The response to an electric field of electrolytic solutions, gels, liquid crystals, and other soft materials is described by the drift-diffusion and Poisson equations. Existing models, used for the interpretation of experimental data, usually consider the system as one dimensional (1D), which is valid only for an infinite electrode size. Here we solve numerically the model equations in 2D, considering a circular electrode with a finite radius, and discuss the limit of validity of the 1D approximation.

A relation between the effective diffusion coefficient in a lattice with random site energies and random transition rates and the macroscopic conductivity in a random resistor network allows for elucidating possible sources of anomalous diffusion in random potential models. We show that subdiffusion is only possible either if the mean Boltzmann factor in the corresponding potential diverges or if the percolation concentration in the system is equal to unity (or both), and that superdiffusion is impossible in our system under any condition. We show also other useful applications of this relation.

We propose the Wigner separability entropy as a measure of complexity of a quantum state. This quantity measures the number of terms that effectively contribute to the Schmidt decomposition of the Wigner function with respect to a chosen phase-space decomposition. We prove that the Wigner separability entropy is equal to the operator space entanglement entropy, measuring entanglement in the space of operators, and, for pure states, twice the entropy of entanglement. The quantum to classical correspondence between the Wigner separability entropy and the separability entropy of the classical phase-space Liouville density is illustrated by means of numerical simulations of chaotic maps. In this way, the separability entropy emerges as an extremely broad complexity quantifier in both the classical and quantum realms.

A hallmark of the changes in dynamics towards the glass transition is the stretched exponential structural relaxation. Quasielastic neutron scattering results on liquid rubidium demonstrate such a nonexponential relaxation process in a simple liquid metal above the melting point. The nonexponential decay is an indication of non-Markovian dynamics and points to the collective character of the relaxation process. Describing the relaxation dynamics by a two-step process, the long lasting part of the decay process is in remarkable quantitative agreement with predictions from mode coupling theory. The feedback mechanism of the slowing down process in the theoretical description suggests that this contribution is at the origin of the structural arrest. With rising temperature the intermediate scattering function transforms into a simple exponential decay at a temperature range which indicates the end of the highly viscous solidlike behavior in the liquid.

The structure of the ripple phase of phospholipid membranes remains poorly understood in spite of a large number of theoretical studies, with many experimentally established structural features of this phase unaccounted for. In this article we present a phenomenological theory of phase transitions in single- and two-component achiral lipid membranes in terms of two coupled order parameters: a scalar order parameter describing lipid chain melting, and a vector order parameter describing the tilt of the hydrocarbon chains below the chain-melting transition. This model reproduces all the salient structural features of the ripple phase, providing a unified description of the phase diagram and microstructure. In addition, it predicts a variant of this phase that does not seem to have been experimentally observed. Using this model we have calculated generic phase diagrams of two-component membranes. We have also determined the phase diagram of a two-component lipid membrane from x-ray diffraction studies on aligned multilayers. This phase diagram is found to be in good agreement with that calculated from the model.

We propose a model that predicts the final sizes of lipid bilayer vesicles produced by pressure extrusion through nanochannels and we conduct large-scale coarse-grained molecular dynamics simulations of the phenomenon. We show that, to a first approximation independent of pressure, vesicle size can be predicted by a simple geometrical argument that considers an invariable inner vesicle volume enclosed by a finitely extensible lipid bilayer. The pressure dependence is then incorporated in our model by arguing that the effective channel radius decreases with increasing pressure due to a thickening of the lubrication layer between the vesicles and the channel wall. We fit our model to the experimental data of Patty and Frisken [Biophys. J. 85, 996 (2003)]. We predict that at high pressure, vesicle size significantly depends on channel length and, therefore, flow rate. The CGMD simulations reproduce the physical principles of the model. They also show the build-up of the stress in the vesicle, and typical rupture scenarios as the pressure gradient is increased.

The effect of geometric confinement on electroconvective instability due to nonequilibrium electro-osmotic slip at the interface of an electrolytic fluid and charge-selective solid is studied. It is shown that the topology of the marginal stability curves and the behavior of the critical parameters depend strongly on both channel geometry and dimensionless Debye length at low voltages for sufficiently deep channels, corresponding to the Rubinstein-Zaltzman instability mechanism, but that stability is governed almost entirely by channel depth for narrow channels at higher voltages. For shallow channels, it is shown that above a transition threshold, determined by both channel depth and Debye length, the low-voltage instability is completely suppressed.

