Physical Review E

Published by American Physical Society
Online ISSN: 1550-2376
Publications
Article
We perform a large-scale Monte Carlo simulation of the three-dimensional Ising model on simple cubic lattices of size L(3) with L=128 and 256. We determine the corresponding structure factor (Fourier transform of the two-point function) and compare it with several approximations and with experimental results. We also compute the turbidity as a function of the momentum of the incoming radiation, focusing in particular on the deviations from the Ornstein-Zernike expression of Puglielli and Ford.
 
Article
We analyze the effect of correlations in a simple model of a small-world network by obtaining exact analytical expressions for the distribution of shortest paths in the network. We enter correlations into a simple model with a distinguished site, by taking the random connections to this site from an Ising distribution. Our method shows how the transfer-matrix technique can be used in the new context of small-world networks.
 
Article
We study a social network consisting of over 10(4) individuals, with a degree distribution exhibiting two power scaling regimes separated by a critical degree k(crit), and a power law relation between degree and local clustering. We introduce a growing random model based on a local interaction mechanism that reproduces the observed scaling features and their exponents. We suggest that the double power law originates from two very different kinds of networks that are simultaneously present in the human social network.
 
Article
An approach aiming to quantify the dynamics of information within a population is developed based on the mapping of the processes underlying the system's evolution into a birth and death type stochastic process and the derivation of a balance equation for the information entropy. Information entropy flux and information entropy production are identified and their time-dependent properties, as well as their dependence on the parameters present in the problem, are analyzed. States of minimum information entropy production are shown to exist for appropriate parameter values. Furthermore, uncertainty and information production are transiently intensified when the population traverses the inflexion point stage of the logisticlike growth process.
 
Article
The work of Barton and Alexander on the fifth-order corrected field expressions for a Hermite-Gaussian (0,0) mode laser beam was extended to more general cases with adjustable parameters C1 and A1. The parametric dependence of the electron dynamics was studied by numerical methods. It was found that such dependence is mainly influenced by the beam width and comes from the second-order corrections in the expansions. Finally, the fifth-order corrected field equations for Hermite-Gaussian (0,1) mode were also detailed.
 
Article
The article reports the dependence of the conductivity relaxation on temperature T and pressure P in the canonical ionic glass former 0.4Ca(NO_{3})_{2}-0.6KNO_{3}(CKN). At constant conductivity relaxation time τ_{σ}, the entire conductivity relaxation spectra obtained at widely different combinations of T and P superpose almost perfectly, and thus it is the ion-ion interaction but not thermodynamics that determines the frequency dispersion. Moreover, on vitrifying CKN by either elevating P or decreasing T, changes of P or T dependence of τ_{σ} at the glass transition pressure P_{g} and temperature T_{g} are observed to occur at the same value, i.e., τ_{σ}(P_{g})=τ_{σ}(T_{g}), indicating that the relation between τ_{σ} and the structural relaxation time τ_{α} is also independent of P and T.
 
Article
Molecular dynamics results are reported concerning cooperatively rearranging regions in simulated Ni0.5Zr0.5 melts down to 700 K . Emphasis is laid on discriminating between clusters of mobile atoms (CMA) from low-frequency dynamics and the all-frequency case, where the former characterize fluctuations and relaxations on the scale of the late beta regime and alpha decay, while the latter include, in addition, reversible high-frequency vibrations. Separation of the low-frequency part of the dynamics is carried out by low-pass filtering, exploiting the separation of time scales below the critical temperature T{c} of the mode-coupling theory. With increasing temperature, the low-frequency and all-frequency dynamics merge in the range of T{c} when the separation of time scales disappears. In the low-frequency CMA, the average size of correlated clusters of connected atoms turns out to be nearly one order of magnitude larger than in the all-frequency CMA. The low-frequency CMA appear as local clusters propagating extremely slowly in space with characteristic time scale of mus at 700 K , the scale of the onset of alpha decay.
 
Measured magnetic field incident laser intensity as determined from harmonic polarimetry. ͑ ᭝ ͒ : second harmonic; ͑ b ͒ : third harmonic; ͑ ᮀ ͒ : fourth harmonic; ͑ ࡗ ͒ : fifth harmonic; ͑ ᭿ ͒ : eleventh–thirteenth harmonics, open cross: peak magnetic field from PIC simulations ( OSIRIS ) ; dashed line: ponderomotive scaling “fit” to simulation results. 
( Color ) Setup for VUV polarimetry. Inset is shown as an example of raw data with eighth–25th harmonic ( wavelength increases left to right ) separated into s and p polarization components ( up/down ) . 
Calculated magnetic field from experiment at I =9 10 19 W/cm 2 : note that this displays the 3 scaling (solid line) which is characteristic of the Cotton-Mouton effect.
( Color ) Simulation of high intensity interaction using 2D particle in cell code, OSIRIS , showing hole-boring effects and regions of 
Article
We report measurements of ultrahigh magnetic fields produced during intense ( approximately 10(20) Wcm(-2) micro m(2) ) laser interaction experiments with solids. We show that polarization measurements of high-order vuv laser harmonics generated during the interaction (up to the 15th order) suggest the existence of magnetic field strengths of 0.7+/-0.1 GG in the overdense plasma. Measurements using higher order harmonics indicate that denser regions of the plasma can be probed. This technique may be useful for measurements of multi- GG level magnetic fields which are predicted to occur at even higher intensities.
 
