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Showing papers in "Physical Review E in 1998"


Journal ArticleDOI
TL;DR: In this article, a dynamical theory of low-temperature shear deformation in amorphous solids is proposed based on molecular-dynamics simulations of a two-dimensional, two-component non-crystalline system.
Abstract: We propose a dynamical theory of low-temperature shear deformation in amorphous solids. Our analysis is based on molecular-dynamics simulations of a two-dimensional, two-component noncrystalline system. These numerical simulations reveal behavior typical of metallic glasses and other viscoplastic materials, specifically, reversible elastic deformation at small applied stresses, irreversible plastic deformation at larger stresses, a stress threshold above which unbounded plastic flow occurs, and a strong dependence of the state of the system on the history of past deformations. Microscopic observations suggest that a dynamically complete description of the macroscopic state of this deforming body requires specifying, in addition to stress and strain, certain average features of a population of two-state shear transformation zones. Our introduction of these state variables into the constitutive equations for this system is an extension of earlier models of creep in metallic glasses. In the treatment presented here, we specialize to temperatures far below the glass transition and postulate that irreversible motions are governed by local entropic fluctuations in the volumes of the transformation zones. In most respects, our theory is in good quantitative agreement with the rich variety of phenomena seen in the simulations. {copyright} {ital 1998} {ital The American Physical Society}

1,769 citations


Journal ArticleDOI
TL;DR: In this article, the authors introduce quantum fluctuations into the simulated annealing process of optimization problems, aiming at faster convergence to the optimal state. But quantum fluctuations cause transitions between states and thus play the same role as thermal fluctuations in the conventional approach.
Abstract: We introduce quantum fluctuations into the simulated annealing process of optimization problems, aiming at faster convergence to the optimal state. Quantum fluctuations cause transitions between states and thus play the same role as thermal fluctuations in the conventional approach. The idea is tested by the transverse Ising model, in which the transverse field is a function of time similar to the temperature in the conventional method. The goal is to find the ground state of the diagonal part of the Hamiltonian with high accuracy as quickly as possible. We have solved the time-dependent Schr\"odinger equation numerically for small size systems with various exchange interactions. Comparison with the results of the corresponding classical (thermal) method reveals that the quantum annealing leads to the ground state with much larger probability in almost all cases if we use the same annealing schedule.

1,710 citations


Journal ArticleDOI
TL;DR: In this article, the authors present a quantitative continuum theory of flock behavior, which predicts the existence of an ordered phase of flocks, in which all members of even an arbitrarily large flock move together with the same mean velocity.
Abstract: We present a quantitative continuum theory of ``flocking'': the collective coherent motion of large numbers of self-propelled organisms. In agreement with everyday experience, our model predicts the existence of an ``ordered phase'' of flocks, in which all members of even an arbitrarily large flock move together with the same mean velocity $〈\stackrel{\ensuremath{\rightarrow}}{v}〉\ensuremath{ e}0.$ This coherent motion of the flock is an example of spontaneously broken symmetry: no preferred direction for the motion is picked out a priori in the model; rather, each flock is allowed to, and does, spontaneously pick out some completely arbitrary direction to move in. By analyzing our model we can make detailed, quantitative predictions for the long-distance, long-time behavior of this ``broken symmetry state.'' The ``Goldstone modes'' associated with this ``spontaneously broken rotational symmetry'' are fluctuations in the direction of motion of a large part of the flock away from the mean direction of motion of the flock as a whole. These ``Goldstone modes'' mix with modes associated with conservation of bird number to produce propagating sound modes. These sound modes lead to enormous fluctuations of the density of the flock, far larger, at long wavelengths, than those in, e.g., an equilibrium gas. Our model is similar in many ways to the Navier-Stokes equations for a simple compressible fluid; in other ways, it resembles a relaxational time-dependent Ginsburg-Landau theory for an $n=d$ component isotropic ferromagnet. In spatial dimensions $dg4,$ the long-distance behavior is correctly described by a linearized theory, and is equivalent to that of an unusual but nonetheless equilibrium model for spin systems. For $dl4,$ nonlinear fluctuation effects radically alter the long distance behavior, making it different from that of any known equilibrium model. In particular, we find that in $d=2,$ where we can calculate the scaling exponents exactly, flocks exhibit a true, long-range ordered, spontaneously broken symmetry state, in contrast to equilibrium systems, which cannot spontaneously break a continuous symmetry in $d=2$ (the ``Mermin-Wagner'' theorem). We make detailed predictions for various correlation functions that could be measured either in simulations, or by quantitative imaging of real flocks. We also consider an anisotropic model, in which the birds move preferentially in an ``easy'' (e.g., horizontal) plane, and make analogous, but quantitatively different, predictions for that model as well. For this anisotropic model, we obtain exact scaling exponents for all spatial dimensions, including the physically relevant case $d=3.$

