Multifractal detrended fluctuation analysis (MF-DFA) is the most popular method to detect multifractal characteristics of considerable signals such as traffic signals. When fractal properties vary from point to point along the series, it leads to multifractality. In this study, we concentrate not only on the fact that traffic signals have multifractal properties, but also that such properties depend on the time scale in which the multifractality is computed. Via the multiscale multifractal analysis (MMA), traffic signals appear to be far more complex and contain more information which MF-DFA cannot explore by using a fixed time scale. More importantly, we do not have to avoid data sets with crossovers or narrow the investigated time scales, which may lead to biased results. Instead, the Hurst surface provides a spectrum of local scaling exponents at different scale ranges, which helps us to easily position these crossovers. Through comparing Hurst surfaces for signals before and after removing periodical trends, we find periodicities of traffic signals are the main source of the crossovers. Besides, the Hurst surface of the weekday series behaves differently from that of the weekend series. Results also show that multifractality of traffic signals is mainly due to both broad probability density function and correlations. The effects of data loss are also discussed, which suggests that we should carefully handle MMA results when the percentage of data loss is larger than 40$\%$.

We investigate a Kuramoto model incorporated with the first-order and the second-order interaction terms. We show that the model displays the coexistence of multiattractors and different attractors may be characterized by the phase distributions of oscillators. By investigating the transition diagrams in both forward continuation and backward continuation, we find that the synchronous state with unimodal phase distribution is the most stable one while the state in cluster synchrony with evenly distributed bimodal phase distribution is the least stable one. We also present the phase diagram of the model in the parameter space.

Refluxing of fast electrons generated by high-intensity, short-pulse lasers was investigated by measuring electron-induced $K$α x rays from a buried tracer layer. Using planar foils of Au/Cu/CH, the 150-J, 0.7-ps TITAN short-pulse laser was focused on the gold foil to generate fast electrons and the 3-ns, 300-J long pulse beam irradiated on the CH side to create expanding plasma as a conducting medium. By delaying the short-pulse beam timing from the long pulse laser irradiation, the plasma size was varied to change electron refluxing in the target rear. The total yields and two-dimensional images of 8.05-keV Cu-$K$α x ray were recorded with an x-ray spectrometer and two monochromatic crystal imagers. The measurements show that the integrated yields decrease by a factor of 10 from refluxing to the nonrefluxing limit. Similar radial profiles of the $K$α images in the rear were observed at all delays. Hybrid-particle-in-cell simulations using plasma profiles calculated by a radiation-hydrodynamic code HYDRA agree well with the measured $K$α yields. The simulations suggest that conducting plasma with the size of ∼300 μm in the laser direction and ∼600 μm in the lateral direction at the density of 2 × 10${}^{20}$ 1/cm${}^3$ is sufficiently large to prevent electrons from refluxing in the target. The parameters found in this study can be useful in designing experiments utilizing a $K$α x-ray source in refluxing regime or a tracer layer in nonrefluxing regime.

We consider the asymmetric simple exclusion process (TASEP) on an open network consisting of three consecutively coupled macroscopic chain segments with a shortcut between the tail of the first segment and the head of the third one. The model was introduced by Y.-M. Yuan et al. [J. Phys. A 40, 12351 (2007)] to describe directed motion of molecular motors along twisted filaments. We report here unexpected results which revise the previous findings in the case of maximum current through the network. Our theoretical analysis, based on the effective rates' approximation, shows that the second (shunted) segment can exist in both low- and high-density phases, as well as in the coexistence (shock) phase. Numerical simulations demonstrate that the last option takes place in finite-size networks with head and tail chains of equal length, provided the injection and ejection rates at their external ends are equal and greater than one-half. Then the local density distribution and the nearest-neighbor correlations in the middle chain correspond to a shock phase with completely delocalized domain wall. Upon moving the shortcut to the head or tail of the network, the density profile takes a shape typical of a high- or low-density phase, respectively. Surprisingly, the main quantitative parameters of that shock phase are governed by a positive root of a cubic equation, the coefficients of which linearly depend on the probability of choosing the shortcut. Alternatively, they can be expressed in a universal way through the shortcut current. The unexpected conclusion is that a shortcut in the bulk of a single lane may create traffic jams.

