Many swimming microorganisms, such as bacteria and sperm, use flexible flagella to move through viscoelastic media in their natural environments. In this paper we address the effects a viscoelastic fluid has on the motion and beating patterns of elastic filaments. We treat both a passive filament which is actuated at one end and an active filament with bending forces arising from internal motors distributed along its length. We describe how viscoelasticity modifies the hydrodynamic forces exerted on the filaments, and how these modified forces affect the beating patterns. We show how high viscosity of purely viscous or viscoelastic solutions can lead to the experimentally observed beating patterns of sperm flagella, in which motion is concentrated at the distal end of the flagella.

Minimum box-covering method is a basic tool to measure fractal dimension of a network but unfortunately belongs to a family of $NP$-hard problems. Finding more accurate approximation in a relative shorter time is an important problem and attracts considerable attention. In this paper, the accuracy of the ball-covering approach for fractal dimension is measured by the relative error $\eta$ to the true fractal dimension, and its upper bound $\epsilon$ is analytically deduced by the linear least-squares method. When the ball-covering algorithm is applied to real-world networks, the relative error $\eta$ always stays in a narrow range which is far below its theoretical upper bound $\epsilon$. It indicates that the ball-covering approach provides a helpful method to approximate the true fractal dimension. Then a rank-driven ball-covering algorithm is presented. It is demonstrated that the ranking mechanism ensures the search steps of our algorithm for finding balls are obviously less than that of the original algorithm introduced by Kim et al. [Chaos 17, 026116 (2007)] and our algorithm is much more efficient.

We study the dynamical generation of entanglement as a signature of chaos in a system of periodically kicked coupled tops, where chaos and entanglement arise from the same physical mechanism. The long-time-averaged entanglement as a function of the position of an initially localized wave packet very closely correlates with the classical phase space surface of section—it is nearly uniform in the chaotic sea, and reproduces the detailed structure of the regular islands. The uniform value in the chaotic sea is explained by the random state conjecture. As classically chaotic dynamics take localized distributions in phase space to random distributions, quantized versions take localized coherent states to pseudorandom states in Hilbert space. Such random states are highly entangled, with an average value near that of the maximally entangled state. For a map with global chaos, we derive that value based on analytic results for the entropy of random states. For a mixed phase space, we use the Percival conjecture to identify a “chaotic subspace” of the Hilbert space. The typical entanglement, averaged over the unitarily invariant Haar measure in this subspace, agrees with the long-time-averaged entanglement for initial states in the chaotic sea. In all cases the dynamically generated entanglement is that of a random complex vector, even though the system is time-reversal invariant, and the Floquet operator is a member of the circular orthogonal ensemble.

We present a quantitative analysis of the reversibility properties of classically chaotic quantum motion. We analyze the connection between reversibility and the rate at which a quantum state acquires a more and more complicated structure in its time evolution. This complexity is characterized by the number $\mathcal{M}\left(t\right)$ of harmonics of the [initially isotropic, i.e., $\mathcal{M}\left(0\right)=0$] Wigner function, which are generated during quantum evolution for the time $t$. We show that, in contrast to the classical exponential increase, this number can grow not faster than linearly and then relate this fact with the degree of reversibility of the quantum motion. To explore the reversibility we reverse the quantum evolution at some moment $T$ immediately after applying at this moment an instant perturbation governed by a strength parameter $\xi$. It follows that there exists a critical perturbation strength ${\xi }_c\approx \sqrt{2}∕\mathcal{M}\left(T\right)$ below which the initial state is well recovered, whereas reversibility disappears when $\xi \gtrsim {\xi }_c\left(T\right)$. In the classical limit the number of harmonics proliferates exponentially with time and the motion becomes practically irreversible. The above results are illustrated in the example of the kicked quartic oscillator model.

A simplified version of the stochastic Fermi-Ulam model is investigated in order to elucidate the effect of a class of rare low-velocity events on the velocity diffusion process and consequently Fermi acceleration. The relative fraction of these events, for sufficiently large times, decreases monotonically with increasing variance of the magnitude of the particle velocity. However, a treatment of the diffusion problem which totally neglects these events, gives rise to a glaring inconsistency associated with the mean value of the magnitude of the velocity in the ensemble. We propose a general scheme for treating the diffusion process in velocity space, which succeeds in capturing the effect of the low-velocity events on the diffusion, providing a consistent description of the acceleration process. The present study exemplifies the influence of low-probability events on the transport properties of time-dependent billiards.

