We discuss the behavior of the largest Lyapunov exponent $\lambda$ in the incoherent phase of large ensembles of heterogeneous, globally coupled, phase oscillators. We show that the scaling with the system size $N$ depends on the details of the spacing distribution of the oscillator frequencies. For sufficiently regular distributions $\lambda \sim 1/N$, while for strong fluctuations of the frequency spacing $\lambda \sim lnN/N$ (the standard setup of independent identically distributed variables belongs to the latter class). In spite of the coupling being small for large $N$, the development of a rigorous perturbative theory is not obvious. In fact, our analysis relies on a combination of various types of numerical simulations together with approximate analytical arguments, based on a suitable stochastic approximation for the tangent space evolution. In fact, the very reason for $\lambda$ being strictly larger than zero is the presence of finite-size fluctuations. We trace back the origin of the logarithmic correction to a weak synchronization between tangent and phase-space dynamics.

In this study, we investigate the α process of a polystyrene thin film using inelastic neutron scattering (INS), dielectric relaxation spectroscopy (DRS), and thermal expansion spectroscopy (TES). The DRS and TES measurements exhibited a decrease in glass transition temperature ($T_{\mathrm{g}}$) with film thickness. On the other hand, an increase in $T_{\mathrm{g}}$ was observed in INS studies. In order to interpret this contradiction, we investigated the temperature dependence of the peak frequency ($f_{\mathrm{m}}$) of the α process probed by DRS and TES. The experiments revealed an increase in the peak frequency ($f_{\mathrm{m}}$) with decreasing film thickness in the frequency region. This observation is consistent with the observed decrease in $T_{\mathrm{g}}$ with thickness. Interestingly, the increase in $T_{\mathrm{g}}$ with film thickness was confirmed by fitting the temperature dependence measurements of the peak frequency with the Vogel-Fulcher-Tammann equation, within the frequency region probed by INS. The discrepancy between INS and DRS or TES descriptions of the α process is likely to be attributed to a decrease in the apparent activation energy with film thickness and reduced mobility, due to the impenetrable wall effect.

Electron attenuation due to inelastic and elastic scattering in condensed media can often be described in terms of the effective attenuation length (EAL) of the electron. The EAL is thus an important parameter for describing electron transport processes as exemplified by dissipation of energy following radiolysis. Focusing on electrons at low electron kinetic energies (10–40 eV) in condensed argon, we determine EAL from x-ray photoelectron spectra of argon nanoparticles and compare to values obtained from valence ionization in thin argon films as well as from gas-phase electron-scattering data. EAL determined from argon clusters shows variation with cluster size. Moreover, the values are significantly lower than those obtained in valence-ionization studies and from scattering data. Our results corroborate recent x-ray photoelectron spectroscopy–based determination of EALs of water showing large differences to the EALs determined by other methods in amorphous ice at low kinetic energies of the photoelectron [Y.-I. Suzuki, K. Nishizawa, N. Kurahashi, and T. Suzuki, Phys. Rev. E 90, 010302 (2014)], underlining that care must be taken when using EAL values from other sources for core-level electrons.

The molecular rearrangements of most fluids under flow and deformation do not directly follow the macroscopic strain field. In this work, we describe a phenomenological method for characterizing such nonaffine deformation via the anisotropic pair distribution function (PDF). We demonstrate how the microscopic strain can be calculated in both simple shear and uniaxial extension, by perturbation expansion of anisotropic PDF in terms of real spherical harmonics. Our results, given in the real as well as the reciprocal space, can be applied in spectrum analysis of small-angle scattering experiments and nonequilibrium molecular dynamics simulations of soft matter under flow.

Simulations of a polydispersed two-dimensional silo were performed using molecular dynamics, with different numbers of grains reaching up to 64 000, verifying numerically the model derived by Janssen and also the main assumption that the walls carry part of the weight due to the static friction between grains with themselves and those with the silo's walls. We vary the friction coefficient, the radii dispersity, the silo width, and the size of grains. We find that the Janssen's model becomes less relevant as the the silo width increases since the behavior of the stresses becomes more hydrostatic. Likewise, we get the normal and tangential stress distribution on the walls evidencing the existence of points of maximum stress. We also obtained the stress matrix with which we observe zones of concentration of load, located always at a height around two thirds of the granular columns. Finally, we observe that the size of the grains affects the distribution of stresses, increasing the weight on the bottom and reducing the normal stress on the walls, as the grains are made smaller (for the same total mass of the granulate), giving again a more hydrostatic and therefore less Janssen-type behavior for the weight of the column.

