Standard thin-double-layer modeling of electro-osmotic flows about metal objects typically predicts an induced zeta-potential distribution whose characteristic magnitude varies linearly with the applied voltage. At moderately large zeta potential, comparable with several thermal voltages, surface conduction enters the dominant electrokinetic transport, throttling that linear scaling. We derive here a macroscale model for induced-charge electro-osmosis accounting for that mechanism. Unlike classical analyses of surface conduction about dielectric surfaces, the present nonlinear problem cannot be linearized about a uniform-zeta-potential reference state. With the transition to moderately large zeta potentials taking place nonuniformly, the Dukhin number, representing the magnitude of surface conduction, is reinterpreted as a local dimensionless group, varying along the boundary. Debye-scale analysis provides effective boundary conditions about two types of generic boundary points, corresponding to small and moderate Dukhin numbers. The boundary decomposition into the respective asymptotic domains is unknown in advance and must be determined throughout the solution of the macroscale problem, itself hinging upon the proper formulation of effective boundary conditions. This conceptual obstacle is surmounted via introduction of a uniform approximation to these conditions.

We develop the method proposed by Chernyshuk and Lev [Phys. Rev. E 81, 041701 (2010)] for theoretical investigation of elastic interactions between colloidal particles of arbitrary shape and chirality (polar as well as azimuthal anchoring) in the confined nematic liquid crystal (NLC). General expressions for six different types of multipole elastic interactions are obtained in the confined NLC: monopole-monopole (Coulomb type), monopole-dipole, monopole-quadrupole, dipole-dipole, dipole-quadrupole, and quadrupole-quadrupole interactions. The obtained formulas remain valid in the presence of the external electric or magnetic fields. The exact equations are found for all multipole coefficients for the weak anchoring case. For the strong anchoring coupling, the connection between the symmetry of the shape or director and multipole coefficients is obtained, which enables us to predict which multipole coefficients vanish and which remain nonzero. The particles with azimuthal helicoid anchoring are considered as an example. Dipole-dipole interactions between helicoid cylinders and cones are found in the confined NLC. In addition, the banana-shaped particles in homeotropic and planar nematic cells are considered. It is found that the dipole-dipole interaction between banana-shaped particles differs greatly from the dipole-dipole interaction between the axially symmetrical particles in the nematic cell. There is a crossover from attraction to repulsion between banana particles along some directions in nematic cells. It is shown that monopoles do not “feel” the type of nematic cell: monopole-monopole interaction turns out to be the same in homeotropic and planar nematic cells and converges to the Coulomb law as thickness increases, $L\to \infty$.

We generate percolating fullerene-polymer bulk heterostructures that are consistent with the experimental characterization of a nanostructure, in particular neutron reflectometry and small-angle neutron scattering data from as-cast and annealed poly(3-hexylthiophene) (P3HT) and [6,6]-phenyl C61-butyric acid methyl ester systems. Transport simulations correlate changes in exciton dissociation efficiency and charge collection efficiency with morphological features including characteristic domain size, fullerene concentration profile, degree of fullerene sequestration, and degree of P3HT crystallization.

The dielectric properties of brain tissue are important for understanding how neural activity is related to local field potentials and electroencephalograms. It is known that the permittivity of brain tissue exhibits strong frequency dependence (dispersion) and that the permittivity is very large in the low-frequency region. However, little is known with regard to the cause of the large permittivity in the low-frequency region. Here, we postulate that the dielectric properties of brain tissue can be partially accounted for by assuming that neurites are of sufficient length to be “electrically long.” To test this idea, we consider a model in which a neurite is treated as a long, narrow body, and it is subjected to a stimulus created by electrodes situated in the region external to it. With regard to this electric stimulus, the neurite can be treated as a passive cable. Assuming adequate symmetry so that the tissue packed with multiple cables is equivalent to an isolated system consisting of a single cable and a surrounding extracellular resistive medium, we analytically calculate the extracellular potential of the tissue in response to such an externally created alternating-current electric field using a Green's function that we obtained previously. Our results show that brain tissue modeled by such a cable existing within a purely resistive extracellular medium exhibits a large effective permittivity in the low-frequency region. Moreover, we obtain results suggesting that an extremely large low-frequency permittivity can coexist with weak low-pass filter characteristics in brain tissue.

