In a recent paper [Mandal et al., Phys. Rev. E 88, 022129 (2013)], the nature of spatial correlations of plasticity in hard-sphere glasses was addressed both via computer simulations and in experiments. It was found that the experimentally obtained correlations obey a power law, whereas the correlations from simulations are better fitted by an exponential decay. We here provide direct evidence—via simulations of a hard-sphere glass in two dimensions (2D)—that this discrepancy is a consequence of the finite system size in the 3D simulations. By extending the study to a 2D soft disk model at zero temperature [Durian, Phys. Rev. Lett. 75, 4780 (1995)], the robustness of the power-law decay in sheared amorphous solids is underlined. Deviations from a power law occur when either reducing the packing fraction towards the supercooled regime in the case of hard spheres or changing the dissipation mechanism from contact dissipation to a mean-field-type drag in the case of soft disks.

Nonlinear dynamics of surface gravity waves trapped by an opposing jet current is studied analytically and numerically. For wave fields narrow band in frequency but not necessarily with narrow angular distributions the developed asymptotic weakly nonlinear theory based on the modal approach of Shrira and Slunyaev [J. Fluid. Mech. 738, 65 (2014)] leads to the one-dimensional modified nonlinear Schrödinger equation of self-focusing type for a single mode. Its solutions such as envelope solitons and breathers are considered to be prototypes of rogue waves; these solutions, in contrast to waves in the absence of currents, are robust with respect to transverse perturbations, which suggests a potentially higher probability of rogue waves. Robustness of the long-lived analytical solutions describing modulated trapped waves and solitary wave groups is verified by direct numerical simulations of potential Euler equations.

We perform path-integral Monte Carlo calculations to study the adsorption of ${}^4\mathrm{He}$ atoms on a ${\text{H}}_2$-plated ${\text{C}}_{20}$ molecular surface. It is found that 32 ${\text{H}}_2$ molecules form a complete solid layer on ${\text{C}}_{20}$, where each ${\text{H}}_2$ molecule is located either above one of the 12 pentagon centers or above one of the 20 carbon atoms. The angular density profiles of the first ${}^4\mathrm{He}$ layer on the (${\text{H}}_2$)${}_{32}$-${\text{C}}_{20}$ surface reveal different quantum states as the number of ${}^4\mathrm{He}$ atoms $N$ varies. Especially, the helium layer exhibits an icosidodecahedron structure for $N=30$, where each ${}^4\mathrm{He}$ atom is located at one of the vertices of 20 corner-sharing triangles. While the ${}^4\mathrm{He}$ density peaks for $N=60$ constitute a truncated icosahedron with 12 pentagonal and 20 hexagonal faces, the additional atoms beyond $N=60$ are found to be placed at the hexagon centers of the truncated icosahedron to form a hexakis truncated icosahedron for $N=80$. The superfluid response of the ${}^4\mathrm{He}$ layer at a temperature of $T=0.6$ K is found to be completely quenched for $N=30$ and to be significantly suppressed for $N=60$ and 80, reflecting the formation of compact buckyball structures.

We introduce and discuss a local kinetic mechanism for an $n$-electron electrochemical reaction at the interface formed by an electrode and diluted electrolyte. We show that the suggested mechanism is in agreement with the Nernst equation in the thermal equilibrium. We also qualitatively characterize the structure of a flat electrode-diluted electrolyte boundary in the meaning of the spatial distribution of electrochemical reactants and electric potential. As the suggested kinetic mechanism is not limited by the duration of relaxation processes in electric double layers, it is suitable for the understanding and simulation of fast transient processes that appear in modern applications such as nanocolloid dielectrophoresis, AC electrospray, AC electroosmosis, or nanopore biosensing.