Understanding the physics of gas giants requires knowledge about the behavior of hydrogen at extreme pressures and temperatures. Molecular hydrogen in these planets is supercritical, and has been considered as a physically homogeneous state where no differences can be made between a liquid and a gas and where all properties undergo no marked or distinct changes with pressure and temperature, the picture believed to hold below the dissociation and metallization transition. Here, we show that in Jupiter and Saturn, supercritical molecular hydrogen undergoes a dynamic transition around 10 GPa and 3000 K from the “rigid” liquid state to the “nonrigid” gas-like fluid state at the Frenkel line recently proposed, with the accompanying qualitative changes of all major physical properties. The consequences of this finding are discussed, including a physically justified way to demarcate the interior and the atmosphere in gas giants.

Recent advances in high-resolution measurements means it is now possible to identify and track the local “fabric” or contact topology of individual grains in a deforming sand throughout loading history. These provide compelling impetus to the development of methods for inferring changes in the contact forces and energies at multiple spatiotemporal scales, using information on grain contacts alone. Here we develop a surrogate measure of the fluctuating kinetic energy based on changes in the local contact topology of individual grains. We demonstrate the method for dense granular materials under quasistatic biaxial shear. In these systems, the initially stable and solidlike response eventually gives way to liquidlike behavior and global failure. This crossover in mechanical behavior, akin to a phase transition, is marked by bursts of kinetic energy and frictional dissipation. Mechanisms underlying this release of energy include the buckling of major load-bearing structures known as force chains. These columns of grains represent major repositories for stored strain energy. Stored energy initially accumulates at all of the contacts along the force chain, but is released collectively when the chain overloads and buckles. The exact quantification of the buildup and release of energy in force chains, and the manner in which force chain buckling propagates in the sample (i.e., diffuse and systemwide versus localized into shear bands), requires detailed knowledge of contact forces. To date, however, the forces at grain contacts continue to elude measurement in natural granular materials like sand. Here, using data from computer simulations, we show that a proxy for the fluctuating kinetic energy in dense granular materials can be suitably constructed solely from the evolving properties of the grain's local contact topology. Our approach directly relates the evolution of fabric to energy flux and makes possible research into the propagation of failure from measurements of grain contacts in real granular materials.

A colloid supported against gravitational settling by means of an imposed electric field behaves, on average, as if it is at equilibrium in a confining potential [T. M. Squires, J. Fluid Mech. 443, 403 (2001)]. We show, however, that the effective Langevin equation for the colloid contains a nonequilibrium noise source, proportional to the field, arising from the thermal motion of dissolved ions. The position fluctuations of the colloid show strong, experimentally testable signatures of nonequilibrium behavior, including a highly anisotropic, frequency-dependent “effective temperature” obtained from the fluctuation-dissipation ratio.

Structural investigations of the de Vries smectic-$A$ (Sm$A$) and smectic-$C$ (Sm$C$) phases of four mesogens containing a trisiloxane end segment reveal a linear molecular conformation in the Sm$A$ phase and a bent conformation resembling a hockey stick in the Sm$C$ phase. The siloxane and the hydrocarbon parts of the molecule tilt at different angles relative to the smectic layer normal and are oriented along different directions. For the compounds investigated, the shape of orientational distribution function (ODF) is found to be sugarloaf shaped and not the widely expected volcano like with positive orientational order parameters: ⟨$P_2$⟩ = 0.53–0.78, ⟨$P_4$⟩ = 0.14–0.45, and ⟨$P_6$⟩∼0.10. The increase in the effective molecular length, and consequently in the smectic layer spacing caused by reduced fluctuations and the corresponding narrowing of the ODF, counteracts the effect of molecular tilt and significantly reduces the Sm$C$ layer contraction. Maximum tilt of the hydrocarbon part of the molecule lies between approximately 18° and 25° and between 6° and 12° for the siloxane part. The critical exponent of the tilt order parameter, β∼0.25, is in agreement with tricritical behavior at the Sm$A$–Sm$C$ transition for two compounds and has lower value for first-order transition in the other compounds with finite enthalpy of transition.

Using hydrodynamic simulations, we demonstrate that confined colloidal suspensions can greatly enhance the unfolding of collapsed single polymers in flow. When colloids come in direct contact with the polymers due to the flow, the collapsed chains become flattened or elongated on the surface of the colloids, increasing the probability of forming large chain protrusions that the flow can pull out to unfold the polymers. This phenomenon may be suppressed if the colloid size is commensurate with the confining channels, where the colloids form well-defined banding structures. Here, we analyze the colloid banding structures in detail and their relation to the chain unfolding. We find that for colloid volume fractions up to 30%, the confined colloids form simple cubic ($sc$), hexagonal (hex), or a mixture of $sc$ + hex structures. By directly changing the heights of the confining channels, we show that the collapsed polymers unfold the most in the mixed $sc$ + hex structures. The diffuse (not well-defined) bands in the mixed $sc$ + hex structures provide the highest collision probability for the colloids and the polymers, thus enhancing unfolding the most. Without colloidal suspensions, we show that the confining channels alone do not have an observable effect on the unfolding of collapsed polymers. The well-defined colloid bands also suppress the unfolding of noncollapsed polymers. In fact, the average size for noncollapsed chains is even smaller in the well-defined bands than in a channel without any colloids. The appearance of well-defined bands in this case also indicates that lift forces experienced by the polymers in confinement are negligible compared to those exerted by the colloidal band structures. Our results may be important for understanding the dynamics of mixed colloid polymer solutions.

