Simulations of maximum drag reduction (MDR) in channel flow using constitutive equations for suspensions of noninteracting rods predict a few-fold larger turbulent kinetic energy than in experiments using rodlike polymers. These differences are attributed to the neglect of interactions between polymers in the simulations. Despite these inconsistencies the simulations correctly reproduce the essential features of MDR, with universal profiles of the mean flow and the shear stress budgets that do not depend on the polymer concentration.

Heat conduction in three two-dimensional (2D) momentum-conserving nonlinear lattices are numerically calculated via both nonequilibrium heat-bath and equilibrium Green-Kubo algorithms. It is expected by mainstream theories that heat conduction in such 2D lattices is divergent and the thermal conductivity $\kappa$ increases with lattice length $N$ logarithmically. Our simulations for the purely quartic lattice firmly confirm it. However, very robust finite-size effects are observed in the calculations for the other two lattices, which well explain some existing studies and imply the extreme difficulties in observing their true asymptotic behaviors with affordable computation resources.

We have investigated the linear response of shear stress to ac electric fields under shear flow in a nematic liquid crystal. The experimental results were compared with the theoretical results derived from the Ericksen-Leslie theory. Although close agreement was obtained at low shear rates, discrepancies were observed at high shear rates. By introducing a two-mode coupling model the experimental results were well reproduced for the entire range of shear rates, and nonconservative forces were found to play an important role in determining the fluctuation dynamics, which is a characteristic of nonequilibrium steady states.

Nonlinear saturation of a beta-induced Alfvén eigenmode, driven by slowing down energetic particles via transit resonance, is investigated by the nonlinear hybrid magnetohyrodynamic gyrokinetic code. Saturation is characterized by frequency chirping and symmetry breaking between co- and counter-passing particles, which can be understood as the evidence of resonance detuning. The scaling of the saturation amplitude with the growth rate is also demonstrated to be consistent with radial resonance detuning due to the radial nonuniformity and mode structure.

We study a reversal process in Stokes flows in the presence of weak diffusion in order to clarify the distinct effects that chaotic flows have on the loss of reversibility relative to nonchaotic flows. In all linear flows, including a representation of the baker's map, we show that the decay of reversibility presents universal properties. In nonlinear chaotic and nonchaotic flows, we show that this universality breaks down due to the distribution of strain rates. In the limit of infinitesimal diffusivity, we predict qualitatively distinct behavior in the chaotic case.

The analysis of dynamic dependencies in complex systems such as the brain helps to understand how emerging properties arise from interactions. Here we propose an information-theoretic framework to analyze the dynamic dependencies in multivariate time-evolving systems. This framework constitutes a fully multivariate extension and unification of previous approaches based on bivariate or conditional mutual information and Granger causality or transfer entropy. We define multi-information measures that allow us to study the global statistical structure of the system as a whole, the total dependence between subsystems, and the temporal statistical structure of each subsystem. We develop a stationary and a nonstationary formulation of the framework. We then examine different decompositions of these multi-information measures. The transfer entropy naturally appears as a term in some of these decompositions. This allows us to examine its properties not as an isolated measure of interdependence but in the context of the complete framework. More generally we use causal graphs to study the specificity and sensitivity of all the measures appearing in these decompositions to different sources of statistical dependence arising from the causal connections between the subsystems. We illustrate that there is no straightforward relation between the strength of specific connections and specific terms in the decompositions. Furthermore, causal and noncausal statistical dependencies are not separable. In particular, the transfer entropy can be nonmonotonic in dependence on the connectivity strength between subsystems and is also sensitive to internal changes of the subsystems, so it should not be interpreted as a measure of connectivity strength. Altogether, in comparison to an analysis based on single isolated measures of interdependence, this framework is more powerful to analyze emergent properties in multivariate systems and to characterize functionally relevant changes in the dynamics.

We examine changes in the dynamics of a semiconductor quantum-dot (QD) laser subject to optical feedback that correlate to changes in the QD laser band structure. By employing a microscopic model for the carrier-carrier scattering processes between the QDs and the carrier reservoir we are able to tune the carrier lifetimes in the QDs, e.g., by modifying the QD confinement energies or the pump current. By using numerical continuation methods as well as asymptotic theory we demonstrate that the feedback sensitivity crucially depends on these lifetimes through the damping of the turn-on oscillations, and small lifetimes on the order of this relaxation time scale lead to an increased feedback resistivity. Thus intelligent band structure engineering can lead to stable continuous wave operation of the laser over a large parameter range.