Experiments and three-dimensional direct numerical simulations were performed to investigate the effects of physical parameters on the repulsion or attraction force affecting the motion of a particle oscillating near a solid wall of a fluid cell under microgravity. The following physical parameters were investigated: fluid cell amplitude, fluid and particle densities, angular frequency of the cell vibration, initial distance between the particle centroid and the closest cell wall, particle radius, and dynamic viscosity. Based on the simulations, a nondimensional relation was developed to relate those physical parameters to the repulsion or attraction force affecting the particle. The relation shows that the repulsion or attraction force is increased by the increase in the cell vibration amplitude and frequency and also the force direction would change from attraction to repulsion above a threshold fluid viscosity. Relations to other physical parameters were also studied and are reported. This paper follows our previous work on the physical mechanism of observed repulsion force on a particle in a viscous fluid cell [M. Saadatmand and M. Kawaji, Phys. Rev. E 88, 023019 (2013)].

We investigate theoretically the possible final stationary configurations that can be reached by a laterally confined uniform liquid film inside a container. The liquid is under the action of gravity, surface tension, and the molecular interaction with the solid substrate. We study the case when the container is in an upright position as well as when it is turned upside down. The governing parameters of the problem are the initial thickness of the film, the size of the recipient that contains the liquid, and a dimensionless number that quantifies the relative strength of gravity with respect to the molecular interaction. The uniform film is always a possible final state and depending on the value of the parameters, up to three different additional final states may exist, each one consisting in a droplet surrounded by a thin film. We derive analytical expressions for the energy of these possible final configurations and from these we analyze which state is indeed reached. A uniform thin film may show three different behaviors after a perturbation: The system recovers its initial shape after any perturbation, the fluid evolves towards a drop (if more than one is possible, it tends toward that with the thinnest precursor film) for any perturbation, or the system ends as a uniform film or a drop depending on the details of the perturbation.

We propose a stochastic model of Zipf's law, namely a power-law relation between rank and size, and clarify as to why a specific value of its power-law exponent is quite universal. We focus on the successive total of a multiplicative stochastic process. By employing properties of a well-known stochastic process, we concisely show that the successive total follows a stationary power-law distribution, which is directly related to Zipf's law. The formula of the power-law exponent is also derived. Finally, we conclude that the universality of the rank-size exponent is brought about by symmetry between an increase and a decrease in the random growth rate.

We present results for the temperature behavior of the Casimir force for a system with a film geometry with thickness $L$ subject to free boundary conditions and described by the $\mathit{n}\to \infty$ limit of the $\mathrm{O}\left(\mathit{n}\right)$ model. These results extend over all temperatures, including the critical regime near the bulk critical temperature $T_c$, where the critical fluctuations determine the behavior of the force, and temperatures well below it, where its behavior is dictated by the Goldstone mode contributions. The temperature behavior when the absolute temperature, $T$, is a finite distance below $T_c$, up to a logarithmic-in-$L$ proximity of the bulk critical temperature, is obtained both analytically and numerically; the critical behavior follows from numerics. The results resemble—but do not duplicate—the experimental curve behavior for the force obtained for ${}^4\mathrm{He}$ films.

We review ideas on temporal dependencies and recurrences in discrete time series from several areas of natural and social sciences. We revisit existing studies and redefine the relevant observables in the language of copulas (joint laws of the ranks). We propose that copulas provide an appropriate mathematical framework to study nonlinear time dependencies and related concepts—like aftershocks, Omori law, recurrences, and waiting times. We also critically argue, using this global approach, that previous phenomenological attempts involving only a long-ranged autocorrelation function lacked complexity in that they were essentially monoscale.

An important class of economic models involve agents whose wealth changes due to transactions with other agents. Several authors have pointed out an analogy with kinetic theory, which describes molecules whose momentum and energy change due to interactions with other molecules. We pursue this analogy and derive a Boltzmann equation for the time evolution of the wealth distribution of a population of agents for the so-called Yard-Sale Model of wealth exchange. We examine the solutions to this equation by a combination of analytical and numerical methods and investigate its long-time limit. We study an important limit of this equation for small transaction sizes and derive a partial integrodifferential equation governing the evolution of the wealth distribution in a closed economy. We then describe how this model can be extended to include features such as inflation, production, and taxation. In particular, we show that the model with taxation exhibits the basic features of the Pareto law, namely, a lower cutoff to the wealth density at small values of wealth, and approximate power-law behavior at large values of wealth.

