A spherical drop of one liquid suspended in another is subjected to an instantaneous initial shear. We simulate the retraction of the drop to its spherical equilibrium and compare the results with recent experiments. In agreement with the experiments, we observe a two-step relaxation process.

It is shown that essentially nonlinear models for solids with complex internal structure may be studied using phenomenological and proper structural approaches. It is found that both approaches give rise to the same nonlinear equation for traveling longitudinal macrostrain waves. However, presence of the connection between macro- and microfields in the proper structural model prevents a realization of some important solutions. First, it is obtained that simultaneous existence of compression and tensile waves is impossible in contrast to the phenomenological approach. Then, it is found that correlation between macro- and internal strains gives rise to the crucial influence of the velocity of the macrostrain wave on the existence of either compression or tensile localized strain waves. Also, it is shown that similar profiles of the macrostrain solitary waves may be accompanied by distinct profiles of the microstrain waves. Finally, the dispersion curves for the waves belong to the different branches. This is important for internal structural deviations caused by the dynamical loading due to the localized macrostrain wave propagation and demonstrates a need in the development of the proper structural approaches relative to the phenomenological ones.

A clarification is due about the paper by Hasegawa and Nemoto [Phys. Rev. E 75, 026105 (2007)], where a clear distinction between the Zeta and Zipf power-law distributions offers an alternative interpretation of the behavior of susceptibility of the model at hand. More precisely, their conclusion that susceptibility diverges for this scale-free network model with power-law distribution $P\left(k\right)\sim k^{-\gamma }$ for the coordination number $k$ for all temperatures, for values of exponent $\gamma \le 4$ (as observed in real networks), stems from the (infinite domain) Zeta distribution power-law assumption for the coordination number distribution. On the other hand, by assuming the Zipf power-law distribution (with an arbitrary finite upper bound on the coordination number), the susceptibility is well behaved, diverges in the interval $0\le T<T_S$, and is finite for $T\ge T_S$, where $T_S$ depends on $P\left(k\right)$.

The self-organized criticality in Ehrenfest’s historical dog-flea model is analyzed by simulating the underlying stochastic process. The fluctuations around the thermal equilibrium in the model are treated as avalanches. We show that the distributions for the fluctuation length differences at subsequent time steps are in the shape of a $q$-Gaussian (the distribution which is obtained naturally in the context of nonextensive statistical mechanics) if one avoids the finite-size effects by increasing the system size. We provide clear numerical evidence that the relation between the exponent $\tau$ of avalanche size distribution obtained by maximum-likelihood estimation and the $q$ value of appropriate $q$-Gaussian obeys the analytical result recently introduced by Caruso et al. [Phys. Rev. E 75, 055101(R) (2007)]. This allows us to determine the value of $q$-parameter a priori from one of the well-known exponents of such dynamical systems.

The $q$-state clock gauge glass model is studied to see the effect of discreteness on the Kosterlitz-Thouless (KT) transition and the ferromagnetic (FM) critical phenomenon in random systems. The nonequilibrium relaxation analysis is applied. In two dimensions, the successive transitions of paramagnetic (PM), KT, and FM phases are investigated along the Nishimori line for $q=6$, 8, 10, 12, 14, 16, and 1024 (recognized as $\infty$) cases. For the upper critical temperature, it is found that the transition temperature is almost the same as in the continuous case for all $q$ values. The lower transition temperature is found to be proportional to $1/q^2$. In three dimensions, the critical behavior of the PM-FM transition is studied along the Nishimori line for $q=6$, 8, 16, and 1024 cases. It is found that the spin discreteness is irrelevant, and the transition belongs to the same universality class as in the (continuous) $XY$ case.

