We consider dynamic response of a cytoskeletal network to both thermal and motor-induced fluctuations. The latter are viewed in two independent ways, as either additive or multiplicative colored noise. Due to a natural upper frequency limit of the motor agitation, the response of a living cell is similar to that of an equilibrium system in the high-frequency domain. At lower frequencies, the role of motor agitation manifests itself in intensified network fluctuations, which is equivalent to effective growth of the environment temperature. The effective temperature becomes frequency dependent, which signifies violation of the conventional fluctuation-dissipation theorem. The motor action affects the dynamic shear modulus in two opposite ways: by stiffening the network through filament prestress and softening it through increased agitation. The latter tendency is isolated when only single-headed motors are present. The theory is in good agreement with experimental measurements of the amplitude of the shear modulus under these conditions.

We present an experimental study of the displacement of a light intruder immersed in a vibrated granular bed. Using high speed video we resolve the motion, during one cycle of oscillation, of a cylindrical object inside a Plexiglas box partially filled with grains. We report experimental evidence that, in the absence of convection, at least two forces are behind the intruder’s motion: an air drag force—due to the airflow through the granular bed—and a buoyancy force produced by an air-mediated granular fluid.

Bimetallic rod-shaped nanomotors swim autonomously in hydrogen peroxide solutions. Here, we present a scaling analysis, computational simulations, and experimental data that show that the nanomotor locomotion is driven by fluid slip around the nanomotor surface due to electrical body forces. The body forces are generated by a coupling of charge density and electric fields induced by electrochemical reactions occurring on the nanomotor surface. We describe the dependence of nanomotor motion on the nanomotor surface potential and reaction-driven flux.

The representation of real systems with network models is becoming increasingly common and critical to both capture and simplify systems’ complexity, notably, via the partitioning of networks into communities. In this respect, the definition of modularity, a common and broadly used quality measure for networks partitioning, has induced a surge of efficient modularity-based community detection algorithms. However, recently, the optimization of modularity has been found to show a resolution limit, which reduces its effectiveness and range of applications. Therefore, one recent trend in this area of research has been related to the definition of novel quality functions, alternative to modularity. In this paper, however, instead of laying aside the important body of knowledge developed so far for modularity-based algorithms, we propose to use a strategy to preprocess networks before feeding them into modularity-based algorithms. This approach is based on the observation that dynamic processes triggered on vertices in the same community possess similar behavior patterns but dissimilar on vertices in different communities. Validations on real-world and synthetic networks demonstrate that network preprocessing can enhance the modularity-based community detection algorithms to find more natural clusters and effectively alleviates the problem of resolution limit.

We study perturbation with period $T_{\text{p}}$ of one of two model Belousov-Zhabotinsky chemical oscillators diffusively coupled through an inhibitory species. We find a variety of resonance regimes, characterized as $N_1:N_2:n$, where $N_1$ $\left(N_2\right)$ and $n$ are the numbers of spikes of the perturbed (unperturbed) oscillator and the external perturbation, respectively, per global period $T_{\text{G}}$. The resonance mode is determined primarily by the ratios $T_{\text{p}}/T_0$ and $T_{\text{p}}/T_{\text{C}}$, where $T_0$ and $T_{\text{C}}$ are the periods of a single oscillator and of two coupled antiphase oscillators, respectively ($T_{\text{C}}\cong 2T_0$ at large coupling strength). The period of the perturbed oscillator can be tuned over a wide range (from $T_0$ to $>10T_0$) by varying $T_{\text{p}}$ between $T_{\text{C}}$ and $T_0$.

We investigate what is called swarm oscillator model where interacting motile oscillators form various kinds of ordered structures. We particularly focus on the dimensionality of clusters which oscillators form. In two-dimensional space, oscillators spontaneously form one-dimensional clusters or two-dimensional clusters. By studying the three-oscillator system, we analytically find the conditions of the appearance of those patterns. The validity of those conditions in applying to systems of more oscillators is demonstrated by numerically investigating a system of twenty oscillators.

Resonance spectra of two-dimensional dielectric microwave resonators of circular and square shapes have been measured. The deduced length spectra of periodic orbits were analyzed and a trace formula for dielectric resonators recently proposed by Bogomolny et al. [Phys. Rev. E 78, 056202 (2008)] was tested. The observed deviations between the experimental length spectra and the predictions of the trace formula are attributed to a large number of missing resonances in the measured spectra. We show that by taking into account the systematics of observed and missing resonances the experimental length spectra are fully understood. In particular, a connection between the most long-lived resonances and certain periodic orbits is established experimentally.

We consider statistics of the disruption and Lyapunov times in an hierarchical restricted three-body problem. We show that at the edge of disruption the orbital periods and the size of the orbit of the escaping body exhibit Lévy flights. Due to them, the time decay of the survival probability is heavy-tailed with the power-law index equal to $-2/3$, while the relation between the Lyapunov and disruption times is quasilinear. Applicability of these results in an “hierarchical resonant scattering” setting for a three-body interaction is discussed.

