 2006 (7 pages)
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    Differential optical reflectivity (DOR) was used to study the temperature dependence of the short helical pitch in freestanding films of a liquid crystal compound. The experimentally measured DOR signal was fitted using Berreman's 4×4 matrix method to get the pitch value in the smectic-Calpha<sup>*</sup> (SmCalpha<sup>*</sup>) phase. The results show continuous evolution of the pitch between the smectic-C* and SmCalpha<sup>*</sup> phases. In SmCalpha<sup>*</sup>, the pitch decreases as temperature increases and is found to level off at 16±1 smectic layers at the SmCalpha<sup>*</sup> to smectic-A* transition.

    Microscopic and macroscopic description of anchoring at the nematic-solid substrate interface
    L. V. Mirantsev
    Published 6 July 2006 (7 pages)
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    A simple microscopic mean-field model for a flat nematic liquid crystal (NLC) sample in a contact to the solid substrate surface is offered. An interaction between NLC molecules is simulated by the well known McMillan model potential, and an orienting action of the solid substrate surface on NLC molecules is modeled by a short-range external field which acts directly only on molecules within the first molecular layer of the nematic sample adjacent to the substrate surface. For an undistorted NLC sample, the model allows the calculation of local order parameter profiles for different values of strength of this external orienting field and temperature of the sample. These profiles are used in a description of a director field distortion caused by a certain external action and in the calculation of the anchoring energy coefficient W used in a macroscopic description of the anchoring at the nematic-solid substrate interface. Dependence of this coefficient on the strength of the short-range orienting field is obtained, and an unequivocal relation between the magnitude of W and the orientational order parameter profile near the substrate surface is established. The temperature dependence of the coefficient W calculated from the offered microscopic model is in good agreement with the experimental data on NLC MBBA.

    Role of molecular weight and phase sequence in the temperature variation of film tension above the bulk isotropic transition in freestanding liquid-crystal films
    M. Veum, M. K. Blees, N. Voshell, H. T. Nguyen, and C. C. Huang
    Published 11 July 2006 (5 pages)
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    Building upon our previous report [Veum et al., Phys. Rev. E 17, 020701(R) (2005)] involving two compounds, we have performed a systematic study of the temperature variation of film tension above the bulk isotropic transition in freestanding films to include a total of six smectic liquid-crystal compounds. Consistent with the previous results, the tension increases sharply with temperature above the transition, the tension-temperature slope is proportional to the film's thickness, and the data can be interpreted in the context of theoretical models for layer thinning. Our data suggest that both molecular weight and bulk phase appearing below its isotropic phase play important roles in the slope values.

    Computer simulation study of a simple cubatic mesogenic lattice model
    Silvano Romano
    Published 11 July 2006 (6 pages)
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    Over the last 15  years, the possible existence of a cubatic mesophase, possessing cubic orientational order (i.e., along three mutually orthogonal axes) but no translational one, has been addressed theoretically, and predicted in some cases, where the investigated interaction models involved hard-core repulsion only; on the other hand, no experimental realizations of such a phase are known at the time being. The present paper addresses a very simple cubatic mesogenic lattice model, involving continuous interactions; we consider particles possessing Oh symmetry, whose centers of mass are associated with a three-dimensional simple-cubic lattice; the pair potential is taken to be isotropic in orientation space, and restricted to nearest neighboring sites; let the two orthonormal triads {uj, j=1,2,3} and {vk, k=1,2,3} define orientations of a pair of interacting particles, and let fjk=vj·uk. The interaction model studied here is defined by the simplest nontrivial (quartic) polynomial in the scalar products fjk, consistent with the assumed symmetry and favoring orientational order; it is, so to speak, the cubatic counterpart of the Lebwohl-Lasher model for uniaxial nematics. The model was investigated by mean field theory and Monte Carlo simulation, and found to produce a low-temperature cubatically ordered phase, undergoing a first order transition to the isotropic phase at higher temperature; the mean field treatment yielded results in reasonable qualitative agreement with simulation.