1,365 citations


Journal ArticleDOI
TL;DR: In this article, a simplified prisoner's game is studied on a square lattice, where the players interacting with their neighbors can follow two strategies: to cooperate or to defect unconditionally, and the players updated in random sequence have a chance to adopt one of the neighboring strategies with a probability depending on the payoff difference.
Abstract: A simplified prisoner's game is studied on a square lattice when the players interacting with their neighbors can follow two strategies: to cooperate $(C)$ or to defect $(D)$ unconditionally. The players updated in random sequence have a chance to adopt one of the neighboring strategies with a probability depending on the payoff difference. Using Monte Carlo simulations and dynamical cluster techniques, we study the density $c$ of cooperators in the stationary state. This system exhibits a continuous transition between the two absorbing states when varying the value of temptation to defect. In the limits $\stackrel{\ensuremath{\rightarrow}}{c}0$ and 1 we have observed critical transitions belonging to the universality class of directed percolation.

1,323 citations


Journal ArticleDOI
TL;DR: In this article, the results of quantitative phase-field simulations of the dendritic crystallization of a pure melt in two and three dimensions were reported, and they were used to test the accuracy of phase field computations performed within the thin interface limit of the phase field model.
Abstract: We report the results of quantitative phase-field simulations of the dendritic crystallization of a pure melt in two and three dimensions. These simulations exploit a recently developed thin-interface limit of the phase-field model [A. Karma and W.-J. Rappel, Phys. Rev. E 53, R3017 (1996)], which is given here a detailed exposition. This limit makes it possible to perform efficient computations with a smaller ratio of capillary length to interface thickness and with an arbitrary interface kinetic coefficient. Simulations in one and two dimensions are first carried out to test the accuracy of phase-field computations performed within this limit. Dendrite tip velocities and tip shapes are found to be in excellent quantitative agreement with exact numerical benchmarks of solvability theory obtained by a boundary integral method, both with and without interface kinetics. Simulations in three dimensions exploit, in addition to the asymptotics, a methodology to calculate grid corrections due to the surface tension and kinetic anisotropies. They are used to test basic aspects of dendritic growth theory that pertain to the selection of the operating state of the tip and to the three-dimensional morphology of needle crystals without sidebranches. For small crystalline anisotropy, simulated values of ${\ensuremath{\sigma}}^{*}$ are slightly larger than solvability theory predictions computed by the boundary integral method assuming an axisymmetric shape, and agree relatively well with experiments for succinonitrile given the uncertainty in the measured anisotropy. In contrast, for large anisotropy, simulated ${\ensuremath{\sigma}}^{*}$ values are significantly larger than the predicted values. This disagreement, however, does not signal a breakdown of solvability theory. It is consistent with the finding that the amplitude of the $\mathrm{cos}4\ensuremath{\varphi}$ mode, which measures the departure of the tip morphology from a shape of revolution, increases with anisotropy. This departure can therefore influence the tip selection in a way that is not accurately captured by the axisymmetric approximation for large anisotropy. Finally, the tail shape at a distance behind the tip that is large compared to the diffusion length is described by a linear law $r\ensuremath{\sim}z$ with a slope $dr/dz$ that is nearly equal to the ratio of the two-dimensional and three-dimensional steady-state tip velocities. Furthermore, the evolution of the cross section of a three-dimensional needle crystal with increasing distance behind the tip is nearly identical to the evolution of a two-dimensional growth shape in time, in accord with the current theory of the three-dimensional needle crystal shape.

1,207 citations


Journal ArticleDOI
TL;DR: Floating car data of car-following behavior in cities were compared to existing microsimulation models, after their parameters had been calibrated to the experimental data and good results were obtained with the proposed generalized force model.
Abstract: Floating car data of car-following behavior in cities were compared to existing microsimulation models, after their parameters had been calibrated to the experimental data. With these parameter values, additional simulations have been carried out, e.g., of a moving car which approaches a stopped car. It turned out that, in order to manage such kinds of situations without producing accidents, improved traffic models are needed. Good results were obtained with the proposed generalized force model.

