Showing papers in "Physical Review E in 2006"
TL;DR: A modularity matrix plays a role in community detection similar to that played by the graph Laplacian in graph partitioning calculations, and a spectral measure of bipartite structure in networks and a centrality measure that identifies vertices that occupy central positions within the communities to which they belong are proposed.
Abstract: We consider the problem of detecting communities or modules in networks, groups of vertices with a higher-than-average density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as ``modularity'' over possible divisions of a network. Here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix, which plays a role in community detection similar to that played by the graph Laplacian in graph partitioning calculations. This result leads us to a number of possible algorithms for detecting community structure, as well as several other results, including a spectral measure of bipartite structure in networks and a centrality measure that identifies vertices that occupy central positions within the communities to which they belong. The algorithms and measures proposed are illustrated with applications to a variety of real-world complex networks.
4,559 citations
TL;DR: The properties of the ground state configuration are elucidated to give a concise definition of communities as cohesive subgroups in networks that is adaptive to the specific class of network under study.
Abstract: Starting from a general ansatz, we show how community detection can be interpreted as finding the ground state of an infinite range spin glass. Our approach applies to weighted and directed networks alike. It contains the ad hoc introduced quality function from [J. Reichardt and S. Bornholdt, Phys. Rev. Lett. 93, 218701 (2004)] and the modularity Q as defined by Newman and Girvan [Phys. Rev. E 69, 026113 (2004)] as special cases. The community structure of the network is interpreted as the spin configuration that minimizes the energy of the spin glass with the spin states being the community indices. We elucidate the properties of the ground state configuration to give a concise definition of communities as cohesive subgroups in networks that is adaptive to the specific class of network under study. Further, we show how hierarchies and overlap in the community structure can be detected. Computationally efficient local update rules for optimization procedures to find the ground state are given. We show how the ansatz may be used to discover the community around a given node without detecting all communities in the full network and we give benchmarks for the performance of this extension. Finally, we give expectation values for the modularity of random graphs, which can be used in the assessment of statistical significance of community structure.
1,845 citations
TL;DR: A measure of similarity based on the concept that two vertices are similar if their immediate neighbors in the network are themselves similar is proposed, which leads to a self-consistent matrix formulation of similarity that can be evaluated iteratively using only a knowledge of the adjacency matrix of the network.
Abstract: We consider methods for quantifying the similarity of vertices in networks. We propose a measure of similarity based on the concept that two vertices are similar if their immediate neighbors in the network are themselves similar. This leads to a self-consistent matrix formulation of similarity that can be evaluated iteratively using only a knowledge of the adjacency matrix of the network. We test our similarity measure on computer-generated networks for which the expected results are known, and on a number of real-world networks.
844 citations
TL;DR: Full electromagnetic simulations of the cylindrical version of this cloaking structure are reported, using ideal and nonideal electromagnetic parameters that show that the low-reflection and power-flow bending properties of the electromagnetic cloaky structure are not especially sensitive to modest permittivity and permeability variations.
Abstract: Pendry et al. have reported electromagnetically anisotropic and inhomogeneous shells that, in theory, completely shield an interior structure of arbitrary size from electromagnetic fields without perturbing the external fields. Neither the coordinate transformation-based analytical formulation nor the supporting ray-tracing simulation indicate how material perturbations and full-wave effects might affect the solution. We report fully electromagnetic simulations of the cylindrical version of this cloaking structure using ideal and nonideal (but physically realizable) electromagnetic parameters that show that the low-reflection and power-flow bending properties of the electromagnetic cloaking structure are not especially sensitive to modest permittivity and permeability variations. The cloaking performance degrades smoothly with increasing loss, and effective low-reflection shielding can be achieved with a cylindrical shell composed of an eight- (homogeneous) layer approximation of the ideal continuous medium. An imperfect but simpler version of the cloaking material is derived and is shown to reproduce the ray bending of the ideal material in a manner that may be easier to experimentally realize.