The three-equation $k\text{−}L\text{−}a$ turbulence model [B. Morgan and M. Wickett, Three-equation model for the self-similar growth of Rayleigh-Taylor and Richtmyer-Meshkov instabilities, Phys. Rev. E 91, 043002 (2015)] is extended by the addition of a second length scale equation. It is shown that the separation of turbulence transport and turbulence destruction length scales is necessary for simultaneous prediction of the growth parameter and turbulence intensity of a Kelvin-Helmholtz shear layer when model coefficients are constrained by similarity analysis. Constraints on model coefficients are derived that satisfy an ansatz of self-similarity in the low-Atwood-number limit and allow the determination of model coefficients necessary to recover expected experimental behavior. The model is then applied in one-dimensional simulations of Rayleigh-Taylor, reshocked Richtmyer-Meshkov, Kelvin-Helmholtz, and combined Rayleigh-Taylor–Kelvin-Helmholtz instability mixing layers to demonstrate that the expected growth rates are recovered numerically. Finally, it is shown in the case of combined instability that the model predicts a mixing width that is a linear combination of Rayleigh-Taylor and Kelvin-Helmholtz mixing processes.

An artificial cilium using ac electro-osmosis (ACEO) is attractive because of its large potentiality for innovative microfluidic applications. However, the ACEO cilium has not been probed experimentally and has a shortcoming that the working frequency range is very narrow. Thus, we here propose an ACEO elastic actuator having a skew structure that broadens a working frequency range and experimentally demonstrate that the elastic actuator in water can be driven with a high-speed ($\sim 10$ Hz) and a wide frequency range ($\sim 0.1$ to $\sim 10$ kHz). Moreover, we propose a simple self-consistent model that explains the broadband characteristic due to the skew structure with other characteristics. By comparing the theoretical results with the experimental results, we find that they agree fairly well. We believe that our ACEO elastic actuator will play an important role in microfluidics in the future.

In this paper, a general lattice Boltzmann (LB) model is proposed for the high-order nonlinear partial differential equation with the form ${\partial }_t\varphi +{\sum }_{k=1}^m{\alpha }_k{\partial }_x^k{\mathrm{\Pi }}_k\left(\varphi \right)=0$ ($1\le k\le m\le 6$), ${\alpha }_k$ are constant coefficients, ${\mathrm{\Pi }}_k\left(\varphi \right)$ are some known differential functions of $\varphi$. As some special cases of the high-order nonlinear partial differential equation, the classical (m)KdV equation, KdV-Burgers equation, $\mathrm{K}(n,n)$-Burgers equation, Kuramoto-Sivashinsky equation, and Kawahara equation can be solved by the present LB model. Compared to the available LB models, the most distinct characteristic of the present model is to introduce some suitable auxiliary moments such that the correct moments of equilibrium distribution function can be achieved. In addition, we also conducted a detailed Chapman-Enskog analysis, and found that the high-order nonlinear partial differential equation can be correctly recovered from the proposed LB model. Finally, a large number of simulations are performed, and it is found that the numerical results agree with the analytical solutions, and usually the present model is also more accurate than the existing LB models [H. Lai and C. Ma, Sci. China Ser. G 52, 1053 (2009); H. Lai and C. Ma, Phys. A (Amsterdam) 388, 1405 (2009)] for high-order nonlinear partial differential equations.

Topological phase transitions constitute a new class of quantum critical phenomena. They cannot be described within the usual framework of the Landau theory since, in general, the different phases cannot be distinguished by an order parameter, neither can they be related to different symmetries. In most cases, however, one can identify a diverging length at these topological transitions. This allows us to describe them using a scaling approach and to introduce a set of critical exponents that characterize their universality class. Here we consider some relevant models of quantum topological transitions associated with well-defined critical exponents that are related by a quantum hyperscaling relation. We extend to these models a finite-size scaling approach based on techniques for calculating the Casimir force in electromagnetism. This procedure allows us to obtain universal Casimir amplitudes at their quantum critical points. Our results verify the validity of finite-size scaling in these systems and confirm the values of the critical exponents obtained previously.

