The electro-osmotic flow driven by a screen pump, composed of a line array of evenly spaced identical rectangular solid blocks, is investigated under the Debye-Hückel approximation. The geometry of the screen pump is determined by the spacing and aspect ratio of the solid blocks. A constant surface zeta potential is assumed on the block surface. The method of eigenfunction series expansion is applied to solve analytically for the applied electric field, electric charge potential in the fluid, and flow field. Because of the low Reynolds number, Stokes equations are applied for the flow. The analytic result is first confirmed by comparing with the exact solution of the electro-osmotic flow in an infinite channel. Then different geometries of the screen pump and the effect of the electrokinetic width are computed for their influence on the flow rate. Recirculating eddies and reversing flow are found even though the applied electric driving field is unidirectional.

The nonlinear interaction between intense laser light and a quantum plasma is modeled by a collective Dirac equation coupled with the Maxwell equations. The model is used to study the nonlinear propagation of relativistically intense laser light in a quantum plasma including the electron spin-1/2 effect. The relativistic effects due to the high-intensity laser light lead, in general, to a downshift of the laser frequency, similar to a classical plasma where the relativistic mass increase leads to self-induced transparency of laser light and other associated effects. The electron spin-1/2 effects lead to a frequency upshift or downshift of the electromagnetic (EM) wave, depending on the spin state of the plasma and the polarization of the EM wave. For laboratory solid density plasmas, the spin-1/2 effects on the propagation of light are small, but they may be significant in superdense plasma in the core of white dwarf stars. We also discuss extensions of the model to include kinetic effects of a distribution of the electrons on the nonlinear propagation of EM waves in a quantum plasma.

In finite-size scaling analyses of Monte Carlo simulations of second-order phase transitions one often needs an extended temperature range around the critical point. By combining the parallel-tempering algorithm with cluster updates and an adaptive routine to find the temperature window of interest, we introduce a flexible and powerful method for systematic investigations of critical phenomena. As a result, we gain one to two orders of magnitude in the performance for two- and three-dimensional Ising models in comparison with the recently proposed Wang-Landau recursion for cluster algorithms based on the multibondic algorithm, which is already a great improvement over the standard multicanonical variant.

A theory for large amplitude compressional electromagnetic solitary pulses in a magnetized electron-positron ($e$-$p$) plasma is presented. The pulses, which propagate perpendicular to the external magnetic field, are associated with the compression of the plasma density and the wave magnetic field. Here the solitary wave magnetic field pressure provides the restoring force, while the inertia comes from the equal mass electrons and positrons. The solitary pulses are formed due to a balance between the compressional wave dispersion arising from the curl of the inertial forces in Faraday's law and the nonlinearities associated with the divergence of the electron and positron fluxes, the nonlinear Lorentz forces, the advection of the $e$-$p$ fluids, and the nonlinear plasma current densities. The compressional solitary pulses can exist in a well-defined speed range above the Alfvén speed. They can be associated with localized electromagnetic field excitations in magnetized laboratory and space plasmas composed of electrons and positrons.

We present a network model in which words over a specific alphabet, called structures, are associated to each node and undirected edges are added depending on some distance measure between different structures. This model shifts the underlying principle of network generation from a purely mathematical one to an information-based one. It is shown how this model differs from the Barábasi-Albert and duplication models and how it can generate networks with topological features similar to biological networks: power law degree distribution, low average path length, clustering coefficient independent from the network size, etc. Two biological networks: S. cerevisiae gene network and E. coli protein-protein interaction network, are replicated using this model.

We study the site percolation under Achlioptas process with a product rule in a two-dimensional square lattice. From the measurement of the cluster size distribution $P_s$, we find that $P_s$ has a very robust power-law regime followed by a stable hump near the transition threshold. Based on the careful analysis on the $P_s$ distribution, we show that the transition should be discontinuous. The existence of the hysteresis loop in order parameter also verifies that the transition is discontinuous in two dimensions. Moreover, we also show that the transition nature from the product rule is not the same as that from a sum rule in two dimensions.

Many random transport phenomena, such as radiation propagation, chemical-biological species migration, or electron motion, can be described in terms of particles performing exponential flights. For such processes, we sketch a general approach (based on the Feynman-Kac formalism) that is amenable to explicit expressions for the moments of the number of collisions and the residence time that the walker spends in a given volume as a function of the particle equilibrium distribution. We then illustrate the proposed method in the case of the so-called rod problem (a one-dimensional system), and discuss the relevance of the obtained results in the context of Monte Carlo estimators.