The laser manipulation technique was effectively used for agarose solutions and the frequency specstrum of the surface response to the periodical laser irradiation yielded shear elasticity $G$ and surface tension $\sigma$ in the gel. The laser spot size, from $60\mu \mathrm{m}\text{to}200\mu \mathrm{m}$ in radius, was chosen so that either the Rayleigh waves or the capillary waves, selectively excited, associated with $G$ or $\sigma$, respectively. The result of $G$ showed a dependence on the agarose concentration that is consistent with the theoretical prediction of the percolation model, while $\sigma$ has little dependence on the concentration. The surface state of $0.2\mathrm{wt.}\%$ agarose solution was controlled with sodium-dodecyl-sulfate (SDS) additives, and $\sigma$ of the gel and the sol was observed at different SDS concentrations: The result showed (i) $\sigma$ decreased with increasing SDS concentration up to $39\times {10}^{-3}\mathrm{mol}∕\mathrm{l}$ and kept a constant value thereafter, and (ii) the gel and the sol have the same value of $\sigma$ and the same dependence on the concentration. These results were considered from a viewpoint of surface pressure and a partially quantitative discussion was made on the surface adsorbed with SDS and agarose molecules.

The linking and writhing numbers are key quantities when characterizing the structure of a piece of supercoiled DNA. Defined as double integrals over the shape of the double helix, these numbers are not always straightforward to compute, though a simplified formula was established in a theorem by Fuller [Proc. Natl. Acad. Sci. U.S.A. 75, 3557 (1978)]. We examine the range of applicability of this widely used simplified formula, and show that it cannot be employed for plectonemic DNA. We show that inapplicability is due to a hypothesis of Fuller theorem that is not met. The hypothesis seems to have been overlooked in many works.

We suggest several stationary state control-based delay identification methods which do not require any structural information about the controlled systems and are applicable to systems described by delayed ordinary differential equations. This proposed technique includes three steps: (i) driving a system to a steady state; (ii) perturbing the control signal for shifting the steady state; and (iii) identifying all delays by detecting the time that the system is abruptly drawn out of stationarity. Some aspects especially important for applications are discussed as well, including interaction delay identification, stationary state convergence speed, performance comparison, and the influence of noise on delay identification. Several examples are presented to illustrate the reliability and robustness of all delay identification methods suggested.

The phase order parameter of oscillators on a network is optimized using two different sets of constraints. First, the maximization is achieved by adjusting the coupling strengths among the oscillators without changing the total coupling strength and the natural frequencies of the oscillators. This optimization reveals that a stronger weight tends to be assigned to a connection between two oscillators with greatly different natural frequencies. Second, we vary both coupling strengths and natural frequencies while maximizing the phase order and minimizing the penalty function which prevents the natural frequencies of the oscillators from taking the same value. This optimization reveals that a large total coupling strength makes oscillators take two natural frequencies (two-group state), whereas a small total coupling strength facilitates the convergence of natural frequencies to one single value (one-group state). Small and large penalty parameters make the optimized network take the one- and two-group states, respectively. This phase transition is observed in all-to-all, lattice, and scale-free networks although the clustering coefficient of the strongest links in the optimized network reflects the difference of the underlying network topologies.

An accurate prediction of the particle charge in plasmas is of fundamental importance for a wide range of problems from the study of dusty or complex plasmas to the controlled synthesis of nanoparticle materials in plasmas. Despite its known deficiencies, the orbital motion limited (OML) theory, which strictly applies only to collisionless plasmas, is the most widely used model to describe particle charging. This paper develops a simple, analytical model to describe the charging of particles in plasmas over a wide range of pressures and particle sizes. In spite of its simplicity, excellent agreement is found with results of a self-consistent molecular dynamics Monte Carlo model and with experimental results found in the literature. In particular, the model presented here provides significant improvements compared to the OML theory.

An analytical model for the soliton-potential interaction is presented by constructing a collective coordinate for the system. Most of the characters of the interaction are derived analytically while they are calculated by other models numerically. We find that the behavior of the soliton is like a point particle “living” under the influence of a complicated potential, that is a function of soliton velocity and the potential parameters. The analytic model does not have a clear prediction for the islands of initial velocities in which the soliton may reflect back or escape over the potential well.

