We consider the single-file motion of colloidal particles interacting via short-range repulsion and placed in a traveling wave potential that varies periodically in time and space. Under suitable driving conditions, a directed time-averaged flow of colloids is generated. We obtain analytic results for the model using a perturbative approach to solve the Fokker-Planck equations. The predictions show good agreement with numerical simulations. We find peaks in the time-averaged directed current as a function of driving frequency, wavelength, and particle density and discuss possible experimental realizations. Surprisingly, unlike a closely related exclusion dynamics on a lattice, the directed current in the present model does not show current reversal with density. A linear response formula relating current response to equilibrium correlations is also proposed.

Thermal transport in liquid $n$-alkanes in the vicinity of α-quartz substrates and thermal boundary resistance between the liquid $n$-alkanes and the α-quartz substrates have been investigated using nonequilibrium molecular dynamics simulations. The study considers two liquid alkanes, methane and decane, and three crystal orientations of α-quartz substrate terminated with -H or -OH groups. The local thermal conductivity (LTC), defined in the same manner as with macroscopic thermal conductivity, is used to measure the efficiency of thermal energy transport of the liquids in the vicinity of the solid surface. The variations in the LTC of the liquid alkanes in the layered region next to the surface of the substrate were examined. The modeled LTC values of the alkanes were found to oscillate in the solid-liquid interface region. These fluctuations were typically proportional to the oscillations in the local density profile. The correlation between the thermal conductivity and density was linear in the bulk liquid region. The correlation between LTC and local density in the first adsorption layer is not a straightforward extension of that of the bulk liquid, which is mostly due to the specific molecular-scale ordering structure that occurs in the liquids formed by the proximity of the solid substrate. Thermal boundary resistance between the liquid alkanes and the quartz substrate was also evaluated. It was observed that thermal boundary resistance is relatively large when the in-plane molecular-scale structure in the first adsorption layer is sparse, and is lower when the liquid structure is dense in the adsorption layer.

Natural languages are full of rules and exceptions. One of the most famous quantitative rules is Zipf's law, which states that the frequency of occurrence of a word is approximately inversely proportional to its rank. Though this “law” of ranks has been found to hold across disparate texts and forms of data, analyses of increasingly large corpora since the late 1990s have revealed the existence of two scaling regimes. These regimes have thus far been explained by a hypothesis suggesting a separability of languages into core and noncore lexica. Here we present and defend an alternative hypothesis that the two scaling regimes result from the act of aggregating texts. We observe that text mixing leads to an effective decay of word introduction, which we show provides accurate predictions of the location and severity of breaks in scaling. Upon examining large corpora from 10 languages in the Project Gutenberg eBooks collection, we find emphatic empirical support for the universality of our claim.

The Ising model in clustered scale-free networks has been studied by Monte Carlo simulations. These networks are characterized by a degree distribution of the form $P\left(k\right)\sim k^{-\gamma }$ for large $k$. Clustering is introduced in the networks by inserting triangles, i.e., triads of connected nodes. The transition from a ferromagnetic (FM) to a paramagnetic (PM) phase has been studied as a function of the exponent $\gamma$ and the triangle density. For $\gamma >3$ our results are in line with earlier simulations, and a phase transition appears at a temperature $T_c\left(\gamma \right)$ in the thermodynamic limit (system size $N\to \infty$). For $\gamma \le 3$, a FM-PM crossover appears at a size-dependent temperature $T_{\mathrm{co}}$, so the system remains in a FM state at any finite temperature in the limit $N\to \infty$. Thus, for $\gamma =3, T_{\mathrm{co}}$ scales as $lnN$, whereas for $\gamma <3$, we find $T_{\mathrm{co}}\sim J{N}^z$, where the exponent $z$ decreases for increasing $\gamma$. Adding motifs (triangles in our case) to the networks causes an increase in the transition (or crossover) temperature for exponent $\gamma >3$ (or $\le 3$). For $\gamma >3$, this increase is due to changes in the mean values $\langle k\rangle$ and $\langle k^2\rangle$, i.e., the transition is controlled by the degree distribution (nearest-neighbor connectivities). For $\gamma \le 3$, however, we find that clustered and unclustered networks with the same size and distribution $P\left(k\right)$ have different crossover temperature, i.e., clustering favors FM correlations, thus increasing the temperature $T_{\mathrm{co}}$. The effect of a degree cutoff $k_{\mathrm{cut}}$ on the asymptotic behavior of $T_{\mathrm{co}}$ is discussed.

A modified Carlson-Langer model for earthquakes is proposed, which includes nonlinear viscoelasticity. Several aftershocks are generated after the main shock owing to the damping of the additional viscoelastic force. Both the Gutenberg-Richter law and Omori's law are reproduced in a numerical simulation of the modified Carlson-Langer model on a critical percolation cluster of a square lattice.

