We report the nature of the transition to generalized synchronization (GS) in a system of two coupled scalar piecewise linear time-delay systems using the auxiliary system approach. We demonstrate that the transition to GS occurs via an on-off intermittency route and that it also exhibits characteristically distinct behaviors for different coupling configurations. In particular, the intermittency transition occurs in a rather broad range of coupling strength for the error feedback coupling configuration and in a narrow range of coupling strength for the direct feedback coupling configuration. It is also shown that the intermittent dynamics displays periodic bursts of periods equal to the delay time of the response system in the former case, while they occur in random time intervals of finite duration in the latter case. The robustness of these transitions with system parameters and delay times has also been studied for both linear and nonlinear coupling configurations. The results are corroborated analytically by suitable stability conditions for asymptotically stable synchronized states and numerically by the probability of synchronization and by the transition of sub-Lyapunov exponents of the coupled time-delay systems. We have also indicated the reason behind these distinct transitions by referring to the unstable periodic orbit theory of intermittency synchronization in low-dimensional systems.

We study slip boundary conditions for simple fluids at surfaces with nanoscale chemical heterogeneities. Using a perturbative approach, we examine the flow of a Newtonian fluid far from a surface described by a heterogeneous Navier slip boundary condition. In the far field, we obtain expressions for an effective slip boundary condition in certain limiting cases. These expressions are compared to numerical solutions which show they work well when applied in the appropriate limits. The implications for experimental measurements and for the design of surfaces that exhibit large slip lengths are discussed.

We formulate the Hamiltonian version of contour dynamics for a model of axially symmetric, equally vortexed jet streams with a free boundary. In particular, we study dominant structural elements which appear in strongly perturbed jet streams at the stage of their decay. The model produces solutions with compact support which can describe such dominant structures, called compactons. Evolution of the compactons can lead to their collapse which virtually does not deform the shape, but gradually intensifies the vortex sheet at the boundary according to the law ${(t_0-t)}^{-1}$, where $t_0$ is the collapse time.

We describe an approximation method to solve the probability density function transport equation, i.e., the Liouville equation, which is encountered in the evolution of uncertainty of the initial values of dynamical systems. A state-space based method is formulated using a least-squares technique that preserves the parabolic nature of the Liouville equation and is flexible in terms of accuracy of representation. This method is based on a global approximation in terms of analytical elementary functions with unknown parameters, whose evolution equations are determined by a global least-squares approximation. The realizability conditions of the probability density, i.e., the non-negativity and normalization conditions are enforced at all times. The method is successfully evaluated in a number of scenarios including the uncertainty evolution in a system governed by a Riccati equation and a particle moving in a fluid under the influence of Stokes drag force. The results obtained in our examples exhibit a reasonable good agreement when compared with the solution of the probability transport equation using the method of characteristics. The cost of the method is proportional to the cost of solving the deterministic system and the number of parameters used to approximate the probability density function, a feature that can make the present method very advantageous in comparison with other methods in problems involving a large number of dimensions.

Due to an extremely rugged structure of the free energy landscape, the determination of spin-glass ground states is among the hardest known optimization problems, found to be $\mathcal{NP}$ hard in the most general case. Owing to the specific structure of local (free) energy minima, general-purpose optimization strategies perform relatively poorly on these problems, and a number of specially tailored optimization techniques have been developed in particular for the Ising spin glass and similar discrete systems. Here, an efficient optimization heuristic for the much less discussed case of continuous spins is introduced, based on the combination of an embedding of Ising spins into the continuous rotators and an appropriate variant of a genetic algorithm. Statistical techniques for insuring high reliability in finding (numerically) exact ground states are discussed, and the method is benchmarked against the simulated annealing approach.

The average pedestrian flow through an exit is one of the most important indices in evaluating pedestrian dynamics. In order to study the flow in detail, the floor field model, which is a crowd model using cellular automata, is extended by taking into account realistic behavior of pedestrians around the exit. The model is studied by both numerical simulations and cluster analysis to obtain a theoretical expression for the average pedestrian flow through the exit. It is found quantitatively that the effects of exit door width, the wall, and the pedestrian mood of competition or cooperation significantly influence the average flow. The results show that there is a suitable width and position of the exit according to the pedestrians’ mood.