796 citations
TL;DR: It is shown that the bursty nature of human behavior is a consequence of a decision based queuing process: when individuals execute tasks based on some perceived priority, the timing of the tasks will be heavy tailed, most tasks being rapidly executed, while a few experiencing very long waiting times.
Abstract: terized by bursts of rapidly occurring events separated by long periods of inactivity. We show that the bursty nature of human behavior is a consequence of a decision based queuing process: when individuals execute tasks based on some perceived priority, the timing of the tasks will be heavy tailed, most tasks being rapidly executed, while a few experiencing very long waiting times. In contrast, priority blind execution is well approximated by uniform interevent statistics. We discuss two queuing models that capture human activity. The first model assumes that there are no limitations on the number of tasks an individual can hadle at any time, predicting that the waiting time of the individual tasks follow a heavy tailed distribution Pw w with =3/2. The second model imposes limitations on the queue length, resulting in a heavy tailed waiting time distribution characterized by = 1. We provide empirical evidence supporting the relevance of these two models to human activity patterns, showing that while emails, web browsing and library visitation display = 1, the surface mail based communication belongs to the =3/2 universality class. Finally, we discuss possible extension of the proposed queuing models and outline some future challenges in exploring the statistical mechanics of human dynamics.
679 citations
TL;DR: A characterization of quantum phase transitions in terms of the the overlap function between two ground states obtained for two different values of external parameters shows that the regions of criticality of a system are marked by the extremal points of the overlap and functions closely related to it.
Abstract: We present a characterization of quantum phase transitions in terms of the the overlap function between two ground states obtained for two different values of external parameters. On the examples of the Dicke and $XY$ models, we show that the regions of criticality of a system are marked by the extremal points of the overlap and functions closely related to it. Further, we discuss the connections between this approach and the Anderson orthogonality catastrophe as well as with the dynamical study of the Loschmidt echo for critical systems.
651 citations
TL;DR: The results indicate that a spatial analysis based on a set of four centrality indices allows an extended visualization and characterization of the city structure and has a certain capacity to distinguish different classes of cities.
Abstract: We study centrality in urban street patterns of different world cities represented as networks in geographical space. The results indicate that a spatial analysis based on a set of four centrality indices allows an extended visualization and characterization of the city structure. A hierarchical clustering analysis based on the distributions of centrality has a certain capacity to distinguish different classes of cities. In particular, self-organized cities exhibit scale-free properties similar to those found in nonspatial networks, while planned cities do not.
599 citations
TL;DR: A simple model of the convergence of opinion in social systems, with a single parameter controlling the balance of the two processes, that undergoes a continuous phase transition as this parameter is varied, from a regime in which opinions are arbitrarily diverse to one in which most individuals hold the same opinion.
Abstract: Models of the convergence of opinion in social systems have been the subject of considerable recent attention in the physics literature. These models divide into two classes, those in which individuals form their beliefs based on the opinions of their neighbors in a social network of personal acquaintances, and those in which, conversely, network connections form between individuals of similar beliefs. While both of these processes can give rise to realistic levels of agreement between acquaintances, practical experience suggests that opinion formation in the real world is not a result of one process or the other, but a combination of the two. Here we present a simple model of this combination, with a single parameter controlling the balance of the two processes. We find that the model undergoes a continuous phase transition as this parameter is varied, from a regime in which opinions are arbitrarily diverse to one in which most individuals hold the same opinion.
586 citations
TL;DR: A generalized routing algorithm is given to find the so-called efficient path, which considers the possible congestion in the nodes along actual paths, to improve the transportation efficiency on complex networks.
Abstract: We propose a routing strategy to improve the transportation efficiency on complex networks. Instead of using the routing strategy for shortest path, we give a generalized routing algorithm to find the so-called efficient path, which considers the possible congestion in the nodes along actual paths. Since the nodes with the largest degree are very susceptible to traffic congestion, an effective way to improve traffic and control congestion, as our strategy, can be redistributing traffic load in central nodes to other noncentral nodes. Simulation results indicate that the network capability in processing traffic is improved more than 10 times by optimizing the efficient path, which is in good agreement with the analysis.