We demonstrate the use of a variational method to determine a quantitative lower bound on the rate of convergence of Markov chain Monte Carlo (MCMC) algorithms as a function of the target density and proposal density. The bound relies on approximating the second largest eigenvalue in the spectrum of the MCMC operator using a variational principle and the approach is applicable to problems with continuous state spaces. We apply the method to one dimensional examples with Gaussian and quartic target densities, and we contrast the performance of the random walk Metropolis-Hastings algorithm with a “smart” variant that incorporates gradient information into the trial moves, a generalization of the Metropolis adjusted Langevin algorithm. We find that the variational method agrees quite closely with numerical simulations. We also see that the smart MCMC algorithm often fails to converge geometrically in the tails of the target density except in the simplest case we examine, and even then care must be taken to choose the appropriate scaling of the deterministic and random parts of the proposed moves. Again, this calls into question the utility of smart MCMC in more complex problems. Finally, we apply the same method to approximate the rate of convergence in multidimensional Gaussian problems with and without importance sampling. There we demonstrate the necessity of importance sampling for target densities which depend on variables with a wide range of scales.

We propose a strategy to achieve the fastest convergence in the Wang-Landau algorithm with varying modification factors. With this strategy, the convergence of a simulation is at least as good as the conventional Monte Carlo algorithm, i.e., the statistical error vanishes as $1∕\sqrt{t}$, where $t$ is a normalized time of the simulation. However, we also prove that the error cannot vanish faster than $1∕t$. Our findings are consistent with the $1∕t$ Wang-Landau algorithm discovered recently, and we argue that one needs external information in the simulation to beat the conventional Monte Carlo algorithm.

Thermodynamic behaviors of a binary monolayer of Ising dipolar particles are studied using particle dynamics simulation, varying the relative intensity between the upward and downward dipole moments. The orientational order of the solid phase changes from tetragonal to hexagonal as the moment ratio increases. On the basis of the arguments of the candidates for ground state structures, the energy of the structures are well estimated. The transition point is also determined theoretically, which is consistent with the value obtained from the simulation results. Critical condensation is also studied. While the system whose moment ratio is unity does not exhibit the gas-liquid critical condensation, the transition appears as the moment ratio changes. The local structure of the liquid phase is found to be characterized by the ground state of the tetramer. The above-mentioned results imply that the gas-liquid critical point comes close to the melting transition point as the local structure of the liquid phase becomes closer to the structure of the solid phase, and therefore, the critical condensation is vanished.

The ideas related to potential-energy landscape and cooperativity of atomic rearrangements are widely discussed in the research field of glass transition. The crossover transition from high-temperature regime to potential-energy-landscape-influenced regime was extensively studied using the concept of inherent structure. However, the interpretation of this crossover behavior in terms of microscopic changes in real structures is still lacking. In this paper we present several observations on the crossover behavior on real structures. We compare fluctuations in the global properties (total number of bonds, total potential energy, pressure) versus fluctuations in the local properties (coordination number, atomic potential energy, local atomic pressure) by means of molecular dynamics simulations. We then show that the total and local fluctuations in the number of atomic bonds in the system depend on temperature differently above and below the temperature of crossover to the landscape-influenced regime. Similarly, the ratio between the global and local fluctuations in the potential energy and pressure changes in the vicinity of the crossover temperature, whereas the change is less distinct than in the case of the bond fluctuations. Our results indicate that local fluctuations become more correlated below the crossover temperature, most likely via the interaction through the dynamic shear elastic field.

Propagating waves on the surface of cells, over many micrometers, involve active forces. We investigate here the mechanical excitation of such waves when the membrane is perturbed by an external oscillatory force. The external perturbation may trigger the propagation of such waves away from the force application. This scheme is then suggested as a method to probe the properties of the excitable medium of the cell, and learn about the mechanisms that drive the wave propagation. We then apply these ideas to a specific model of active cellular membrane waves, demonstrating how the response of the system to the external perturbation depends on the properties of the model. The most outstanding feature that we find is that the excited waves exhibit a resonance phenomenon at the frequency corresponding to the tendency of the system to develop a linear instability. Mechanical excitation of membrane waves in cells at different frequencies can therefore be used to characterize the properties of the mechanism underlying the existence of these waves.