958 citations


Journal ArticleDOI
TL;DR: In this article, the photonic band structure of both face center cubic and hexagonal close packed photonic crystals is evaluated, and it is shown that the LDOS may exhibit considerable pseudogap structure even for systems that do not exhibit a complete band gap.
Abstract: We present a detailed study of photonic band structure in certain self-organizing systems that self-assemble into large-scale photonic crystals with photonic band gaps (PBGs) or pseudogaps in the near-visible frequency regime. These include colloidal suspensions, inverted opals, and macroporous silicon. We show that complete three-dimensional PBGs spanning roughly 10% and 15% of the gap center frequency are attainable by incomplete infiltration of an opal with silicon and germanium, respectively. The photonic band structure of both face center cubic and hexagonal close packed photonic crystals are evaluated. We delineate how the PBG is modified by sintering the opal prior to infiltration and by applying strain along various crystallographic directions. We evaluate the total photon density of states as well as the local density of states (LDOS) projected onto various points within the photonic crystal. It is shown that the LDOS may exhibit considerable pseudogap structure even for systems that do not exhibit a complete PBG. These results are directly relevant to quantum optical experiments in which atoms, dye molecules, or other active materials are inserted into specific locations within the photonic crystal. When the resonant optical transition of these dopants is tuned close to a pseudogap or other abrupt structure in the LDOS, novel effects in radiative dynamics associated with a ``colored vacuum'' may be realized.

807 citations


Journal ArticleDOI
TL;DR: In this article, a procedure for reconstructing the structure of general random heterogeneous media from limited morphological information is proposed based on the methodology of Rintoul and Torquato [J. Colloid Interface Sci. 1998] developed for dispersions.
Abstract: We formulate a procedure to reconstruct the structure of general random heterogeneous media from limited morphological information by extending the methodology of Rintoul and Torquato [J. Colloid Interface Sci. {bold 186}, 467 (1997)] developed for dispersions. The procedure has the advantages that it is simple to implement and generally applicable to multidimensional, multiphase, and anisotropic structures. Furthermore, an extremely useful feature is that it can incorporate any type and number of correlation functions in order to provide as much morphological information as is necessary for accurate reconstruction. We consider a variety of one- and two-dimensional reconstructions, including periodic and random arrays of rods, various distribution of disks, Debye random media, and a Fontainebleau sandstone sample. We also use our algorithm to construct heterogeneous media from specified hypothetical correlation functions, including an exponentially damped, oscillating function as well as physically unrealizable ones. {copyright} {ital 1998} {ital The American Physical Society}

789 citations


Journal ArticleDOI
TL;DR: Sollich et al. as mentioned in this paper proposed a simplified scalar model for low frequency shear rheology of foams, emulsions, slurries, etc. The model attributes similarities in the rheological of such soft glassy materials to the shared features of structural disorder and metastability.
Abstract: We solve exactly and describe in detail a simplified scalar model for the low frequency shear rheology of foams, emulsions, slurries, etc. [P. Sollich, F. Lequeux, P. H\'ebraud, and M. E. Cates, Phys. Rev. Lett. 78, 2020 (1997)]. The model attributes similarities in the rheology of such ``soft glassy materials'' to the shared features of structural disorder and metastability. By focusing on the dynamics of mesoscopic elements, it retains a generic character. Interactions are represented by a mean-field noise temperature $x$, with a glass transition occurring at $x=1$ (in appropriate units). The exact solution of the model takes the form of a constitutive equation relating stress to strain history, from which all rheological properties can be derived. For the linear response, we find that both the storage modulus ${G}^{\ensuremath{'}}$ and the loss modulus ${G}^{\ensuremath{''}}$ vary with frequency as ${\ensuremath{\omega}}^{x\ensuremath{-}1}$ for $1lxl2$, becoming flat near the glass transition. In the glass phase, aging of the moduli is predicted. The steady shear flow curves show power-law fluid behavior for $xl2$, with a nonzero yield stress in the glass phase; the Cox-Merz rule does not hold in this non-Newtonian regime. Single and double step strains further probe the nonlinear behavior of the model, which is not well represented by the Bernstein-Kearseley-Zapas relation. Finally, we consider measurements of ${G}^{\ensuremath{'}}$ and ${G}^{\ensuremath{''}}$ at finite strain amplitude $\ensuremath{\gamma}$. Near the glass transition, ${G}^{\ensuremath{''}}$ exhibits a maximum as $\ensuremath{\gamma}$ is increased in a strain sweep. Its value can be strongly overestimated due to nonlinear effects, which can be present even when the stress response is very nearly harmonic. The largest strain ${\ensuremath{\gamma}}_{c}$ at which measurements still probe the linear response is predicted to be roughly frequency independent.