We analyze the consequences of symmetry breaking in the coupling in a network of globally coupled identical Stuart-Landau oscillators. We observe that symmetry breaking leads to increased disorderliness in the dynamical behavior of oscillatory states and consequently results in a rich variety of dynamical states. Depending on the strength of the nonisochronicity parameter, we find various dynamical states such as amplitude chimera, amplitude cluster, frequency chimera, and frequency cluster states. In addition we also find disparate transition routes to recently observed chimera death states in the presence of symmetry breaking even with global coupling. We also analytically verify the chimera death region, which corroborates the numerical results. These results are compared with that of the symmetry-preserving case as well.

The dynamics of random weakly nonlinear waves is studied in the framework of vibrating thin elastic plates. Although it has been previously predicted that no stationary inverse cascade of constant wave action flux could exist in the framework of wave turbulence for elastic plates, we present substantial evidence of the existence of a time-dependent inverse cascade, opening up the possibility of self-organization for a larger class of systems. This inverse cascade transports the spectral density of the amplitude of the waves from short up to large scales, increasing the distribution of long waves despite the short-wave fluctuations. This dynamics appears to be self-similar and possesses a power-law behavior in the short-wavelength limit which significantly differs from the exponent obtained via a Kolmogorov dimensional analysis argument. Finally, we show explicitly a tendency to build a long-wave coherent structure in finite time.

Reduced models for the (defocusing) nonlinear Schrödinger equation are developed. In particular, we develop reduced models that only involve the low-frequency modes given noisy observations of these modes. The ansatz of the reduced parametric models are obtained by employing a rational approximation and a colored-noise approximation, respectively, on the memory terms and the random noise of a generalized Langevin equation that is derived from the standard Mori-Zwanzig formalism. The parameters in the resulting reduced models are inferred from noisy observations with a recently developed ensemble Kalman filter-based parametrization method. The forecasting skill across different temperature regimes are verified by comparing the moments up to order four, a two-time correlation function statistics, and marginal densities of the coarse-grained variables.

We give a simple and intuitive proof that the only states which are completely passive, i.e., those states from which work cannot be extracted even with infinitely many copies, are Gibbs states at positive temperatures. The proof makes use of the idea of virtual temperatures, i.e., the association of temperatures to pairs of energy levels (transitions). We show that (1) passive states are those where every transition is at a positive temperature and (2) completely passive states are those where every transition is at the same positive temperature.

We develop a novel model of drainage of microscale thin aqueous film separating a gas bubble and a solid wall. In contrast to previous studies, the electrostatic effects are accounted for not only in the normal but also in the shear stress balance at the liquid-gas interface. We show that the action of the tangential component of the electric field leads to potentially strong spatially variable shear stress at the deforming charged interface. This previously overlooked effect turns out to be essential for correctly estimating the long-time drainage rates. Comparison of time-dependent fluid interface shapes predicted by our model with the experimental data is discussed.

The effects of surface interactions on the ordering dynamics of self-assembled monolayers (SAM) of chain molecules were studied using molecular dynamics simulations. When the strength of surface–chain interactions was equal to or less than that of chain–chain interactions, domains of chain molecules adsorbed perpendicular to the surface (“upright” chains) formed on the surface. Although chain molecules adsorbed parallel to the surface (“lying” chains) were initially observed on the surface, they did not develop into two-dimensionally aligned structures. In contrast, when the strength of surface–chain interactions was at least twice that of chain–chain interactions, the proportion of upright chain molecules was initially small, and the reorientation of lying chains was observed shortly afterwards. In this case, the reorientation from lying to upright configuration developed slowly from the domain boundaries of two-dimensionally aligned structures late in the calculation period. Although the orientation processes of chain molecules on surfaces were strongly influenced by the strength of surface–chain interactions, the total adsorption rate on the surface was not. We also analyzed the maximum area of domains formed by lying chains. The development of two-dimensionally aligned domains required strong surface–chain interactions to prevent the spontaneous formation of nuclei of upright domains.

We investigate the relaxation behavior of thin films of a polyamide random copolymer, PA66/6I, with various film thicknesses using dielectric relaxation spectroscopy. Two dielectric signals are observed at high temperatures, the $\alpha$ process and the relaxation process due to electrode polarization (the EP process). The relaxation time of the EP process has a Vogel-Fulcher-Tammann type of temperature dependence, and the glass transition temperature, $T_{\mathrm{g}}$, evaluated from the EP process agrees very well with the $T_{\mathrm{g}}$ determined from the thermal measurements. The fragility index derived from the EP process increases with decreasing film thickness. The relaxation time and the dielectric relaxation strength of the EP process are described by a linear function of the film thickness $d$ for large values of $d$, which can be regarded as experimental evidence for the validity of attributing the observed signal to the EP process. Furthermore, there is distinct deviation from this linear law for thicknesses smaller than a critical value. This deviation observed in thinner films is associated with an increase in the mobility and/or diffusion constant of the charge carriers responsible for the EP process. The $\alpha$ process is located in a higher-frequency region than the EP process at high temperatures but merges with the EP process at lower temperatures near the glass transition region. The thickness dependence of the relaxation time of the $\alpha$ process is different from that of the EP process. This suggests that there is decoupling between the segmental motion of the polymers and the translational motion of the charge carriers in confinement.