568 citations
TL;DR: A simple closed formula is derived that determines the feasibility of cooperation in finite populations, whenever cooperation is modeled in terms of any symmetric two-person game, and is valid at all intensities of selection and for any initial condition.
Abstract: We study evolutionary game dynamics in finite populations. We analyze an evolutionary process, which we call pairwise comparison, for which we adopt the ubiquitous Fermi distribution function from statistical mechanics. The inverse temperature in this process controls the intensity of selection, leading to a unified framework for evolutionary dynamics at all intensities of selection, from random drift to imitation dynamics. We derive a simple closed formula that determines the feasibility of cooperation in finite populations, whenever cooperation is modeled in terms of any symmetric two-person game. In contrast with previous results, the present formula is valid at all intensities of selection and for any initial condition. We investigate the evolutionary dynamics of cooperators in finite populations, and study the interplay between intensity of selection and the remnants of interior fixed points in infinite populations, as a function of a given initial number of cooperators, showing how this interplay strongly affects the approach to fixation of a given trait in finite populations, leading to counterintuitive results at different intensities of selection.
536 citations
TL;DR: The onset of a typical plastic event is studied with precision, and it is shown that the mode of the system which is responsible for the loss of stability has structure in real space which is consistent with a quadrupolar source acting on an elastic matrix.
Abstract: We present results on a series of two-dimensional atomistic computer simulations of amorphous systems subjected to simple shear in the athermal, quasistatic limit The athermal quasistatic trajectories are shown to separate into smooth, reversible elastic branches which are intermittently broken by discrete catastrophic plastic events The onset of a typical plastic event is studied with precision, and it is shown that the mode of the system which is responsible for the loss of stability has structure in real space which is consistent with a quadrupolar source acting on an elastic matrix The plastic events themselves are shown to be composed of localized shear transformations which organize into lines of slip which span the length of the simulation cell, and a mechanism for the organization is discussed Although within a single event there are strong spatial correlations in the deformation, we find little correlation from one event to the next, and these transient lines of slip are not to be confounded with the persistent regions of localized shear---so-called ``shear bands''---found in related studies The slip lines give rise to particular scalings with system length of various measures of event size Strikingly, data obtained using three differing interaction potentials can be brought into quantitative agreement after a simple rescaling, emphasizing the insensitivity of the emergent plastic behavior in these disordered systems to the precise details of the underlying interactions The results should be relevant to understanding plastic deformation in systems such as metallic glasses well below their glass temperature, soft glassy systems (such as dense emulsions), or compressed granular materials
TL;DR: In this paper, the authors exploit three methods of sampling and investigate the topological properties such as degree and betweenness centrality distribution, average path length, assortativity, and clustering coefficient of sampled networks compared with those of original networks.
Abstract: We study the statistical properties of the sampled scale-free networks, deeply related to the proper identification of various real-world networks. We exploit three methods of sampling and investigate the topological properties such as degree and betweenness centrality distribution, average path length, assortativity, and clustering coefficient of sampled networks compared with those of original networks. It is found that the quantities related to those properties in sampled networks appear to be estimated quite differently for each sampling method. We explain why such a biased estimation of quantities would emerge from the sampling procedure and give appropriate criteria for each sampling method to prevent the quantities from being overestimated or underestimated.
TL;DR: A flocking model is constructed that exhibits a continuous transition to the ordered phase, while assuming only short-range interactions and no explicit information about the knowledge of the directions of motion of neighbors.
Abstract: We have recorded the swarming-like collective migration of a large number of keratocytes (tissue cells obtained from the scales of goldfish) using long-term videomicroscopy. By increasing the overall density of the migrating cells, we have been able to demonstrate experimentally a kinetic phase transition from a disordered into an ordered state. Near the critical density a complex picture emerges with interacting clusters of cells moving in groups. Motivated by these experiments we have constructed a flocking model that exhibits a continuous transition to the ordered phase, while assuming only short-range interactions and no explicit information about the knowledge of the directions of motion of neighbors. Placing cells in microfabricated arenas we found spectacular whirling behavior which we could also reproduce in simulations.