Article
This paper presents a detailed investigation of the temporal, spatial, and spectroscopic properties of L-shell radiation from 0.8 to 1.0 MA Mo x pinches. Time-resolved measurements of x-ray radiation and both time-gated and time-integrated spectra and pinhole images are presented and analyzed. High-current x pinches are found to have complex spatial and temporal structures. A collisional-radiative kinetic model has been developed and used to interpret L-shell Mo spectra. The model includes the ground state of every ionization stage of Mo and detailed structure for the O-, F-, Ne-, Na-, and Mg-like ionization stages. Hot electron beams generated by current-carrying electrons in the x pinch are modeled by a non-Maxwellian electron distribution function and have significant influence on L-shell spectra. The results of 20 Mo x-pinch shots with wire diameters from 24 to 62 microm have been modeled. Overall, the modeled spectra fit the experimental spectra well and indicate for time-integrated spectra electron densities between 2 x 10(21) and 2 x 10(22) cm(-3), electron temperatures between 700 and 850 eV, and hot electron fractions between 3% and 7%. Time-gated spectra exhibit wide variations in temperature and density of plasma hot spots during the same discharge.
 
Article
The distributions of the size of islands and of the capture zones are discussed comparatively, both experimentally and numerically, for the case of a sudden nucleation process with and without coarsening. The experiments were performed by growing InAs islands on GaAs(001) and the coarsening was altered by varying the temperature. In the two-dimensional kinetic Monte Carlo simulations a single-species diffusing adatom was taken into account, and the coarsening was altered in this case by modifying the binding energy between adatoms and islands. The results show that size and capture zone distributions overlap only when coarsening can be disregarded.
 
Snapshot of a Si(001) surface at T = 580 K. Open squares represent the initial positions, solid circles the positions after 10 6 MCS. Dashed lines indicate anti-phase domains walls.
Article
A classical, hybrid Monte Carlo-molecular dynamic (MC-MD) algorithm is introduced for the study of phenomena like two-dimensional (2D) island stability or step-edge evolution on semiconductor surfaces. This method presents the advantages of working off lattice and utilizing bulk-fitted potentials. It is based on the introduction of collective moves, such as dimer jumps, in the MC algorithm. MD-driven local relaxations are considered as trial moves for the MC. The algorithm is applied to the analysis of 2D Si islands on Si(001). Results on early stages of island formation, island stability versus temperature and system size, and step-edge evolution are presented. In all cases good qualitative agreement with experimental results is found.
 
Article
Using standard numerical Monte Carlo lattice methods, we study non-universal properties of the phase transition of three-dimensional straight phi(4) theory of a two-component real field phi=(phi(1),phi(2)) with O(2) symmetry. Specifically, we extract the renormalized values of <phi(2)>/u and r/u(2) at the phase transition, where the continuum action of the theory is integral d(3)x[1/2/inverted Delta phi/(2) + 1 2r phi(2)+(u/4!)phi(4)]. These values have applications to calculating the phase-transition temperature of dilute or weakly interacting Bose gases (both relativistic and nonrelativistic). In passing, we also provide perturbative calculations of various O(a) lattice-spacing errors in three-dimensional O(N) scalar field theory, where a is the lattice spacing.
 
Article
We consider the dynamic behavior in driven phase transitions dominated either by attachment-detachment or by surface diffusion mass transport mechanisms. As the driving force increases, we numerically demonstrate for both cases that the spatiotemporal faceted structure of the surface undergoes a sequential transition from slow coarsening turning to accelerated coarsening followed by fixed length scale structures before finally becoming spatiotemporally chaotic. For the attachment-detachment dominated phase transition problem we compare in the accelerated coarsening regime the simulation results with an intrinsic dynamical system governing the leading-order piecewise-affine dynamic surface (PADS), which can be obtained through a matched asymptotic analysis. The PADS predicts the numerically observed coarsening law for the growth in time of the characteristic morphological length scale L_{M} . In particular we determine the prefactor of the scaling law which allows for quantitative predictions necessary for any use of the theory in preparing patterned surfaces through modifications of the driving force.
 
Fractal dimension of the aggregates of DPPC liposomes at different concentration of La 3+ calculated by scattering intensity 
TEM photograph of DPPC liposomes in the presence of 0.2 M of La 3+ . RCLA clusters with closed and compact structures. 
Variation of the number of liposomes aggregated with the concentration of La 3+ ions. The insets represent the secondary 
Article
A study of the fractal dimension of the aggregation of three different types of large unilamellar vesicles, formed by egg yolk phosphatidylcholine (EYPC), dimyristoyl-phosphocholine (DMPC), and dipalmitoyl-phosphocholine (DPPC), in the presence of La3+, is presented. Aggregate liposome fractal dimensions were calculated by two methods, aggregation kinetics, using the approaches diffusion-limited cluster aggregation (DLCA) and reaction-limited cluster aggregation (RLCA) and angle-scattering light dispersion. Electrophoretic measurements show a similar variation of the zeta potential (zeta potential) for EYPC and DPPC, with a small increase of initial positive values. However, the zeta potential of DMPC changes from a initial negative value to near zero with increasing La3+ concentration. The evolution of the aggregate sizes was followed by light scattering. DPPC and DMPC show a RLCA regimen growth at low La3+ concentrations and a DLCA regimen at higher concentrations. In the case of EYPC, the final size of aggregation strongly depends on La3+ concentration. The calculated fractal dimension is in the range 1.8 to 2.1.
 