The partition function of the symmetric (zero electric field) eight-vertex model on a square lattice can be formulated either in the original “electric” vertex format or in an equivalent “magnetic” Ising-spin format. In this paper, both electric and magnetic versions of the model are studied numerically by using the corner transfer matrix renormalization-group method which provides reliable data. The emphasis is put on the calculation of four specific critical exponents, related by two scaling relations, and of the central charge. The numerical method is first tested in the magnetic format, the obtained dependencies of critical exponents on the model's parameters agree with Baxter's exact solution, and weak universality is confirmed within the accuracy of the method due to the finite size of the system. In particular, the critical exponents $\eta$ and $\delta$ are constant as required by weak universality. On the other hand, in the electric format, analytic formulas based on the scaling relations are derived for the critical exponents ${\eta }_{\mathrm{e}}$ and ${\delta }_{\mathrm{e}}$ which agree with our numerical data. These exponents depend on the model's parameters which is evidence for the full nonuniversality of the symmetric eight-vertex model in the original electric formulation.

How and why stock prices move is a centuries-old question still not answered conclusively. More recently, attention shifted to higher frequencies, where trades are processed piecewise across different time scales. Here we reveal that price impact has a universal nonlinear shape for trades aggregated on any intraday scale. Its shape varies little across instruments, but drastically different master curves are obtained for order-volume and -sign impact. The scaling is largely determined by the relevant Hurst exponents. We further show that extreme order-flow imbalance is not associated with large returns. To the contrary, it is observed when the price is pinned to a particular level. Prices move only when there is sufficient balance in the local order flow. In fact, the probability that a trade changes the midprice falls to zero with increasing (absolute) order-sign bias along an arc-shaped curve for all intraday scales. Our findings challenge the widespread assumption of linear aggregate impact. They imply that market dynamics on all intraday time scales are shaped by correlations and bilateral adaptation in the flows of liquidity provision and taking.

The flow curve of various yield stress materials is singular as the strain rate vanishes and can be characterized by the so-called Herschel-Bulkley exponent $n=1/\beta$. A mean-field approximation due to Hebraud and Lequeux (HL) assumes mechanical noise to be Gaussian and leads to $\beta =2$ in rather good agreement with observations. Here we prove that the improved mean-field model where the mechanical noise has fat tails instead leads to $\beta =1$ with logarithmic correction. This result supports that HL is not a suitable explanation for the value of $\beta$, which is instead significantly affected by finite-dimensional effects. From considerations on elastoplastic models and on the limitation of speed at which avalanches of plasticity can propagate, we argue that $\beta =1+1/(d-d_f)$, where $d_f$ is the fractal dimension of avalanches and $d$ the spatial dimension. Measurements of $d_f$ then supports that $\beta \approx 2.1$ and $\beta \approx 1.7$ in two and three dimensions, respectively. We discuss theoretical arguments leading to approximations of $\beta$ in finite dimensions.