Much recent progress has been made in the study of nematic solids, both glassy and elastomeric, particularly in the realm of stress-free, defect-driven deformation in thin sheets of material. In this paper we consider a subset of texture domains in nematic glasses that are simple to synthesize, and explore the ways that these simple domains may be compatibly combined to yield analogs of the traditional smooth disclination defect textures seen in standard liquid crystals. We calculate the deformation properties of these constructed textures, and show that, subject to the compatibility constraints of the construction, these textures may be further combined to achieve shape blueprinting of three-dimensional structures from flat sheets.

The association between oppositely charged branched polyethylenimine (BPEI) and polymethacrylic acid (PMA) in the dilute regime is investigated using turbidimetric titration and electrophoretic mobility measurements. The complexation is controlled by tuning continuously the pH-sensitive charge of the polyacid in acidic solution. The formation of soluble and stable positively charged complexes is a cooperative process characterized by the existence of two regimes of weak and strong complexation. In the regime of weak complexation, a long PMA chain overcharged by several BPEI molecules forms a binary complex. As the charge of the polyacid increases, these binary complexes condense at a well defined charge ratio of the mixture to form large positively charged aggregates. The overcharging and the existence of two regimes of complexation are analyzed in the light of recent theories. The structure of the polyelectrolytes is investigated at higher polymer concentration by small angle neutron scattering. Binary complexes of finite size present an open structure where the polyacid chains connecting a small number of BPEI molecules have shrunk slightly. In the condensed complexes, BPEI molecules, wrapped by polyacid chains, form networks of stretched necklaces.

A rigorous solution for the spectrum of a quasioptical cylindrical cavity resonator with a randomly rough side boundary has been obtained. To accomplish this task, we have developed a method for the separation of variables in a wave equation, which enables one, in principle, to rigorously examine any limiting case—from negligibly weak to arbitrarily strong disorder at the resonator boundary. It is shown that the effect of disorder-induced scattering can be properly described in terms of two geometric potentials, specifically, the “amplitude” and the “gradient” potentials, which appear in wave equations in the course of conformal smoothing of the resonator boundaries. The scattering resulting from the gradient potential appears to be dominant, and its impact on the whole spectrum is governed by the unique sharpness parameter $\Xi$, the mean tangent of the asperity slope. As opposed to the resonator with bulk disorder, the distribution of nearest-neighbor spacings (NNS) in the rough-resonator spectrum acquires Wigner-like features only when the governing wave operator loses its unitarity, i.e., with the availability in the system of either openness or dissipation channels. It is shown that the reason for this is that the spectral line broadening related to the oscillatory mode scattering due to random inhomogeneities is proportional to the dissipation rate. Our numeric experiments suggest that in the absence of dissipation loss the randomly rough resonator spectrum is always regular, whatever the degree of roughness. Yet, the spectrum structure is quite different in the domains of small and large values of the parameter $\Xi$. For the dissipation-free resonator, the NNS distribution changes its form with growing the asperity sharpness from Poissonian-like distribution in the limit of $\Xi \ll 1$ to the bell-shaped distribution in the domain where $\Xi \gg 1$.

We analyze theoretically a high-speed drainage of liquid films squeezed between a hydrophilic sphere and a textured superhydrophobic plane that contains trapped gas bubbles. A superhydrophobic wall is characterized by parameters $L$ (texture characteristic length), $b_1$ and $b_2$ (local slip lengths at solid and gas areas), and ${\phi }_1$ and ${\phi }_2$ (fractions of solid and gas areas). Hydrodynamic properties of the plane are fully expressed in terms of the effective slip-length tensor with eigenvalues that depend on texture parameters and $H$ (local separation). The effect of effective slip is predicted to decrease the force as compared with what is expected for two hydrophilic surfaces and described by the Taylor equation. The presence of additional length scales, $L$, $b_1$, and $b_2$, implies that a film drainage can be much richer than in the case of a sphere moving toward a hydrophilic plane. For a large (compared to $L$) gap the reduction of the force is small, and for all textures the force is similar to expected when a sphere is moving toward a smooth hydrophilic plane that is shifted down from the superhydrophobic wall. The value of this shift is equal to the average of the eigenvalues of the slip-length tensor. By analyzing striped superhydrophobic surfaces, we then compute the correction to the Taylor equation for an arbitrary gap. We show that at a thinner gap the force reduction becomes more pronounced, and that it depends strongly on the fraction of the gas area and local slip lengths. For small separations we derive an exact equation, which relates a correction for effective slip to texture parameters. Our analysis provides a framework for interpreting recent force measurements in the presence of a superhydrophobic surface.

