We exactly prove the no-passing rule in the ground state evolution of the random-field Ising model with monotonically varying external field. In particular, we show that the application of the no-passing rule can speed up the calculation of the zero-temperature equilibrium $M\left(H\right)$ curve dramatically.

We investigate the dynamics of a partially saturated grain-liquid mixture with a rotating drum apparatus. The drum is partially filled with the mixture and then rotated about its horizontal axis. We focus on the continuous avalanching regime and measure the impact of the volume fraction and viscosity of the liquid on the dynamic surface angle. The inclination angle of the surface is observed to increase sharply to a peak and then decrease as a function of liquid volume fraction. The height of the peak is observed to increase with rotation rate. For higher liquid volume fractions, the inclination angle of the surface can decrease with viscosity before increasing. The viscosity where the minimum occurs decreases with the rotation rate of the drum. Limited measurements of the flow depth were made, and these were observed to show only fractional changes with volume fraction and rotation speeds. We show that the qualitative features of our observations can be understood by analyzing the effect of lubrication forces on the time scale over which particles come in contact.

At the air-water interface, $4^{\prime }\text{−}8\text{−}\text{alkyl}[1,1^{\prime }\text{−}\text{biphenyl}]$-4-carbonitrile (8CB) domains with different thicknesses coexist in the same Langmuir film, as multiple bilayers on a monolayer. The edge dislocation at the domain boundary leads to line tension, which determines the domain shape and dynamics. By observing the domain relaxation process starting from small distortions, we find that the line tension $\lambda$ is linearly dependent on the thickness difference $\Delta L$ between the coexisting phases in the film, $\lambda =(3.3\pm 0.2)\mathrm{mN}∕\mathrm{m}$ $\Delta L$. Comparisons with theoretical treatments in the literature suggest that the edge dislocation at the boundary locates near the center of the film, which means that the 8CB multilayers are almost symmetric with respect to the air-water interface.

Using scaled-particle theory for binary mixtures of two-dimensional hard particles with orientational degrees of freedom, we analyze the stability of phases with orientational order and the demixing phase behavior of a variety of mixtures. Our study is focused on cases where at least one of the components consists of hard rectangles, or a particular case of these, hard squares. A pure fluid of hard rectangles has recently been shown to exhibit, aside from the usual uniaxial nematic phase, an additional oriented phase, called tetratic phase, possessing two directors, which is the analog of the biaxial or cubatic phases in three-dimensional fluids. There is evidence, based on computer simulation studies, that the tetratic phase might be stable with respect to phases with lower translational symmetry for rectangles with low aspect ratios. As hard rectangles are mixed, in increasing concentration, with other particles not possessing stable tetratic order by themselves, the tetratic phase is destabilized, via a first- or second-order phase transition, to uniaxial nematic or isotropic phases; for hard rectangles of low aspect ratio (hard squares, in particular), tetratic order persists in a relatively large range of volume fractions. The order of these transitions depends on the particle geometry and dimensions, and also on the thermodynamic conditions of the mixture. The second component of the mixture has been chosen to be hard disks or discorectangles, the geometry of which is different from that of rectangles, leading to packing frustration and demixing behavior, or simply rectangles of different aspect ratio but with the same particle area, or different particle area but with the same aspect ratio. These mixtures may be good candidates for observing thermodynamically stable tetratic phases in monolayers of hard particles. Finally, demixing between fluid (isotropic-tetratic or tetratic-tetratic) phases is seen to occur in mixtures of hard squares of different sizes when the size ratio is sufficiently large.

We use a highly sensitive, noncontact, optical interferometric technique to quantify the red blood cell membrane fluctuations at the nanometer and millisecond scales. The results reveal significant properties of both temporal and spatial coherence associated with the membrane dynamics. We show that these correlations can be accounted for by the viscoelastic properties of the cell membrane. From this measurement, we extract the loss and storage moduli associated with the membrane and find a crossover frequency at which the buffer viscosity seems to become dominant.

We present an empirical study of the networks created by users within internet news groups and forums and show that they organize themselves into scale-free trees. The structure of these trees depends on the topic under discussion; specialist topics have trees with a short shallow structure whereas more universal topics are discussed widely and have a deeper tree structure. For news groups we find that the distribution of the time intervals between when a message is posted and when it receives a response exhibits a composite power-law behavior. From our statistics we can see if the news group or forum is free or is overseen by a moderator. The correlation function of activity, the number of messages posted in a given time, shows long-range correlations connected with the users’ daily routines. The distribution of distances between each message and its root is exponential for most news groups and power law for the forums. For both formats we find that the relation between the supremacy (the total number of nodes that are under the node $i$, including node $i$) and the degree is linear $s\left(k\right)\sim k$, in contrast to the analytical relation for the Barabási-Albert network.

