In Pires et al. [Phys. Rev. E 84, 066210 (2011)], intermittent maps were considered, and the tight relationship between correlation decay of smooth observables and large deviation estimates as, for instance, employed in Artuso and Manchein [Phys. Rev. E 80, 036210 (2009)], was questioned. We try to clarify the problem and to provide rigorous arguments and an analytic estimate that disprove the objections raised in Pires et al. [Phys. Rev. E 84, 066210 (2011)] when ergodic systems are considered.

We investigate mass transfer during the isothermal absorption of atmospheric trace soluble gases by a single droplet whose size is comparable to the molecular mean free path in air at normal conditions. It is assumed that the trace reactant diffuses to the droplet surface and then reacts with the substances inside the droplet according to the first-order rate law. Our analysis applies a flux-matching theory of transport processes in gases and assumes constant thermophysical properties of the gases and liquids. We derive an integral equation of Volterra type for the transient molecular flux density to a liquid droplet and solve it numerically. Numerical calculations are performed for absorption of sulfur dioxide (${\mathrm{SO}}_2$), dinitrogen trioxide (N${}_2$O${}_3$), and chlorine (Cl${}_2$) by liquid nanoaerosols accompanied by chemical dissociation reaction. It is shown that during gas absorption by nanoaerosols, the kinetic effects play a significant role, and neglecting kinetic effects leads to a significant overestimation of the soluble gas flux into a droplet during the entire period of gas absorption.

We study the effects of ambient air humidity on the dynamics of imbibition in a paper. We observed that a quick increase of ambient air humidity leads to depinning and non-Washburn motion of wetting fronts. Specifically, we found that after depinning the wetting front moves with decreasing velocity $v\propto {(h_p/h_D)}^{\gamma }$, where $h_D$ is the front elevation with respect to its pinned position at lower humidity $h_p$, while $\gamma \cong 1/3$. The spatiotemporal maps of depinned front activity are established. The front motion is controlled by the dynamics of local avalanches directed at 30° to the balk flow direction. Although the roughness of the pinned wetting front is self-affine and the avalanche size distribution displays a power-law asymptotic, the roughness of the moving front becomes multiaffine a few minutes after depinning.

We study the restricted solid-on-solid model for surface growth in spatial dimension $d=4$ by means of a multisurface coding technique that allows us to analyze samples of size up to ${256}^4$ in the steady-state regime. For such large systems we are able to achieve a controlled asymptotic regime where the typical scale of the fluctuations are larger than the lattice spacing used in the simulations. A careful finite-size scaling analysis of the critical exponents clearly indicate that $d=4$ is not the upper critical dimension of the model.

Random walks constitute a fundamental mechanism for a large set of dynamics taking place on networks. In this article, we study random walks on weighted networks with an arbitrary degree distribution, where the weight of an edge between two nodes has a tunable parameter. By using the spectral graph theory, we derive analytical expressions for the stationary distribution, mean first-passage time (MFPT), average trapping time (ATT), and lower bound of the ATT, which is defined as the average MFPT to a given node over every starting point chosen from the stationary distribution. All these results depend on the weight parameter, indicating a significant role of network weights on random walks. For the case of uncorrelated networks, we provide explicit formulas for the stationary distribution as well as ATT. Particularly, for uncorrelated scale-free networks, when the target is placed on a node with the highest degree, we show that ATT can display various scalings of network size, depending also on the same parameter. Our findings could pave a way to delicately controlling random-walk dynamics on complex networks.

We study the idea spreading process by extending a recent model proposed by Bornholdt et al. [Phys. Rev. Lett. 106, 058701 (2011)] to the population on a two-dimensional square area either in the presence of static topological randomness or in which agents are allowed to freely move. We find that the static topological randomness induced by the random distribution of agents in the square area disfavors the common pattern of scientific paradigms, which is characterized by quick rise and slow decline of an arbitrary dominant idea. However, the common pattern of scientific paradigms is recovered when the movement of agents is enabled. In addition, we find that, when the moving speed of agents is low, the average lifetime of a dominant idea displays an optimal behavior. In contrast, the evolution of the model is no more sensitive to the movement speed once it is high enough.