Article
On the basis of a modified bouncing-ball model, we investigated whether human movements utilize principles of dynamic stability in their performance of a similar movement task. Stability analyses of the model provided predictions about conditions indicative of a dynamically stable period-one regime. In a series of experiments, human subjects bounced a ball rhythmically on a racket and displayed these conditions supporting that they attuned to and exploited the dynamic stability properties of the task.
 
Article
The Smoluchowski-Chapman-Kolmogorov functional equation is applied to the electric signals that precede rupture. The results suggest a non-Markovian character of the analyzed data. The rescaled range Hurst and detrended fluctuation analyses, as well as that related with the "mean distance a walker spanned," lead to power-law exponents, which are consistent with the existence of long-range correlations. A "universality" in the power spectrum characteristics of these signals emerges, if an analysis is made (not in the conventional time frame, but) in the "natural" time domain. Within this frame, it seems that certain power spectrum characteristics of ion current fluctuations in membrane channels distinguish them from the electric signals preceding rupture. The latter exhibit a behavior compatible with that expected from a model based on the random field Ising Hamiltonian at the critical point.
 
Article
Helicase proteins move along double-stranded nucleic-acid molecules and unwind the double helix. This paper presents a theoretical study of the coupling between helicase translocation and duplex unwinding. Two different cases-active and passive opening-are usually distinguished. In active opening, the helicase directly destabilizes the double-stranded nucleic acid (dsNA) to promote opening. Passive opening implies that the helicase binds ssNA available when a thermal fluctuation partially opens the dsNA. We formulate a discrete model for helicase motion. An interaction potential describes how the helicase affects duplex unwinding when near a junction between single-stranded and double-stranded NA. Different choices of the potential correspond to the cases of active and passive opening. An optimal choice of interaction potential leads to a helicase which can unwind NA as rapidly as it translocates on single strands.
 
Dynamic range as a function of the system size L for p = q = 1. Lines are just guides to the eye. 
Experimental response curves (normalized firing rate vs. light intensity) of retinal on-center ganglion cells in linearlog (main plot) and log-log (inset) scales (data extracted from Fig. 6 of Ref. [4]). Filled (open) circles are for WT (Cx36KO) mice, solid (dashed) lines show the results of the pair approximation, thus L → ∞, with p = q = 1 (p = q = 0). Upper curves are for n = 10, lower curves are for n = 3. The dot-dashed line corresponds to simulations with n = 10, p = q = 1 and L = 20. 
Article
Experimental data suggest that some classes of spiking neurons in the first layers of sensory systems are electrically coupled via gap junctions or ephaptic interactions. When the electrical coupling is removed, the response function (firing rate vs. stimulus intensity) of the uncoupled neurons typically shows a decrease in dynamic range and sensitivity. In order to assess the effect of electrical coupling in the sensory periphery, we calculate the response to a Poisson stimulus of a chain of excitable neurons modeled by n-state Greenberg-Hastings cellular automata in two approximation levels. The single-site mean field approximation is shown to give poor results, failing to predict the absorbing state of the lattice, while the results for the pair approximation are in good agreement with computer simulations in the whole stimulus range. In particular, the dynamic range is substantially enlarged due to the propagation of excitable waves, which suggests a functional role for lateral electrical coupling. For probabilistic spike propagation the Hill exponent of the response function is alpha=1, while for deterministic spike propagation we obtain alpha=1/2, which is close to the experimental values of the psychophysical Stevens exponents for odor and light intensities. Our calculations are in qualitative agreement with experimental response functions of ganglion cells in the mammalian retina.
 
Article
We provide two complementary approaches to the treatment of disorder in a fundamental nonequilibrium model, the asymmetric simple exclusion process. First, a mean-field steady-state mapping is generalized to the disordered case, where it provides a mapping of probability distributions and demonstrates how disorder results in a new flat regime in the steady-state current-density plot for periodic boundary conditions. This effect was earlier observed by Phys. Rev. E 58, 1911 (1998)] but we provide a treatment for more general distributions of disorder, including both numerical results and analytic expressions for the width 2 Delta(C) of the flat section. We then apply an argument based on moving shock fronts [Europhys. Lett. 48, 257 (1999)]] to show how this leads to an increase in the high-current region of the phase diagram for open boundary conditions. Second, we show how equivalent results can be obtained easily by taking the continuum limit of the problem and then using a disordered version of the well-known Cole-Hopf mapping to linearize the equation. Within this approach we show that adding disorder induces a localization transformation (verified by numerical scaling), and Delta(C) maps to an inverse localization length, helping to give a physical interpretation to the problem.
 
Article
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.
 
Article
The well-established universality classes of absorbing critical phenomena are directed percolation (DP) and directed Ising (DI) classes. Recently, the pair contact process with diffusion (PCPD) has been investigated extensively and claimed to exhibit a different type of critical phenomenon distinct from both DP and DI classes. Noticing that the PCPD possesses a long-term memory effect, we introduce a generalized version of the PCPD (GPCPD) with a parameter controlling the memory strength. The GPCPD connects the DP fixed point to the PCPD point continuously. Monte Carlo simulations strongly suggest that the GPCPD displays, to our knowledge, novel critical phenomena which are characterized by continuously varying critical exponents. The same critical behaviors are also observed in models where two species of particles are coupled cyclically. We present one possible scenario that the long-term memory may serve as a marginal perturbation to the ordinary DP fixed point.
 
