We study the designing principles of the simplest colloidal propeller, an architecture built from four identical spheres that can couple translation with rotation to produce controlled drift motion. By considering superparamagnetic beads, we show that the simultaneous action of a magnetic field and a shear flow leads to the migration of the cluster in the vorticity direction. We investigate the dependence of the migration velocity on the geometrical parameters of the cluster and find that significant cluster separation can be achieved under the typical operation conditions of microfluidic devices.

The homogeneous partly pinned fluid systems are simple models of a fluid confined in a disordered porous matrix obtained by arresting randomly chosen particles in a one-component bulk fluid or one of the two components of a binary mixture. In this paper, their configurational properties are investigated. It is shown that a peculiar complementarity exists between the mobile and immobile phases, which originates from the fact that the solid is prepared in presence of and in equilibrium with the adsorbed fluid. Simple identities follow, which connect different types of configurational averages, either relative to the fluid-matrix system or to the bulk fluid from which it is prepared. Crucial simplifications result for the computation of important structural quantities, both in computer simulations and in theoretical approaches. Finally, possible applications of the model in the field of dynamics in confinement or in strongly asymmetric mixtures are suggested.

Tumor angiogenesis is a landmark of solid tumor development, but it is also directly relevant to chemotherapy. Indeed, the density and quality of neovessels may influence the effectiveness of therapies based on blood-born agents. In this paper, first we define a deterministic model of antiproliferative chemotherapy in which the drug efficacy is a unimodal function of vessel density, and then we show that under constant continuous infusion therapy the tumor-vessel system may be multistable. However, the actual drug concentration profiles are affected by bounded even if possibly large fluctuations. Through numerical simulations, we show that the tumor volume may undergo transitions to the higher equilibrium value induced by the bounded noise. In case of periodically delivered boli-based chemotherapy, we model the fluctuations due to time variability of both the drug clearance rate and the distribution volume, as well as those due to irregularities in drug delivery. We observed noise-induced transitions also in case of periodic delivering. By applying a time dense scheduling with constant average delivered drug (metronomic scheduling), we observed an easier suppression of the transitions. Finally, we propose to interpret the above phenomena as an unexpected non-genetic kind of resistance to chemotherapy.

Despite degree distributions give some insights about how heterogeneous a network is, they fail in giving a unique quantitative characterization of network heterogeneity. This is particularly the case when several different distributions fit for the same network, when the number of data points is very scarce due to network size, or when we have to compare two networks with completely different degree distributions. Here we propose a unique characterization of network heterogeneity based on the difference of functions of node degrees for all pairs of linked nodes. We show that this heterogeneity index can be expressed as a quadratic form of the Laplacian matrix of the network, which allows a spectral representation of network heterogeneity. We give bounds for this index, which is equal to zero for any regular network and equal to one only for star graphs. Using it we study random networks showing that those generated by the Erdös-Rényi algorithm have zero heterogeneity, and those generated by the preferential attachment method of Barabási and Albert display only 11% of the heterogeneity of a star graph. We finally study 52 real-world networks and we found that they display a large variety of heterogeneities. We also show that a classification system based on degree distributions does not reflect the heterogeneity properties of real-world networks.

There is convincing evidence showing that the probability distributions of stock returns in mature markets exhibit power-law tails and both the positive and negative tails conform to the inverse cubic law. It supports the possibility that the tail exponents are universal at least for mature markets in the sense that they do not depend on stock market, industry sector, and market capitalization. We investigate the distributions of intraday returns at different time scales ($\Delta t=1$, 5, 15, and 30 min) of all the A-share stocks traded in the Chinese stock market, which is the largest emerging market in the world. We find that the returns can be well fitted by the $q$-Gaussian distribution and the tails have power-law relaxations with the exponents increasing with $\Delta t$ and being well outside the Lévy stable regime for individual stocks. We provide statistically significant evidence showing that, at small time scales $\Delta t<15\text{min}$, the exponents logarithmically decrease with the turnover rate and increase with the market capitalization. When $\Delta t>15\text{min}$, no conclusive evidence is found for a possible dependence of the tail exponent on the turnover rate or the market capitalization. Our findings indicate that the intraday return distributions at small time scales are not universal in emerging stock markets but might be universal at large time scales.