Dense hard-particle packings are intimately related to the structure of low-temperature phases of matter and are useful models of heterogeneous materials and granular media. Most studies of the densest packings in three dimensions have considered spherical shapes, and it is only more recently that nonspherical shapes (e.g., ellipsoids) have been investigated. Superballs (whose shapes are defined by ${\left|x_1\right|}^{2p}+{\left|x_2\right|}^{2p}+{\left|x_3\right|}^{2p}\le 1$) provide a versatile family of convex particles $\left(p\ge 0.5\right)$ with both cubic-like and octahedral-like shapes as well as concave particles $\left(0<p<0.5\right)$ with octahedral-like shapes. In this paper, we provide analytical constructions for the densest known superball packings for all convex and concave cases. The candidate maximally dense packings are certain families of Bravais lattice packings (in which each particle has 12 contacting neighbors) possessing the global symmetries that are consistent with certain symmetries of a superball. We also provide strong evidence that our packings for convex superballs $\left(p\ge 0.5\right)$ are most likely the optimal ones. The maximal packing density as a function of $p$ is nonanalytic at the sphere point $\left(p=1\right)$ and increases dramatically as $p$ moves away from unity. Two more nontrivial nonanalytic behaviors occur at $p_c^{\ast }=1.1509\dots$ and $p_o^{\ast }=\text{ln}3/\text{ln}4=0.7924\dots$ for “cubic” and “octahedral” superballs, respectively, where different Bravais lattice packings possess the same densities. The packing characteristics determined by the broken rotational symmetry of superballs are similar to but richer than their two-dimensional “superdisk” counterparts [Y. Jiao et al., Phys. Rev. Lett. 100, 245504 (2008)] and are distinctly different from that of ellipsoid packings. Our candidate optimal superball packings provide a starting point to quantify the equilibrium phase behavior of superball systems, which should deepen our understanding of the statistical thermodynamics of nonspherical-particle systems.

The structural properties of a binary colloidal quasi-one-dimensional system confined in a narrow channel are investigated through modified Monte Carlo simulations. Two species of particles with different magnetic moment interact through a repulsive dipole-dipole force are confined in a quasi-one-dimensional channel. The impact of three decisive parameters (the density of particles, the magnetic-moment ratio, and the fraction between the two species) on the transition from disordered phase to crystal-like phases and the transitions among the different mixed phases are summarized in a phase diagram.

Although a lot of experimental and model results for roughness evolution exhibit anomalous scaling, the origins of such a behavior remain still unclear. In this paper, the possible contribution of material inhomogeneities to the appearance of anomalous scaling behavior in kinetic roughening is investigated by a simple modeling of roughness evolution in the etching of porous and composite films. It is found that the roughness evolution during the etching of both kinds of inhomogeneous films displays anomalous scaling behavior with peculiar features (no expansion of correlations vs time and square-root time increase in surface width roughness) defining a new universality class. Furthermore, the insertion of correlations between film pores or fillers along etching direction leads to roughness instability, i.e., linear increase in surface width roughness. The latter observation may be exploited for the detection of correlations between pores or fillers using roughness evolution as a diagnostic tool.

We show that the simplest stochastic epidemiological models with spatial correlations exhibit two types of oscillatory behavior in the endemic phase. In a large parameter range, the oscillations are due to resonant amplification of stochastic fluctuations, a general mechanism first reported for predator-prey dynamics. In a narrow range of parameters that includes many infectious diseases which confer long lasting immunity the oscillations persist for infinite populations. This effect is apparent in simulations of the stochastic process in systems of variable size and can be understood from the phase diagram of the deterministic pair approximation equations. The two mechanisms combined play a central role in explaining the ubiquity of oscillatory behavior in real data and in simulation results of epidemic and other related models.

The influence of helicity on the stability of the Kolmogorov scaling regime in fully developed turbulence in space dimension $d=3$ based on the stochastic Navier-Stokes equation with the self-similar Gaussian random stirring force $\delta$-correlated in time and with the correlator proportional to $k^{4-d-2\epsilon }$ is investigated by the field-theoretic renormalization-group technique within two-loop approximation. The two-loop renormalization constant, the $\beta$ function, and the coordinate of the fixed point are found as functions of the helicity parameter. It is shown that the presence of helicity in the system does not destroy the stability of the Kolmogorov scaling regime.

