Granular mixtures may segregate because of external driving forces, which play an important role in industry and geophysics. We investigate experimentally the mechanism of density-driven spontaneous streak segregation patterns in a thin rotating drum. We find that a spontaneous streak segregation pattern can occur in such a system, which we call a $D$-system. A phase diagram identifies three segregation pattern regimes in this study: the mixing regime, the core segregation regime, and the streak segregation regime.

We present here the measurement of the diffusivity of spherical particles closely confined by narrow microchannels. Our experiments yield a two-dimensional map of the position-dependent diffusion coefficients parallel and perpendicular to the channel axis with a resolution down to 129 nm. The diffusivity was measured simultaneously in the channel interior, the bulk reservoirs, as well as the channel entrance region. In the channel interior we found strongly anisotropic diffusion. While the perpendicular diffusion coefficient close to the confining walls decreased down to approximately $25\%$ of the value on the channel axis, the parallel diffusion coefficient remained constant throughout the entire channel width. In addition to the experiment, we performed finite element simulations for the diffusivity in the channel interior and found good agreement with the measurements. Our results reveal the distinctive influence of strong confinement on Brownian motion, which is of significance to microfluidics as well as quantitative models of facilitated membrane transport.

The reliable persistence of an adhered monolayer film on a substrate is critical for film function. The process by which monolayers degrade or disperse remains unclear. Our study investigates the properties and dynamics of a solute of dipolar molecules initially adhered as a monolayer on a substrate in a water-like Stockmayer solvent. We find that for a rigid solute, both the solute and solvent show qualitatively different dynamics than for a flexible solute and its solvent. For the rigid solute, spreading is hindered and solvent orientation is more pronounced. We formulate a simple kinetic model that shows qualitatively similar results to the molecular dynamics simulations of the time evolution of the monolayer. Simple kinetics of molecules on substrates is a starting point for understanding important industrial monolayer applications and complex interactions on membranes.

The global effects of sudden changes in the interface growth dynamics are studied using models of the Edwards-Wilkinson (EW) and Kardar-Parisi-Zhang (KPZ) classes during their growth regimes in dimensions $d=1$ and $d=2$. Scaling arguments and simulation results are combined to predict the relaxation of the difference in the roughness of the perturbed and the unperturbed interfaces, $\Delta W^2\sim s^c{t}^{-\gamma }$, where $s$ is the time of the change and $t>s$ is the observation time after that event. The previous analytical solution for the EW-EW changes is reviewed and numerically discussed in the context of lattice models, with possible decays with $\gamma =3/2$ and $\gamma =1/2$. Assuming the dominant contribution to $\Delta W^2$ to be predicted from a time shift in the final growth dynamics, the scaling of KPZ-KPZ changes with $\gamma =1-2\beta$ and $c=2\beta$ is predicted, where $\beta$ is the growth exponent. Good agreement with simulation results in $d=1$ and $d=2$ is observed. A relation with the relaxation of a local autoresponse function in $d=1$ cannot be discarded, but very different exponents are shown in $d=2$. We also consider changes between different dynamics, with the KPZ-EW as a special case in which a faster growth, with dynamical exponent $z_i$, changes to a slower one, with exponent $z$. A scaling approach predicts a crossover time $t_c\sim s^{z/z_i}\gg s$ and $\Delta W^2\sim s^{c}F(t/t_c)$, with the decay exponent $\gamma =1/2$ of the EW class. This rules out the simplified time shift hypothesis in $d=2$ dimensions. These results help to understand the remarkable differences in EW smoothing of correlated and uncorrelated surfaces, and the approach may be extended to sudden changes between other growth dynamics.