We study the evolution of binary opinions on a simple adaptive network of $N$ nodes. At each time step, a randomly selected node updates its state (“opinion”) according to the majority opinion of the nodes that it is linked to; subsequently, all links are reassigned with probability $\tilde{p}$ $\left(\tilde{q}\right)$ if they connect nodes with equal (opposite) opinions. In contrast to earlier work, we ensure that the average connectivity (“degree”) of each node is independent of the system size (“intensive”), by choosing $\tilde{p}$ and $\tilde{q}$ to be of $O\left(1/N\right)$. Using simulations and analytic arguments, we determine the final steady states and the relaxation into these states for different system sizes. We find two absorbing states, characterized by perfect consensus, and one metastable state, characterized by a population split evenly between the two opinions. The relaxation time of this state grows exponentially with the number of nodes, $N$. A second metastable state, found in the earlier studies, is no longer observed.

Recently, we have presented spatially modulated delayed feedback as a novel mechanism, which generically generates chimera states, remarkable spatiotemporal patterns in which coherence coexists with incoherence [O. E. Omel’chenko et al., Phys. Rev. Lett. 100, 044105 (2008)]. Remarkably, such chimera states serve as a natural link between completely coherent states and completely incoherent states. So far, we have studied this mechanism with a self-consistency-based numerical analysis only. In contrast, in this paper we perform a thorough dynamical description and, in particular, a stability analysis of the emerging chimera states. For this, we apply a recently developed reduction procedure [A. Pikovsky and M. Rosenblum, Phys. Rev. Lett. 101, 264103 (2008)]. By combining analytical and numerical approaches, we systematically describe the relationship between the parameters of the delayed feedback on one hand and the properties of the chimera states on the other hand. We provide the general rules for an effective control and manipulation of the chimera states.

Recent studies have suggested that in some cases transition can be triggered by some purely nonlinear mechanisms. Here we aim at verifying such an hypothesis, looking for a localized perturbation able to lead a boundary-layer flow to a chaotic state, following a nonlinear route. Nonlinear optimal localized perturbations have been computed by means of an energy optimization which includes the nonlinear terms of the Navier-Stokes equations. Such perturbations lie on the turbulent side of the laminar-turbulent boundary, whereas, for the same value of the initial energy, their linear counterparts do not. The evolution of these perturbations toward a turbulent flow involves the presence of streamwise-inclined vortices at short times and of hairpin structures prior to breakdown.

This paper is focused on the fundamental mechanism(s) of viscoelastic turbulence that leads to polymer-induced turbulent drag reduction phenomenon. A great challenge in this problem is the computation of viscoelastic turbulent flows, since the understanding of polymer physics is restricted to mechanical models. An effective state-of-the-art numerical method to solve the governing equation for polymers modeled as nonlinear springs, without using any artificial assumptions as usual, was implemented here on a three-dimensional channel flow geometry. The capability of this algorithm to capture the strong polymer-turbulence dynamical interactions is depicted on the results, which are much closer qualitatively to experimental observations. This allowed a more detailed study of the polymer-turbulence interactions, which yields an enhanced picture on a mechanism resulting from the polymer-turbulence energy transfers.

The paper studies the nonlinear mechanisms at work in magnetized plasmas when wave packets interact resonantly with particle distributions presenting loss-cone-like structures. Lower hybrid waves are considered in view of the great importance, in space and laboratory plasmas, of waves with frequencies below the electron cyclotron frequency. Owing to a three-dimensional Hamiltonian model and a numerical symplectic code, the authors study the nonlinear stage of the loss-cone instability for various particle distributions and wave spectra involving symmetric and asymmetric features. In particular, the wave-particle interaction process of dynamical resonance merging, which results from an instability of the trapped particles’ motion and leads to complex stochastic phenomena, is discussed. Whereas interactions at normal cyclotron resonances are mostly considered, the role of the Landau and the anomalous cyclotron resonances is also studied to explain thoroughly the nonlinear wave-particle dynamics as well as the competition between loss-cone, fan, and beam instabilities. The relaxed particle distributions and the saturated wave spectra are analyzed. The time necessary for filling the loss-cone structures is determined as a function of the characteristics of the particle distributions. Whereas most of the previous works analyzed the asymptotic stage of the system’s evolution in the frame of the well-known quasilinear theory, the paper considers the case when the energy carried by the wave packet is sufficiently large so that the description of the physical processes at work cannot be limited to the frame of weak turbulence theories.