We propose a general framework to study the stability of the subspace spanned by $P$ consecutive eigenvectors of a generic symmetric matrix ${\mathbf{H}}_0$ when a small perturbation is added. This problem is relevant in various contexts, including quantum dissipation (${\mathbf{H}}_0$ is then the Hamiltonian) and financial risk control (in which case ${\mathbf{H}}_0$ is the assets' return covariance matrix). We argue that the problem can be formulated in terms of the singular values of an overlap matrix, which allows one to define an overlap distance. We specialize our results for the case of a Gaussian orthogonal ${\mathbf{H}}_0$, for which the full spectrum of singular values can be explicitly computed. We also consider the case when ${\mathbf{H}}_0$ is a covariance matrix and illustrate the usefulness of our results using financial data. The special case where the top eigenvalue is much larger than all the other ones can be investigated in full detail. In particular, the dynamics of the angle made by the top eigenvector and its true direction defines an interesting class of random processes.

It is common to determine the effective conductivity of heterogeneous media by assuming stationarity of the random local properties. This assumption is not obeyed in a boundary layer of a body of finite size. The effect of different types of boundaries is examined for a two-phase medium with spherical inclusions of given conductivity distributed randomly in a matrix of a different conductivity. Exact solutions are derived for the apparent conductivity and the boundary layer thickness. The interaction between the spheres and the boundaries is fully incorporated in the solutions using a spherical harmonics expansion and the method of images. As applications, the corrections for the effective conductivity are given for two cases of finite bodies: the Maxwell sphere and a cylinder of flow parallel to the axis.

Sexually reproducing populations with a small number of individuals may go extinct by stochastic fluctuations in sex determination, causing all their members to become male or female in a generation. In this work we calculate the time to extinction of isolated populations with fixed number $N$ of individuals that are updated according to the Moran birth and death process. At each time step, one individual is randomly selected and replaced by its offspring resulting from mating with another individual of the opposite sex; the offspring can be male or female with equal probability. A set of $N$ time steps is called a generation, the average time it takes for the entire population to be replaced. The number $k$ of females fluctuates in time, similarly to a random walk, and extinction, which is the only asymptotic possibility, occurs when $k=0$ or $k=N$. We show that it takes only one generation for an arbitrary initial distribution of males and females to approach the binomial distribution. This distribution, however, is unstable and the population eventually goes extinct in $2^N/N$ generations. We also discuss the robustness of these results against bias in the determination of the sex of the offspring, a characteristic promoted by infection by the bacteria Wolbachia in some arthropod species or by temperature in reptiles.

Anisotropy effects on the finite-size critical behavior of a two-dimensional Ising model on a general triangular lattice in an infinite-strip geometry with periodic, antiperiodic, and free boundary conditions (bc) in the finite direction are investigated. Exact results are obtained for the scaling functions of the finite-size contributions to the free energy density. With ${\xi }_{>}$ the largest and ${\xi }_{<}$ the smallest bulk correlation length at a given temperature near criticality, we find that the dependence of these functions on the ratio ${\xi }_{<}/{\xi }_{>}$ and on the angle parametrizing the orientation of the correlation volume is of geometric nature. Since the scaling functions are independent of the particular microscopic realization of the anisotropy within the two-dimensional Ising model, our results provide a limited verification of universality. We explain our observations by considering finite-size scaling of free energy densities of general weakly anisotropic models on a $d$-dimensional film (i.e., in an $L\times {\infty }^{d-1}$ geometry) with bc in the finite direction that are invariant under a shear transformation relating the anisotropic and isotropic cases. This allows us to relate free energy scaling functions in the presence of an anisotropy to those of the corresponding isotropic system. We interpret our results as a simple and transparent case of anisotropic universality, where, compared to the isotropic case, scaling functions depend additionally on the shape and orientation of the correlation volume. We conjecture that this universality extends to cases where the geometry and/or the bc are not invariant under the shear transformation and argue in favor of validity of two-scale factor universality for weakly anisotropic systems.

Brownian ratchets enable the use of thermal motion in performing useful work. They typically employ spatial asymmetry to rectify nondirected external forces that drive the system out of equilibrium (cf. running marbles on a shaking washboard). The major application foreseen for Brownian ratchets is high-selectivity fractionation of particle or molecule distributions. Here, we investigate the functioning of an important model system, the on/off ratchet for water-suspended particles, in which interdigitated finger electrodes can be switched on and off to create a time-dependent, spatially periodic but asymmetric potential. Surprisingly, we find that mainly dielectrophoretic rather than electrophoretic forces are responsible for the ratchet effect. This has major implications for the (a)symmetry of the ratchet potential and the settings needed for optimal performance. We demonstrate that by applying a potential offset the ratchet can be optimized such that its particle displacement efficiency reaches the theoretical upper limit corresponding to the electrode geometry and particle size. Efficient fractionation based on size selectivity is therefore not only possible for charged species, but also for uncharged ones, which greatly expands the applicability range of this type of Brownian ratchet.