674 citations


Journal ArticleDOI
TL;DR: In this paper, surface-enhanced Raman scattering (SERS) on colloidal silver clusters at near-infrared (NIR) excitation was shown to be an excellent technique for single molecule detection.
Abstract: Nonresonant Raman cross sections of $\ensuremath{\sim}{10}^{\ensuremath{-}16} {\mathrm{cm}}^{2}$ per molecule are shown to be related to surface-enhanced Raman scattering (SERS) on colloidal silver clusters at near-infrared (NIR) excitation. The enhancement is found to be independent of cluster sizes between 100 nm and 20 \ensuremath{\mu}m. These experimental findings demonstrate that NIR SERS on colloidal silver clusters is an excellent technique for single molecule detection that is applicable for a broad range of molecules including ``colorless'' biomolecules, for example nucleotides in DNA sequencing. As an example, we present the detection of a single adenine molecule without any labeling based on its intrinsic surface-enhanced Raman scattering.

566 citations


Journal ArticleDOI
TL;DR: In this paper, a discrete model based on the Boltzmann equation with a body force and a single relaxation time collision model is derived for simulations of nonideal-gas flow, and the interparticle interaction is treated using a mean-field approximation.
Abstract: A discrete model based on the Boltzmann equation with a body force and a single relaxation time collision model is derived for simulations of nonideal-gas flow. The interparticle interaction is treated using a mean-field approximation. The Boltzmann equation is discretized in a way that preserves the derivation of the hydrodynamic equations from the Boltzmann equation, using either the Chapman-Enskog method or the Grad 13-moment method. The previously proposed nonideal-gas lattice Boltzmann equation model can be analyzed with rigor.

Journal ArticleDOI
TL;DR: Inverse nematic emulsions, in which surfactant-coated water droplets are dispersed in a nematic host fluid, have distinctive properties that set them apart from dispersions of two isotropic fluids or of nematic droplets in an isotropical fluid.
Abstract: Inverse nematic emulsions, in which surfactant-coated water droplets are dispersed in a nematic host fluid, have distinctive properties that set them apart from dispersions of two isotropic fluids or of nematic droplets in an isotropic fluid. We present a comprehensive theoretical study of the distortions produced in the nematic host by the dispersed droplets and of solvent-mediated dipolar interactions between droplets that lead to their experimentally observed chaining. A single droplet in a nematic host acts like a macroscopic hedgehog defect. Global boundary conditions force the nucleation of compensating topological defects in the nematic host. Using variational techniques, we show that in the lowest energy configuration, a single water droplet draws a single hedgehog out of the nematic host to form a tightly bound dipole. Configurations in which the water droplet is encircled by a disclination ring have higher energy. The droplet dipole induces distortions in the nematic host that lead to an effective dipole-dipole interaction between droplets, and hence to chaining.

Journal ArticleDOI
TL;DR: In this article, the distribution of normal forces exerted by granular material under uniaxial compression onto the interior surfaces of a confining vessel is studied. But the authors focus on the distribution and the value of the exponential decay constant.
Abstract: We report on systematic measurements of the distribution of normal forces exerted by granular material under uniaxial compression onto the interior surfaces of a confining vessel. Our experiments on three-dimensional, random packings of monodisperse glass beads show that this distribution is nearly uniform for forces below the mean force and decays exponentially for forces greater than the mean. The shape of the distribution and the value of the exponential decay constant are unaffected by changes in the system preparation history or in the boundary conditions. An empirical functional form for the distribution is proposed that provides an excellent fit over the whole force range measured and is also consistent with recent computer simulation data.

Journal ArticleDOI
TL;DR: In this article, the authors used morphological information obtained from a 2D slice of a thin section of a random medium to reconstruct the full three-dimensional (3D) medium.
Abstract: We report on an investigation concerning the utilization of morphological information obtained from a two-dimensional (2D) slice (thin section) of a random medium to reconstruct the full three-dimensional (3D) medium. We apply a procedure that we developed in an earlier paper that incorporates any set of statistical correlation functions to reconstruct a Fontainebleau sandstone in three dimensions. Since we have available the experimentally determined 3D representation of the sandstone, we can probe the extent to which intrinsically 3D information (such as connectedness) is captured in the reconstruction. We considered reconstructing the sandstone using the two-point probability function and lineal-path function as obtained from 2D cuts (cross sections) of the sample. The reconstructions are able to reproduce accurately certain 3D properties of the pore space, such as the pore-size distribution, the mean survival time of a Brownian particle, and the fluid permeability. The degree of connectedness of the pore space also compares remarkably well with the actual sandstone. However, not surprisingly, visualization of the 3D pore structures reveals that the reconstructions are not perfect. A more refined reconstruction can be produced by incorporating higher-order information at the expense of greater computational cost. Finally, we remark that our reconstruction study sheds lightmore » on the nature of information contained in the employed correlation functions. thinsp {copyright} {ital 1998} {ital The American Physical Society}« less