The properties of the leader-laggard chaos synchronization (LLCS) in two mutually coupled external-cavity semiconductor lasers are studied systematically. We theoretically analyze the general conditions for the LLCS based on the symmetric operation mechanism and numerically investigate the influences of operation parameters, the mismatch robustness, the chaos pass filtering effects, the communication performance, and the security of the system. It is demonstrated that stable LLCS, which allows simultaneous bidirectional message exchange in virtue of mutual chaos pass filtering effect, can be achieved in a wide operation region; moreover, high-quality LLCS and satisfactory communication performance can be maintained under a relatively large device parameter mismatch. Compared with the isochronal chaos synchronization in the same system, LLCS provides a wider operation region, a better mismatch robustness, and a stronger chaos pass filtering effect. In addition, the investigations on the security of private key message transmission under some potential attacks indicate that the security can be enhanced by increasing the bit rate moderately, exchanging messages with different bit rates, or monitoring the LLCS.

The problem of linear stability of confined V-shaped flames with arbitrary gas expansion is addressed. Using the on-shell description of flame dynamics, a general equation governing propagation of disturbances of an anchored flame is obtained. This equation is solved analytically for V-flames anchored in high-velocity channel streams. It is demonstrated that dynamics of the flame disturbances in this case is controlled by the memory effects associated with vorticity generated by the perturbed flame. The perturbation growth rate spectrum is determined, and explicit analytical expressions for the eigenfunctions are given. It is found that the piecewise linear V structure is unstable for all values of the gas expansion coefficient. Despite the linearity of the basic pattern, however, evolutions of the V-flame disturbances are completely different from those found for freely propagating planar flames or open anchored flames. The obtained results reveal strong influence of the basic flow and the channel walls on the stability properties of confined V-flames.

We present numerical simulations as well as experimental results concerning transitions between Taylor vortices and spiral vortices in the Taylor-Couette system with rigid, nonrotating lids at the cylinder ends. These transitions are performed by wavy structures appearing via a secondary bifurcation out of Taylor vortices and spirals, respectively. In the presence of these axial end walls, pure spiral solutions do not occur as for axially periodic boundary conditions but are substituted by primary bifurcating, stable wavy spiral structures. Similarly to the periodic system, we found a transition from Taylor vortices to wavy spirals mediated by so-called wavy Taylor vortices and, on the other hand, a transition from wavy spirals to Taylor vortices triggered by a propagating defect. We furthermore observed and investigated the primary bifurcation of wavy spirals out of the basic circular Couette flow with Ekman vortices at the cylinder ends.

Bubbles can be trapped inside textured structures such as grooves, forming a superhydrophobic surface. A superhydrophobic surface has a large effective hydrodynamic slip length compared to a smooth hydrophobic surface and holds the promise of enhancing electrokinetic flows that find many interesting applications in microfluidics. However, recent theoretical studies suggested that electro-osmotic flows over a weakly charged superhydrophobic surface [the zeta potential of the surface is smaller than the thermal potential (25 mV)] can only be enhanced when liquid-gas interfaces are charged [T. M. Squires, Phys. Fluids 20, 092105 (2008); Bahga et al., J. Fluid Mech. 644, 245 (2010)]. So far there is little work reported when the zeta potential of the surface is comparable or even larger than the thermal potential. In this paper we numerically investigate electro-osmotic flows over a periodically striped slip-stick surface by solving the standard Poisson-Nernst-Planck equations. Our results indicate that at large zeta potentials, even if liquid-gas interfaces are charged, the nonuniform surface conduction due to the mismatch between surface conductions over no-shear and no-slip regions leads to electric field lines penetrating the double layer and thus the nonuniform surface conduction weakens the tangential component of the electric field which primarily drives electro-osmotic flows. Our results imply that, in the presence of strong nonuniform surface conduction, enhanced electro-osmotic flows over a superhydrophobic surface are possible only in certain conditions. In particular, the enhancement due to the slip can potentially be lost at large zeta potentials. Similar loss of the enhancement of a charged particle’s electrophoretic mobility due to the slip was reported by Khair and Squires [Phys. Fluids 21, 042001 (2009)].

We analyze the phonon spectra of periodic structures formed by two-dimensional mixtures of dipolar colloidal particles. These mixtures display an enormous variety of complex ordered configurations [J. Fornleitner et al., Soft Matter 4, 480 (2008)], allowing for the systematic investigation of the ensuing phonon spectra and the control of phononic gaps. We show how the shape of the phonon bands and the number and width of the phonon gaps can be controlled by changing the susceptibility ratio, the composition, and the mass ratio between the two components.