Article
We study the phenomenon of spatial coherence resonance in a two-dimensional model of excitable media with FitzHugh-Nagumo local dynamics. In particular, we show that there exists an optimal level of additive noise for which an inherent spatial scale of the excitable media is best pronounced. We argue that the observed phenomenon occurs due to the existence of a noise robust excursion time that is characteristic for the local dynamics whereby the diffusion constant, representing the rate of diffusive spread, determines the actual resonant spatial frequency. Additionally, biological implications of presented results in the field of neuroscience are outlined.
 
Article
Bulk fluid flow induced by an ac electric potential with a peak voltage below the ionization potential of water is described. The potential is applied to an ionic solution with a planar array of electrodes arranged in pairs so that one edge of a large electrode is close to an opposing narrow electrode. During half the cycle, the double layer on the surface of the electrodes charges as current flows between the electrodes. The electrodes charge in a nonuniform manner producing a gradient in potential parallel to the surface of the electrodes. This gradient drives the ions in the double layer across the surface of the electrode and this in turn drags the fluid across the electrode surface. The anisotropic nature of the pairs of electrodes is used to produce a net flow of fluid. The flow produced is approximately uniform at a distance from the electrodes that is greater than the periodicity of the electrode array. The potential and frequency dependence of this flow is reported and compared to a simple model. This method of producing fluid flow differs from electrical and thermal traveling-wave techniques as only a low voltage is required and the electrode construction is much simpler.
 
Article
The electrostatic potential and plasma density variations around a pointlike charged object in a plasma flow are studied. These objects can represent small charged dust particles, for instance. The radiation patterns can be interpreted as the result of sound waves being radiated by the obstacle. Two limits are considered: one where the electron-ion temperature ratio is large, Te>Ti , and one where Te/Ti approximately 1 . The former limit can be described by a simple model based on geometrical optics, while the latter requires a kinetic model in order to account for the effects of ion Landau damping. The results are illustrated by numerical simulation using a particle-in-cell code, where the electrons are treated as an isothermal massless fluid, giving a nonlinear Poisson equation. The analytical results are in good agreement with the numerical simulations.
 
Article
The computation of superconfiguration partition functions relies upon independent electron statistics, with electron-electron contributions included as an average first-order correction factor. The decomposition into a first-order correction and reference independent electron system has degrees of freedom not exploited by current methods. We present a derivation for the conventional choice of decomposition and propose a different method for obtaining an optimal decomposition for each superconfiguration. This constitutes an alternative procedure to recomputing self-consistent fields for the refinement of superconfiguration partition functions. Numerical results are presented and discussed.
 
Article
Optical emission spectroscopy (OES) was used to study the evolution behavior of the neutral Si atoms in the plasma produced by nanosecond pulsed-laser beam irradiating on SiC crystal targets. The OES measurements indicated that the electron temperature and density in the plasma had maximum values around a region about 2mm from the target surface. Based on the temporal and spatial evolution of the spectral line at 633.19 nm originating from excited Si atoms, it was found that these Si atoms have short decay times and long range spatial distribution in vacuum. At the initial growth stage of SiC thin films using pulsed-laser deposition (PLD) technique, these Si atoms were found possibly to arrive at the Si substrate to form defects near the SiC/Si interface. By comparing the OES result measured in vacuum and that measured in ambient air, it was deduced that by properly adjusting the background gas species and pressure, the quality of the films prepared by PLD technique may be improved.
 
Article
Electric-field measurements inside a negative-permeability-positive-permittivity metamaterial composed of arrays of split-ring resonators directly show that the theoretically predicted enhancement of evanescent waves in passive materials is physically realizable. To circumvent the extreme sensitivity of this phenomenon to the material parameters, we show how the basic phenomenon occurs under relaxed conditions for a single transverse wave number and use this approach in our measurements. Measurements of the spatial distribution of the electric field in a three-slab configuration confirm that the evanescent wave enhancement responsible for the subwavelength focusing effect occurs in an electromagnetic material in a manner in close agreement with theory.
 
Article
This Rapid Communication addresses the relationship between hyperbolic equations of heat conduction and microscopic models of dielectrics. Effects of the nonstationary heat conduction are investigated in two one-dimensional models with conserved momentum: Fermi-Pasta-Ulam (FPU) chain and chain of rotators (CR). These models belong to different universality classes with respect to stationary heat conduction. Direct numeric simulations reveal in both models a crossover from oscillatory decay of short-wave perturbations of the temperature field to smooth diffusive decay of the long-wave perturbations. Such behavior is inconsistent with parabolic Fourier equation of the heat conduction. The crossover wavelength decreases with increase in average temperature in both models. For the FPU model the lowest-order hyperbolic Cattaneo-Vernotte equation for the nonstationary heat conduction is not applicable, since no unique relaxation time can be determined.
 