We study the effects of the anharmonic strand-separation dynamics of double-stranded DNA on the infrared spectra of the intramolecular base-pairing hydrogen bonds. Using the extended Peyrard-Bishop-Dauxois model for the DNA breathing dynamics coupled with the Lippincott-Schroeder potential for $\mathrm{N}-\mathrm{H}$$\cdots$N and $\mathrm{N}-\mathrm{H}$$\cdots$O hydrogen bonding, we identify a high-frequency ($\sim$96 THz) feature in the infrared spectra. We show that this sharp peak arises as a result of the anharmonic base-pair breathing dynamics of DNA. In addition, we study the effects of friction on the infrared spectra. For higher temperatures ($\sim$300 K), where the anharmonicity of DNA dynamics is pronounced, the high-frequency peak is always present irrespective of the friction strength.

Monte Carlo computer simulation is employed to determine the local, wave-number-dependent, high-frequency elastic properties of a Lennard-Jones fluid that is confined between two walls. In particular, the elastic constants are calculated from coarse-grained stress correlation functions and then related to the local fluid structure via planar radial distribution functions. We find that local fluid properties correlate with the inhomogeneous fluid density and the strength of the wall-fluid interaction. Finally, we discuss the utility of this analysis in the interpretation of experiments involving the characterization of confined fluids.

Within the framework of the Lifshitz-Slyozov-Wagner theory of Ostwald ripening, the amount of volume of the second (solid) phase in a liquid solution that is newly formed by recrystallization is investigated. It is shown that in the late stage, the portion of the newly generated volume formed within an interval from time $t_0$ to $t$ is a certain function of $t/t_0$ and an explicit expression of this volume is given. To achieve this, we introduce the notion of the return radius $r(t,t_0)$, which is the unique radius of a particle at time $t_0$ such that this particle has—after growing and shrinking—the same radius at time $t$. We derive a formula for the return radius, which later on is used to obtain the newly formed volume. Moreover, formulas for the growth rate of the return radius and the recrystallized material at time $t_0$ are derived.

We show that the long-established concept of a linewidth-enhancement factor $\alpha$ to describe carrier-induced refractive index changes in semiconductor lasers breaks down in quantum-dot (QD) lasers when describing complex dynamic scenarios, found, for example, under high-excitation or optical injection. By comparing laser simulations using a constant $\alpha$ factor with results from a more complex nonequilibrium model that separately treats gain and refractive index dynamics, we examine the conditions under which an approximation of the amplitude-phase coupling by an $\alpha$ factor becomes invalid. The investigations show that while a quasiequilibrium approach for conventional quantum well lasers is valid over a reasonable parameter range, allowing one to introduce an $\alpha$ factor as a constant parameter, the concept is in general not applicable to predict QD laser dynamics due to the different time scales of the involved scattering processes.

We study the wealth distribution of the Bouchaud-Mézard model on complex networks. It is known from numerical simulations that this distribution depends on the topology of the network; however, no one has succeeded in explaining it. Using “adiabatic” and “independent” assumptions along with the central-limit theorem, we derive equations that determine the probability distribution function. The results are compared to those of simulations for various networks. We find good agreement between our theory and the simulations, except for the case of Watts-Strogatz networks with a low rewiring rate due to the breakdown of independent assumption.

Finding efficient algorithms to explore large networks with the aim of recovering information about their structure is an open problem. Here, we investigate this challenge by proposing a model in which random walkers with previously assigned home nodes navigate through the network during a fixed amount of time. We consider that the exploration is successful if the walker gets the information gathered back home, otherwise no data are retrieved. Consequently, at each time step, the walkers, with some probability, have the choice to either go backward approaching their home or go farther away. We show that there is an optimal solution to this problem in terms of the average information retrieved and the degree of the home nodes and design an adaptive strategy based on the behavior of the random walker. Finally, we compare different strategies that emerge from the model in the context of network reconstruction. Our results could be useful for the discovery of unknown connections in large-scale networks.