The formation kinetics of open half-monolayer films on solid substrates is studied by the deposition of particles from a gaseous (vapor) phase to a cold substrate (room temperature) provided the lateral interaction between the particles of adsorbed layer (adlayer) is attractive. A detailed analysis of two limiting cases is presented: when the half-monolayer film formation rate is limited by the adsorption of particles from the gas phase and when the formation of the half-monolayer film surface is determined by the rate of surface diffusion of the adsorbed particles. The asymptotic analysis of the coverage dispersion evolution and the characteristic spatial scale of coverage inhomogeneities at the early and late stages of relaxation of a submonolayer film after quenching under the spinodal is carried out. It is found that separation of the adlayer occurs, so inhomogeneities of submonolayer films at the later stages of the process tend to equilibrium values of coverage in any case. However, asymptotic and numerical analysis shows that in the second case for some relationship between the kinetic and thermodynamic parameters of the adlayer an intermediate asymptotic relaxation process can be observed. It testifies to a kinetic slowdown of the separation process at the spinodal values of coverages. This fact manifests as the appearance of the intermediate plateau in the evolution curves for the coverage dispersion and nonmonotonic change of the characteristic spatial scale of coverage inhomogeneities. Moreover, at the early stages of the coverage evolution, the incubation period is revealed in the development of its inhomogeneities. It is shown that at the later stages of the separation of the half-monolayer film, the characteristic spatial scale of coverage inhomogeneities increases with time according to the law ${\tau }^{1/2}$ and the width of the transition region between enriched and depleted regions of adlayer decreases as $1/{\tau }^{1/2}$.

We introduce a short correlation length for torque in twisting-stiff biomolecules, which is necessary for the physical property that torque fluctuations be finite in amplitude. We develop a nonequilibrium theory of dynamics of DNA twisting which predicts two crossover time scales for temporal torque correlations in single-molecule experiments. Bending fluctuations can be included, and at linear order we find that they do not affect the twist dynamics. However, twist fluctuations affect bending, and we predict the spatial inhomogeneity of twist, torque, and buckling arising in nonequilibrium “rotor-bead” experiments.

Although Gibrat's law and its generalized versions have been widely used, the organizing principle behind its phenomenological theory has been poorly studied for network-structured systems. More important, its fluctuation behavior, which contradicts the prediction of the preferential attachment (PA), indicates a nontrivial mechanism that goes beyond our present knowledge based on the traditional mean-field approach. Here, we take advantage of the rich data of the Internet and aim to identify the origin of Gibrat's law by studying the empirical fluctuation behavior. We show how the correlation between the fluctuations of the node degree increment affects the dynamics of the network. Specifically, if the distribution of the correlation is symmetric, the network evolves as the classical PA, while if such symmetry breaks, the fluctuation becomes macroscopically positively correlated and contributes to the emergence of Gibrat's law. These results indicate a local collective increase in the actual network evolution, which provides a new paradigm and understanding of the related microcosmic dynamics.

To investigate nonautonomous matter waves with time-dependent modulation in a one-dimensional trapped spin-1 Bose-Einstein condensate, we hereby work on the generalized three-coupled Gross-Pitaevskii equations by means of the Hirota bilinear method. By modulating the external trap potential, atom gain or loss, and coupling coefficients, we can obtain several nonautonomous matter-wave solitons and rogue waves including “bright” and “dark” shapes and arrive at the following conclusions: (i) the external trap potential and atom gain or loss can influence the propagation of matter-wave solitons and the duration and frequency of bound solitonic interaction, but they have little effect on the head-on solitonic interaction; (ii) through numerical simulation, stable evolution of the matter-wave solitons is realized with a perturbation of $5\%$ initial random noise, and the spin-exchange interaction of atoms can be affected by the time-dependent modulation; (iii) under the influence of a periodically modulated trap potential and periodic atom gain or loss, rogue waves can emerge in the superposition of localized character and periodic oscillating properties.

Multiscale methods built purely on the kinetic theory of gases provide information about the molecular velocity distribution function. It is therefore both important and feasible to establish new breakdown parameters for assessing the appropriateness of a fluid description at the continuum level by utilizing kinetic information rather than macroscopic flow quantities alone. We propose a new kinetic criterion to indirectly assess the errors introduced by a continuum-level description of the gas flow. The analysis, which includes numerical demonstrations, focuses on the validity of the Navier-Stokes-Fourier equations and corresponding kinetic models and reveals that the new criterion can consistently indicate the validity of continuum-level modeling in both low-speed and high-speed flows at different Knudsen numbers.