Article
The correlations within the time series of the seismic electric signal (SES) activities have been studied in a previous paper [P. Varotsos, N. Sarlis, and E. Skordas, Phys. Rev. E 66, 011902 (2002)]. Here, we analyze the time series of successive high- and low-level states' durations. The existence of correlation between the states is investigated by means of Hurst and detrended fluctuation analysis (DFA). The multifractal DFA (MF-DFA) is also employed. The results point to a stronger correlation, and hence longer memory, in the series of the high-level states. Furthermore, an analysis in the "natural" time domain reveals that certain power spectrum characteristics seem to distinguish SES activities from "artificial" (man-made) electric noises. More precisely, for natural frequencies 0<phi<0.5, the curves of the SES activities and artificial noises lie above and below, respectively, that of the "uniform" distribution (UD). A classification of these two types of electric signals (SES activities, artificial noises), cannot be achieved on the basis of the values of the power-law exponents alone, if the Hurst analysis, DFA, and MF-DFA are applied to the original time series. The latter two methods, however, seem to allow a distinction between the SES activities and artificial noises when treating them (not in conventional the time frame, but) in the natural time domain. To further test the techniques, a time series produced by another system was examined. We chose a signal of ion current fluctuations in membrane channels (ICFMCs). The following conclusions, among others, have been obtained: First, the power spectrum analysis in the natural time domain shows that the ICFMC curve almost coincides (in the range 0<phi<0.5) with that of the UD, and hence ICFMC lies just in the boundary between the SES activities and artificial noises. Second, MF-DFA indicates monofractality for the ICFMCs with a generalized Hurst exponent h=0.84+/-0.03 in the range 7-70 ms.
 
Article
Established expressions for entropy production in irreversible processes are generalized to include friction explicitly, as a source of irreversibility in the interaction between a system and its surroundings. The net amount of heat delivered to the system does not come now only from the reservoir, but may have an additional component coming from the work done against friction forces and dissipated as heat. To avoid ambiguities in interpreting the different contributions to entropy increase, the latter is also written in terms of the heat directly exchanged between the system and surroundings and of the fraction of frictional work that is lost in the system.
 
(Color online) Plot of the function y2(r) at T * = 0 (top panel), T * = 1 (middle panel), and T * = 2 (bottom panel). The solid lines are the exact results, the dashed lines are the HNC predictions, and the dotted lines are the PY predictions.
(Color online) Plot of the fourth virial coefficient b4(T * ) (top panel) and of the scaled fourth virial coefficient b4(T * )/x 4 (bottom panel), where x = 1 − e −1/T * , as given exactly and by the HNC and PY approximations.  
Article
The simplest bounded potential is that of penetrable spheres, which takes a positive finite value epsilon if the two spheres are overlapped, being zero otherwise. In this paper we derive the cavity function to second order in density and the fourth virial coefficient as functions of T* identical with k(B)T/epsilon (where k(B is the Boltzmann constant and T is the temperature) for penetrable sphere fluids. The expressions are exact, except for the function represented by an elementary diagram inside the core, which is approximated by a polynomial form in excellent agreement with accurate results obtained by Monte Carlo integration. Comparison with the hypernetted-chain (HNC) and Percus-Yevick (PY) theories shows that the latter is better than the former for T* < or similar to 1 only. However, even at zero temperature (hard sphere limit), the PY solution is not accurate inside the overlapping region, where no practical cancellation of the neglected diagrams takes place. The exact fourth virial coefficient is positive for T* < or similar to 0.73, reaches a minimum negative value at T* approximately 1.1, and then goes to zero from below as 1/T(*4) for high temperatures. These features are captured qualitatively, but not quantitatively, by the HNC and PY predictions. In addition, in both theories the compressibility route is the best one for T* < or similar to 0.7, while the virial route is preferable if T* > or similar to 0.7.
 
Article
We investigate a phase separation instability that occurs in a system of nearly elastically colliding hard spheres driven by a thermal wall. If the aspect ratio of the confining box exceeds a threshold value, granular hydrostatics predict phase separation: the formation of a high-density region coexisting with a low-density region along the wall that is opposite to the thermal wall. Event-driven molecular dynamics simulations confirm this prediction. The theoretical bifurcation curve agrees with the simulations quantitatively well below and well above the threshold. However, in a wide region of aspect ratios around the threshold, the system is dominated by fluctuations, and the hydrostatic theory breaks down. Two possible scenarios of the origin of the giant fluctuations are discussed.
 
(a) Static structure factor S(q) of CRN (solid line, measured on G41 at the Laboratoire Léon Brillouin) and of CRN (dotted line, scanned from Ref. [19]), both obtained by neutron diffraction at about room temperature. (b) Dynamic window of our inelastic scattering experiment on the time-of-flight spectrometer IN 5 for an incident neutron wavelength λi = 8.0 ˚ A. The solid curves show q(ν) for every second detector. The scattering law S(q, ν) is obtained by interpolating the constant-angle data to constant-q sections. The vertical dashed-dotted lines indicate the limits of the q range used in the data analysis. 
Susceptibility χ ′′ ns (ν) = χ ′′ (q, ν)/hq averaged over q between 0.5 and 1.3 ˚ A −1 (excluding the q-dependent α relaxation in the low-frequency, high-temperature limit). Solid lines are fits to the MCT asymptote with fixed λ = 0.79. 
Article
The fast dynamics of viscous calcium rubidium nitrate is investigated by depolarized light scattering, neutron scattering, and dielectric loss. Fast beta relaxation evolves as in calcium potassium nitrate. The dynamic susceptibilities can be described by the asymptotic scaling law of mode-coupling theory with a shape parameter lambda=0.79; the temperature dependence of the amplitudes extrapolates to T(c) approximately equal 378 K. However, the frequencies of the minima of the three different spectroscopies never coincide, in conflict with the factorization prediction, indicating that the true asymptotic regime is unreachable.
 