Based on previous instability experiments of the double mode perturbed interface in initially nonuniform flows, we numerically investigate the effect of the nonuniformity of flows on the evolution of instability in a nonlinear regime after reshock by adopting two different nonuniform coefficients (${\delta }_1$ $=$ 0.6162 and ${\delta }_2$ $=$ 0.4961) in the Gaussian distribution of the initial nonuniform density. We obtain the evolution of the mixing zone width and vortex structure of the air-SF${}_6$ interface and compare the circulation discrepancies of the nonuniform and uniform flows before and after reshock. These results indicate that the nonuniformity of the initial flow has great effect on the evolution of instability in the linear regime and the weak nonlinear regime prior to reshock. However, the mixing layer has little dependence on the nonuniformity of the initial flow in the nonlinear regime after reshock; namely, the effect of the nonuniformity is reduced significantly as the instability enters the strongly nonlinear regime after reshock. Although the growth rate of the perturbations has a significant increase, the characteristics of the flow like the mixing width, vorticity, and circulation are close to those of a uniform flow.

The decay rate of isotropic and homogeneous turbulence is known to be affected by the large-scale spectrum of the initial perturbations, associated with at least two canonical self-preserving solutions of the von Kármán–Howarth equation: the so-called Batchelor and Saffman spectra. The effect of long-range correlations in the decay of anisotropic flows is less clear, and recently it has been proposed that the decay rate of rotating turbulence may be independent of the large-scale spectrum of the initial perturbations. We analyze numerical simulations of freely decaying rotating turbulence with initial energy spectra $\sim k^4$ (Batchelor turbulence) and $\sim k^2$ (Saffman turbulence) and show that, while a self-similar decay can not be identified for the total energy, the decay is indeed affected by long-range correlations. The decay of two- and three-dimensional modes follows distinct power laws in each case, which are consistent with predictions derived from the anisotropic von Kármán–Howarth equation, and with conservation of anisotropic integral quantities by the flow evolution.

An inextensible vesicle under shear flow experiences a tank-treading motion on its membrane if the viscosity contrast between the interior and exterior fluids is small. Above a critical threshold of viscosity contrast, the vesicle undergoes a tumbling bifurcation. In this paper, we extend our previous work [Kim and Lai, J. Comput. Phys. 229, 4840 (2010)] to the case of different viscosity and investigate the transition between the tank-treading and tumbling motions in detail. The present numerical results are in a good agreement with other numerical and theoretical studies qualitatively. In addition, we study the inertial effect on this transition and find that the inertial effect might inhibit the tumbling motion in favor of the tank-treading motion, which is observed recently in the literature. The critical viscosity contrast for the transition to the tumbling motion usually increases as the reduced area increases in the Stokes regime. However, we surprisingly observe that the critical viscosity contrast decreases as the reduced area increases to some point in the flow of slightly higher Reynolds number. Our numerical result also shows that the inertial effect has stronger inhibition to tumbling motion when the reduced area is small.

The present-day Universe is highly magnetized, even though the first magnetic seed fields were most probably extremely weak. To explain the growth of the magnetic field strength over many orders of magnitude, fast amplification processes need to operate. The most efficient mechanism known today is the small-scale dynamo, which converts turbulent kinetic energy into magnetic energy leading to an exponential growth of the magnetic field. The efficiency of the dynamo depends on the type of turbulence indicated by the slope of the turbulence spectrum $v\left(\ell \right)\propto {\ell }^{\vartheta }$, where $v\left(\ell \right)$ is the eddy velocity at a scale $\ell$. We explore turbulent spectra ranging from incompressible Kolmogorov turbulence with $\vartheta =1/3$ to highly compressible Burgers turbulence with $\vartheta =1/2$. In this work, we analyze the properties of the small-scale dynamo for low magnetic Prandtl numbers Pm, which denotes the ratio of the magnetic Reynolds number, Rm, to the hydrodynamical one, Re. We solve the Kazantsev equation, which describes the evolution of the small-scale magnetic field, using the WKB approximation. In the limit of low magnetic Prandtl numbers, the growth rate is proportional to ${\mathrm{Rm}}^{(1-\vartheta )/(1+\vartheta )}$. We furthermore discuss the critical magnetic Reynolds number ${\mathrm{Rm}}_{\mathrm{crit}}$, which is required for small-scale dynamo action. The value of ${\mathrm{Rm}}_{\mathrm{crit}}$ is roughly 100 for Kolmogorov turbulence and 2700 for Burgers. Furthermore, we discuss that ${\mathrm{Rm}}_{\mathrm{crit}}$ provides a stronger constraint in the limit of low Pm than it does for large Pm. We conclude that the small-scale dynamo can operate in the regime of low magnetic Prandtl numbers if the magnetic Reynolds number is large enough. Thus, the magnetic field amplification on small scales can take place in a broad range of physical environments and amplify week magnetic seed fields on short time scales.