TL;DR: A multiphase-field model previously proposed by the authors is reformulated in a thermodynamically consistent form and extended to multicomponent systems and shows that this extrapolation scheme, used in a "multibinary" approximation, reproduces the former model without restriction to dilute solutions.
Abstract: A multiphase-field model previously proposed by the authors is reformulated in a thermodynamically consistent form and extended to multicomponent systems. The phase-field and diffusion equations, derived from a free energy functional, are compared to those postulated in the previous model in the limit of a binary alloy. The constraint of local quasiequilibrium, which is equivalent to the postulate of equal diffusion potentials for coexisting phases, is deduced from a variational principle. Solute partitioning and evaluation of the thermodynamic driving force for phase transformation are done by numerical minimization of the free energy of the multiphase system using the Calphad approach. A local extrapolation scheme which enhances the computational efficiency for complex numerical simulations of technical alloys is presented. It is shown that this extrapolation scheme, used in a "multibinary" approximation, reproduces the former model without restriction to dilute solutions.
TL;DR: These calculations demonstrate that, notwithstanding its seductive simplicity, the basic Langevin equation does a remarkably poor job of capturing the decay rate of the velocity autocorrelation function in the colloidal regime, strongly underestimating it at short times and strongly overestimated it at long times.
Abstract: We describe in detail how to implement a coarse-grained hybrid molecular dynamics and stochastic rotation dynamics simulation technique that captures the combined effects of Brownian and hydrodynamic forces in colloidal suspensions. The importance of carefully tuning the simulation parameters to correctly resolve the multiple time and length scales of this problem is emphasized. We systematically analyze how our coarse-graining scheme resolves dimensionless hydrodynamic numbers such as the Reynolds number Re, which indicates the importance of inertial effects, the Schmidt number Sc, which indicates whether momentum transport is liquidlike or gaslike, the Mach number, which measures compressibility effects, the Knudsen number, which describes the importance of noncontinuum molecular effects, and the Peclet number, which describes the relative effects of convective and diffusive transport. With these dimensionless numbers in the correct regime the many Brownian and hydrodynamic time scales can be telescoped together to maximize computational efficiency while still correctly resolving the physically relevant processes. We also show how to control a number of numerical artifacts, such as finite-size effects and solvent-induced attractive depletion interactions. When all these considerations are properly taken into account, the measured colloidal velocity autocorrelation functions and related self-diffusion and friction coefficients compare quantitatively with theoretical calculations. By contrast, these calculations demonstrate that, notwithstanding its seductive simplicity, the basic Langevin equation does a remarkably poor job of capturing the decay rate of the velocity autocorrelation function in the colloidal regime, strongly underestimating it at short times and strongly overestimating it at long times. Finally, we discuss in detail how to map the parameters of our method onto physical systems and from this extract more general lessons—keeping in mind that there is no such thing as a free lunch—that may be relevant for other coarse-graining schemes such as lattice Boltzmann or dissipative particle dynamics.
TL;DR: The propagation of acoustic waves in a phononic crystal slab consisting of piezoelectric inclusions placed periodically in an isotropic host material is analyzed and it is observed that the band gaps of a phononics crystal slab are distinct from those of bulk acoustic waves propagating in the plane of an infinite two-dimensional phononic Crystal.
Abstract: The propagation of acoustic waves in a phononic crystal slab consisting of piezoelectric inclusions placed periodically in an isotropic host material is analyzed. Numerical examples are obtained for a square lattice of quartz cylinders embedded in an epoxy matrix. It is found that several complete band gaps with a variable bandwidth exist for elastic waves of any polarization and incidence. In addition to the filling fraction, it is found that a key parameter for the existence and the width of these complete band gaps is the ratio of the slab thickness, d, to the lattice period, a. Especially, we have explored how these absolute band gaps close up as the parameter d/a increases. Significantly, it is observed that the band gaps of a phononic crystal slab are distinct from those of bulk acoustic waves propagating in the plane of an infinite two-dimensional phononic crystal with the same composition. The band gaps of the slab are strongly affected by the presence of cutoff frequency modes that cannot be excited in infinite media.