Fibrillar assemblies by peptides are becoming one of the most promising nanomaterials due to their exceptional properties. The self-assembly of peptides into β sheets is a critical step in the fibrillization pathway. We investigated the length-dependent β-sheet growth mechanisms of polyalanine [poly(A)] peptides consisting of 6 to 24 alanines (A6 to A24) in water and on the hydrophobic surface, respectively, by molecular dynamics simulations. β-sheet growth behavior in water fits negative exponential growth model, showing that β-sheet growth rate decays exponentially with time. Meanwhile, increasing chain length leads to an accelerated decay of the β-sheet growth rate. By contrast, β-sheet growth on the surface from A6 to A18 occurs in two consecutive stages, both of which fit linear growth models. β-sheet growth rate in the first stage increases as chain length is increased, while the intermediate length peptide A12 has the highest β-sheet growth rate in the second stage. β-sheet growth behavior of A24 on the surface still fits negative exponential model. Overall, the hydrophobic surface accelerates β-sheet growth by enhancing local concentration and reducing conformational entropy of poly(A) peptide, and the β-sheet growth of the intermediate length peptide A12 is the fastest on the surface. Our simulation results shed light on understanding the accelerated peptide fibrillization on the hydrophobic surface.

We derive the asymptotes for the ratio of the thermal to viscous boundary layer thicknesses for infinite and infinitesimal Prandtl numbers $\text{Pr}$ as functions of the angle $\beta$ between the large-scale circulation and an isothermal heated or cooled surface for the case of turbulent thermal convection with laminar-like boundary layers. For this purpose, we apply the Falkner-Skan ansatz, which is a generalization of the Prandtl-Blasius one to a nonhorizontal free-stream flow above the viscous boundary layer. Based on our direct numerical simulations (DNS) of turbulent Rayleigh-Bénard convection for $\text{Pr}=0.1$, 1, and 10 and moderate Rayleigh numbers up to ${10}^8$ we evaluate the value of $\beta$ that is found to be around $0.7\pi$ for all investigated cases. Our theoretical predictions for the boundary layer thicknesses for this $\beta$ and the considered $\text{Pr}$ are in good agreement with the DNS results.

A lattice Boltzmann (LB) formulation, which is consistent with the phase-field model for two-phase incompressible fluid, is proposed to model the interface dynamics of droplet impingement. The interparticle force is derived by comparing the macroscopic transport equations recovered from LB equations with the governing equations of the continuous phase-field model. The inconsistency between the existing LB implementations and the phase-field model in calculating the relaxation time at the phase interface is identified and an approximation is proposed to ensure the consistency with the phase-field model. It is also shown that the commonly used equilibrium velocity boundary for the binary fluid LB scheme does not conserve momentum at the wall boundary and a modified scheme is developed to ensure the momentum conservation at the boundary. In addition, a geometric formulation of the wetting boundary condition is proposed to replace the popular surface energy formulation and results show that the geometric approach enforces the prescribed contact angle better than the surface energy formulation in both static and dynamic wetting. The proposed LB formulation is applied to simulating droplet impingement dynamics in three dimensions and results are compared to those obtained with the continuous phase-field model, the LB simulations reported in the literature, and experimental data from the literature. The results show that the proposed LB simulation approach yields not only a significant speed improvement over the phase-field model in simulating droplet impingement dynamics on a submillimeter length scale, but also better accuracy than both the phase-field model and the previously reported LB techniques when compared to experimental data. Upon validation, the proposed LB modeling methodology is applied to the study of multiple-droplet impingement and interactions in three dimensions, which demonstrates its powerful capability of simulating extremely complex interface phenomena.