By considering a general discrete nonlinear Schrödinger model with arbitrary values of nonlinearity power and disorder, the existence and stability of a discrete breather (DB) in a general nonlinear lattice are discussed. It is found that nonlinearity and disorder play important roles in determining the existence and stability of the DB. Nonlinearity (expressed by the interparticle interaction) and disorder can enhance the stability of the DB. Remarkably, we find that the DB is most stable when the nonlinearity power is equal to a critical value. The effects of nonlinearity, nonlinearity power, and disorder on the stability of the DB are strongly coupled.

Monte Carlo switching moves (“perturbations”) are defined between two or more classical Hamiltonians sharing a common ground-state energy. The ratio of the density of states (DOS) of one system to that of another is related to the ensemble averages of the microcanonical acceptance probabilities of switching between these Hamiltonians, analogously to the case of Bennett's acceptance ratio method for the canonical ensemble [C. H. Bennett, J. Comput. Phys. 22, 245 (1976)]. Thus, if the DOS of one of the systems is known, one obtains those of the others and, hence, the partition functions. As a simple test case, the vapor pressure of an anharmonic Einstein crystal is computed, using the harmonic Einstein crystal as the reference system in one dimension; an auxiliary calculation is also performed in three dimensions. As a further example of the algorithm, the energy dependence of the ratio of the DOS of the square-well and hard-sphere tetradecamers is determined, from which the temperature dependence of the constant-volume heat capacity of the square-well system is calculated and compared with canonical Metropolis Monte Carlo estimates. For these cases and reference systems, the perturbation calculations exhibit a higher degree of convergence per Monte Carlo cycle than Wang-Landau (WL) sampling, although for the one-dimensional oscillator the WL sampling is ultimately more efficient for long runs. Last, we calculate the vapor pressure of liquid gold using an empirical Sutton-Chen many-body potential and the ideal gas as the reference state. Although this proves the general applicability of the method, by its inherent perturbation approach the algorithm is suitable for those particular cases where the properties of a related system are well known.

An explicit local boundary condition is proposed for finite-domain simulations of the linear Schrödinger equation on an unbounded domain. Based on an exact boundary condition in terms of the Bessel functions, it takes a simple form with 16 neighboring grid points, and it involves no empirical parameter. While the computing load is rather low, the proposed boundary condition is effective in reflection suppression, comparable to the exact convolution treatments. An extension to nonlinear Schrödinger equations is also proposed. Numerical comparisons clearly demonstrate the effectiveness of this ALmost EXact (ALEX) boundary condition for both the linear and the cubic nonlinear Schrödinger equations.

Rheological measurements have been applied to study the tautomerization of the pharmaceutically active compound glibenclamide. The rate constant and activation energy of the imidic-acid-amide transformation have been successfully determined by monitoring the evolution of shear viscosity. The kinetic parameters from rheological measurements agree reasonably well with the data previously obtained from dielectric spectroscopy. The present Brief Report demonstrates that rheology can provide a fast and precise way to characterize the reaction kinetics of tautomerization.

We study multiple scattering of electromagnetic waves by an array of parallel gyrotropic circular rods and show that such an array can exhibit fairly unusual scattering properties and provide, under certain conditions, a giant enhancement of the scattered field. Among the scattering patterns of such an array at its resonant frequencies, the most interesting is the distribution of the total field in the form of a perfect self-similar structure of chessboard type. The scattering characteristics of the array are found to be essentially determined by the resonant properties of its gyrotropic elements and cannot be realized for arrays of nongyrotropic rods. It is expected that the results obtained can lead to a wide variety of practical applications.