In an earlier work [Cheng and Cui, Phys. Rev. B 72, 113112 (2005)], we have shown theoretically that extremely high power densities can be generated and transmitted in a super waveguide which is filled with homogeneous bilayers of right- and left-handed materials. In this paper, we realize such a super waveguide using right-handed transmission-line (RHTL) and left-handed transmission-line (LHTL) circuits. After a rigorous design of the RHTL-LHTL structure, we observe the generation and transmission of high-power densities in the super circuit waveguide from accurate simulation results. Both lossless and lossy cases have been studied for the LHTL circuit. From the simulation results and the rigorous analysis of energy speeds, we show that high-power flows with opposite directions are excited in the RHTL and LHTL parts of the super waveguide, which form the energy vortices in the waveguide cross section.

A thermal lattice Boltzmann model for a van der Waals fluid is proposed. In the continuum, the model reproduces at second order of a Chapman-Enskog expansion, the theory recently introduced by A. Onuki [Phys. Rev. Lett. 94, 054501 (2005)]. Phase separation has been studied in a system quenched by contact with external walls. Pressure waves favor the thermalization of the system at initial times and the temperature, soon with respect to typical times of phase separation, becomes homogeneous in the bulk. Alternate layers of liquid and vapor form on the walls and disappear at late times.

We propose a simple one-dimensional linear model to describe the formation of localized traveling waves due to material parameter ramps in nematic liquid crystals. We assume that due to some external perturbation the material parameters (conductivity, dielectric constants, viscosity, elasticity) of the liquid crystal become slowly varying functions of position. Temperature gradient in localized regions induced by a laser beam could be one such perturbation. We obtain a $4\times 4$ system of electrohydrodynamic equations [partial derivative equations (PDE) with respect to time and position]. At first we assume that all parameters change from their nonperturbed value by the same ramp function. Then, to reveal the parameters which slowly change are predominant in the formation of localized traveling waves, we obtain four more systems of equations. Each time we assume that just one of the material parameters changes while the others are held constant. Accordingly, by reducing $4\times 4$ systems of equations into one equation and using a WKB-like approach for nonuniform media, we obtain the relevant dispersion relations. We show that ramps of elasticity and dielectric parameters play the dominant role in the formation of localized traveling waves in nonuniform nematic media.

We report dynamic Monte Carlo simulations of binary polymer blends. The blends exhibit liquid-liquid phase separation influenced by the nearby crystallization of one component. We found that both binodal and spinodal boundaries of liquid-liquid phase separation shift up above the predictions of the mean-field lattice theory. The enhancement of immiscibility can be assigned to the thermal fluctuations toward better parallel order of the crystallizable chains in the blends, which has been neglected in the mean-field theory. This result serves as a theoretical background to explain the related experimental observations.

Modularity is one of the most prominent properties of real-world complex networks. Here, we address the issue of module identification in two important classes of networks: bipartite networks and directed unipartite networks. Nodes in bipartite networks are divided into two nonoverlapping sets, and the links must have one end node from each set. Directed unipartite networks only have one type of node, but links have an origin and an end. We show that directed unipartite networks can be conveniently represented as bipartite networks for module identification purposes. We report on an approach especially suited for module detection in bipartite networks, and we define a set of random networks that enable us to validate the approach.

We describe a fast and accurate method to compute the pressure and equilibrium states for maps of the interval $T:[0,1]\to [0,1]$ with respect to potentials $\varphi :[0,1]\to \mathbb{R}$. An approximate Ruelle-Perron-Frobenius operator is constructed and the pressure read off as the logarithm of the leading eigenvalue of this operator. By setting $\varphi \equiv 0$, we recover the topological entropy. The conformal measure and the equilibrium state are computed as eigenvectors. Our approach is extremely efficient and very simple to implement. Rigorous convergence results are stated for piecewise expanding maps.

We investigate a solvable model for energy-conserving nonequilibrium steady states. The time-reversal asymmetry of the dynamics leads to the violation of detailed balance and to ergodicity breaking, as manifested by the presence of dynamically inaccessible states. Two such systems in contact do not reach the same effective temperature if standard definitions are used. However, we identify the effective temperature that controls energy flow. Although this operational temperature does reach a common value upon contact, the total entropy of the joint system can decrease.