Recently, different numerical studies of coarsening in disordered systems have shown the existence of a crossover from an initial, transient, power-law domain growth to a slower, presumably logarithmic, growth. However, due to the very slow dynamics and the long-lasting transient regime, one is usually not able to fully enter the asymptotic regime when investigating the relaxation of these systems toward equilibrium. We here study two simple driven systems—the one-dimensional $ABC$ model and a related domain model with simplified dynamics—that are known to exhibit anomalous slow relaxation where the asymptotic logarithmic growth regime is readily accessible. Studying two-times correlation and response functions, we focus on aging processes and dynamical scaling during logarithmic growth. Using the time-dependent growth length as the scaling variable, a simple aging picture emerges that is expected to also prevail in the asymptotic regime of disordered ferromagnets and spin glasses.

The diffusion of a system of ferromagnetic dipoles confined in a quasi-one-dimensional parabolic trap is studied using Brownian dynamics simulations. We show that the dynamics of the system is tunable by an in-plane external homogeneous magnetic field. For a strong applied magnetic field, we find that the mobility of the system, the exponent of diffusion, and the crossover time among different diffusion regimes can be tuned by the orientation of the magnetic field. For weak magnetic fields, the exponent of diffusion in the subdiffusive regime is independent of the orientation of the external field.

We study the spatiotemporal low-frequency microrheology of a gelatin gel during the sol-gel transition after a fast temperature quench by tracking the motion of embedded colloidal particles. From the particle dynamics two different mechanisms responsible for the gelation of the sol phase can be identified: a fast process associated to the local nucleation of triple helices and a slow fiber growth triggered by presence of an intact network. We associate the latter to a gelation front propagating into the sol phase whose speed depends linearly on the quench depth and which accelerates the local rate of the sol-gel transition.

A free-energy functional for a crystal proposed by Singh and Singh [Europhys. Lett. 88, 16005 (2009)] which contains both the symmetry conserved and symmetry broken parts of the direct pair correlation function has been used to investigate the crystallization of a two-dimensional fluid. The results found for fluids interacting via the inverse power potential $u\left(r\right)=\epsilon {\left(\sigma /r\right)}^n$ for $n=3,6$, and 12 are in good agreement with experimental and simulation results. The contribution made by the symmetry broken part to the grand thermodynamic potential at the freezing point is found to increase with the softness of the potential. Our results explain why the Ramakrishnan-Yussouff [Phys. Rev. B 19, 2775 (1979)] free-energy functional gave good account of freezing transitions of hard-core potentials but failed for potentials that have soft core and/or attractive tail.

This theoretical and numerical study deals with evaporation of a fluid wedge in contact with its pure vapor. The model describes a regime where the continuous wetting film is absent and the actual line of the triple gas-liquid-solid contact appears. A constant temperature higher than the saturation temperature is imposed at the solid substrate. The fluid flow is solved in the lubrication approximation. The introduction of the surface forces in the case of the partial wetting is discussed. The apparent contact angle (the gas-liquid interface slope far from the contact line) is studied numerically as a function of the substrate superheating, contact line velocity, and parameters related to the solid-fluid interaction (Young and microscopic contact angles, Hamaker constant, etc.). The dependence of the apparent contact angle on the substrate temperature is in agreement with existing approaches. For water, the apparent contact angle may be ${20}^{\circ }$ larger than the Young contact angle for 1 K superheating. The effect of the surface forces on the apparent contact angle is found to be weak.