Journal ArticleDOI
TL;DR: In this article, the authors investigate the structures that form when small colloidal particles are suspended in a nematic solvent and demonstrate that they can be controlled by the anchoring of the liquid crystal molecules at the surfaces of the droplets.
Abstract: We investigate experimentally the structures that form when small colloidal particles are suspended in a nematic solvent. These structures are anisotropic, and their formation is driven by interactions arising from the orientational elasticity of the nematic solvent. By using inverted and multiple nematic emulsions composed of water droplets dispersed in a thermotropic liquid crystal, we identify the nature of these interactions, and demonstrate that they can be controlled by the anchoring of the liquid crystal molecules at the surfaces of the droplets. When the anchoring is normal, the droplets form linear chains, suggesting a long-range dipole-dipole attraction between the particles. By contrast, the interactions are repulsive at short range, and prevent contact of the droplets, thereby stabilizing them against coalescence. When the anchoring is planar, the droplets generate distortions that have a quadrupolar character. The resultant elastic interactions lead to more compact, but still anisotropic, clusters.

Journal ArticleDOI
TL;DR: In this paper, the density of a vibrated granular material was measured as a function of time and the frequency dependence and amplitude of these fluctuations were investigated as the function of vibration intensity.
Abstract: We report systematic measurements of the density of a vibrated granular material as a function of time. Monodisperse spherical beads were confined to a cylindrical container and shaken vertically. Under vibrations, the density of the pile slowly reaches a final steady-state value about which the density fluctuates. We have investigated the frequency dependence and amplitude of these fluctuations as a function of vibration intensity \ensuremath{\Gamma}. The spectrum of density fluctuations around the steady state value provides a probe of the internal relaxation dynamics of the system and a link to recent thermodynamic theories for the settling of granular material. In particular, we propose a method to evaluate the compactivity of a powder, first put forth by Edwards and co-workers, that is the analog to temperature for a quasistatic powder. We also propose a stochastic model based on free volume considerations that captures the essential mechanism underlying the slow relaxation. We compare our experimental results with simulations of a one-dimensional model for random adsorption and desorption.

Journal ArticleDOI
TL;DR: The authors conclude that the logical structure of the lane changing rules, as proposed here, is at least as important as the microscopic details of the rules for producing realistic results.
Abstract: Microscopic modeling of multi-lane traffic is usually done by applying heuristic lane changing rules, and often with unsatisfying results. Recently, a cellular automaton model for two-lane traffic was able to overcome some of these problems and to produce a correct density inversion at densities somewhat below the maximum flow density. In this paper, we summarize different approaches to lane changing and their results, and propose a general scheme, according to which realistic lane changing rules can be developed. We test this scheme by applying it to several different lane changing rules, which, in spite of their differences, generate similar and realistic results. We thus conclude that, for producing realistic results, the logical structure of the lane changing rules, as proposed here, is at least as important as the microscopic details of the rules.

Journal ArticleDOI
TL;DR: In this paper, the authors present analytical results and computer simulations of the nonlinear evolution of wake field waves in inhomogeneous plasmas and show that stable beams of energetic electrons are formed.
Abstract: We present analytical results and computer simulations of the nonlinear evolution of wake field waves in inhomogeneous plasmas. The wake wave break that occurs due to the inhomogeneity of the Langmuir frequency makes it possible to inject electrons into the acceleration phase of the wave. Particle-in-cell simulations show that stable beams of energetic electrons are formed. These beams are well bunched in coordinate and velocity space and contain a considerable fraction of the pulse energy

Journal ArticleDOI
TL;DR: In this paper, the optimal velocity model with explicit delay is analyzed and the properties of congestion and the delay time of car motion are investigated by analytical and numerical methods, and it is shown that the small explicit delay time has almost no effects.
Abstract: We analyze the optimal velocity model (OVM) with explicit delay. The properties of congestion and the delay time of car motion are investigated by analytical and numerical methods. It is shown that the small explicit delay time has almost no effects. In the case of the large explicit delay time, a new phase of congestion pattern of OVM seems to appear.