Entropy production rate (EPR) is often effective to describe how a structure is self-organized in a nonequilibrium thermodynamic system. The “minimum EPR principle” is widely applicable to characterizing self-organized structures, but is sometimes disproved by observations of “maximum EPR states.” Here we delineate a dual relation between the minimum and maximum principles; the mathematical representation of the duality is given by a Legendre transformation. For explicit formulation, we consider heat transport in the boundary layer of fusion plasma [Z. Yoshida and S. M. Mahajan, Phys. Plasmas 15, 032307 (2008)]. The mechanism of bifurcation and hysteresis (which are the determining characteristics of the so-called H-mode, a self-organized state of reduced thermal conduction) is explained by multiple tangent lines to a pleated graph of an appropriate thermodynamic potential. In the nonlinear regime, we have to generalize Onsager’s dissipation function. The generalized function is no longer equivalent to EPR; then EPR ceases to be the determinant of the operating point, and may take either minimum or maximum values depending on how the system is driven.

This paper generalizes the two-component algorithm of Sec. II, extending it, in Sec. III, to describe $N>2$ mutually immiscible fluids in the isothermal continuum regime. Each fluid has an independent interfacial tension. While retaining all its computational advantages, we remove entirely the empiricism associated with contact behavior in our previous multiple immiscible fluid models [M. M. Dupin et al., Phys. Rev. E 73, 055701(R) (2006); Med. Eng. Phys. 28, 13 (2006)] while solidifying the physical foundations. Moreover, the model relies upon a fluid-fluid segregation which is simpler, computationally faster, more free of artifacts (i.e., the interfacial microcurrent), and upon an interface-inducing force distribution which is analytic. The method is completely symmetric between any numbers of immiscible fluids and stable over a wide range of directly input interfacial tension. We present data on the steady-state properties of multiple interface model, which are in good agreement with theory [R. E. Johnson and S. S. Sadhal, Annu. Rev. Fluid Mech. 17, 289 (1985)], specifically on the shapes of multidrop systems. Section II is an analysis of the kinetic and continuum-scale descriptions of the underlying two-component lattice Boltzmann model for immiscible fluids, extendable to more than two immiscible fluids. This extension requires (i) the use of a more local kinetic equation perturbation which is (ii) free from a reliance on measured interfacial curvature. It should be noted that viewed simply as a two-component method, the continuum algorithm is inferior to our previous methods, reported by Lishchuk et al. [Phys. Rev. E 67, 036701 (2003)] and Halliday et al. [Phys. Rev. E 76, 026708 (2007)]. Greater stability and parameter range is achieved in multiple drop simulations by using the forced multi-relaxation-time lattice Boltzmann method developed, along with (for completeness) a forced exactly incompressible Bhatnagar-Gross-Krook lattice Boltzmann model, in the Appendix. These appended schemes closely follow those developed by Guo et al. [Phys. Rev. E 65, 046308 (2002)] for the single-relaxation-time scheme.

Extending a Padé approximant method used for studying compactons in the Rosenau-Hyman (RH) equation, we study the numerical stability of single compactons of the Cooper-Shepard-Sodano (CSS) equation and their pairwise interactions. The CSS equation has a conserved Hamiltonian which has allowed various approaches for studying analytically the nonlinear stability of the solutions. We study three different compacton solutions and find they are numerically stable. Similar to the collisions between RH compactons, the CSS compactons re-emerge with same coherent shape when scattered. The time evolution of the small-amplitude ripple resulting after scattering depends on the values of the parameters $l$ and $p$ characterizing the corresponding CSS equation. The simulation of the CSS compacton scattering requires a much smaller artificial viscosity to obtain numerical stability than in the case of RH compacton propagation.

In complex systems with fractal properties the scale invariance has an important rule to classify different statistical properties. In two dimensions the Loewner equation can classify all the fractal curves. Using the Weierstrass-Mandelbrot (WM) function as the drift of the Loewner equation we introduce a large class of fractal curves with discrete scale invariance (DSI). We show that the fractal dimension of the curves can be extracted from the diffusion coefficient of the trend of the variance of the WM function. We argue that, up to the fractal dimension calculations, all the WM functions follow the behavior of the corresponding Brownian motion. Our study opens a way to classify all the fractal curves with DSI. In particular, we investigate the contour lines of two-dimensional WM function as a physical candidate for our new stochastic curves.

Directed transport of overdamped Brownian particles driven by fractional Gaussian noises is investigated in asymmetrically periodic potentials. By using Langevin dynamics simulations, we find that rectified currents occur in the absence of any external driving forces. Unlike white Gaussian noises, fractional Gaussian noises can break thermodynamical equilibrium and induce directed transport. Remarkably, the average velocity for persistent fractional noise is opposite to that for antipersistent fractional noise. The velocity increases monotonically with Hurst exponent for the persistent case, whereas there exists an optimal value of Hurst exponent at which the velocity takes its maximal value for the antipersistent case.

