As in electrochemical cyclic voltammetry, time-periodic reverse voltage bias across a bipolar membrane is shown to exhibit hysteresis due to transient effects. This is due to the incomplete depletion of mobile ions, at the junction between the membranes, within two adjoining polarized layers; the layer thickness depends on the applied voltage and the surface charge densities. Experiments show that the hysteresis consists of an Ohmic linear rise in the total current with respect to the voltage, followed by a decay of the current. A limiting current is established for a long period when all the mobile ions are depleted from the polarized layer. If the resulting high field within the two polarized layers is sufficiently large, water dissociation occurs to produce proton and hydroxyl traveling wave fronts which contribute to another large jump in the current. We use numerical simulation and asymptotic analysis to interpret the experimental results and to estimate the amplitude of the transient hysteresis and the water-dissociation current.

The classical theory of electrokinetic phenomena is based on the mean-field approximation that the electric field acting on an individual ion is self-consistently determined by the local mean charge density. This paper considers situations, such as concentrated electrolytes, multivalent electrolytes, or solvent-free ionic liquids, where the mean-field approximation breaks down. A fourth-order modified Poisson equation is developed that captures the essential features in a simple continuum framework. The model is derived as a gradient approximation for nonlocal electrostatics of interacting effective charges, where the permittivity becomes a differential operator, scaled by a correlation length. The theory is able to capture subtle aspects of molecular simulations and allows for simple calculations of electrokinetic flows in correlated ionic fluids. Charge-density oscillations tend to reduce electro-osmotic flow and streaming current, and overscreening of surface charge can lead to flow reversal. These effects also help to explain the suppression of induced-charge electrokinetic phenomena at high salt concentrations.

We present experimental observations of the hierarchy of rational breather solutions of the nonlinear Schrödinger equation (NLS) generated in a water wave tank. First, five breathers of the infinite hierarchy have been successfully generated, thus confirming the theoretical predictions of their existence. Breathers of orders higher than five appeared to be unstable relative to the wave-breaking effect of water waves. Due to the strong influence of the wave breaking and relatively small carrier steepness values of the experiment these results for the higher-order solutions do not directly explain the formation of giant oceanic rogue waves. However, our results are important in understanding the dynamics of rogue water waves and may initiate similar experiments in other nonlinear dispersive media such as fiber optics and plasma physics, where the wave propagation is governed by the NLS.

We compare the behavior of the finite-temperature Hartree-Fock model with that of thermal density functional theory using both ground-state and temperature-dependent approximate exchange functionals. The test system is bcc Li in the temperature-density regime of warm dense matter (WDM). In this exchange-only case, there are significant qualitative differences in results from the three approaches. Those differences may be important for Born-Oppenheimer molecular dynamics studies of WDM with ground-state approximate density functionals and thermal occupancies. Such calculations require reliable regularized potentials over a demanding range of temperatures and densities. By comparison of pseudopotential and all-electron results at $T=0$ K for small Li clusters of local bcc symmetry and bond lengths equivalent to high density bulk Li, we determine the density ranges for which standard projector augmented wave (PAW) and norm-conserving pseudopotentials are reliable. Then, we construct and use all-electron PAW data sets with a small cutoff radius that are valid for lithium densities up to at least 80 g/cm${}^3$.

We study a Vicsek-style model of self-propelled particles where ferromagnetic and nematic alignment compete in both the usual “metric” version and in the “metric-free” case where a particle interacts with its Voronoi neighbors. We show that the phase diagram of this out-of-equilibrium $\mathit{XY}$ model is similar to that of its equilibrium counterpart: The properties of the fully nematic model, studied before by Ginelli et al. [Phys. Rev. Lett. 104, 184502 (2010)], are thus robust to the introduction of a modest bias of interactions toward ferromagnetic alignment. The direct transitions between polar and nematic ordered phases are shown to be discontinuous in the metric case, and continuous, belonging to the Ising universality class, in the metric-free version.