We present a molecular dynamics analysis of the static friction between two thick slabs. The upper block is formed by ${\mathrm{N}}_2$ molecules and the lower block by Pb atoms. We study the effects of the temperature as well as the effects produced by the structure of the surface of the lower block on the static friction. To put in evidence the temperature effects we will compare the results obtained with the lower block formed by still atoms with those obtained when the atoms are allowed to vibrate (e.g., with phonons). To investigate the importance of the geometry of the surface of the lower block we apply the external force in different directions, with respect to a chosen crystallographic direction of the substrate. We show that the interaction between the lattice dynamics of the two blocks is responsible for the strong dependence of the static friction on the temperature. The lattice dynamics interaction between the two blocks strongly reduces the static friction, with respect to the case of the rigid substrate. This is due to the large momentum transfer between atoms and the ${\mathrm{N}}_2$ molecules which disorders the molecules of the interface layer. A further disorder is introduced by the temperature. We perform calculations at $T=20\mathrm{K}$ which is a temperature below the melting, which for our slab is at $50\mathrm{K}$. We found that because of the disorder the static friction becomes independent of the direction of the external applied force. The very low value of the static friction seems to indicate that we are in a regime of thermolubricity similar to that observed in dynamical friction.

We study a modified version of the naming game, a recently introduced model which describes how shared vocabulary can emerge spontaneously in a population without any central control. In particular, we introduce a mechanism that allows a continuous interchange with the external inventory of words. A playing strategy, influenced by the hierarchical structure that individuals’ reputation defines in the community, is implemented. We analyze how these features influence the convergence times, the cognitive efforts of the agents, and the scaling behavior in memory and time.

Turbulence of scroll waves is a sort of spatiotemporal chaos that exists in three-dimensional excitable media. Cardiac tissue and the Belousov-Zhabotinsky reaction are examples of such media. In cardiac tissue, chaotic behavior is believed to underlie fibrillation which, without intervention, precedes cardiac death. In this study we investigate suppression of the turbulence using stimulation of two different types, “modulation of excitability” and “extra transmembrane current.” With cardiac defibrillation in mind, we used a single pulse as well as repetitive extra current with both constant and feedback controlled frequency. We show that turbulence can be terminated using either a resonant modulation of excitability or a resonant extra current. The turbulence is terminated with much higher probability using a resonant frequency perturbation than a nonresonant one. Suppression of the turbulence using a resonant frequency is up to fifty times faster than using a nonresonant frequency, in both the modulation of excitability and the extra current modes. We also demonstrate that resonant perturbation requires strength one order of magnitude lower than that of a single pulse, which is currently used in clinical practice to terminate cardiac fibrillation. Our results provide a robust method of controlling complex chaotic spatiotemporal processes. Resonant drift of spiral waves has been studied extensively in two dimensions, however, these results show for the first time that it also works in three dimensions, despite the complex nature of the scroll wave turbulence.

The effect of physically realizable wall potentials (soft walls) on the dynamics of two interacting particles in a one-dimensional (1D) billiard is examined numerically. The 1D walls are modeled by the error function and the transition from hard to soft walls can be analyzed continuously by varying the softness parameter $\sigma$. For $\sigma \to 0$ the 1D hard wall limit is obtained and the corresponding wall force on the particles is the $\delta$ function. In this limit the interacting particle dynamics agrees with previous results obtained for the 1D hard walls. We show that the two interacting particles in the 1D soft walls model is equivalent to one particle inside a soft right triangular billiard. Very small values of $\sigma$ substantiously change the dynamics inside the billiard and the mean finite-time Lyapunov exponent decreases significantly as the consequence of regular islands which appear due to the low-energy double collisions (simultaneous particle-particle-1D wall collisions). The rise of regular islands and sticky trajectories induced by the 1D wall softness is quantified by the number of occurrences of the most probable finite-time Lyapunov exponent. On the other hand, chaotic motion in the system appears due to the high-energy double collisions. In general we observe that the mean finite-time Lyapunov exponent decreases when $\sigma$ increases, but the number of occurrences of the most probable finite-time Lyapunov exponent increases, meaning that the phase-space dynamics tends to be more ergodiclike. Our results suggest that the transport efficiency of interacting particles and heat conduction in periodic structures modeled by billiards will strongly be affected by the smoothness of physically realizable walls.