Many natural and artificial networks evolve in time. Nodes and connections appear and disappear at various time scales, and their dynamics has profound consequences for any processes in which they are involved. The first empirical analysis of the temporal patterns characterizing dynamic networks are still recent, so that many questions remain open. Here, we study how random walks, as a paradigm of dynamical processes, unfold on temporally evolving networks. To this aim, we use empirical dynamical networks of contacts between individuals, and characterize the fundamental quantities that impact any general process taking place upon them. Furthermore, we introduce different randomizing strategies that allow us to single out the role of the different properties of the empirical networks. We show that the random walk exploration is slower on temporal networks than it is on the aggregate projected network, even when the time is properly rescaled. In particular, we point out that a fundamental role is played by the temporal correlations between consecutive contacts present in the data. Finally, we address the consequences of the intrinsically limited duration of many real world dynamical networks. Considering the fundamental prototypical role of the random walk process, we believe that these results could help to shed light on the behavior of more complex dynamics on temporally evolving networks.

The historical interplay between societies is governed by many factors, including in particular the spreading of languages, religion, and other symbolic traits. Cultural development, in turn, is coupled to the emergence and maintenance of information spreading. Strong centralized cultures exist due to attention from their members, whose faithfulness in turn relies on the supply of information. Here we discuss a culture evolution model on a planar geometry that takes into account aspects of the feedback between information spreading and its maintenance. Features of the model are highlighted by comparing it to cultural spreading in ancient and medieval Europe, where it suggests in particular that long-lived centers should be located in geographically remote regions.

We report the experimental studies on interaction of two vesicles trapped in a microfluidic four-roll mill, where a plane linear flow is realized. We found that the dynamics of a vesicle in tank-treading motion is significantly altered by the presence of another vesicle at separation distances up to $3.2–3.7$ times of the vesicle effective radius. This result is supported by measurement of a single vesicle back-reaction on the velocity field. Thus the experiment provides the upper bound for the volume fraction $\phi =0.08–0.13$ of noninteracting vesicle suspensions.

We report the results of an experimental study on the multiplicity of states in Taylor-Couette flow as a result of axial localization of azimuthally rotating waves. Localized states have been found to appear hysteretically from time-dependent Taylor-Couette flow at Reynolds numbers significantly above the onset of wavy Taylor vortices. These localized states have the shape of a modulated rotating wave and differ significantly from global modulated wavy Taylor vortex states in their spatial characteristics. Axial localization of rotating waves is accompanied with a significant increase in size of the underlying pair of Taylor vortices. Our work reveals that localization provides a mechanism for the appearance of multiple time-dependent states in Taylor-Couette flow.

This article presents a new formulation of the solution for fully nonlinear and unsteady planar flow of an electron beam in a diode. Using characteristic variables (i.e., variables that follow particle paths) the solution is expressed through an exact analytic, but implicit, formula for any choice of incoming velocity $v_0$, electric field $E_0$, and current $J_0$. For steady solutions, this approach clarifies the origin of the maximal current $J_{\max }$, derived by Child and Langmuir for $v_0=0$ and by Jaffe for $v_0>0$. The implicit formulation is used to find (1) unsteady solutions having constant incoming flux $J_0>J_{\max }$, which leads to formation of a virtual cathode, and (2) time-periodic solutions whose average flux exceeds the adiabatic average of $J_{\max }$.

The electrical characteristics of a photoelectric Franck-Hertz cell are measured in argon gas over a wide range of pressure, covering conditions where elastic collisions play an important role, as well as conditions where ionization becomes significant. Photoelectron pulses are induced by the fourth harmonic UV light of a diode-pumped Nd:YAG laser. The electron kinetics, which is far more complex compared to the naive picture of the Franck-Hertz experiment, is analyzed via Monte Carlo simulation. The computations provide the electrical characteristics of the cell, the energy and velocity distribution functions, and the transport parameters of the electrons, as well as the rate coefficients of different elementary processes. A good agreement is obtained between the cell's measured and calculated electrical characteristics, the peculiarities of which are understood by the simulation studies.

In this report, we present a dynamical systems approach to study the exact nonlinear wave-particle interaction in relativistic regime. We give particular attention to the effect of wave obliquity on the dynamics of the orbits by studying the specific cases of parallel ($\theta =0$) and perpendicular ($\theta =-\pi /2$) propagations in comparison to the general case of oblique propagation $\theta =]-\pi /2,0[$. We found that the fixed points of the system correspond to Landau resonance and that the dynamics can evolve from trapping to surfatron acceleration for propagation angles obeying a Hopf bifurcations condition. Cyclotron-resonant particles are also studied by the construction of a pseudo-potential structure in the Lorentz factor $\gamma$. We derived a condition for which Arnold diffusion results in relativistic stochastic acceleration. Hence, two general conclusions are drawn: (1) The propagation angle $\theta$ can significantly alter the dynamics of the orbits at both Landau and cyclotron-resonances. (2) Considering the short-time scales upon which the particles are accelerated, these two mechanisms for Landau and cyclotron resonant orbits could become potential candidates for problems of particle energization in collisionless space and cosmic plasmas.