The effect of surfactants on the radial dynamics of a single sonoluminescing bubble has been investigated. Experimentally, it is observed that an increase in the surfactant concentration leads to a decline in the oscillation amplitude and hence light emission intensity. Numerical simulations support this result, showing that under the driving pressures required to achieve single bubble sonoluminescence (SBSL), the surface properties, namely, the surface elasticity and dilatational viscosity, contribute to the damping of the radial amplitude in the bubble oscillation. In most cases this stabilizes the bubble surface, and contributes to a decreased light intensity. A stronger driving pressure is necessary to achieve equivalent light emission to a surfactant-free bubble. However, as the driving pressure is increased, the surface stability also decreases, making it practically very difficult for a bubble to achieve high SBSL intensities in concentrated surfactant solutions. Although more stable owing to more mild pulsations, the instability mechanism for a surfactant-coated bubble at higher ambient radii is more likely to be of the Rayleigh-Taylor type than that of a clean bubble at the same given acoustic parameters, which can lead to bubble disintegration before correcting mechanisms can bring the bubble back into the stable sonoluminescence regime.

We study the stability of coherent structures in plane Couette flow against long-wavelength perturbations in wide domains that cover several pairs of coherent structures. For one and two pairs of vortices, the states retain the stability properties of the small domains, but for three pairs new unstable modes are found. They are shown to be connected to bifurcations that break the translational symmetry and drive the coherent structures from the spanwise extended state to a modulated one that is a precursor to spanwise localized states. Tracking the stability of the orbits as functions of the spanwise wave length reveals a rich variety of additional bifurcations.

In this Comment, I point out that the physical origin of molecular tilt in the smectic phase, found in the Monte Carlo simulations of systems of rodlike molecules with two terminal antiparallel transverse dipole moments by Bose and Saha [Phys. Rev. E 86, 050701(R) (2012)], is similar to the one proposed by McMillan. In particular, unlike in smectic-$C$ liquid crystals, in which the molecules are known to have practically free rotations about their long axes, the molecular rotations are found to be partially frozen in the simulations. Further, I suggest that the attractive interaction between correlated splay fluctuations of the antiparallel polarized sublayers which lie close to each other in adjacent molecular layers give rise to the tilting, rather than a reduced attractive interaction between dipoles belonging to the two dipolar sublayers within one molecular layer, as proposed by the authors.

In a recent article [T. K. Bose and J. Saha, Phys. Rev. E 86, 050701 (2012)], we have presented the results of a Monte Carlo simulation study of the systems of dipolar Gay-Berne ellipsoids where two terminal antiparallel dipoles are placed symmetrically on the long axis of each ellipsoid, and the results revealed the combined contribution of dipolar separation and transverse orientations in controlling the tilt angle in the tilted hexatic smectic phase. The tilt angle changed from zero to a significant value, in the case of transverse dipoles, with a change in the dipolar separation. In the related comment, Madhusudana [preceding Comment, Phys. Rev. E 89, 046501 (2014)] has claimed that the physical origin of the molecular tilt in the significantly tilted phases found in the simulations is similar to that proposed by McMillan [Phys. Rev. A 8, 1921 (1973)]. Here, we explain that the claim is not correct and make it clear that the two compared pictures are quite different. In the preceding Comment, Madhusudana has also suggested an alternative explanation for tilt generation in the simulations by criticizing the original one proposed by us. We argue here in support of the original explanation and clarify that his explanation does not follow the simulation results.

We consider sequences of measurements implemented by positive operator valued measures (POVMs). Starting from the assumption that these sequences may be described as consistent and Markovian, even and especially for closed quantum systems, we identify properties of the equilibrium state that coincide with the properties of typical pure quantum states. We define a physical entropy that converges against the standard entropies in the approach to equilibrium. Furthermore, strict limits to its possible decrease are derived on the basis of Renyi entropies. It is demonstrated that Landauer's principle follows directly from these limits. Since the above assumptions are rather strong, we exemplify the fact that they may nevertheless apply by checking them numerically for some transition paths in a concrete model.