Journal ArticleDOI
TL;DR: In this paper, the authors discuss the generation and statistics of density fluctuations in highly compressible polytropic turbulence, based on a simple model and one-dimensional numerical simulations, and suggest that Burgers flow is a singular case not approached by the high-$\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{M}$ limit.
Abstract: We discuss the generation and statistics of the density fluctuations in highly compressible polytropic turbulence, based on a simple model and one-dimensional numerical simulations. Observing that density structures tend to form in a hierarchical manner, we assume that density fluctuations follow a random multiplicative process. When the polytropic exponent $\ensuremath{\gamma}$ is equal to unity, the local Mach number is independent of the density, and our assumption leads us to expect that the probability density function (PDF) of the density field is a log-normal. This isothermal case is found to be special, with a dispersion ${\ensuremath{\sigma}}_{s}^{2}$ scaling as the square turbulent Mach number ${M}^{2},$ where $s\ensuremath{\equiv}\mathrm{ln}\ensuremath{\rho}$ and $\ensuremath{\rho}$ is the fluid density. Density fluctuations are stronger than expected on the sole basis of shock jumps. Extrapolating the model to the case $\ensuremath{\gamma}\ensuremath{ e}1,$ we find that as the Mach number becomes large, the density PDF is expected to asymptotically approach a power-law regime at high densities when $\ensuremath{\gamma}l1,$ and at low densities when $\ensuremath{\gamma}g1.$ This effect can be traced back to the fact that the pressure term in the momentum equation varies exponentially with $s,$ thus opposing the growth of fluctuations on one side of the PDF, while being negligible on the other side. This also causes the dispersion ${\ensuremath{\sigma}}_{s}^{2}$ to grow more slowly than ${M}^{2}$ when $\ensuremath{\gamma}\ensuremath{ e}1.$ In view of these results, we suggest that Burgers flow is a singular case not approached by the high-$\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{M}$ limit, with a PDF that develops power laws on both sides.

Journal ArticleDOI
TL;DR: In this article, the authors derived the hydrodynamic equations for a gas of hard spheres with dissipative dynamics from the Boltzmann equation and derived the heat and momentum fluxes to Navier-Stokes order and the transport coefficients as explicit functions of the coefficient of restitution.
Abstract: The hydrodynamic equations for a gas of hard spheres with dissipative dynamics are derived from the Boltzmann equation. The heat and momentum fluxes are calculated to Navier-Stokes order and the transport coefficients are determined as explicit functions of the coefficient of restitution. The dispersion relations for the corresponding linearized equations are obtained and the stability of this linear description is discussed. This requires consideration of the linear Burnett contributions to the energy balance equation from the energy sink term. Finally, it is shown how these results can be imbedded in simpler kinetic model equations with the potential for analysis of more complex states.

Journal ArticleDOI
TL;DR: In this article, a mixture of identically sized but optically different particles having hard-sphere-like interactions is projected out the incoherent (or self-) intermediate scattering functions by adjusting the refractive index of the suspending liquid until scattering from the structure is suppressed.
Abstract: Dynamic light-scattering measurements are reported for suspensions at concentrations in the vicinity of the glass transition. In a mixture of identically sized but optically different particles having hard-sphere-like interactions, we project out the incoherent (or self-) intermediate scattering functions by adjusting the refractive index of the suspending liquid until scattering from the structure is suppressed. Due to polydispersity, crystallization is sufficiently slow so that good estimates of ensemble-averaged quantities can be measured for the metastable fluid states. Crystallization of the suspensions is still exploited, however, to set the volume fraction scale in terms of effective hard spheres and to eliminate (coherent) scattering from the structure. The glass-transition volume fraction is identified by the value where large-scale particle motion ceases. The nonequilibrium nature of the glass state is evidenced by the dependence on the waiting time of the long time decay of the relaxation functions. The self-intermediate scattering functions show negligible deviation from Gaussian behavior up to the onset of large-scale diffusion in the fluid or the onset of waiting time effects in the glass.