A thermodynamiclike formalism is developed for superstatistical systems based on conditional entropies. This theory takes into account large-scale variations of intensive variables of systems in nonequilibrium stationary states. Ordinary thermodynamics is recovered as a special case of the present theory, and corrections to it can systematically be evaluated. A generalization of Einstein’s relation for fluctuations is presented using a maximum entropy condition.

Building upon the ideas of Gerischer et al., we have developed a cellular automaton for the growth dynamics of nanowhiskers. We present two models for the whisker growth. The first is a simple extension of the surface model, whereas the second includes diffusion on the rim of the whiskers. Results for one-dimensional calculations are presented and discussed, together with a comparison between the two models and with experimental results as well.

We have studied the polar structures in the binary mixtures of bent-core liquid crystals $\mathrm{P}\text{−}n\text{−}\mathrm{O}\text{−}\mathrm{PIMB}{(n-2)}^{*}\text{−}(n-4)\mathrm{O}$ showing the ferroelectric smectic-$C_A{P}_F$ $\left(\mathrm{Sm}\text{−}{C}_A{P}_F\right)$ ($n=8$ and 10) and antiferroelectric $\mathrm{Sm}\text{−}{C}_S{P}_A$ $(n=9)$ $B2$ phase. Although the polar structure of the one-to-one mixture is governed by the compound with longer end chains, it is much more complicated in the mixtures with slightly less fraction of compounds with longer end chains. Even if the mixtures show the antiferroelectric phase before field application, the ferroelectric domains remain once the field is applied and coexist with the antiferroelectric domains. The coexistence structure was modeled by comparing the microscope real image with that of second-harmonic generation. The fraction of the ferroelectric domains is larger at higher temperature region of the $B2$ phase and decreases with decreasing temperature. The stable phase structures were discussed based on the phenomenological theory. We suggest that the coupling energy of the layer chirality is higher than the energies of the orientation correlations of tilts and polarizations between adjacent layers.

We report molecular dynamics simulations of the segregation of two overlapping chains in cylindrical confinement. We find that the entropic repulsion between chains can be sufficiently strong to cause segregation on a time scale that is short compared to the one for diffusion. This result implies that entropic driving forces are sufficiently strong to cause rapid bacterial chromosome segregation.

Ion-acoustic double layers has been studied in multicomponent plasma with positrons. Using the reductive perturbation method, the modified Korteweg–de Vries (mKdV) equation is derived for the system. The double-layer solution of the mKdV equation is discussed in detail. It is found that there exist two critical concentrations of positrons, ${\alpha }_R$ and ${\alpha }_Q$, which decide the existence and nature of the ion-acoustic double layers. It is also found that the system supports ion-acoustic double layers only when the positron concentration $\left(\alpha \right)$ is less than the critical concentration ${\alpha }_R$ (i.e., $\alpha <{\alpha }_R$). It is also investigated that for the given set of parameter values, if ${\alpha }_R<{\alpha }_Q$, the system supports only rarefactive double layers for the values of $\alpha$ lying in the range $0<\alpha <{\alpha }_R$. However, for the given set of parameter values ${\alpha }_R>{\alpha }_Q$, the system supports rarefactive double layers for $\alpha <{\alpha }_Q$, and for $\alpha >{\alpha }_Q$, compressive double layers exist. The present theory also predicts that for a given set of parameter values on increasing the positron concentration, the amplitude of the rarefactive (compressive) double layer decreases (increases), whereas as positron concentration is increased, the width of the rarefactive (compressive) double layer increases (decreases). The effects of positron concentration and temperature ratio on the characteristics of the double layers (namely amplitude and width) are discussed in detail.

It is shown that the computer simulations of Hele-Shaw flows around a wedge reported by Bogoyavlenskiy and Cotts [Phys. Rev. E 69, 016310 (2004)] do not reproduce with a high degree of accuracy the exact solutions known for this problem.

As pointed out by Vasconcelos in his Comment, our computer simulations of Hele-Shaw flows around series of wedges differ from analytical solutions existing for this problem. We attribute the discrepancy to the notion that these analytical solutions correspond to ideal, steady-state flow regimes which are hardly applicable when a rigid obstacle interacts with a moving liquid-gas interface.