We investigate next-nearest-neighbor correlations of the contact number in simulations of polydisperse, frictionless packings in two dimensions. We find that disks with few contacting neighbors are predominantly in contact with disks that have many neighbors and vice versa at all packing fractions. This counterintuitive result can be explained by drawing a direct analogy to the Aboav-Weaire law in cellular structures. We find an empirical one parameter relation similar to the Aboav-Weaire law that satisfies an exact sum rule constraint. Surprisingly, there are no correlations in the radii between neighboring particles, despite correlations between contact number and radius.

Atomic force microscopy (AFM) of cadmium stearate (CdSt) and cobalt stearate (CoSt) Langmuir-Blodgett films show differences in their in-plane morphologies. CdSt films, with a huge number of in-plane “pinhole” defects, follow self-affine behavior, whereas CoSt films, which are almost void of such in-plane defects, show deviation from self-affinity especially at small length scales, suggesting liquidlike behavior, imparting flexibility to the system, in plane. Phase images of CoSt obtained from tapping mode AFM show gentle undulations or hemispherelike features in contrast to its smooth topography, unlike the CdSt system where both height and phase images show self-affine domains. Near edge x-ray absorption fine structure spectroscopy indicates no preferred in-plane orientation of the head group in CoSt films. The undulating features in CoSt is explained by invoking a radially symmetric orientational distribution in the tilt of adjacent hydrocarbon tails, causing a small in-plane density variation which shows up in the phase image. These orientational disorders in adjacent tails probably allow “filling up” of in-plane defects thereby giving rise to its excellent in-plane coverage and hence a “liquidlike” behavior in CoSt. Brewster angle microscopy shows that parent Langmuir monolayers of stearic acid in the presence of Cd and Co ions in the aqueous subphase behave as two-dimensional “solids” and “liquids,” respectively, suggesting the phenomena to be inherent in the amphiphiles and probably independent of their organization as monolayers and multilayers.

The viscoelastic properties of a binary mixture of a mesogenic side-chain block copolymer in a low molecular weight nematic liquid crystal are studied for mass concentrations ranging from the diluted regime up to a liquid crystalline gel state at about 3%. In the gel state, the system does not flow, exhibits a polydomain structure on a microscopic level, and strongly scatters light. Below the gelation point, the system is homogeneous and behaves like a usual nematic, so the continuum theory of liquid crystals can be applied for interpreting the experimental data. Using the dynamic Fréedericksz transition technique, the dependence of the splay elastic constant and the rotational viscosity on the polymer concentration have been obtained. Comparing the dynamic behavior of block copolymer solutions with the respective homopolymer solutions reveals that, above a mass concentration of 1%, self-assembling of the block copolymer chain segments in clusters occurred, resulting in a gel state at higher concentrations. The effective cluster size is estimated as a function of the concentration, and a scaling-law behavior near the sol-gel transition is confirmed. This technique may serve as an alternative method for determining the gelation point.

Noise-induced excitability is a prevalent feature in many nonlinear dynamical systems. The optically injected semiconductor laser is one of the simplest such systems and is readily amenable to both experimental and theoretical analysis. We show that the dimensionality of this system may be tuned experimentally and that this has a strong signature on the interspike statistics. The phase of the slave laser is resolved experimentally in the frame of the master laser, allowing an examination of the dynamics at extremely low injection strengths where intensity measurements alone cannot determine the dynamics fully. Generic phase equations are found for the different dimensional scenarios. When the dimensionality is greater than 1, we show that a precursor of a homoclinic bifurcation generates a noise-induced frequency and that the homoclinic bifurcation admits a bistability in the system.

Core-annular flow is common in nature, representing, for example, how streams of oil, surrounded by water, move in petroleum reservoirs. Oil, typically a nonwetting fluid, tends to occupy the middle (core) part of a channel, while water forms a surrounding wall-wetting film. What is the thickness of the wetting film? A classic theory has been in existence for nearly 50 years offering a solution, although in a controversial manner, for moving gas bubbles. On the other hand, an acceptable, experimentally verified theory for a body of one liquid flowing in another has not been available. Here we develop a hydrodynamic, testable theory providing an explicit relationship between the thickness of the wetting film and fluid properties for a blob of one fluid moving in another, with neither phase being gas. In its relationship to the capillary number Ca, the thickness of the film is predicted to be proportional to Ca${}^2$ at lower Ca and to level off at a constant value of ∼20% the channel radius at higher Ca. The thickness of the film is deduced to be approximately unaffected by the viscosity ratio of the fluids. We have conducted our own laboratory experiments and compiled experimental data from other studies, all of which are mutually consistent and confirm the salient features of the theory. At the same time, the classic law, originally deduced for films surrounding moving gas bubbles but often believed to hold for liquids as well, fails to explain the observations.