The photonic force microscope (PFM) is an opto-mechanical technique that uses an optically trapped probe to measure forces in the range of pico to femto Newton. For a correct use of the PFM, the force field has to be homogeneous on the scale of the Brownian motion of the trapped probe. This condition implicates that the force field must be conservative, excluding the possibility of a rotational component. However, there are cases where these assumptions are not fulfilled. Here, we show how to expand the PFM technique in order to deal with these cases. We introduce the theory of this enhanced PFM and we propose a concrete analysis workflow to reconstruct the force field from the experimental time series of the probe position. Furthermore, we experimentally verify some particularly important cases, namely, the case of a conservative and of a rotational force field.

We propose a model for the elastic properties of RNA gels. The model predicts anomalous elastic properties in the form of a negative Poisson ratio and shape instabilities. The anomalous elasticity is generated by the non-Gaussian force-deformation relation of single-stranded RNA. The effect is greatly magnified by broken rotational symmetry produced by double-stranded sequences and the concomitant soft modes of uniaxial elastomers.

We propose a continuum theory for the conformational transitions of viral shells. Conformational transitions of viral shells, as encountered during viral maturation, are associated with a soft mode instability of the capsid proteins [F. Tama and C. L. Brooks, J. Mol. Biol. 345(2), 299 (2005)]. The continuum theory presented here is an adaptation of the Ginzburg-Landau theory of soft-mode structural phase transitions of solids to viral shells. The theory predicts that the conformational transitions are characterized by a pronounced softening of the shell elasticity in the critical region. We demonstrate that the thermodynamics of the conformational transition can be probed quantitatively by a micromechanical atomic force microscope study. The external force can drive a capsid into a state of phase coexistence characterized by a highly nonlinear force deformation curve.

Coordinated cellular activity is a major characteristic of nervous system function. Coupled oscillator theory offers unique avenues to address cellular coordination phenomena. In this study, we focus on the characterization of the dynamics of epileptiform activity, based on some seizures that manifest themselves with very periodic rhythmic activity, termed absence seizures. Our approach consists in obtaining experimentally the phase response curves (PRCs) in the neocortex and thalamus, and incorporating these PRCs into a model of coupled oscillators. Phase preferences of the stationary states and their stability are determined, and these results from the model are compared with the experimental recordings, and interpreted in physiological terms.

One of the main elements of the self-consistent generalized Langevin equation (SCGLE) theory of colloid dynamics [Phys. Rev. E 62, 3382 (2000); 72, 031107 (2005)] is the introduction of exact short-time moment conditions in its formulation. The need to previously calculate these exact short-time properties constitutes a practical barrier for its application. In this Brief Report, we report that a simplified version of this theory, in which this short-time information is eliminated, leads to the same results in the intermediate and long-time regimes. Deviations are only observed at short times, and are not qualitatively or quantitatively important. This is illustrated by comparing the two versions of the theory for representative model systems.

Synchronization cluster analysis is an approach to the detection of underlying structures in data sets of multivariate time series, starting from a matrix $R$ of bivariate synchronization indices. A previous method utilized the eigenvectors of $R$ for cluster identification, analogous to several recent attempts at group identification using eigenvectors of the correlation matrix. All of these approaches assumed a one-to-one correspondence of dominant eigenvectors and clusters, which has however been shown to be wrong in important cases. We clarify the usefulness of eigenvalue decomposition for synchronization cluster analysis by translating the problem into the language of stochastic processes, and derive an enhanced clustering method harnessing recent insights from the coarse-graining of finite-state Markov processes. We illustrate the operation of our method using a simulated system of coupled Lorenz oscillators, and we demonstrate its superior performance over the previous approach. Finally we investigate the question of robustness of the algorithm against small sample size, which is important with regard to field applications.

We present an adaptive similarity-based approach to detect generalized synchronization (GS) with $n:m$ phase synchronization (PS), where $n$ and $m$ are integers and one of them is 1. This approach is based on the similarity index (SI) and Gaussian mixture model with the minimum description length criterion. The clustering method, which is shown to be superior to the closeness and connectivity of a continuous function, is employed in this study to detect the existence of GS with $n:m$ PS. We conducted a computer simulation and a finger-lifting experiment to illustrate the effectiveness of the proposed method. In the simulation of a Rössler-Lorenz system, our method outperformed the conventional SI, and GS with 2:1 PS within the coupled system was found. In the experiment of self-paced finger-lifting movement, cortico-muscular GS with 1:2 and 1:3 PS was found between the surface electromyogram signals on the first dorsal interossei muscle and the magnetoencephalographic data in the motor area. The GS with $n:m$ PS ($n$ or $m=1$) has been simultaneously resolved from both simulation and experiment. The proposed approach thereby provides a promising means for advancing research into both nonlinear dynamics and brain science.