We consider the antiferromagnetic spin-$1/2$ Ising model on the recursive tetrahedron lattice on which two elementary tetrahedrons are connected at each site. The model represents the simplest approximation of the antiferromagnetic Ising model on the real three-dimensional tetrahedron lattice which takes into account effects of frustration. An exact analytical solution of the model is found and discussed. It is shown that the model exhibits neither the first-order nor the second-order phase transitions. A detailed analysis of the magnetization of the model in the presence of the external magnetic field is performed and the existence of the magnetization plateaus for low temperatures is shown. All possible ground states of the model are found and discussed. The existence of nontrivial singular ground states is proven and exact explicit expressions for them are found.

The temperature dependence of a charge mobility in a model DNA based on a Holstein Hamiltonian is calculated for four types of homogeneous sequences It has turned out that upon rescaling all four types are quite similar. Two types of rescaling, i.e., those for low and intermediate temperatures, are found. The curves obtained are approximated on a logarithmic scale by cubic polynomials. We believe that for model homogeneous biopolymers with parameters close to the designed ones, one can assess the value of the charge mobility without carrying out resource-intensive direct simulation, just by using a suitable approximating function.

Step-meandering instabilities can manifest during step-flow growth on vicinal surfaces [Bales and Zangwill, Phys. Rev. B 41, 5500 (1990); Pierre-Louis, D'Orsogna, and Einstein, Phys. Rev. Lett. 82, 3661 (1999)]. A phase diagram based on the various growth regimes of a vicinal surface allows us to study the impact of nucleation on these meanders and to predict a meandering instability caused by the nucleation and the coalescence of both islands and steps. Using an accelerated kinetic Monte Carlo method, we find that the coalescence of islands with steps produces large protrusions and deep ripples and that the resulting meandering instability is reinforced by the growth of the islands at almost the same positions from one monolayer to the other. A coarsening phenomenon occurs for the instability wavelength until mounds appear, favored by a large Ehrlich-Schwoebel barrier. Such a meandering instability could be exploited for periodic self-assembly.

We study the mutual percolation of a system composed of two interdependent random regular networks. We introduce a notion of distance to explore the effects of the proximity of interdependent nodes on the cascade of failures after an initial attack. We find a nontrivial relation between the nature of the transition through which the networks disintegrate and the parameters of the system, which are the degree of the nodes and the maximum distance between interdependent nodes. We explain this relation by solving the problem analytically for the relevant set of cases. In the process, we solve a variant of Rényi's parking problem on treelike graphs.

Most algorithms to detect communities in networks typically work without any information on the cluster structure to be found, as one has no a priori knowledge of it, in general. Not surprisingly, knowing some features of the unknown partition could help its identification, yielding an improvement of the performance of the method. Here we show that, if the number of clusters was known beforehand, standard methods, like modularity optimization, would considerably gain in accuracy, mitigating the severe resolution bias that undermines the reliability of the results of the original unconstrained version. The number of clusters can be inferred from the spectra of the recently introduced nonbacktracking and flow matrices, even in benchmark graphs with realistic community structure. The limit of such a two-step procedure is the overhead of the computation of the spectra.

Networks often possess mesoscale structures, and studying them can yield insights into both structure and function. It is most common to study community structure, but numerous other types of mesoscale structures also exist. In this paper, we examine core-periphery structures based on both density and transport. In such structures, core network components are well-connected both among themselves and to peripheral components, which are not well-connected to anything. We examine core-periphery structures in a wide range of examples of transportation, social, and financial networks—including road networks in large urban areas, a rabbit warren, a dolphin social network, a European interbank network, and a migration network between counties in the United States. We illustrate that a recently developed transport-based notion of node coreness is very useful for characterizing transportation networks. We also generalize this notion to examine core versus peripheral edges, and we show that the resulting diagnostic is also useful for transportation networks. To examine the properties of transportation networks further, we develop a family of generative models of roadlike networks. We illustrate the effect of the dimensionality of the embedding space on transportation networks, and we demonstrate that the correlations between different measures of coreness can be very different for different types of networks.

We investigate the effect of an external magnetic field on the velocity autocorrelation function and the “caging” of the particles in a two-dimensional strongly coupled Yukawa liquid, via numerical simulations. The influence of the coupling strength on the position of the dominant peak in the frequency spectrum of the velocity autocorrelation function confirms the onset of a joint effect of the magnetic field and strong correlations at high coupling. Our molecular dynamics simulations quantify the decorrelation of the particles' surroundings: the magnetic field is found to increase significantly the caging time, which reaches values well beyond the time scale of plasma oscillations. The observation of the increased caging time is in accordance with findings that the magnetic field decreases diffusion in similar systems.