A performance optimization for minimally nonlinear heat engines and refrigerators is conducted under an optimization criterion of $\Omega$. The results show that under tight-coupling conditions, the efficiency and coefficient of performance (COP) bounds in asymmetric dissipation limits are the same as those obtained by de Tomas et al. [Phys. Rev. E 87, 012105 (2013)] for low dissipation heat devices. The efficiency bounds for heat engines under nontight-coupling conditions are also analyzed and the experimental results lie between theoretical results obtained under different coupling strengths. For refrigerators, the theoretical results are also in good agreement with some observed results. The efficiency and COP bounds under the $\Omega$ criterion are refined, which are closer to real heat engines and refrigerators.

We perform a numerical study of the long-range (LR) ferromagnetic Ising model with power law decaying interactions ($J\propto r^{-d-\sigma }$) on both a one-dimensional chain ($d=1$) and a square lattice ($d=2$). We use advanced cluster algorithms to avoid the critical slowing down. We first check the validity of the relation connecting the critical behavior of the LR model with parameters $(d,\sigma )$ to that of a short-range (SR) model in an equivalent dimension $D$. We then study the critical behavior of the $d=2$ LR model close to the lower critical $\sigma$, uncovering that the spatial correlation function decays with two different power laws: The effect of the subdominant power law is much stronger than finite-size effects and actually makes the estimate of critical exponents very subtle. By including this subdominant power law, the numerical data are consistent with the standard renormalization group (RG) prediction by Sak [Phys. Rev. B 8, 281 (1973)], thus making not necessary (and unlikely, according to Occam's razor) the recent proposal by Picco [arXiv:1207.1018] of having a new set of RG fixed points in addition to the mean-field one and the SR one.

We propose a “phase diagram” for particulate systems with purely repulsive contact forces, such as granular media and colloids. We characterize two classes of behavior as a function of the input kinetic energy per degree of freedom $T_0$ and packing fraction deviation from jamming onset $\Delta \varphi =\varphi -{\varphi }_J$ using simulations of frictionless disks. Isocoordinated solids (ICS) exist above jamming; they possess an average contact number equal to the isostatic value $z_{\mathrm{iso}}$. ICS display “strict” harmonic response, where the density of vibrational modes from the Fourier transform of the velocity autocorrelation function is a set of sharp peaks at eigenfrequencies ${\omega }_k^d$ of the dynamical matrix. In contrast, hypocoordinated solids (HCS) occur above and below jamming and possess fluctuating networks of interparticle contacts but do not undergo cage-breaking particle rearrangements. The density of vibrational frequencies for the HCS is not a collection of sharp peaks at ${\omega }_k^d$, but it does possess a common form over a range of $\Delta \varphi$ and $T_0$.

We describe an efficient and parsimonious matrix-based theory for studying the ensemble behavior of self-propellers and active swimmers, such as nanomotors or motile bacteria, that are typically studied by differential-equation-based Langevin or Fokker-Planck formalisms. The kinematic effects for elementary processes of motion are incorporated into a matrix, called the “kinematrix,” from which we immediately obtain correlators and the mean and variance of angular and position variables (and thus effective diffusivity) by simple matrix algebra. The kinematrix formalism enables us recast the behaviors of a diverse range of self-propellers into a unified form, revealing universalities in their ensemble behavior in terms of new emergent time scales. Active fluctuations and hydrodynamic interactions can be expressed as an additive composition of separate self-propellers.

Stack, chimneylike, and threadlike assemblies have previously been proposed for the structure of disodium cromoglycate (DSCG) aggregates in aqueous solutions. The results of the synchrotron x-ray scattering investigations reported here reveal the formation of simple columnar assemblies with π-π stacking at a separation of 3.4 Å between the DSCG molecules. Lateral separation between the assemblies is concentration and temperature dependent, varying from ∼35 to 42 Å in the orientationally ordered nematic ($N$) phase and from 27 to 32 Å in the columnar or middle ($M$) phase having long range lateral positional order. The assemblies’ length depends on concentration and consists of ∼23 molecules in the $N$ phase, becoming three to ten times larger in the $M$ phase. The scission energy is concentration dependent in the $N$ phase with values ∼7.19 ± 0.14 $k_{B}T$ (15 wt %), 2.73 ± 0.4 $k_{B}T$ (20 wt %), and 3.05 ± 0.2 $k_{B}T$ (25 wt %). Solutions of all concentrations undergo a spinodal decomposition at temperatures above ∼40 °C, resulting in DSCG-rich regions with the $M$ phase and water-rich regions in the $N$ and isotropic phases.