Dense granular flows have been well described by the Bagnold rheology, even when the particles are in the multibody contact regime and the coordination number is greater than 1. This is surprising, because the Bagnold law should be applicable only in the instantaneous collision regime, where the time between collisions is much larger than the period of a collision. Here, the effect of particle stiffness on rheology is examined. It is found that there is a rheological threshold between a particle stiffness of ${10}^4\text{–}{10}^5$ for the linear contact model and ${10}^5\text{–}{10}^6$ for the Hertzian contact model above which Bagnold rheology (stress proportional to square of the strain rate) is valid and below which there is a power-law rheology, where all components of the stress and the granular temperature are proportional to a power of the strain rate that is less then 2. The system is in the multibody contact regime at the rheological threshold. However, the contact energy per particle is less than the kinetic energy per particle above the rheological threshold, and it becomes larger than the kinetic energy per particle below the rheological threshold. The distribution functions for the interparticle forces and contact energies are also analyzed. The distribution functions are invariant with height, but they do depend on the contact model. The contact energy distribution functions are well fitted by Gamma distributions. There is a transition in the shape of the distribution function as the particle stiffness is decreased from ${10}^7$ to ${10}^6$ for the linear model and ${10}^8$ to ${10}^7$ for the Hertzian model, when the contact number exceeds 1. Thus, the transition in the distribution function correlates to the contact regime threshold from the binary to multibody contact regime, and is clearly different from the rheological threshold. An order-disorder transition has recently been reported in dense granular flows. The Bagnold rheology applies for both the ordered and disordered states, even though the rheological constants differ by orders of magnitude. The effect of particle stiffness on the order-disorder transition is examined here. It is found that when the particle stiffness is above the rheological threshold, there is an order-disorder transition as the base roughness is increased. The order-disorder transition disappears after the crossover to the soft-particle regime when the particle stiffness is decreased below the rheological threshold, indicating that the transition is a hard-particle phenomenon.

The entropic lattice Boltzmann algorithm of Karlin et al. [Phys. Rev. E 90, 031302 (2014)] is partially extended to magnetohydrodynamics, based on the Dellar model of introducing a vector distribution for the magnetic field. This entropic ansatz is now applied only to the scalar particle distribution function so as to permit the many problems entailing magnetic field reversal. A 9-bit lattice is employed for both particle and magnetic distributions for our two-dimensional simulations. The entropic ansatz is benchmarked against our earlier multiple relaxation lattice-Boltzmann model for the Kelvin-Helmholtz instability in a magnetized jet. Other two-dimensional simulations are performed and compared to results determined by more standard direct algorithms: in particular the switch over between the Kelvin-Helmholtz or tearing mode instability of Chen et al. [J. Geophys. Res.: Space Phys. 102, 151 (1997)], and the generalized Orszag-Tang vortex model of Biskamp-Welter [Phys. Fluids B 1, 1964 (1989)]. Very good results are achieved.

The dynamics of coherent nonlinear wave groups is shown to be drastically different from the classical scenario of weakly nonlinear wave interactions. The coherent groups generate nonresonant (bound) waves which can be synchronized with other linear waves. By virtue of the revealed mechanism, the groups may emit waves with similar or different lengths, which propagate in the same or opposite direction.

The theory of magnetic flux conservation is developed for a subsonic plasma implosion and used to describe the magnetic flux degradation in the MagLIF concept [S. A. Slutz et al., Phys. Plasmas 17, 056303 (2010)]. Depending on the initial magnetic Lewis and Péclet numbers and the electron Hall parameter, the implosion falls into either a superdiffusive regime in which the magnetization decreases or a magnetized regime in which the magnetization increases. Scaling laws for magnetic field, temperature, and magnetic flux losses in the hot spot of radius $R$ are obtained for both regimes. The Nernst velocity convects the magnetic field outwards, pushing it against the liner and enhancing the magnetic field diffusion, thereby reducing the magnetic field compression and degrading the implosion performance. However, in the magnetized regime, the core of the hot spot becomes magnetically insulated and undergoes an ideal adiabatic compression ($T\sim R^{-4/3}$ compared to $T\sim R^{-2/3}$ without magnetic field), while the detrimental Nernst term is confined to the outer part of the hot spot. Its effect is drastically reduced, improving the magnetic flux conservation.

The Ornstein-Uhlenbeck particle (OUP) model imagines a microscopic swimmer propelled by an active force which is correlated with itself on a finite time scale. Here we investigate the influence of external potentials on an ideal suspension of OUPs, in both one and two spatial dimensions, with particular attention paid to the pressure exerted on “confining walls.” We employ a mathematical connection between the local density of OUPs and the statistics of their propulsion force to demonstrate the existence of an equation of state in one dimension. In higher dimensions we show that active particles generate a nonconservative force field in the surrounding medium. A simplified far-from-equilibrium model is proposed to account for OUP behavior in the vicinity of potentials. Building on this, we interpret simulations of OUPs in more complicated situations involving asymmetrical and spatially curved potentials, and characterize the resulting inhomogeneous stresses in terms of competing active length scales.