We have computed current-current correlation functions in chains of anharmonic oscillators described by various models (FPU-$\beta$, FPU-$\alpha \beta$, ${\varphi }^4$), considering both the total current and the currents associated with individual phonon modes, which are important in view of the Green-Kubo relation for heat conductivity. Our simulations show that, contrary to the common hypothesis, there are, under some circumstances, significant correlations between neighboring modes. These cross-mode correlations are the dominant contribution to the conductivity in the low anharmonicity regime. The inverse of the timescale over which they are significant, $1/{\tau }_c$, is related to the anharmonicity level in a way similar to the largest Lyapunov exponent, suggesting that the two quantities are related. Cross-mode correlations exist in both anomalous and regular heat-conducting systems although we are unable to observe a transition to the independent-mode regime in the latter case.

The evaporation characteristics of sessile water droplets on smooth hydrophobic and structured superhydrophobic heated surfaces are experimentally investigated. Droplets placed on the hierarchical superhydrophobic surface subtend a very high contact angle ($\sim$160°) and demonstrate low roll-off angle ($\sim$1°), while the hydrophobic substrate supports corresponding values of 120° and $\sim$10°. The substrates are heated to different constant temperatures in the range of 40–60 °C, which causes the droplet to evaporate much faster than in the case of natural evaporation without heating. The geometric parameters of the droplet, such as contact angle, contact radius, and volume evolution over time, are experimentally tracked. The droplets are observed to evaporate primarily in a constant-contact-angle mode where the contact line slides along the surface. The measurements are compared with predictions from a model based on diffusion of vapor into the ambient that assumes isothermal conditions. This vapor-diffusion-only model captures the qualitative evaporation characteristics on both test substrates, but reasonable quantitative agreement is achieved only for the hydrophobic surface. The superhydrophobic surface demonstrates significant deviation between the measured evaporation rate and that obtained using the vapor-diffusion-only model, with the difference being amplified as the substrate temperature is increased. A simple model considering thermal diffusion through the droplet is used to highlight the important role of evaporative cooling at the droplet interface in determining the droplet evaporation characteristics on superhydrophobic surfaces.

Stability of an idealized hyperbolic hedgehog in a nematic liquid crystal against a twist transition is investigated by extending the methodology of Rüdinger and Stark [Liq. Cryst. 26, 753 (1999)], where the hedgehog is confined between two concentric spheres. In the ideal hyperbolic-hedgehog the molecular orientation is assumed to rotate proportionally with respect to the inclination angle, $\theta$ (and in the opposite sense). However, when splay, $k_{11}$, and bend, $k_{33}$, moduli differ this proportionality is lost and the liquid crystal deforms relative to the ideal with bend and splay. Although slight, these deformations are shown to significantly shift the transition if $k_{11}/k_{33}$ is small. By increasing the degree of confinement the twist transition can be inhibited, a characteristic both hyperbolic and radial hedgehogs have in common. The twist transition of a hyperbolic defect that accompanies a particle is found to be well predicted by the earlier stability analysis of a thick shell.

We study the bond percolation on a one-parameter family of a hierarchical small-world network and find the metatransition between an inverted Berezinskii-Kosterlitz-Thouless (iBKT) transition and an abrupt transition driven by changing the network topology. It is found that the order parameter is continuous and the fractal exponent is discontinuous in the iBKT transition, and oppositely, the former is discontinuous and the latter is continuous in the abrupt transition. The gaps of the order parameter and the fractal exponent in each transition vanish as they approach the metatransition point. This point corresponds to a marginal power-law transition. In the renormalization group formalism, this metatransition corresponds to the transition between transcritical and saddle-node bifurcations of the fixed point via a pitchfork bifurcation.