In the binary mixture phase diagram of MC881 and MC452, the borderline between anticlinic antiferroelectric Sm$C_A^{*}$ and synclinic ferroelectric Sm$C^{*}$ becomes apparently parallel to the temperature ordinate axis at the critical concentration $r_{\mathrm{c}}$. The free energy difference between Sm$C_A^{*}$ and Sm$C^{*}$ is extremely small in a wide temperature range near $r_{\mathrm{c}}$. In such circumstances, by observing Bragg reflection spectra due to the director helical structure and electric-field-induced birefringence, we have observed the continuous change from Sm$C_A^{*}$ to Sm$C^{*}$ for $r\lesssim r_{\mathrm{c}}$ and the gradual growth of the full-pitch band over 5 ${}^{\circ }$C or more in the apparent Sm$C^{*}$ temperature region for $r\gtrsim r_{\mathrm{c}}$. These intriguing phenomena have been explained, successfully at least in the high-temperature region, by a thermal equilibrium between the synclinic and anticlinic orderings and the resulting Boltzmann distribution for the ratio between them; the thermal equilibrium is considered to be attained in a nonuniform defect-assisted way through solitary waves moving around dynamically. We have also discussed qualitatively an important role played by the effective long-range interlayer interactions in the low-temperature region.

In the coevolving voter model, each voter has one of two diametrically opposite opinions, and a voter encountering a neighbor with the opposite opinion may either adopt it or rewire the connection to another randomly chosen voter sharing the same opinion. As we smoothly change the relative frequency of rewiring compared to that of adoption, there occurs a phase transition between an active phase and a frozen phase. By performing extensive Monte Carlo calculations, we show that the phase transition is characterized by critical exponents $\beta =0.54\left(1\right)$ and $\overline{\nu }=1.5\left(1\right)$, which differ from the existing mean-field-type prediction. We furthermore extend the model by introducing a contrarian type that tries to have neighbors with the opposite opinion, and show that the critical behavior still belongs to the same universality class irrespective of such contrarians' fraction.

We discuss rigorous results on the rate of mixing for an idealized model of a class of fluid mixing device. These show that the decay of correlations of a scalar field is governed by the presence of boundaries in the domain, and in particular by the behavior of the modeled fluid at such boundaries.

A variety of complex spatial patterns relevant to chemical and biological systems can be generated through reaction-diffusion mechanisms. In this paper, we show that diffusive coupling through the inactivating component in a system of relaxation oscillators extends such complexity to the temporal domain, generating remarkable spatiotemporal phenomena. We provide analytic explanations of the antiphase synchronization and spatially patterned oscillatory death regimes. We report a chimera state where patches with distinct dynamics coexist and also observe propagating phase defects resembling persistent structures in cellular automata that may be used for computation.

Symbolic dynamics method and time reversal asymmetry analysis are both important approaches in the study of heartbeat interval series. However, there is limited research work reported on combining these two methods. We provide a method of time reversal asymmetry analysis which focuses on the differences between the forward and backward embedding “$m$ words” after the operation of equiprobable symbolization. To investigate the total amplitude as well as the distribution features of the difference, four indices are proposed. Based on the application to simulation series, we found that these measures can successfully detect time reversal asymmetry in chaos series. With application to human heartbeat interval series ($RR$ series), it is suggested that the distribution features of the forward-backward difference can sensitively capture the dynamical changes caused by diseases or aging. In particular, the index $E_D$, which reflects the random degree of the forward-backward difference distribution, can significantly discriminate healthy subjects from diseased ones. We conclude that RR series from healthy subjects show more asymmetry in temporal structure on the original time scale from the perspective of equiprobable symbolization, whereas diseases account for loss of this asymmetry.