We compute statistical properties of the lowest-order multipole coefficients of the magnetic field generated by a dynamo of arbitrary shape. To this end we expand the field in a complete biorthogonal set of base functions, viz. $\mathit{B}={\sum }_k{a}^k\left(t\right){\mathit{b}}^k\left(\mathit{r}\right)$. The properties of these biorthogonal function sets are treated in detail. We consider a linear problem and the statistical properties of the fluid flow are supposed to be given. The turbulent convection may have an arbitrary distribution of spatial scales. The time evolution of the expansion coefficients $a^k$ is governed by a stochastic differential equation from which we infer their averages $⟨a^k⟩$, autocorrelation functions $⟨a^k\left(t\right)a^{k\ast }\left(t+\tau \right)⟩$, and an equation for the cross correlations $⟨a^k{a}^{\ell \ast }⟩$. The eigenfunctions of the dynamo equation (with eigenvalues ${\lambda }_k$) turn out to be a preferred set in terms of which our results assume their simplest form. The magnetic field of the dynamo is shown to consist of transiently excited eigenmodes whose frequency and coherence time is given by $\mathfrak{I}{\lambda }_k$ and $-1/\mathfrak{R}{\lambda }_k$, respectively. The relative rms excitation level of the eigenmodes, and hence the distribution of magnetic energy over spatial scales, is determined by linear theory. An expression is derived for $⟨{\left|a^k\right|}^2⟩/⟨{\left|a^0\right|}^2⟩$ in case the fundamental mode ${\mathit{b}}^0$ has a dominant amplitude, and we outline how this expression may be evaluated. It is estimated that $⟨{\left|a^k\right|}^2⟩/⟨{\left|a^0\right|}^2⟩\sim 1/N$, where $N$ is the number of convective cells in the dynamo. We show that the old problem of a short correlation time (or first-order smoothing approximation) has been partially eliminated. Finally we prove that for a simple statistically steady dynamo with finite resistivity all eigenvalues obey $\mathfrak{R}{\lambda }_k<0$.

We study the transport and deposition dynamics of colloids in saturated porous media under unfavorable filtering conditions. As an alternative to traditional convection-diffusion or more detailed numerical models, we consider a mean-field description in which the attachment and detachment processes are characterized by an entire spectrum of rate constants, ranging from shallow traps which mostly account for hydrodynamic dispersivity, all the way to the permanent traps associated with physical straining. The model has an analytical solution which allows analysis of its properties including the long-time asymptotic behavior and the profile of the deposition curves. Furthermore, the model gives rise to a filtering front whose structure, stability, and propagation velocity are examined. Based on these results, we propose an experimental protocol to determine the parameters of the model.

The effect of the Reynolds number on the wavelet-decomposed turbulent structures in a self-preserving plane wake has been investigated for ${\text{Re}}_{\theta }$ (based on the free-stream velocity and momentum thickness, $\theta$, of the wake) $=1350$ and 4600. Measurements were made at $x/\theta$ ($x$ is the streamwise distance downstream of the cylinder) $=580$ for the circular cylinder using two orthogonal arrays of 16 X wires, eight in the $\left(x,y\right)$ plane, and eight in the $\left(x,z\right)$ plane. A wavelet multiresolution technique is used to analyze the measured hot-wire data. This technique decomposes turbulence structures into a number of components based on their central frequencies, which are linked with the turbulence scales. Sectional streamlines and vorticity contours at the same central frequency, i.e., the comparable scales of turbulent structures, are examined and compared between the two Reynolds numbers. Discernible differences are observed in the turbulent structures of relatively large to intermediate scales. The differences are further quantified in terms of contributions from the turbulent structures of different scales to the Reynolds stresses, vorticity variance, and probability density functions of the fluctuating velocities. The large-scale structure contributes most to the Reynolds stresses and this contribution drops for the higher ${\text{Re}}_{\theta }$.

Contractor renormalization (CORE) is a real-space renormalization-group method to derive effective Hamiltionians for microscopic models. The original CORE method is based on a real-space decomposition of the lattice into small blocks and the effective degrees of freedom on the lattice are tensor products of those on the small blocks. We present an extension of the CORE method that overcomes this restriction. Our generalization allows the application of CORE to derive arbitrary effective models whose Hilbert space is not just a tensor product of local degrees of freedom. The method is especially well suited to search for microscopic models to emulate low-energy exotic models and can guide the design of quantum devices.

We propose a practical realization of electromagnetic spherical cloaking by layered structure of homogeneous isotropic materials. By mimicking the classic anisotropic cloak by many alternating thin layers of isotropic dielectrics, the permittivity and permeability in each isotropic layer can be properly determined by effective medium theory in order to achieve invisibility. The model greatly facilitates modeling by Mie theory and realization by multilayer coating of dielectrics. Eigenmode analysis is also presented to provide insights of the discretization in multilayers.