Rescaled distributions of the hole amplitudes Φµ 1 (η) for µ1 = 2.5, 2, 1.5, and 1 (the latter corresponding to the limiting distribution). Smaller µ1 are shown by thicker lines.  
Article
We employ hydrodynamic equations to investigate nonstationary channel flows of freely cooling dilute gases of hard and smooth spheres with nearly elastic particle collisions. This work focuses on the regime where the sound travel time through the channel is much shorter than the characteristic cooling time of the gas. As a result, the gas pressure rapidly becomes almost homogeneous, while the typical Mach number of the flow drops well below unity. Eliminating the acoustic modes and employing Lagrangian coordinates, we reduce the hydrodynamic equations to a single nonlinear and nonlocal equation of a reaction-diffusion type. This equation describes a broad class of channel flows and, in particular, can follow the development of the clustering instability from a weakly perturbed homogeneous cooling state to strongly nonlinear states. If the heat diffusion is neglected, the reduced equation becomes exactly soluble, and the solution develops a finite-time density blowup. The blowup has the same local features at singularity as those exhibited by the recently found family of exact solutions of the full set of ideal hydrodynamic equations [I. Fouxon, Phys. Rev. E 75, 050301(R) (2007); I. Fouxon,Phys. Fluids 19, 093303 (2007)]. The heat diffusion, however, always becomes important near the attempted singularity. It arrests the density blowup and brings about previously unknown inhomogeneous cooling states (ICSs) of the gas, where the pressure continues to decay with time, while the density profile becomes time-independent. The ICSs represent exact solutions of the full set of granular hydrodynamic equations. Both the density profile of an ICS and the characteristic relaxation time toward it are determined by a single dimensionless parameter L that describes the relative role of the inelastic energy loss and heat diffusion. At L>1 the intermediate cooling dynamics proceeds as a competition between "holes": low-density regions of the gas. This competition resembles Ostwald ripening (only one hole survives at the end), and we report a particular regime where the "hole ripening" statistics exhibits a simple dynamic scaling behavior.
 
Article
A microscopic theory for the dependence on external strain, stress, and shear rate of the transient localization length, elastic modulus, alpha relaxation time, shear viscosity, and other dynamic properties of glassy colloidal suspensions is formulated and numerically applied. The approach is built on entropic barrier hopping as the elementary physical process. The concept of an ideal glass transition plays no role, and dynamical slowing down is a continuous, albeit precipitous, process with increasing colloid volume fraction. The relative roles of mechanically driven motion versus thermally activated barrier hopping and transport have been studied. Various scaling behaviors are found for the relaxation time and shear viscosity in both the controlled stress and shear rate mode of rheological experiments. Apparent power law and/or exponential dependences of the elastic modulus and perturbative and absolute yield stresses on colloid volume fraction are predicted. A nonmonotonic dependence of the absolute yield strain on volume fraction is also found. Qualitative and quantitative comparisons of calculations with experiments on high volume fraction glassy colloidal suspensions show encouraging agreement, and multiple testable predictions are made. The theory is generalizable to treat nonlinear rheological phenomena in other soft glassy complex fluids including depletion gels.
 
Article
The rheological properties of a dilute suspension of ellipsoidal ferromagnetic particles in the presence of a magnetic field are studied on the basis of a kinetic model, where the flow and magnetic external fields couple in qualitatively different ways to the orientational behavior of the suspension. In the uniaxial phase the stress tensor is found to be of the same form as in the Ericksen-Leslie theory for nematic liquid crystals in the steady state. Expressions for a complete set of viscosity coefficients in terms of orientational order parameters are worked out. In the low Péclet number regime, the viscosity coefficients are given as explicit functions of the magnetic field and a particle shape factor, where the shape factor may equally represent a nonspherical unit (agglomerate, chain) composed of spherical particles. Effects due to possible flow-induced breakup of units are not covered in this work. Further, by considering the magnetization as the only relevant variable, a magnetization equation within an effective field approach is derived from the kinetic equation and compared to existing magnetization equations. The alignment angle of the magnetization and the first and second normal stress coefficient are studied for the special case of plane Couette flow. The assumptions employed are tested against a Brownian dynamics simulation of the full kinetic model, and a few comparisons with experimental data are made.
 
Article
Multilamellar vesicles can be formed upon shearing lamellar phases (L(alpha)) and phase-separated lamellar-sponge (L(alpha)/L(3)) mixtures. In the first case, the vesicle volume fraction is always 100% and the vesicle size is monitored by elasticity ("onion textures"). In the second system the vesicle volume fraction can be tuned from 0 to 100% and the mean size results from a balance between capillary and viscous forces ("Taylor droplets"). However, despite these differences, in both systems we show that the formation of vesicles is a strain-controlled process monitored by a universal primary buckling instability of the lamellae.
 
Article
An expression for the anisotropy of the solid-liquid interfacial energy has been determined experimentally by an inverse method for the Al-43.4 wt%Zn-1.6 wt%Si system. Assuming that dendrite growth directions correspond to the minima of the surface stiffness, the anisotropy of the solid-liquid interfacial energy could be described by minimizing the errors between the calculated minima of a parametric interface stiffness function and experimentally measured growth directions of dendrites in thin coatings. In order to adequately describe the interfacial energy, it is found that a cubic harmonic expansion up to the third order is necessary to obtain the minima of interface stiffness along directions that depart from <100> or <110>. Best agreement with observed growth directions is obtained for first, second, and third harmonic coefficients (epsilon1, epsilon2, and epsilon3, respectively) satisfying the following relationships: epsilon2/epsilon1 = -0.188; epsilon3/epsilon1 = -0.00776. The corresponding interface stiffness function shows 24 minima lying along directions between <100> and <110>. The minima are located at 28.5 degrees from <100> and only 5.1 degrees from <320>, which was the growth direction suggested by Sémoroz for this alloy [A. Sémoroz, Y. Durandet, and M. Rappaz, Acta Mater. 49, 529 (2001).]. It was also found that the strength of the effective in-plane anisotropy is directly reflected by the morphology of the dendritic microstructure.
 