A multistream model for spinless electrons in a relativistic quantum plasma is introduced by means of a suitable fluidlike version of the Klein-Gordon-Maxwell system. The one- and two-stream cases are treated in detail. A new linear instability condition for two-stream quantum plasmas is obtained, generalizing the previously known nonrelativistic results. In both the one- and two-stream cases, steady-state solutions reduce the model to a set of coupled nonlinear ordinary differential equations, which can be numerically solved, yielding a manifold of nonlinear periodic and soliton structures. The validity conditions for the applicability of the model are addressed.

A model for two-dimensional colloids confined laterally by “structured boundaries” (i.e., ones that impose a periodicity along the slit) is studied by Monte Carlo simulations. When the distance $D$ between the confining walls is reduced at constant particle number from an initial value $D_0$, for which a crystalline structure commensurate with the imposed periodicity fits, to smaller values, a succession of phase transitions to imperfectly ordered structures occur. These structures have a reduced number of rows parallel to the boundaries (from $n$ to $n-1$ to $n-2$, etc.) and are accompanied by an almost periodic strain pattern, due to “soliton staircases” along the boundaries. Since standard simulation studies of such transitions are hampered by huge hysteresis effects, we apply the phase switch Monte Carlo method to estimate the free energy difference between the structures as a function of the misfit between $D$ and $D_0$, thereby locating where the transitions occur in equilibrium. For comparison, we also obtain this free energy difference from a thermodynamic integration method: The results agree, but the effort required to obtain the same accuracy as provided by phase switch Monte Carlo would be at least three orders of magnitude larger. We also show for a situation where several “candidate structures” exist for a phase, that phase switch Monte Carlo can clearly distinguish the metastable structures from the stable one. Finally, applying the method in the conjugate statistical ensemble (where the normal pressure conjugate to $D$ is taken as an independent control variable), we show that the standard equivalence between the conjugate ensembles of statistical mechanics is violated.

We report results of systematic numerical studies of two-dimensional matter-wave soliton families supported by an external potential, in a vicinity of the junction between stable and unstable branches of the families, where the norm of the solution attains a minimum, facilitating the creation of the soliton. The model is based on the Gross-Pitaevskii equation for the self-attractive condensate loaded into a quasiperiodic (QP) optical lattice (OL). The same model applies to spatial optical solitons in QP photonic crystals. Dynamical properties and stability of the solitons are analyzed with respect to variations of the depth and wave number of the OL. In particular, it is found that the single-peak solitons are stable or not in exact accordance with the Vakhitov-Kolokolov (VK) criterion, while double-peak solitons, which are found if the OL wave number is small enough, are always unstable against splitting.

We study asymptotic properties of diffusion and other transport processes (including self-avoiding walks and electrical conduction) on large, randomly branched polymers using renormalized dynamical field theory. We focus on the swollen phase and the collapse transition, where loops in the polymers are irrelevant. Here the asymptotic statistics of the polymers is that of lattice trees, and diffusion on them is reminiscent of the climbing of a monkey on a tree. We calculate a set of universal scaling exponents including the diffusion exponent and the fractal dimension of the minimal path to two-loop order and, where available, compare them to numerical results.

A synergetic model allowing the description of a Brownian motion of active nanoparticles within the framework of the Lorenz three-parameter system is developed. The fluctuation's influence on the transition between different motion regimes is investigated. A diagram of possible motion modes of an active nanoparticle group and the corresponding stationary values of velocity are analyzed.

Hyperbolic structures are obtained by tiling a hyperbolic surface with negative Gaussian curvature. These structures generally exhibit two percolation transitions: a system-wide connection can be established at a certain occupation probability $p=p_{c1}$, and there emerges a unique giant cluster at $p_{c2}>p_{c1}$. There have been debates about locating the upper transition point of a prototypical hyperbolic structure called the enhanced binary tree (EBT), which is constructed by adding loops to a binary tree. This work presents its lower bound as $p_{c2}\gtrsim 0.55$ by using phenomenological renormalization-group methods and discusses some solvable models related to the EBT.