Within the framework of quantum field theory, we present the superfluid state of photons in a blackbody whose interior is filled by a Kerr nonlinear crystal. The thermodynamic properties of a Kerr nonlinear blackbody are investigated. At the transition temperature, the Gibbs free energy of the two phases is continuous but the entropy density of the two phases is discontinuous. Hence, there is a jump in the entropy density and this leads to a latent heat density. The photon system undergoes a first-order phase transition from the normal to the superfluid state. The transition temperature is characteristic of a concrete crystal. The entropy density and specific heat capacity are monotonically increasing functions of the temperature but are monotonically decreasing functions of the Kerr nonlinear coefficient.

Percolation is one of the most widely studied models in which a unique giant cluster emerges after the phase transition. Recently, a new phenomenon, where multiple giant clusters are observed in the so called Bohman-Frieze-Wormald (BFW) model, has attracted much attention, and how multiple giant clusters could emerge in generic percolation processes on random networks will be discussed in this paper. By introducing the merging probability and inspecting the distinct mechanisms which contribute to the growth of largest clusters, a sufficient condition to generate multiple stable giant clusters is given. Based on the above results, the BFW model and a multi-Erdös-Rényi (ER) model given by us are analyzed, and the mechanism of multiple giant clusters of these two models is revealed. Furthermore, large fluctuations are observed in the size of multiple giant clusters in many models, but the sum size of all giant clusters exhibits self-averaging as that in the size of unique giant cluster in ordinary percolation. Besides, the growth modes of different giant clusters are discussed, and we find that the large fluctuations observed are mainly due to the stochastic behavior of the evolution in the critical window. For all the discussion above, numerical simulations on the BFW model and the multi-ER model are done, which strongly support our analysis. The investigation of merging probability and the growth mechanisms of largest clusters provides insight for the essence of multiple giant clusters in the percolation processes and can be instructive for modeling or analyzing real-world networks consisting of many large clusters.

Inverse freezing is analyzed in a cluster spin-glass (SG) model that considers infinite-range disordered interactions between magnetic moments of different clusters (intercluster interaction) and short-range antiferromagnetic coupling $J_1$ between Ising spins of the same cluster (intracluster interaction). The intercluster disorder $J$ is treated within a mean-field theory by using a framework of one-step replica symmetry breaking. The effective model obtained by this treatment is computed by means of an exact diagonalization method. With the results we build phase diagrams of temperature $T/J$ versus $J_1/J$ for several sizes of clusters $n_s$ (number of spins in the cluster). The phase diagrams show a second-order transition from the paramagnetic phase to the SG order at the freezing temperature $T_f$ when $J_1/J$ is small. The increase in $J_1/J$ can then destroy the SG phase. It decreases $T_f/J$ and introduces a first-order transition. In addition, inverse freezing can arise at a certain range of $J_1/J$ and large enough $n_s$. Therefore, the nontrivial frustration generated by disorder and short-range antiferromagnetic coupling can introduce inverse freezing spontaneously.

We establish a quantum Otto engine cycle in which the working substance contacts with squeezed reservoirs during the two quantum isochoric processes. We consider two working substances: (1) a qubit and (2) two coupled qubits. Due to the effects of squeezing, the working substance can be heated to a higher effective temperature, which leads to many interesting features different from the ordinary ones, such as (1) for the qubit as working substance, if we choose the squeezed parameters properly, the positive work can be exported even when $T_H<T_L$, where $T_H$ and $T_L$ are the temperatures of the hot and cool reservoirs, respectively; (2) the efficiency can be higher than classical Carnot efficiency. These results do not violate the second law of thermodynamics and it can be understood as quantum fuel is more efficient than the classical one.

Experimental and theoretical studies were carried out to investigate the problem of magnetophoresis in a thin layer of concentrated magnetic fluids, concerning the aspect of particle aggregation. A heuristic theoretical model, describing diffusion fluxes of individual and aggregated particles, is suggested. The solution of related diffusion and magnetostatic problems are compared with the experimental data. The analysis of the data shows that the aggregates essentially change the concentration profile. Good agreement between experimental and theoretical curves is observed in the case when the aggregates contain, on average, more than ten particles.