Article
We performed neutron reflectivity measurements on multilayered polymer thin films consisting of alternatively stacked deuterated polystyrene (d-PS) and hydrogenated polystyrene (h-PS) layers ∼200 Å thick as a function of temperature covering the glass-transition temperature T(g), and we found a wide distribution of T(g) as well as a distribution of the thermal expansivity α within the thin films, implying the dynamic heterogeneity of the thin films along the depth direction. The reported anomalous film thickness dependences of T(g) and α were reasonably understood in terms of the distributions, showing that the surface mobile layer and the bottom hard interfacial layer are, respectively, responsible for the depressions of T(g) and α with decreasing film thickness. The molecular mobility in each layer is also discussed in relation to the distribution of T(g), based on the results on mutual diffusion at the layer interface.
 
Article
We consider a lattice Boltzmann simulation of blood flow in a vessel deformed by the presence of an aneurysm. Modern clinical treatments involve introducing a stent (a tubular mesh of wires) into the cerebral artery in order to reduce the flow inside the aneurysm and favor its spontaneous reabsorption. A crucial question is to design the stent with suitable porosity so as to produce the most effective flow reduction. We propose a stent positioning factor as a characterizing tool for stent pore design in order to describe the flow reduction effect and reveal the several flow reduction mechanisms using this effect.
 
Article
This paper reports the results of an experimental and theoretical study of the segregation of heavy (sand) and light [polyvinyl chloride (PVC)] grains under the action of intense nonlinear water waves, solitons. The tests are carried out with initially carefully mixed grains at the bottom of a wave flume used in resonant mode. Ripples form on the bed and the segregation process is considered after the stopping of the wave paddle. The waves are damped and the PVC grains concentrate in a narrow region close to the ripple crest. A theoretical model explaining this grain density segregation is developed.
 
The auxiliary functions s 1 (v) and s 2 (v), and their ratio, as a function of v (the plasma drift velocity normalized by 2k B T i /m i ). 
f N (solid line) and its Gaussian approximation (dashed line) for a 10 nm sphere in a hydrogenic plasma with a λ D , v = 0, Θ = 0.001, and 1 eV electrons. 
Contour plot of f N 's skewness for a large grain in a hydrogenic plasma with 1 eV electrons and ions, v ≫ 1, and γ = 3. 
Article
A dust grain in a plasma has a fluctuating electric charge, and past work concludes that spherical grains in a stationary, collisionless plasma have an essentially Gaussian charge probability distribution. This paper extends that work to flowing plasmas and arbitrarily large spheres, deriving analytic charge probability distributions up to normalizing constants. We find that these distributions also have good Gaussian approximations, with analytic expressions for their mean and variance.
 
Article
We study empirically the time evolution of scientific collaboration networks in physics and biology. In these networks, two scientists are considered connected if they have coauthored one or more papers together. We show that the probability of a pair of scientists collaborating increases with the number of other collaborators they have in common, and that the probability of a particular scientist acquiring new collaborators increases with the number of his or her past collaborators. These results provide experimental evidence in favor of previously conjectured mechanisms for clustering and power-law degree distributions in networks.
 
Finite size behaviour for the magnetisation |m| versus the temperature T in the regular, 2D-Ising model for L1 = 80 (squares) and L2 = 160 (circles). The dashed line shows Yang's solution [16]. In the dynamical Ising model, the cooling and heating rates, h(L) and ǫ(L) prescribe the magnetisation |m(L)| = h(L)/ǫ(L) ∝ L κ−ω , indicated by horizontal lines. The system is forced to move to an effective temperature t eff (L), indicated by arrows. 
Article
We investigate a suggested path to self-organized criticality. Originally, this path was devised to "generate criticality" in systems displaying an absorbing-state phase transition, but nothing in its definition forbids the mechanism to be used in any other continuous phase transition. We used the Ising model as well as the Manna model to demonstrate how the finite-size scaling exponents depend on the tuning of driving and dissipation rates with system size. Our findings limit the explanatory power of the mechanism as it is to nonuniversal critical behavior, suggesting that the explanation of self-organized criticality in terms of absorbing-state phase transitions is incomplete.
 
Article
By use of a reduced model focusing on the in-plane dependence of plane Couette flow, it is shown that the turbulent-->laminar relaxation process can be understood as a nucleation problem similar to that occurring at a thermodynamic first-order phase transition. The approach, apt to deal with the large extension of the system considered, challenges the current interpretation in terms of chaotic transients typical of temporal chaos. The study of the distribution of the sizes of laminar domains embedded in turbulent flow proves that an abrupt transition from sustained spatiotemporal chaos to laminar flow can take place at some given value of the Reynolds number Rlow, whether or not the local chaos lifetime, as envisioned within low-dimensional dynamical systems theory, diverges at finite R beyond Rlow.
 