A non-Markovian one-dimensional random walk model is studied with emphasis on the phase-diagram, showing all the diffusion regimes, along with the exactly determined critical lines. The model, known as the Alzheimer walk, is endowed with memory-controlled diffusion, responsible for the model's long-range correlations, and is characterized by a rich variety of diffusive regimes. The importance of this model is that superdiffusion arises due not to memory per se, but rather also due to loss of memory. The recently reported numerically and analytically estimated values for the Hurst exponent are hereby reviewed. We report the finding of two, previously overlooked, phases, namely, evanescent log-periodic diffusion and log-periodic diffusion with escape, both with Hurst exponent $H=1/2$. In the former, the log-periodicity gets damped, whereas in the latter the first moment diverges. These phases further enrich the already intricate phase diagram. The results are discussed in the context of phase transitions, aging phenomena, and symmetry breaking.

This paper presents a detailed comparative study of published order-parameter experimental data of nematic liquid crystals. Throughout a simple linear transformation, it is shown that three distinct nematic mesophases exhibit the same and unique universal behavior for all temperatures below the nematic-isotropic phase transition. This paper generalizes a previous one [M. Simões, D. S. Simeão, S. M. Domiciano, and A. de Campos, Phys. Lett. A 372, 5346 (2008)], in which only the nematic mesophase delimited by the crystalline phase at low temperature was studied. Here we have assembled order-parameter experimental data of 61 different compounds, forming a set with data of 96 experiments, aiming to show that the nematic universal behavior is independent of what is the actual phase or mesophase bordering the nematic phase at low temperatures; our results show that all experimental data of all nematic mesophases coalesce along a common line that extends over the entire range of mesophases.

We present an expression for the effective slip length of a nanoscale rough chemically heterogeneous surface. A heterogeneous surface may be regarded as having an effective slip length generated by extrapolating the uniform velocity profile found in the far field. We consider two-dimensional steady-state Stokes flow over a surface that has periodic roughness and an intrinsic slip length varying over the same period. Using weak convergence methods for partial differential equations, we derive an expression for the effective slip length in terms of the intrinsic slip length and contact area of the surface. The result predicts that roughness causes a significant reduction in effective slip and that slip effects are dominated by the minimum intrinsic slip length of the system.

We consider the effective surface motion of a particle that intermittently unbinds from a planar surface and performs bulk excursions. Based on a random-walk approach, we derive the diffusion equations for surface and bulk diffusion including the surface-bulk coupling. From these exact dynamic equations, we analytically obtain the propagator of the effective surface motion. This approach allows us to deduce a superdiffusive, Cauchy-type behavior on the surface, together with exact cutoffs limiting the Cauchy form. Moreover, we study the long-time dynamics for the surface motion.

We study heat conduction in one-, two-, and three-dimensional anharmonic lattices connected to stochastic Langevin heat baths. The interatomic potential of the lattices is double-well type, i.e., $V_{\mathrm{DW}}\left(x\right)=k_2{x}^2/2+k_4{x}^4/4$ with $k_2<0$ and $k_4>0$. We observe two different temperature regimes of transport: a high-temperature regime where asymptotic length dependence of nonequilibrium steady state heat current is similar to the well-known Fermi-Pasta-Ulam lattices with an interatomic potential, $V_{\mathrm{FPU}}\left(x\right)=k_2{x}^2/2+k_4{x}^4/4$ with $k_2,k_4>0$, and a low-temperature regime where heat conduction is most likely diffusive normal, satisfying Fourier's law. We present our simulation results for different temperature regimes in all dimensions.

We investigate the growth of the total number of particles in a symmetric exclusion process driven by a localized source. The average total number of particles entering an initially empty system grows with time as $\sqrt{t}$ in one dimension, $t/\ln t$ in two dimensions, and linearly in higher dimensions. In one and two dimensions, the leading asymptotic behaviors for the average total number of particles are independent of the intensity of the source. We also discuss fluctuations of the total number of particles and determine the asymptotic growth of the variance in one dimension.