Recently a Poisson-Helmholtz-Boltzmann (PHB) model [Bohinc et al., Phys. Rev. E 85, 031130 (2012)] was developed by accounting for solvent-mediated nonelectrostatic ion-ion interactions. Nonelectrostatic interactions are described by a Yukawa-like pair potential. In the present work, we modify the PHB model by adding steric effects (finite ion size) into the free energy to derive governing equations. The modified PHB model is capable of capturing both ion specificity and ion crowding. This modified model is then employed to study the capacitance of the double layer. More specifically, we focus on the influence of nonelectrostatic ion-ion interactions on charging a double layer near a flat surface in the presence of steric effects. We numerically compute the differential capacitance as a function of the voltage under various conditions. At small voltages and low salt concentrations (dilute solution), we find out that the predictions from the modified PHB model are the same as those from the classical Poisson-Boltzmann theory, indicating that nonelectrostatic ion-ion interactions and steric effects are negligible. At moderate voltages, nonelectrostatic ion-ion interactions play an important role in determining the differential capacitance. Generally speaking, nonelectrostatic interactions decrease the capacitance because of additional nonelectrostatic repulsion among excess counterions inside the double layer. However, increasing the voltage gradually favors steric effects, which induce a condensed layer with crowding of counterions near the electrode. Accordingly, the predictions from the modified PHB model collapse onto those computed by the modified Poisson-Boltzmann theory considering steric effects alone. Finally, theoretical predictions are compared and favorably agree with experimental data, in particular, in concentrated solutions, leading one to conclude that the modified PHB model adequately predicts the diffuse-charge dynamics of the double layer with ion specificity and steric effects.

We use molecular dynamics simulations to examine how the spatial patterns formed by the diffusive motion of water molecules are influenced by confinement between hydrophilic and hydrophobic surfaces. For bulk liquid water, Higo et al. found that the long-range orientational order of spatial dipole moments can form vortex-like spatial patterns for as long as 300 ps [Higo et al., Proc. Natl. Acad. Sci. USA 98, 5961 (2001)]. We perform a similar analysis for confined water and we find that the existence of vortices in these systems is dependent on both the surface separation and the surface hydrophilicity. Vortices perpendicular to the surface normal disappear when the surface separation is reduced to a thickness where the system is comprised of mostly interfacial water molecules. Vortices exist at slightly smaller separations for hydrophobic surfaces than for hydrophilic surfaces because the dipoles are less aligned at the hydrophobic surfaces. The dipole alignment that is induced by the hydrophilic surfaces is counter to the direction required by vortices.

We report on the contrasting phase behavior of a bent-core liquid crystal with a large opening angle between the mesogenic units in the bulk and in freely suspended films. Second-harmonic generation experiments and direct observation of director inversion walls in films in an applied electric field reveal that the nonpolar smectic $C$ phase observed in bulk samples becomes a ferroelectric “banana” phase in films, showing that a mesogen with a small steric moment can give a phase with polar order in freely suspended films even when the corresponding bulk phase is paraelectric.

We use a minimal model to study the processive motion of coupled synthetic molecular motors along a DNA track and we present data from Monte Carlo (MC) computer simulations based on this model. The model was originally proposed by Bromley et al. [HFSP J. 3, 204 (2009)] for studying the properties of a synthetic protein motor, the “Tumbleweed” (TW), and involves rigid Y-shaped motors diffusively rotating along the track while controlled by a series of periodically injected ligand pulses into the solution. The advantage of the model is that it mimics the mechanical properties of the TW motor in detail. Both the average first passage time which measures the diffusive motion of the motors, and the average dwell time on the track which measures their processivity are investigated by varying the parameters of the model. The latter includes ligand concentration and the range and strength of the binding interaction between motors and the track. In particular, it is of experimental interest to study the dependence of these dynamic time scales of the motors on the ligand concentration. Single rigid TW motors were first studied since no previous MC simulations of these motors have been performed. We first studied single motors for which we found a logarithmic decrease of the average first passage time and a logarithmic increase of the average dwell time with increasing ligand concentration. For two coupled motors, the dependence on ligand concentration is still logarithmic for the average first passage time but becomes linear for the average dwell time. This suggests a much greater stability in the processive motion of coupled motors as compared to single motors in the limit of large ligand concentration. By increasing the number of coupled motors, $m$, it was found that the average first passage time of the coupled motors only increases slowly with $m$ while the average dwell time increases exponentially with $m$. Thus the stability of coupled motors on the track can be considerably enhanced by their cooperative motion.