In a mesoscopic reaction-diffusion system with an Oregonator reaction model, we show that intrinsic noise can drive a resonant stable pattern in the presence of the initial subthreshold perturbations. Both spatially periodic and aperiodic stochastic resonances are demonstrated by employing the Gillespies stochastic simulation algorithm. The mechanisms for these phenomena are discussed.

Experimental evidence of vibrational resonance in a multistable vertical-cavity surface-emitting laser (VCSEL) is reported. The VCSEL is characterized by a coexistence of four polarization states and driven by low-frequency (LF) and high-frequency (HF) periodic signals. In these conditions a series of resonances on the low frequency depending on the HF amplitude is observed. The location of resonances in a parameter space (dc current, amplitude of HF signal) is experimentally studied. For a fixed value of the dc current an evolution of the resonance curves with an increase of the LF amplitude is experimentally investigated.

A phenomenological theory is proposed to analyze the asymptotic dynamics of perturbed inviscid Kolmogorov shear flows in two dimensions. The phase diagram provided by the theory is in qualitative agreement with numerical observations, which include three phases depending on the aspect ratio of the domain and the size of the perturbation: a steady shear flow, a stationary dipole, and four traveling vortices. The theory is based on a precise study of the inviscid damping of the linearized equation and on an analysis of nonlinear effects. In particular, we show that the dominant Landau pole controlling the inviscid damping undergoes a bifurcation, which has important consequences on the asymptotic fate of the perturbation.

We examine the dynamics of two coalescing liquid drops in the “inertial regime,” where the effects of viscosity are negligible and the propagation of the front of the bridge connecting the drops can be considered as “local.” The solution fully computed in the framework of classical fluid mechanics allows this regime to be identified, and the accuracy of the approximating scaling laws proposed to describe the propagation of the bridge to be established. It is shown that the scaling law known for this regime has a very limited region of accuracy, and, as a result, in describing experimental data it has frequently been applied outside its limits of applicability. The origin of the scaling law's shortcoming appears to be the fact that it accounts for the capillary pressure due only to the longitudinal curvature of the free surface as the driving force for the process. To address this deficiency, the scaling law is extended to account for both the longitudinal and azimuthal curvatures at the bridge front, which, fortuitously, still results in an explicit analytic expression for the front's propagation speed. This expression is shown to offer an excellent approximation for both the fully computed solution and for experimental data from a range of flow configurations for a remarkably large proportion of the coalescence process. The derived formula allows one to predict the speed at which drops coalesce for the duration of the inertial regime, which should be useful for the analysis of experimental data.

The competition between cluster spin glass (CSG) and ferromagnetism or antiferromagnetism is studied in this work. The model considers clusters of spins with short-range ferromagnetic or antiferromagnetic (FE-AF) interactions ($J_0$) and long-range disordered couplings ($J$) between clusters. The problem is treated by adapting the correlated cluster mean-field theory of D. Yamamoto [Phys. Rev. B 79, 144427 (2009)]. Phase diagrams $T/J\times J_0/J$ are obtained for different cluster sizes $n_s$. The results show that the CSG phase is found below the freezing temperature $T_f$ for lower intensities of $J_0/J$. The increase of short-range FE interaction can favor the CSG phase, while the AF one reduces the CSG region by decreasing the $T_f$. However, there are always critical values of $J_0$ where AF or FE orders become stable. The results also indicate a strong influence of the cluster size in the competition of magnetic phases. For AF cluster, the increase of $n_s$ diminishes $T_f$ reducing the CSG phase region, which indicates that the cluster surface spins can play an important role in the CSG arising.

We study motor traffic on Bethe networks subject to hard-core exclusion for both tightly coupled one-state machines and loosely coupled two-state machines that perform work against a constant load. In both cases we find an interaction-induced enhancement of the efficiency at maximum power (EMP) as compared to noninteracting motors. The EMP enhancement occurs for a wide range of network and single-motor parameters and is due to a change in the characteristic load-velocity relation caused by phase transitions in the system. Using a quantitative measure of the trade-off between the EMP enhancement and the corresponding loss in the maximum output power we identify parameter regimes where motor traffic systems operate efficiently at maximum power without a significant decrease in the maximum power output due to jamming effects.