TL;DR: In simulations with individual particles, it is found that particle clustering is facilitated by a sufficiently large packing fraction eta or length-to-width ratio kappa, which is well captured by a mean-field model for the cluster size distribution.
Abstract: Motivated by aggregation phenomena in gliding bacteria, we study collective motion in a two-dimensional model of active, self-propelled rods interacting through volume exclusion. In simulations with individual particles, we find that particle clustering is facilitated by a sufficiently large packing fraction $\ensuremath{\eta}$ or length-to-width ratio $\ensuremath{\kappa}$. The transition to clustering in simulations is well captured by a mean-field model for the cluster size distribution, which predicts that the transition values ${\ensuremath{\kappa}}_{c}$ of the aspect ratio for a fixed packing fraction $\ensuremath{\eta}$ are given by ${\ensuremath{\kappa}}_{c}=C∕\ensuremath{\eta}\ensuremath{-}1$ where $C$ is a constant.
TL;DR: A homogeneous spontaneous motion emerges below a transition line in the noise-density plane, and is shown to be unstable against spatial perturbations, suggesting that more complicated structures should eventually appear.
Abstract: We study analytically the emergence of spontaneous collective motion within large bidimensional groups of self-propelled particles with noisy local interactions, a schematic model for assemblies of biological organisms. As a central result, we derive from the individual dynamics the hydrodynamic equations for the density and velocity fields, thus giving a microscopic foundation to the phenomenological equations used in previous approaches. A homogeneous spontaneous motion emerges below a transition line in the noise-density plane. Yet, this state is shown to be unstable against spatial perturbations, suggesting that more complicated structures should eventually appear.
TL;DR: This work investigates the number of packets of each node depending on its degree in the free flow state and observes the power law behavior to indicate that some fundamental relationships exist between the dynamics of synchronization and traffic on the scale-free networks.
Abstract: We propose a packet routing strategy with a tunable parameter based on the local structural information of a scale-free network. As free traffic flow on the communication networks is key to their normal and efficient functioning, we focus on the network capacity that can be measured by the critical point of phase transition from free flow to congestion. Simulations show that the maximal capacity corresponds to alpha= -1 in the case of identical nodes' delivering ability. To explain this, we investigate the number of packets of each node depending on its degree in the free flow state and observe the power law behavior. Other dynamic properties including average packets traveling time and traffic load are also studied. Inspiringly, our results indicate that some fundamental relationships exist between the dynamics of synchronization and traffic on the scale-free networks.
TL;DR: This work studies the basic properties of twenty 1-square-mile samples of street patterns of different world cities and finds that cities of the same class, e.g., grid-iron or medieval, exhibit roughly similar properties.
Abstract: Recent theoretical and empirical studies have focused on the structural properties of complex relational networks in social, biological, and technological systems. Here we study the basic properties of twenty 1-square-mile samples of street patterns of different world cities. Samples are turned into spatial valued graphs. In such graphs, the nodes are embedded in the two-dimensional plane and represent street intersections, the edges represent streets, and the edge values are equal to the street lengths. We evaluate the local properties of the graphs by measuring the meshedness coefficient and counting short cycles (of three, four, and five edges), and the global properties by measuring global efficiency and cost. We also consider, as extreme cases, minimal spanning trees (MST) and greedy triangulations (GT) induced by the same spatial distribution of nodes. The measures found in the real and the artificial networks are then compared. Surprisingly, cities of the same class, e.g., grid-iron or medieval, exhibit roughly similar properties. The correlation between a priori known classes and statistical properties is illustrated in a plot of relative efficiency vs cost.