Periodical patterns of vegetation in an arid or semiarid ecosystem are described using statistical mechanics and Monte Carlo numerical simulation technique. Plants are characterized by the area that each individual occupies and a facilitation-competition pairwise interaction. Assuming that external resources (precipitation, solar radiation, nutrients, etc.) are available to the ecosystem, it is possible to obtain the persistent configurations of plants compatible with an equitable distribution of resources maximizing the Shannon entropy. Variation of vegetation patterns with density, critical cluster size, and facilitation distance are predicted. Morphological changes of clusters are shown to be a function of the external resources. As a final remark, it is proposed that an early warning of desertification could be detected from the coefficient of variation of the mean cluster size together with the distribution of cluster sizes.

We derive a generalized equation that governs the spreading of liquid films under high-frequency (MHz-order) substrate vibration in the form of propagating surface waves and show that this single relationship is universally sufficient to collectively describe the rich and diverse dynamic phenomena recently observed for the transport of oil films under such substrate excitation, in particular, Rayleigh surface acoustic waves. In contrast to low-frequency (Hz- to kHz-order) vibration-induced wetting phenomena, film spreading at such high frequencies arises from convective drift generated by the viscous periodic flow localized in a region characterized by the viscous penetration depth ${\beta }^{-1}\equiv {(2\mu /\rho \omega )}^{1/2}$ adjacent to the substrate that is invoked directly by its vibration; $\mu$ and $\rho$ are the viscosity and the density of the liquid, respectively, and $\omega$ is the excitation frequency. This convective drift is responsible for driving the spreading of thin films of thickness $h\ll k_l^{-1}$, which spread self-similarly as $t^{1/4}$ along the direction of the drift corresponding to the propagation direction of the surface wave, $k_l$ being the wave number of the compressional acoustic wave that forms in the liquid due to leakage of the surface wave energy from the substrate into the liquid and $t$ the time. Films of greater thicknesses $h\sim k_l^{-1}\gg {\beta }^{-1}$, in contrast, are observed to spread with constant velocity but in a direction that opposes the drift and surface wave propagation due to the attenuation of the acoustic wave in the liquid. The universal equation derived allows for the collective prediction of the spreading of these thin and thick films in opposing directions.

The role of the radiation reaction force in ultraintense laser-driven ion acceleration is investigated. For laser intensities $\sim {10}^{23}{\mathrm{W}/\mathrm{cm}}^2$, the action of this force on electrons is demonstrated in relativistic particle-in-cell simulations to significantly enhance the energy transfer to ions in relativistically transparent targets, but strongly reduce the ion energy in dense plasma targets. An expression is derived for the revised piston velocity, and hence ion energy, taking account of energy loses to synchrotron radiation generated by electrons accelerated in the laser field. Ion mass is demonstrated to be important by comparing results obtained with proton and deuteron plasma. The results can be verified in experiments with cryogenic hydrogen and deuterium targets.

The paper states that magnetic balls preferably assemble in a tube geometry if the number of particles exceeds $N\ge 14$. We find that for substantially higher particle counts, such as $N>1300$, a round cluster of densely packed magnetic balls with an fcc lattice can outmatch the described tube structure.

The authors of the Comment [Phys. Rev. E 91, 057201 (2015)] propose compact round clusters as, energetically, better candidates than stacked rings found in Messina et al. [Phys. Rev. E 89, 011202 (2014)] (forming open tubes) at a pretty large number of constitutive magnets, typically for $N\gtrsim 1300$. Our new findings show that elongated rodlike structures can even outmatch the reported structures in Friedrich et al. [Phys. Rev. E 91, 057201 (2015)] and in Messina et al. [Phys. Rev. E 89, 011202 (2014)] from typically $N\gtrsim 460$.

Learning in restricted Boltzmann machine is typically hard due to the computation of gradients of log-likelihood function. To describe the network state statistics of the restricted Boltzmann machine, we develop an advanced mean-field theory based on the Bethe approximation. Our theory provides an efficient message-passing-based method that evaluates not only the partition function (free energy) but also its gradients without requiring statistical sampling. The results are compared with those obtained by the computationally expensive sampling-based method.

We propose a quantum absorption refrigerator driven by photons. The model uses a four-level system as its working substance and couples simultaneously to hot, cold, and solar heat reservoirs. Explicit expressions for the cooling power ${\dot{Q}}_c$ and coefficient of performance (COP) ${\eta }_{\text{COP}}$ are derived, with the purpose of revealing and optimizing the performance of the device. Our model runs most efficiently under the tight coupling condition, and it is consistent with the third law of thermodynamics in the limit $T\to 0$.

We present results of molecular dynamics simulations for two-dimensional repulsively interacting colloids driven by a one-dimensional asymmetric and commensurate ratchet potential, switching on and off stochastically. This drives a time-averaged directed current of colloids, exhibiting resonance with change in ratcheting frequency, where the resonance frequency itself depends nonmonotonically on density. Using scaling arguments, we obtain analytic results that show good agreement with numerical simulations. With increasing ratcheting frequency, we find nonequilibrium reentrant transitions between solid and modulated liquid phases.