Article
We study via renormalization group (RG), numerics, exact bounds, and qualitative arguments the equilibrium Gibbs measure of a particle in a d-dimensional Gaussian random potential with translationally invariant logarithmic spatial correlations. We show that for any d>/=1 it exhibits a transition at T=T(c)>0. The low-temperature glass phase has a nontrivial structure, being dominated by a few distant states (with replica symmetry breaking phenomenology). In finite dimension this transition exists only in this "marginal glass" case (energy fluctuation exponent straight theta=0) and disappears if correlations grow faster (single ground-state dominance straight theta>0) or slower (high-temperature phase). The associated extremal statistics problem for correlated energy landscapes exhibits universal features which we describe using a nonlinear Kolmogorov (KPP) RG equation. These include the tails of the distribution of the minimal energy (or free energy) and the finite-size corrections, which are universal. The glass transition is closely related to Derrida's random energy models. In d=2, the connection between this problem and Liouville and sinh-Gordon models is discussed. The glass transition of the particle exhibits interesting similarities with the weak- to strong-coupling transition in Liouville (c=1 barrier) and with a transition that we conjecture for the sinh-Gordon model, with correspondence in some exact results and RG analysis. Glassy freezing of the particle is associated with the generation under RG of new local operators and of nonsmooth configurations in Liouville. Applications to Dirac fermions in random magnetic fields at criticality reveal a peculiar "quasilocalized" regime (corresponding to the glass phase for the particle), where eigenfunctions are concentrated over a finite number of distant regions, and allow us to recover the multifractal spectrum in the delocalized regime.
 
Article
Nacre causes the shining beauty of pearl due to its remarkable layered structure, which is also strong. We reconsider a simplified layered model of nacre proposed previously [Okumura and de Gennes, Eur. Phys. J. E 4, 121 (2001)] and obtain an analytical solution to a fundamental crack problem. The result asserts that the fracture toughness is enhanced due to a large displacement around the crack tip (even if the crack-tip stress is not reduced). The derivation offers ideas for solving a number of boundary problems for partial differential equations important in many fields.
 
Article
A three-dimensional Ising model with the plaquette-type (next-nearest-neighbor and four-spin) interactions is investigated numerically. This extended Ising model, the so-called gonihedric model, was introduced by Savvidy and Wegner as a discretized version of the interacting (closed) surfaces without surface tension. The gonihedric model is notorious for its slow relaxation to the thermal equilibrium (glassy behavior), which deteriorates the efficiency of the Monte Carlo sampling. We employ the transfer-matrix (TM) method, implementing Novotny's idea, which enables us to treat an arbitrary number of spins N for one TM slice even in three dimensions. This arbitrariness admits systematic finite-size-scaling analyses. Accepting the extended parameter space by Cirillo et al., we analyzed the (multi-) criticality of the gonihedric model for N</=13. Thereby, we found that, as first noted by Cirillo et al. analytically (cluster-variation method), the data are well described by the multicritical (crossover) scaling theory. That is, the previously reported nonstandard criticality for the gonihedric model is reconciled with a crossover exponent and the ordinary three-dimensional-Ising universality class. We estimate the crossover exponent and the correlation-length critical exponent at the multicritical point as phi=0.6(2) and nu; =0.45(15), respectively.
 
Article
Although the inference of global community structure in networks has recently become a topic of great interest in the physics community, all such algorithms require that the graph be completely known. Here, we define both a measure of local community structure and an algorithm that infers the hierarchy of communities that enclose a given vertex by exploring the graph one vertex at a time. This algorithm runs in time O(k2d) for general graphs when d is the mean degree and k is the number of vertices to be explored. For graphs where exploring a new vertex is time consuming, the running time is linear, O(k). We show that on computer-generated graphs the average behavior of this technique approximates that of algorithms that require global knowledge. As an application, we use this algorithm to extract meaningful local clustering information in the large recommender network of an online retailer.
 
Article
We investigate experimentally the detailed dynamics of how an existing microbubble B1 is impacted and shattered by another nearby pulsed-laser-induced microbubble B2, and the backward interaction on B2 in a thin liquid layer. Mediated by the flow field, potential energy can be accumulated or lost through the alternate compression and expansion of the two bubbles. The symmetry breaking induced by the presence of the nearby counterbubble generates push-pull-type alternate forward and backward axial jetting on the compressed bubble associated with the elongated shape or even entrainment of the counterexpanding bubble into the jet-indented boundary. The strong penetrating axial jet through B1, and its interplay with the transverse jets by the flow field surrounding B1 in the first compression stage and the second expanding stage of B1 lead to a complicated fragmentation pattern of B1. Increasing the interbubble interaction by decreasing the interbubble distance causes B2 to become entangled with B1 through its entrainments into the backward axial jet-indented region of B2, in the expansion phase of B2. At the extreme of large laser energy for B2, the leftward reexpansion of B1 is suppressed. The strong shear flow field generates many tiny bubbles around the liquid-gas boundaries of the two axial jet-induced major daughter bubbles from B1. The detailed interaction behaviors over a broad range of the energy of B2, 0.14-0.55 microJ (corresponding to the maximum bubble expansion energy), and of the interbubble distance (170-500 microm) are presented and discussed.
 
Top-cited authors
H. Eugene Stanley
  • Boston University
Juergen Kurths
  • Potsdam Institute for Climate Impact Research
Santo Fortunato
  • Indiana University Bloomington
Shlomo Havlin
  • Bar Ilan University
Wei-Xing Zhou
  • East China University of Science and Technology