TL;DR: Interestingly, it is found that the frequency of cooperation of the MBSG on a scale-free network peaks at a specific value of the payoff parameter, indicating that properly encouraging selfish behaviors can optimally enhance the cooperation.
Abstract: We present a memory-based snowdrift game (MBSG) taking place on networks. We found that, when a lattice is taken to be the underlying structure, the transition of spatial patterns at some critical values of the payoff parameter is observable for both four- and eight-neighbor lattices. The transition points as well as the styles of spatial patterns can be explained by local stability analysis. In sharp contrast to previously reported results, cooperation is promoted by the spatial structure in the MBSG. Interestingly, we found that the frequency of cooperation of the MBSG on a scale-free network peaks at a specific value of the payoff parameter. This phenomenon indicates that properly encouraging selfish behaviors can optimally enhance the cooperation. The memory effects of individuals are discussed in detail and some non-monotonous phenomena are observed on both lattices and scale-free networks. Our work may shed some new light on the study of evolutionary games over networks.
TL;DR: The results suggest that upon pressurization, hydrophobic plates behave as "soft" surfaces (in the sense of accommodating pressure-dependent changes in water structure) while hydrophilic walls behave as 'hard' surfaces.
Abstract: We perform systematic molecular dynamics simulations of water confined between two nanoscale plates at $T=300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. We investigate the effect of pressure $(\ensuremath{-}0.15\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}\ensuremath{\leqslant}P\ensuremath{\leqslant}0.2\phantom{\rule{0.3em}{0ex}}\mathrm{GPa})$ and plate separation $(0.4\phantom{\rule{0.3em}{0ex}}\mathrm{nm}\ensuremath{\leqslant}d\ensuremath{\leqslant}1.6\phantom{\rule{0.3em}{0ex}}\mathrm{nm})$ on the phase behavior of water when the plates are either hydrophobic or hydrophilic. When water is confined between hydrophobic plates, capillary evaporation occurs between the plates at low enough $P$. The threshold value of $d$ at which this transition occurs decreases with $P$ (e.g., $1.6\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ at $P\ensuremath{\approx}\ensuremath{-}0.05\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$, $0.5\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ at $P\ensuremath{\approx}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$), until, at high $P$, no capillary evaporation occurs. For $d\ensuremath{\approx}0.6\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ and $P\ensuremath{\geqslant}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$, the system crystallizes into a bilayer ice. A $P$-$d$ phase diagram showing the vapor, liquid, and bilayer ice phases is proposed. When water is confined by hydrophilic (hydroxylated silica) plates, it remains in the liquid phase at all $P$ and $d$ studied. Interestingly, we observe for this case that even at the $P$ at which bulk water cavitates, the confined water remains in the liquid state. We also study systematically the state of hydration at different $P$ for both kinds of plates. For the range of conditions studied here, we find that in the presence of hydrophobic plates the effect of $P$ is to enhance water structure and to push water molecules toward the plates. The average orientation of water molecules next to the hydrophobic plates does not change upon pressurization. In contrast, in the presence of hydrophilic plates, water structure is insensitive to $P$. Hence, our results suggest that upon pressurization, hydrophobic plates behave as ``soft'' surfaces (in the sense of accommodating pressure-dependent changes in water structure) while hydrophilic walls behave as ``hard'' surfaces.
TL;DR: Although the stable phase at high density is a crystalline solid, nucleation appears to be strongly suppressed with increasing dimension, consistent with a recently proposed "decorrelation principle".