    Theory of the intermediate tilted smectic phases and their helical rotation
    A. V. Emelyanenko, Atsuo Fukuda, and J. K. Vij
    Published 13 July 2006 (17 pages)
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    A molecular-statistical theory for the entire sequence of the chiral tilted smectic phases is derived. Uniaxial and biaxial subphases were found to be stable in different temperature ranges depending on the molecular parameters. The model of a chiral molecule possessing a strong transverse terminal dipole moment and a quadrupole moment located in the molecular core was used. Direct dispersion and electrostatic interactions (modulated by shape) between molecules located in the same or in the neighboring smectic layers are taken into account. An effective long-range interaction arises after the minimization of the free energy with respect to polarization vectors. If the molecular quadrupole moment is small, only uniaxial phases with different periodicities arise. Their periodicity may be tens and hundreds of layers (Sm-C*), or approximately two layers (Sm-CA<sup>*</sup>), or several layers (Sm-Calpha<sup>*</sup>). In the presence of the nonpolar biaxial ordering (in addition to polarization) there is a cap-shaped border in the phase diagram that separates Sm-CA<sup>*</sup>, Sm-C*, and Sm-Calpha<sup>*</sup>. If the molecules are nonchiral, Sm-CA, Sm-C, and the de Vries's phases arise instead of the three phases mentioned above. If the molecular quadrupole moment is large, the left "arm" of the border breaks into two lines, and a sequence of biaxial subphases arises in the area between these two lines. Among these biaxial subphases, the one with periodicity of three smectic layers appears to be the broadest in the temperature range. In addition, the subphases with different periodicities were found to be stable in narrow temperature ranges. The long helical rotation in every biaxial subphase is calculated. It is found to change sign between the three-layer subphase and Sm-C*, and may diverge in the four-layer subphase if it arises. All calculations are done with help of (A)FLC Phase Diagram Plotter software developed by the first author and available at his web-page.

    Memory effects in nematics with quenched disorder
    M. Buscaglia, T. Bellini, C. Chiccoli, F. Mantegazza, P. Pasini, M. Rotunno, and C. Zannoni
    Published 17 July 2006 (8 pages)
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    We present a combined experimental and Monte Carlo study of a nematic phase in the presence of quenched disorder. The turbidity of a nematic liquid crystal embedded in a porous polymer membrane is measured under different applied field conditions for field-cooled and zero-field-cooled samples. We find that a significant permanent alignment of the nematic can be induced by fields as low as 0.1  V/µm applied during the isotropic to nematic transition. An analogous effect and dependence on sample history is found by studying the order parameter of a sprinkled disorder Lebwohl-Lasher spin model, indicating that dilute quenched randomness is sufficient to produce memory effects in nematics. The large memory induced by field cooling appears to be written in the system during the transition as a result of the field action on freely oriented nematic nuclei. At lower temperature the nuclei consolidate into permanent nematic textures developed from the interaction with quenched disorder.

    Optical and electro-optical derivation of the pretransitional behavior of orientational and shear viscosities in the isotropic phase of liquid crystals
    M. L. Jiménez, F. Mantegazza, L. Gallazzi, G. Zanchetta, and T. Bellini
    Published 19 July 2006 (10 pages)
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    The pretransitional equilibrium properties of isotropic liquids in the proximity of the isotropic-nematic phase transition are well known and successfully modeled. Much less is known about the dynamic behavior, and in particular about the pretransitional viscosity. In this work we combine two techniques [dynamic light scattering (DLS) and electric birefringence spectroscopy (EBS)] offering complementary insights into both static and dynamic pretransitional behavior of the homologous nCB family (n-alkyl cyanobiphenyl). EBS explores the single molecule flipping dynamics retarded by a paranematic potential barrier and enables extracting the associated transport coefficient, which is found to be of Arrhenius type in the whole temperature range explored. DLS reflects the collective dynamics of correlated domains and depends on the viscous damping of the orientational order. Such a viscosity displays Arrhenius behavior only sufficiently far from the transition temperature, with deviations growing as a power law of the appropriate reduced temperature with exponents around 0.1.

    Dispersion of the ordinary refractive indices of smectic liquid crystals in free standing films
    R. Jaquet and F. Schneider
    Published 19 July 2006 (16 pages)
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    The ordinary refractive indices of some smectic-A liquid crystals have been measured by means of interference spectra of free standing films as a function of wavelength and temperature. Numerical data are presented for further use. In the Sm-C phase one of the principal indices can be measured. If the three principal indices in the Sm-C phase would be known the tilt angle could be measured by means of the interference technique with high precision. Predictions of the refractive index of liquid crystals based on quantum chemical calculations of polarizabilities are presented. Using an expression derived by de Jeu and Bordewijk [J. Chem. Phys. 68, 109 (1978)] values for the principal refractive indices have been calculated that can be compared with our experimental results.