A spatially randomized fractal interpolation algorithm to construct three-dimensional synthetic turbulence from original coarse field is reported. As in the one-dimensional case by Ding et al.(Phys. Rev. E 82, 036311, 2010), during the fractal interpolation, positions mapping between large and small scale cubes are chosen randomly, and the stretching factors are drawn from a log-Poisson random multiplicative process. A linear combination function defined as the base part in fractal interpolation and a theoretical energy spectrum model for fully developed turbulence are introduced into the procedure. Statistical analysis shows that the synthetic field displays some properties very close to the direct numeric simulated field, such as probability distributions of velocity, velocity gradient, velocity increment, and the anomalous scaling behavior of the longitude velocity structure functions, which follows the SL94 model precisely. After a short time using direct numeric simulation with the synthetic field as initial data, the typical local dynamical structures described by the teardrop shape of the Q-R plane for empirical turbulence can be reproduced.

A theory for the dynamic permeability in deformable porous media is developed. The analysis is based on the momentum flux transfer from the slow compressional into the slow shear wave (a proxy for the viscous wave in a Newtonian fluid) in the presence of random pore-scale heterogeneities. A first-order statistical smoothing approximation is used to infer a dynamic permeability in the form of an integral over the covariance function modulated by the slow shear wave. In a smooth pore-throat limit the results reproduce the model proposed by Johnson et al. [J. Fluid Mech. 176, 379 (1987)].

The nonlinear propagation of Gardner solitons (GSs) in a nonplanar (cylindrical and spherical) four-component dusty plasma (composed of inertial positively and negatively dust, Boltzmann electrons, and ions) is studied by the reductive perturbation method. The modified Gardner equation is derived and numerically solved. It has been found that the basic characteristics of the dust-acoustic (DA) GSs, which are shown to exist for $\mu$ around its critical value ${\mu }_c$ [where $\mu =Z_{dp}{m}_{dn}/Z_{dn}{m}_{dp}$, $Z_{dn}$ $\left(Z_{dp}\right)$ is the number of electrons (protons) residing on a negative (positive) dust, $m_{dp}$ $\left(m_{dn}\right)$ is the mass of the positive (negative) dust, ${\mu }_c$ is the value of $\mu$ corresponding to the vanishing of the nonlinear coefficient of the Korteweg–de Vries (KdV) equation, e.g., ${\mu }_c\simeq 0.174$ for ${\mu }_e=n_{e0}/Z_{dn}{n}_{dn0}=0.2$, ${\mu }_i=n_{i0}/Z_{dn}{n}_{dn0}=0.4$, and $\sigma =T_i/T_e=0.1$, $n_{e0}$, $n_{i0}$, and $n_{dn0}$ are, respectively, electron, ion, and dust number densities, and $T_i$ ($T_e$) is the ion (electron) temperature], are different from those of the KdV solitons, which do not exist for $\mu$ around ${\mu }_c$. It has been also found that the propagation characteristics of nonplanar DA GSs significantly differ from those of planar ones.

We study the localization of energy in a nonlinear coupled system, exhibiting so-called breather modes, using quantized Hamilton dynamics (QHD). Already at the lowest order, which is only twice as complex as classical mechanics, this simple semiclassical method incorporates quantum-mechanical effects. The transition between the localized and delocalized regimes is instantaneous in classical mechanics, while it is gradual due to tunneling in both quantum mechanics and QHD. In contrast to classical mechanics, which predicts an abrupt appearance of breathers, quantum mechanics and QHD show an alternation of localized and delocalized behavior in the transient region. QHD includes zero-point energy that is reflected in a shifted energy asymptote for the localized states, providing another improvement on the classical perspective. By detailed analysis of the distribution and transfer of energy within classical mechanics, QHD, and quantum dynamics, we conclude that QHD is an efficient approach that accounts for moderate quantum effects and can be used to identify quantum breathers in large nonlinear systems.