Basic properties of the incompressible fluid motion in a rectangular cavity located along one wall of a plane channel are considered. For Mach numbers of the order of $1\times {10}^{-3}$ and using the incompressible formulation, we look for observable properties that can be associated with acoustic emission, which is normally observed in this kind of flow beyond a critical value of Reynolds number. The focus is put on the energy dynamics, in particular on the accumulation of energy in the cavity which takes place in the form of pressure and kinetic energy. By increasing the external forcing, we observe that the pressure flow into the cavity increases very rapidly, then peaks. However, the flow of kinetic energy, which is many orders of magnitude lower than that of the pressure, slowly but continuously grows. This leads to the pressure–kinetic energy flows ratio reaching an asymptotic state around the value 1000 for the channel bulk speed Reynolds number. It is interesting to note that beyond this threshold when the channel flow is highly unsteady—a sort of coarse turbulent flow—a sequence of high and low pressure spots is seen to depart from the downward cavity step in the statistically averaged field. The set of spots forms a steady spatial structure, a sort of damped standing wave stretching along the spanwise direction. The line joining the centers of the spots has an inclination similar to the normal to the fronts of density or pressure waves, which are observed to propagate from the downstream cavity edge in compressible cavity flows (at Mach numbers of $1\times {10}^2$ to $1\times {10}^3$, larger than those considered here). The wavelength of the standing wave is of the order of 1/8 the cavity depth and observed at the channel bulk Reynolds number, $\text{Re}\sim 2900$. In this condition, the measure of the maximum pressure differences in the cavity field shows values of the order of $1\times {10}^{-1}$ Pa. We interpret the presence of this sort of wave as the fingerprint of the noise emission spots which could be observed in simulations where the full compressible formulation is used. The flow is studied by means of a sequence of direct numerical simulations in the Reynolds number range 25–2900. This allows the study to span across the steady laminar regime up to a first coarse turbulent regime. These results are confirmed by the good agreement with a set of laboratory results obtained at a Reynolds number one order of magnitude larger in a different cavity geometry [M. Gharib and A. Roshko, J. Fluid Mech. 177, 501 (1987)]. This leaves room for a certain degree of qualitative universality to be associated with the present findings.

A critical, albeit simple experimental and/or molecular-dynamic (MD) simulation test is proposed whose outcome would, in principle, establish the viability of the Navier-Stokes-Fourier (NSF) equations for compressible fluid continua. The latter equation set, despite its longevity as constituting the fundamental paradigm of continuum fluid mechanics, has recently been criticized on the basis of its failure to properly incorporate volume transport phenomena—as embodied in the proposed bivelocity paradigm [H. Brenner, Int. J. Eng. Sci. 54, 67 (2012)]—into its formulation. Were the experimental or simulation results found to accord, even only qualitatively, with bivelocity predictions, the temperature distribution in a gas-filled, thermodynamically and mechanically isolated circular cylinder undergoing steady rigid-body rotation in an inertial reference frame would not be uniform; rather, the temperature would be higher at the cylinder wall than along the axis of rotation. This radial temperature nonuniformity contrasts with the uniformity of the temperature predicted by the NSF paradigm for these same circumstances. Easily attainable rates of rotation in centrifuges and readily available tools for measuring the expected temperature differences render experimental execution of the proposed scheme straightforward in principle. As such, measurement—via experiment or MD simulation—of, say, the temperature difference $\Delta T$ between the gas at the wall and along the axis of rotation would provide quantitative tests of both the NSF and bivelocity hydrodynamic models, whose respective solutions for the stated set of circumstances are derived in this paper. Independently of the correctness of the bivelocity model, any temperature difference observed during the proposed experiment or simulation, irrespective of magnitude, would preclude the possibility of the NSF paradigm being correct for fluid continua, except for incompressible flows.

Granular ensembles subjected to confinement forces can reach metastable states that often break down via formation of shear bands for sufficiently high deviatoric stress. In this article we investigate the flow induced in a granular ensemble that is perturbed by a vertically moving finger in a quasiplanar geometry. The flow exhibits spiral-like shear bands and evolves discontinuously in time, in concert with an oscillating penetration force. We characterize the nature of this nucleation-relaxation type process for loose to dense packing fractions. The nucleation dynamics is reasonably well described by a simple Mohr-Coulomb failure criterium in which the friction coefficient is a function of packing fraction. We contrast our findings with the recent work of Gravish et al. [Phys. Rev. Lett. 105, 128301 (2010)].