For soft matter systems strongly driven by stationary flow, we discuss an extended fluctuation-dissipation theorem (FDT). Beyond the linear-response regime, the FDT for the stress acquires an additional contribution involving the observable that is conjugate to the strain rate with respect to the dissipation function. This extended FDT is evaluated both analytically for Rouse polymers and in numerical simulations for colloidal suspensions. More generally, our results suggest an extension of Onsager’s regression principle to nonequilibrium steady states.

We study the properties of the Barabási model of queuing [A.-L. Barabási, Nature (London) 435, 207 (2005); J. G. Oliveira and A.-L. Barabási, Nature (London) 437, 1251 (2005)] in the hypothesis that the number of tasks grows with time steadily. Our analytical approach is based on two ingredients. First we map exactly this model into an invasion percolation dynamics on a Cayley tree. Second we use the theory of biased random walks. In this way we obtain the following results: the stationary-state dynamics is a sequence of causally and geometrically connected bursts of execution activities with scale-invariant size distribution. We recover the correct waiting-time distribution $P_W\left(\tau \right)\sim {\tau }^{-3/2}$ at the stationary state (as observed in different realistic data). Finally we describe quantitatively the dynamics out of the stationary state quantifying the power-law slow approach to stationarity both in single dynamical realization and in average. These results can be generalized to the case of a stochastic increase in the queue length in time with limited fluctuations. As a limit case we recover the situation in which the queue length fluctuates around a constant average value.

The geometric percolation thresholds for circular, elliptical, square, and triangular plates in the three-dimensional space are determined precisely by Monte Carlo simulations. These geometries represent oblate particles in the limit of zero thickness. The normalized percolation points, which are estimated by extrapolating the data to zero radius, are ${\eta }_c=0.9614\pm 0.0005$, $0.8647\pm 0.0006$, and $0.7295\pm 0.0006$ for circles, squares, and equilateral triangles, respectively. These results show that the noncircular shapes and corner angles in the plate geometry tend to increase the interparticle connectivity and therefore reduce the percolation point. For elliptical plates, the percolation threshold is found to decrease moderately, when the aspect ratio $\epsilon$ is between 1 and 1.5, but decrease rapidly for $\epsilon$ greater than 1.5. For the binary dispersion of circular plates with two different radii, ${\eta }_c$ is consistently larger than that of equisized plates, with the maximum value located at around $r_1/r_2=0.5$.

We study numerically the autocatalytic irreversible reaction $A+B\to 2A$ on a one-dimensional lattice for the case of subdiffusive reactants performing symmetric continuous-time random walks with the power-law waiting time density function $\psi \left(t\right)\propto t^{-1-\alpha }$ with $0<\alpha <1$ in a large range of other relevant parameters. We show that the propagation failure previously found by the same authors [Phys. Rev. E 78, 011128 (2008)] essentially corresponds to a propagation of a front of a stable form at a velocity which decays with time.

The influence of random axially homogeneous surface roughness on spectral properties of dielectric resonators of circular disk form is studied both theoretically and experimentally. To solve the equations governing the dynamics of electromagnetic fields, the method of eigenmode separation is applied previously developed with reference to inhomogeneous systems subject to arbitrary external static potential. We prove theoretically that it is the gradient mechanism of wave-surface scattering that is highly responsible for nondissipative loss in the resonator. The influence of side-boundary inhomogeneities on the resonator spectrum is shown to be described in terms of effective renormalization of mode wave numbers jointly with azimuth indices in the characteristic equation. To study experimentally the effect of inhomogeneities on the resonator spectrum, the method of modeling in the millimeter wave range is applied. As a model object, we use a dielectric disk resonator (DDR) fitted with external inhomogeneities randomly arranged at its side boundary. Experimental results show good agreement with theoretical predictions as regards the predominance of the gradient scattering mechanism. It is shown theoretically and confirmed in the experiment that TM oscillations in the DDR are less affected by surface inhomogeneities than TE oscillations with the same azimuth indices. The DDR model chosen for our study as well as characteristic equations obtained thereupon enable one to calculate both the eigenfrequencies and the $Q$ factors of resonance spectral lines to fairly good accuracy. The results of calculations agree well with obtained experimental data.