The evolutions of isotropy and the Kármán-Howarth-Kolmogorov (KHK) relation are studied experimentally and numerically in the lifetime of turbulence, i.e., developing, fully developed, and decaying states. The isotropy relations and the KHK relation are well satisfied when the turbulence is fully developed, but they are broken when the turbulence is developing or decaying. The turbulence shows opposite anisotropy in the developing and the decaying states. In response to the isotropy change, the KHK relation shows a variation of energy budget at each scale, which is consistent with an energy transfer from large to small scales. We also find that Taylor’s frozen-eddy hypothesis and periodic boundary conditions, respectively, lead to an inherent phenomenon at large scales.

We calculate analytically the electron-ion temperature equilibration rate in a fully ionized, weakly to moderately coupled plasma, using an exact treatment of the Fermi-Dirac electrons. The temperature is sufficiently high so that the quantum-mechanical Born approximation to the scattering is valid. It should be emphasized that we do not build a model of the energy exchange mechanism, but rather, we perform a systematic first principles calculation of the energy exchange. At the heart of this calculation lies the method of dimensional continuation, a technique that we borrow from quantum field theory and use in a different fashion to regulate the kinetic equations in a consistent manner. We can then perform a systematic perturbation expansion and thereby obtain a finite first-principles result to leading and next-to-leading order. Unlike model building, this systematic calculation yields an estimate of its own error and thus prescribes its domain of applicability. The calculational error is small for a weakly to moderately coupled plasma, for which our result is nearly exact. It should also be emphasized that our calculation becomes unreliable for a strongly coupled plasma, where the perturbative expansion that we employ breaks down, and one must then utilize model building and computer simulations. Besides providing different and potentially useful results, we use this calculation as an opportunity to explain the method of dimensional continuation in a pedagogical fashion. Interestingly, in the regime of relevance for many inertial confinement fusion experiments, the degeneracy corrections are comparable in size to the subleading quantum correction below the Born approximation. For consistency, we therefore present this subleading quantum-to-classical transition correction in addition to the degeneracy correction.

Starting from the governing equations for a quantum magnetoplasma including the quantum Bohm potential and electron spin-$1∕2$ effects, we show that the system of quantum magnetohydrodynamic (QMHD) equations admits rarefactive solitons due to the balance between nonlinearities and quantum diffraction and tunneling effects. It is found that the electron spin-$1∕2$ effect introduces a pressurelike term with negative sign in the QMHD equations, which modifies the shape of the solitary magnetosonic waves and makes them wider and shallower. Numerical simulations of the time-dependent system shows the development of rarefactive QMHD solitary waves that are modified by the spin effects.

The Epstein-Barr virus (EBV) infects more than $90\%$ of the human population, and causes glandular fever as well as several more serious diseases. It is a tumor virus, and has been widely studied as a model system for cell transformation in humans. A central feature of the EBV life cycle is its ability to persist in human B cells in different latency states, denoted latency I, II, and III. In latency III the host cell is driven to cell proliferation and hence expansion of the viral population without entering the lytic pathway, while the latency I state is almost completely dormant. We here study the effective cooperativity of the viral C promoter, active in latency III EBV cell lines. We show that the unusually large number of binding sites of two competing transcription factors, one viral and one from the host, serves to make the switch sharper (higher Hill coefficient), either by cooperative binding between molecules of the same species when they bind, or by competition between the two species if there is sufficient steric hindrance.

In a recent paper [Phys. Rev. E 76, 031202 (2007)], Schmidt proposed a fundamental measure density functional theory for one-dimensional nonadditive hard-rod fluid mixtures and compared its predictions for the bulk structural properties with Monte Carlo simulations. The aim of this Brief Report is to recall that the problem admits an exact solution in the bulk, which is briefly summarized in a self-contained way.

The paper shows that under certain circumstances a monochromatic filament source located above a plane surface coated with a metamaterial does not illuminate the upper half space. New designs of electromagnetic field absorbers and resonators are suggested. They can be constructed with the help of metamaterials.

We address the problem of using feedback control for the purpose of suppressing rare intense events in spatially extended systems. As an example, we investigate the use of control to suppress turbulent spikes in the complex Ginzburg-Landau equation in the limit of small dissipation. We explore how information obtained by forecasting can be used to implement spatially and temporally localized control parameter changes and how control strength and cost are related to effectiveness in this framework. The effects of model error and imperfect state measurement are also considered.