Journal ArticleDOI
TL;DR: In this paper, high-supercooled liquids with soft core potentials are studied via molecular-dynamics simulations in two and three dimensions in quiescent and sheared conditions.
Abstract: Highly supercooled liquids with soft-core potentials are studied via molecular-dynamics simulations in two and three dimensions in quiescent and sheared conditions. We may define bonds between neighboring particle pairs unambiguously owing to the sharpness of the first peak of the pair correlation functions. Upon structural rearrangements, they break collectively in the form of clusters whose sizes grow with lowering the temperature T. The bond lifetime ${\ensuremath{\tau}}_{b},$ which depends on $T$ and the shear rate $\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\gamma}}$, is on the order of the usual structural or $\ensuremath{\alpha}$ relaxation time ${\ensuremath{\tau}}_{\ensuremath{\alpha}}$ in weak shear $\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\gamma}}{\ensuremath{\tau}}_{\ensuremath{\alpha}}\ensuremath{\ll}1,$ while it decreases as $1/\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\gamma}}$ in strong shear $\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\gamma}}{\ensuremath{\tau}}_{\ensuremath{\alpha}}\ensuremath{\gg}1$ due to shear-induced cage breakage. Accumulated broken bonds in a time interval $(\ensuremath{\sim}0.05{\ensuremath{\tau}}_{b})$ closely resemble the critical fluctuations of Ising spin systems. For example, their structure factor is well fitted to the Ornstein-Zernike form, which yields the correlation length $\ensuremath{\xi}$ representing the maximum size of the clusters composed of broken bonds. We also find a dynamical scaling relation, ${\ensuremath{\tau}}_{b}\ensuremath{\sim}{\ensuremath{\xi}}^{z},$ valid for any T and $\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\gamma}}$ with $z=4$ in two dimensions and $z=2$ in three dimensions. The viscosity is of order ${\ensuremath{\tau}}_{b}$ for any T and $\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\gamma}},$ so marked shear-thinning behavior emerges. The shear stress is close to a limiting stress in a wide shear region. We also examine motion of tagged particles in shear in three dimensions. The diffusion constant is found to be of order ${\ensuremath{\tau}}_{b}^{\ensuremath{-}\ensuremath{ u}}$ with $\ensuremath{ u}=0.75\ensuremath{\sim}0.8$ for any T and $\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\gamma}},$ so it is much enhanced in strong shear compared with its value at zero shear. This indicates a breakdown of the Einstein-Stokes relation in accord with experiments. Some possible experiments are also proposed.

Journal ArticleDOI
TL;DR: In this paper, the circuit equations for certain series arrays of Josephson junctions can be mapped onto a simple model originally introduced by Kuramoto [in Proceedings of the International Symposium on Mathematical Problems in Theoretical Physics, edited by H Araki, Lecture Notes in Physics Vol 39 (Springer, Berlin, 1975)] to study fundamental aspects of frequency locking in large populations of nonlinear oscillators.
Abstract: The circuit equations for certain series arrays of Josephson junctions can be mapped onto a simple model originally introduced by Kuramoto [in Proceedings of the International Symposium on Mathematical Problems in Theoretical Physics, edited by H Araki, Lecture Notes in Physics Vol 39 (Springer, Berlin, 1975)] to study fundamental aspects of frequency locking in large populations of nonlinear oscillators This correspondence makes it possible to derive accurate theoretical predictions of transitions signaling the onset of partial and complete locking, respectively We calculate that both transitions should be observable experimentally using present fabrication tolerances

Journal ArticleDOI
TL;DR: In this paper, Monte Carlo simulations were performed to study bond percolation on the simple cubic (sc), face-centered-cubic (fcc), and body-centered cubic lattices, using an epidemic approach.
Abstract: Extensive Monte Carlo simulations were performed to study bond percolation on the simple cubic (sc), face-centered-cubic (fcc), and body-centered-cubic (bcc) lattices, using an epidemic approach. These simulations provide very precise values of the critical thresholds for each of the lattices: ${p}_{c}(\mathrm{sc})=0.2488126\ifmmode\pm\else\textpm\fi{}0.0000005,$ ${p}_{c}(\mathrm{fcc})=0.1201635\ifmmode\pm\else\textpm\fi{}0.0000010,$ and ${p}_{c}(\mathrm{bcc})=0.1802875\ifmmode\pm\else\textpm\fi{}0.0000010$. For $p$ close to ${p}_{c},$ the results follow the expected finite-size and scaling behavior, with values for the Fisher exponent \ensuremath{\tau} $(2.189\ifmmode\pm\else\textpm\fi{}0.002),$ the finite-size correction exponent \ensuremath{\Omega} $(0.64\ifmmode\pm\else\textpm\fi{}0.02),$ and the scaling function exponent \ensuremath{\sigma} $(0.445\ifmmode\pm\else\textpm\fi{}0.01)$ confirmed to be universal.

Journal ArticleDOI
TL;DR: In this article, the relativistic ponderomotive force in the case of a Gaussian transverse profile was investigated and a detailed demonstration of the ponderomic force was established.
Abstract: In order to investigate ponderomotive force in the relativistic regime, the interaction of ultraintense laser pulses with free electrons in vacuum is studied both theoretically and numerically. Various expressions for the electromagnetic field of the laser in the case of a Gaussian transverse profile are given, which take into account corrections to the monochromatic paraxial approximation, and the effects of finite pulse duration. A detailed demonstration of relativistic ponderomotive force (RPF) is established which makes apparent the domain of validity of this concept. Computer simulations are carried out using a three-dimensional test-particle code. They show the importance of the correct description of the fields, and confirm the domain of validity of the RPF which is $1\ensuremath{-}{v}_{z}/c\ensuremath{\gg}{1/kw}_{0}$, where ${v}_{z}$ is the component of the electron velocity parallel to the laser propagation direction, $c$ is the velocity of light, $k$ is the laser wave vector, and ${w}_{0}$ the beam waist at focus. Outside of this domain, the electron motion is more complicated, with a high sensitivity on the initial distance from the laser propagation axis and a relatively low energy gain.