Abstract: We present a study of disordered jammed hard-sphere packings in four-, five-, and six-dimensional Euclidean spaces. Using a collision-driven packing generation algorithm, we obtain the first estimates for the packing fractions of the maximally random jammed MRJ states for space dimensions d =4, 5, and 6t o be MRJ0.46, 0.31, and 0.20, respectively. To a good approximation, the MRJ density obeys the scaling form MRJ=c1/2 d +c2d/2 d , where c1=2.72 and c2=2.56, which appears to be consistent with the highdimensional asymptotic limit, albeit with different coefficients. Calculations of the pair correlation function g2r and structure factor Sk for these states show that short-range ordering appreciably decreases with increasing dimension, consistent with a recently proposed “decorrelation principle,” which, among other things, states that unconstrained correlations diminish as the dimension increases and vanish entirely in the limit d →. As in three dimensions where MRJ0.64, the packings show no signs of crystallization, are isostatic, and have a power-law divergence in g2r at contact with power-law exponent 0.4. Across dimensions, the cumulative number of neighbors equals the kissing number of the conjectured densest packing close to where g2r has its first minimum. Additionally, we obtain estimates for the freezing and melting packing fractions for the equilibrium hard-sphere fluid-solid transition, F0.32 and M0.39, respectively, for d=4, and F0.20 and M0.25, respectively, for d=5. Although our results indicate the stable phase at high density is a crystalline solid, nucleation appears to be strongly suppressed with increasing dimension.
TL;DR: Experimental results agreed reasonably well with the long-wave approximation and numerical calculations based on the Hertz interaction law for particles interactions.
Abstract: One-dimensional strongly nonlinear phononic crystals were assembled from chains of PTFE (polytetrafluoroethylene) and stainless-steel spheres with gauges installed inside the beads. Trains of strongly nonlinear solitary waves were excited by impacts. A significant modification of the signal shape and an increase of solitary wave speed up to two times (at the same magnitude of dynamic contact force) were achieved through a noncontact magnetically induced precompression of the chains. The data for the PTFE based chains are presented for the first time and the data for the stainless-steel beads chains are extended into a range of maximum dynamic forces more than one order of magnitude lower than previously reported. Experimental results agreed reasonably well with the long-wave approximation and numerical calculations based on the Hertz interaction law for particles interactions.
TL;DR: Full-scale, discrete-element simulations in realistic geometries are performed of Pebble-bed nuclear reactor technology to analyze the mean velocity, diffusion and mixing, local ordering and porosity, the residence-time distribution, and the effects of wall friction and discuss implications for reactor design and the basic physics of granular flow.
Abstract: Pebble-bed nuclear reactor technology, which is currently being revived around the world, raises fundamental questions about dense granular flow in silos. A typical reactor core is composed of graphite fuel pebbles, which drain very slowly in a continuous refueling process. Pebble flow is poorly understood and not easily accessible to experiments, and yet it has a major impact on reactor physics. To address this problem, we perform full-scale, discrete-element simulations in realistic geometries, with up to 440,000 frictional, viscoelastic 6-cm-diam spheres draining in a cylindrical vessel of diameter 3.5m and height 10 m with bottom funnels angled at 30 degrees or 60 degrees. We also simulate a bidisperse core with a dynamic central column of smaller graphite moderator pebbles and show that little mixing occurs down to a 1:2 diameter ratio. We analyze the mean velocity, diffusion and mixing, local ordering and porosity (from Voronoi volumes), the residence-time distribution, and the effects of wall friction and discuss implications for reactor design and the basic physics of granular flow.
TL;DR: A detailed description is provided of a new worm algorithm, enabling the accurate computation of thermodynamic properties of quantum many-body systems in continuous space, at finite temperature, within the general path integral Monte Carlo scheme.
Abstract: A detailed description is provided of a new worm algorithm, enabling the accurate computation of thermodynamic properties of quantum many-body systems in continuous space, at finite temperature. The algorithm is formulated within the general path integral Monte Carlo (PIMC) scheme, but also allows one to perform quantum simulations in the grand canonical ensemble, as well as to compute off-diagonal imaginary-time correlation functions, such as the Matsubara Green function, simultaneously with diagonal observables. Another important innovation consists of the expansion of the attractive part of the pairwise potential energy into elementary (diagrammatic) contributions, which are then statistically sampled. This affords a complete microscopic account of the long-range part of the potential energy, while keeping the computational complexity of all updates independent of the size of the simulated system. The computational scheme allows for efficient calculations of the superfluid fraction and off-diagonal correlations in space-time, for system sizes which are orders of magnitude larger than those accessible to conventional PIMC. We present illustrative results for the superfluid transition in bulk liquid $^{4}\mathrm{He}$ in two and three dimensions, as well as the calculation of the chemical potential of hcp $^{4}\mathrm{He}$.