We study how the order of $N$ independent random walks in one dimension evolves with time. Our focus is statistical properties of the inversion number $m$, defined as the number of pairs that are out of sort with respect to the initial configuration. In the steady state, the distribution of the inversion number is Gaussian with the average $⟨m⟩\simeq N^2/4$ and the standard deviation $\sigma \simeq N^{3/2}/6$. The survival probability, $S_m\left(t\right)$, which measures the likelihood that the inversion number remains below $m$ until time $t$, decays algebraically in the long-time limit, $S_m\sim t^{-{\beta }_m}$. Interestingly, there is a spectrum of $N\left(N-1\right)/2$ distinct exponents ${\beta }_m\left(N\right)$. We also find that the kinetics of first passage in a circular cone provides a good approximation for these exponents. When $N$ is large, the first-passage exponents are a universal function of a single scaling variable, ${\beta }_m\left(N\right)\to \beta \left(z\right)$, with $z=\left(m-⟨m⟩\right)/\sigma$. In the cone approximation, the scaling function is a root of a transcendental equation involving the parabolic cylinder equation, $D_{2\beta }\left(-z\right)=0$, and surprisingly, numerical simulations show this prediction to be exact.

The presence of long-term persistence of climate records on scales from 2 to 15 yr has been reported in the literature, even if the universality of this result is controversial. In the present paper results from monthly temperature records measured for about 250 yr in Prague and Milan are reported. Because of the nonlinear and nonstationary character of temperature time series the seasonal contribution has been identified through the empirical mode decomposition. We find that the seasonal component of the climate records is characterized by some time scales showing both amplitude and phase fluctuations. By using a more suitable definition of temperature anomalies, and thus excluding persistence effects due to seasonal oscillations and trends, the occurrence of long-term persistence has been investigated through the detrended fluctuation analysis. Our results indicate persistence on scales from 3 to 10 yr with similar values for the detrended fluctuation analysis indices.

A technique for measuring the mean impulse response function of stationary homogeneous isotropic turbulence is proposed. Such a measurement is carried out here on the basis of direct numerical simulation (DNS). A zero-mean white-noise volume forcing is used to probe the turbulent flow, and the response function is obtained by accumulating the space-time correlation between the white forcing and the velocity field. This technique to measure the turbulent response in a DNS numerical experiment is a research tool in that field of spectral closures where the linear-response concept is invoked either by resorting to renormalized perturbations theories or by introducing the well-known fluctuation-dissipation relation (FDR). Although the results obtained in the present work are limited to relatively low values of the Reynolds number, a preliminary analysis is possible. Both the characteristic form and the time scaling properties of the response function are investigated in the universal subrange of dissipative wave numbers; a comparison with the response approximation given by the FDR is proposed through the independent DNS measurement of the correlation function. Very good agreement is found between the measured response and Kraichnan’s description of random energy-range advection effects.

Sedimentation of the neutron rich isotope ${}^{22}\text{N}\text{e}$ may be an important source of gravitational energy during the cooling of white dwarf stars. This depends on the diffusion constant for ${}^{22}\text{N}\text{e}$ in strongly coupled plasma mixtures. We calculate self-diffusion constants $D_i$ from molecular dynamics simulations of carbon, oxygen, and neon mixtures. We find that $D_i$ in a mixture does not differ greatly from earlier one component plasma results. For strong coupling (coulomb parameter $\Gamma >$ few), $D_i$ has a modest dependence on the charge $Z_i$ of the ion species, $D_i\propto Z_i^{-2/3}$. However, $D_i$ depends more strongly on $Z_i$ for weak coupling (smaller $\Gamma$). We conclude that the self-diffusion constant $D_{\text{Ne}}$ for ${}^{22}\text{N}\text{e}$ in carbon, oxygen, and neon plasma mixtures is accurately known so that uncertainties in $D_{\text{Ne}}$ should be unimportant for simulations of white dwarf cooling.

We show that the Hermitian Hamiltonian formalism in the paper “Scattering-theory analysis of waveguide-resonator coupling” by Xu et al. [Phys. Rev. E 62, 7389 (2000)] is incompatible with the standard perturbation analysis in a strict sense and hence needs to be used with caution. To improve, a perturbation analysis strictly compatible Hermitian Hamiltonian formalism for modeling the adiabatic time evolution of electromagnetic wave in dielectric medium is outlined. Using a quantum $T$-matrix based approach, we demonstrate the validity of our Hermitian Hamiltonian formalism and more importantly the effectiveness of the application of quantum formal scattering theory in electromagnetics by exactly rederiving the Rayleigh formula for the total cross section of a nonmagnetic dielectric sphere at the long-wavelength limit.