Journal ArticleDOI
TL;DR: In this paper, a model for the dynamic shear modulus of entangled or crosslinked networks of semi-lexible polymers was proposed to account for the high-frequency scaling behavior observed in solutions of the biopolymer F-actin.
Abstract: We construct a model for the dynamic shear modulus $G(\ensuremath{\omega})$ of entangled or crosslinked networks of semiflexible polymer that can account for the high-frequency scaling behavior, $G(\ensuremath{\omega})\ensuremath{\sim}{\ensuremath{\omega}}^{3/4},$ that has recently been observed in solutions of the biopolymer $F$-actin. As we argue, this behavior should not be unique to F-actin, but rather should be a clear characteristic of semiflexible polymers in general. We also report molecular dynamics simulations that support the single filament response that is the basis of our model for the network shear modulus.

Journal ArticleDOI
TL;DR: The physical aspects of a recently introduced method for data clustering, based on an inhomogeneous Potts model, are considered in detail and the spatial resolution of the clustering method is argued to be connected to the correlation length of spin fluctuations.
Abstract: The physical aspects of a recently introduced method for data clustering are considered in detail. This method is based on an inhomogeneous Potts model; no assumption concerning the underlying distribution of the data is made. A Potts spin is assigned to each data point and short range interactions between neighboring points are introduced. Spin-spin correlations (measured by Monte Carlo computations) serve to partition the data points into clusters. In this paper we examine the effects of varying different details of the method such as the definition of neighbors, the type of interaction, and the number of Potts states $q$. In addition, we present and solve a granular mean field Potts model relevant to the clustering method. The model consists of strongly coupled groups of spins coupled to noise spins, which are themselves weakly coupled. The phase diagram is computed by solving analytically the model in various limits. Our main result is that in the range of parameters of interest the existence of the superparamagnetic phase is independent of the ordering process of the noise spins. Next we use the known properties of regular and inhomogeneous Potts models in finite dimensions to discuss the performance of the clustering method. In particular, the spatial resolution of the clustering method is argued to be connected to the correlation length of spin fluctuations. The behavior of the method, as more and more data points are sampled, is also investigated.

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TL;DR: In this article, the dominant aspects of chemical transport in fracture networks are derived from subtle features of the steady flow-field distribution through the network, which is an outcome of a theory, based on a continuous time random walk formalism, structured to retain the key space-time correlations of particles as they are advected across each fracture segment.
Abstract: We show that dominant aspects of chemical (particle) transport in fracture networks\char22{}non-Gaussian propagation\char22{}result from subtle features of the steady flow-field distribution through the network. This is an outcome of a theory, based on a continuous time random walk formalism, structured to retain the key space-time correlations of particles as they are advected across each fracture segment. The approach is designed to treat the complex geometries of a large variety of fracture networks and multiscale interactions. Monte Carlo simulations of steady flow in these networks are used to determine the distribution of velocities in individual fractures as a function of their orientation. The geometry and velocity distributions are used, in conjunction with particle mixing rules, to map the particle movement between fracture intersections onto a joint probability density $\ensuremath{\psi}(\mathbf{r},t).$ The chemical concentration plume and breakthrough curves can then be calculated analytically. Particle tracking simulations on these networks exhibit the same non-Gaussian profiles, demonstrating quantitative agreement with the theory. The analytic plume shapes display the same basic behavior as extensive field observations at the Columbus Air Force Base, Mississippi. The quantitative correlation between the time dependence of the mean and standard deviation of the field plumes, and their shape, is predicted by the theory.

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TL;DR: In this article, a phenomenological model of the underlying microscopic Langevin equation of the nonlinear Fokker-Planck equation is derived, which is used to describe anomalous correlated diffusion.
Abstract: We derive a phenomenological model of the underlying microscopic Langevin equation of the nonlinear Fokker-Planck equation, which is used to describe anomalous correlated diffusion. The resulting distribution-dependent stochastic equation is then analyzed and properties such as long-time scaling and the Hurst exponent are calculated both analytically and from simulations. Results of this microscopic theory are compared with those of fractional Brownian motion.