The dynamics of red blood cells (RBCs) in oscillatory shear flow was studied using differential equations of three variables: a shape parameter, the inclination angle $\theta$, and phase angle $\varphi$ of the membrane rotation. In steady shear flow, three types of dynamics occur depending on the shear rate and viscosity ratio. (i) tank-treading (TT): $\varphi$ rotates while the shape and $\theta$ oscillate. (ii) tumbling (TB): $\theta$ rotates while the shape and $\varphi$ oscillate. (iii) intermediate motion: both $\varphi$ and $\theta$ rotate synchronously or intermittently. In oscillatory shear flow, RBCs show various dynamics based on these three motions. For a low shear frequency with zero mean shear rate, a limit-cycle oscillation occurs, based on the TT or TB rotation at a high or low shear amplitude, respectively. This TT-based oscillation well explains recent experiments. In the middle shear amplitude, RBCs show an intermittent or synchronized oscillation. As shear frequency increases, the vesicle oscillation becomes delayed with respect to the shear oscillation. At a high frequency, multiple limit-cycle oscillations coexist. The thermal fluctuations can induce transitions between two orbits at very low shear amplitudes. For a high mean shear rate with small shear oscillation, the shape and $\theta$ oscillate in the TT motion but only one attractor exists even at high shear frequencies. The measurement of these oscillatory modes is a promising tool for quantifying the viscoelasticity of RBCs, synthetic capsules, and lipid vesicles.

We propose a stochastic dynamical model of noisy neural networks with complex architectures and discuss activation of neural networks by a stimulus, pacemakers, and spontaneous activity. This model has a complex phase diagram with self-organized active neural states, hybrid phase transitions, and a rich array of behaviors. We show that if spontaneous activity (noise) reaches a threshold level then global neural oscillations emerge. Stochastic resonance is a precursor of this dynamical phase transition. These oscillations are an intrinsic property of even small groups of 50 neurons.

We employ a pseudopotential approach to investigate the screening of ionic cores in partially ionized plasmas. Here, the effect of the tightly bound electrons is condensed into an effective potential between the (free) valence electrons and the ionic cores. Even for weak electron-ion coupling, the corresponding screening clouds show strong modifications from the Debye result for elements heavier than helium. Modifications of the theoretically predicted x-ray scattering signal and implications on measurements are discussed.

We introduce and discuss a nonlinear kinetic equation of Boltzmann type which describes the evolution of wealth in a pure gambling process, where the entire sum of wealths of two agents is up for gambling, and randomly shared between the agents. For this equation the analytical form of the steady states is found for various realizations of the random fraction of the sum which is shared to the agents. Among others, the exponential distribution appears as steady state in case of a uniformly distributed random fraction, while Gamma distribution appears for a random fraction which is Beta distributed. The case in which the gambling game is only conservative-in-the-mean is shown to lead to an explicit heavy tailed distribution.

Recently it was shown that financial time series are not completely random process but exhibit long-term or short-term dependences, which offer promises for predictability. However, we do not clearly understand the potential relationship between serial structure and predictability. This paper proposed a framework to magnify the correlations and regularities contained in financial time series through constructing accumulative return series. This method can help us distinguish the real world financial time series from random-walk process effectively by examining the change patterns of volatility, Hurst exponent, and approximate entropy. Furthermore, we have found that the predictable degree increases continually with the increasing length of accumulative return. Our results suggest that financial time series are predictable to some extent and approximate entropy is a good indicator to characterize the predictable degree of financial time series if we take the influence of their volatility into account.

Recently, synchronization was proved for permutation parity machines, multilayer feed-forward neural networks proposed as a binary variant of the tree parity machines. This ability was already used in the case of tree parity machines to introduce a key-exchange protocol. In this paper, a protocol based on permutation parity machines is proposed and its performance against common attacks (simple, geometric, majority and genetic) is studied.

We present a numerical analysis of solutal buoyancy effects on the shape and the velocity of autocatalytic reaction fronts, propagating in thin tilted rectangular channels. We use two-dimensional (2D) lattice Bathnagar-Gross-Krook (BGK) numerical simulations of gap-averaged equations for the flow and the concentration, namely a Stokes-Darcy equation coupled with an advection-diffusion-reaction equation. We do observe stationary-shaped fronts, spanning the width of the cell and propagating along the cell axis. We show that the model accounts rather well for experiments we performed using an Iodate Arsenous Acid reaction propagating in tilted Hele-Shaw cells, hence validating our 2D modelization of a three-dimensional problem. This modelization is also able to account for results found for another chemical reaction (chlorite tetrathionate) in a horizontal cell. In particular, we show that the shape and the traveling velocity of such fronts are linked with an eikonal equation. Moreover, we show that the front velocity varies nonmonotonically with the tilt of the cell, and nonlinearly with the width of the cell.