TL;DR: The cascaded digital lattice Boltzmann automata described here, provides a method with which to achieve stable collision operators down to the limit of zero viscosity.
Abstract: Lattice Boltzmann methods are of limited applicability for direct numerical simulation of turbulent flow due to instabilities in the zero viscosity limit. We observe that this is caused by an insufficient degree of Galilean invariance of the relaxation-type Lattice Boltzmann collision operator. The cascaded digital lattice Boltzmann automata described here, provides a method with which to achieve stable collision operators down to the limit of zero viscosity.
TL;DR: It is shown that the high-order harmonic spectrum is universal, i.e., it does not depend on the interaction details, and the cornerstone of the theory is the new physical phenomenon: spikes in the relativistic gamma factor of the plasma surface.
Abstract: High-order harmonic generation due to the interaction of a short ultrarelativistic laser pulse with overdense plasma is studied analytically and numerically. On the basis of the ultrarelativistic similarity theory we show that the high-order harmonic spectrum is universal, i.e., it does not depend on the interaction details. The spectrum includes the power-law part ${I}_{n}\ensuremath{\propto}{n}^{\ensuremath{-}8∕3}$ for $nl\sqrt{8\ensuremath{\alpha}}{\ensuremath{\gamma}}_{\mathrm{max}}^{3}$, followed by exponential decay. Here ${\ensuremath{\gamma}}_{\mathrm{max}}$ is the largest relativistic $\ensuremath{\gamma}$ factor of the plasma surface and $\ensuremath{\alpha}$ is the second derivative of the surface velocity at this moment. The high-order harmonic cutoff at $\ensuremath{\propto}{\ensuremath{\gamma}}_{\mathrm{max}}^{3}$ is parametrically larger than the $4{\ensuremath{\gamma}}_{\mathrm{max}}^{2}$ predicted by the simple ``oscillating mirror'' model based on the Doppler effect. The cornerstone of our theory is the new physical phenomenon: spikes in the relativistic $\ensuremath{\gamma}$ factor of the plasma surface. These spikes define the high-order harmonic spectrum and lead to attosecond pulses in the reflected radiation.
TL;DR: A complete surface acoustic wave band gap is found experimentally in a two-dimensional square-lattice piezoelectric phononic crystal etched in lithium niobate, in good agreement with theoretical predictions.
Abstract: A complete surface acoustic wave band gap is found experimentally in a two-dimensional square-lattice piezoelectric phononic crystal etched in lithium niobate. Propagation in the phononic crystal is studied by direct generation and detection of surface waves using interdigital transducers. The complete band gap extends from 203 to 226 MHZ, in good agreement with theoretical predictions. Near the upper edge of the complete band gap, it is observed that radiation to the bulk of the substrate dominates. This observation is explained by introducing the concept of the sound line.
TL;DR: The experiment shows that external focusing strongly influences the plasma density and the diameter of femtosecond Ti-sapphire laser filaments generated in air and is in good qualitative agreement with the results of numerical simulations.
Abstract: Our experiment shows that external focusing strongly influences the plasma density and the diameter of femtosecond Ti-sapphire laser filaments generated in air. The control of plasma filament parameters is suitable for many applications such as remote spectroscopy, laser induced electrical discharge, and femtosecond laser material interactions. The measurements of the filament showed the plasma density increases from 10(15)cm(-3) to 2 x 10(18)cm(-3) when the focal length decreases from 380 cm to 10 cm while the diameter of the plasma column varies from 30 microm to 90 microm. The experimental results are in good qualitative agreement with the results of numerical simulations.