We study a driven lattice gas model for the length dynamics of treadmilling filaments in the presence of molecular motors. A treadmilling filament grows by subunit addition at one end and shrinks by subunit removal at the other. Molecular motors can attach to the filament, move towards the shrinking end, and detach from the filament. We consider motors that are also capable of inducing subunit removal at the shrinking filament end. Stochastic simulations reveal a phase of unimodal length distribution and a phase of unbounded growth. Exploiting a condition on the motor flux, we explore the system's phase diagram. In certain limits we can define random walks that allow us to estimate the full length distribution. The width of steady state distributions decreases with increasing motor activity. Our analysis indicates possible ways that cells can use to regulate the size of cytoskeletal structures such as mitotic spindles by controlling various motor properties.

We present a general framework to study stability of the synchronous solution for a hypernetwork of coupled dynamical systems. We are able to reduce the dimensionality of the problem by using simultaneous block diagonalization of matrices. We obtain necessary and sufficient conditions for stability of the synchronous solution in terms of a set of lower-dimensional problems and test the predictions of our low-dimensional analysis through numerical simulations. Under certain conditions, this technique may yield a substantial reduction of the dimensionality of the problem. For example, for a class of dynamical hypernetworks analyzed in the paper, we discover that arbitrarily large networks can be reduced to a collection of subsystems of dimensionality no more than 2. We apply our reduction technique to a number of different examples, including the class of undirected unweighted hypermotifs with 3 nodes.

We consider the problem of the control of transport in higher-dimensional periodic structures by applied ac fields. In a generic crystal, transverse degrees of freedom are coupled, and this makes the control of motion difficult to implement. We show, both with simulations and with an analytical functional expansion on the driving amplitudes, that the use of quasiperiodic driving significantly suppresses the coupling between transverse degrees of freedom. This allows a precise control of the transport, and does not require a detailed knowledge of the crystal geometry.

We study the effects of discrete, randomly distributed time delays on the dynamics of a coupled system of self-propelling particles. Bifurcation analysis on a mean field approximation of the system reveals that the system possesses patterns with certain universal characteristics that depend on distinguished moments of the time delay distribution. Specifically, we show both theoretically and numerically that although bifurcations of simple patterns, such as translations, change stability only as a function of the first moment of the time delay distribution, more complex patterns arising from Hopf bifurcations depend on all of the moments.

Reaction-diffusion systems may lead to the formation of steady-state heterogeneous spatial patterns, known as Turing patterns. Their mathematical formulation is important for the study of pattern formation in general and plays central roles in many fields of biology, such as ecology and morphogenesis. Here we show that Turing patterns may have a decisive role in shaping the abundance distribution of predators and prey living in patchy landscapes. We extend the original model proposed by Nakao and Mikhailov [Nat. Phys. 6, 544 (2010)] by considering food chains with several interacting pairs of prey and predators distributed on a scale-free network of patches. We identify patterns of species distribution displaying high degrees of apparent competition driven by Turing instabilities. Our results provide further indication that differences in abundance distribution among patches can be generated dynamically by self organized Turing patterns and not only by intrinsic environmental heterogeneity.

Mixtures of materials that move relative to each other arise in a variety of applications, especially in biophysical problems where the mixture consists of materials with different material properties. The variety of applications leads to a bewildering array of multiphase models, each with slightly different behaviors and interpretations, depending on the application. Some of the behaviors include phase separation, traveling waves, and linear instabilities. Because of the variability of the predicted behaviors, there has been considerable attention paid to minimal models to determine the fundamental solutions, bifurcations, and instabilities. In this paper we describe a new solution for the simplest two-phase system where both phases are dominated by viscous forces, one-phase response to osmotic forces, and the phases interact through a drag term. The system develops a traveling front separating an unstable, uniform solution from a patterned, phase separated solution. We seek the velocity of the traveling front and show that, for large diffusion, marginal stability gives a simple and accurate prediction for the velocity. For smaller diffusion constants, the front is “pushed,” and the linear prediction fails.