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We investigated phase dynamics of sinusoidal forearm tracking with delayed visual feedback. To this end we introduced two data analysis tools which enabled us to find several delay-induced transitions between qualitatively different regimes. Our results show that the investigation of delay-induced transitions of the phase dynamics in tracking movements provides us with insights into the underlying neuronal signal processing. In particular, we experimentally verified predictions of a recently presented mathematical model [P. Tass, A. Wunderlin, and M. Schanz, J. Biol. Phys. 21, 83 (1995)].

We construct exact ring soliton-like solutions of the cylindrically symmetric (i.e., radial) Gross- Pitaevskii equation with a potential, using the similarity transformation method. Depending on the choice of the allowed free functions, the solutions can take the form of stationary dark or bright rings whose time dependence is in the phase dynamics only, or oscillating and bouncing solutions, related to the second Painlev\'e transcendent. In each case the potential can be chosen to be time-independent., Comment: 8 pages, 7 figures. Version 2: stability analysis of the dark solution

We consider the phase dynamics of an ensemble of Kuramoto oscillators whose eigenfrequencies are perturbed to model the openness of living systems, and we show that it exhibits time-localized epochs of synchrony. A new quantitative measure is used to show that the model compares well with electroencephalography data recorded from a healthy awake human.

We examine the mutual coherence and phase dynamics of two solid-state lasers, generated adjacent to each other in a single Nd:YAG rod. The coupling of the lasers is varied by changing the separation of the pump beams. A model is formulated to interpret the experimental results, and theoretical predictions are obtained that are in excellent agreement with the measurements.

Recent advances in subpicosecond generation and amplification with semiconductor lasers have shown the necessity of extending and modifying existing theoretical models1 to include phenomena influencing subpicosecond pulse amplification. To model subpicosecond pulse evolution in semiconductor laser amplifiers (SLA), spectral dependence of both real and imaginary parts of the complex susceptibility (index and gain) within the pulse bandwidth must be included. In addition to the well known gain saturation and selfphase modulation (SPM) due to carrier depletion1, it is necessary to account for the recently observed rapid gain and phase dynamics which have been attributed to carrier heating2. The effects of an instantaneous nonlinear index n2 must also be included.

Concerning the spontaneous THz electromagnetic wave emission from intrinsic Josephson junctions, we revisit the theory for intrinsic Josephson effects from standpoints of the couplings between stacked junctions and consequent superconducting phase dynamics. After reviewing the previous simulation works based on the theory, we present recent multi-physics simulation studies suggested by authors to systematically reproduce the emission experiments. Some typical simulation results are exhibited and the future perspective of the simulation is also given.

The phase dynamics of the coupled Josephson junctions in the framework of CCJJ and CCJJ+DC models is studied. The current voltage characteristics (CVC) are numerically calculated for the stacks with different number of junctions at different model parameters. We manifest the difference of these models for the branching at I = Ic and in the hysteretic region. The essential difference is observed in the breakpoint region, where the longitudinal plasma wave is created. We discuss the main features of both models, related with the role of the diffusion current between the superconducting layers.

To model the IV-characteristics of shunted intrinsic Josephson junctions we calculated phase dynamics of a chain of two identical junctions covered by a resistive shunt and with a resistive crosspiece between the shunt and the junctions. The coherent solution of dynamic equations for this system is unstable at some bias currents above critical currents of junctions. We have shown that this instability leads to the multibranch structure of IV-curves in the hysteretic region. The multibranch structure appears due to the random switching of junctions to the superconducting state above their critical currents. We found that the resistance of the interface between a covering shunt and the junctions can regulate the multibranch behaviour.

The physics of pizza tossing and the next generation of micromotors Is diamagnetism possible classically? Phase dynamics of two coupled oscillators under external periodic force Optical communications through dense matter

The effect of synchronization has been studied in a system of two coupled Van der Pol oscillators under external harmonic force. The analysis has been carried out using the phase approach. The mechanisms of complete and partial synchronization have been established. The main type of bifurcation described in this paper is the saddle-node bifurcation of invariant curves that corresponds to the saddle-node bifurcation of two-dimensional tori in the complete system of differential equations for the dynamical system under study.

To reveal the dynamic mechanism underlying Parkinsonian resting tremor, we applied a phase dynamics modelling technique to local field potentials and accelerometer signals recorded in three Parkinsonian patients with implanted depth electrodes. We detect a bidirectional coupling between the subcortical oscillation and the tremor. The tremor → brain driving is a linear effect with a small delay corresponding to the neural transmission time. In contrast, the brain → tremor driving is a nonlinear effect with a long delay in the order of 1–2 mean tremor periods. Our results are well reproduced for an ensemble of 41 tremor epochs in three Parkinsonian patients and confirmed by surrogate data tests and model simulations. The uncovered mechanism of tremor generation suggests to specifically counteract tremor by desynchronizing the subcortical oscillatory neural activity.

A classical many-body model for the phase dynamics of randomly pinned charge density waves is found to exhibit stretched exponential relaxation below threshold. The statistics of single particle relaxation is highly non-trivial and can only be deduced from known scaling behaviour of intermittent trajectories in an uncoupled approximation. This is compared with results from present single-particle approaches. The self-similarity properties at the dynamical phase transition at threshold are investigated.

In this note we will introduce in the first section the concept of phase dynamics, followed by an outline of some recent developments associated with the properties of nonlinear phase equations, and we will conclude with an extensive list of references on phase dynamics and closely related subjects including envelope equations, the motion of defects, and the coupling between amplitude and phase equations.

Much attention has been attracted in recent years to the dynamics of distorted two-dimensional patterns in non-equilibrium systems, in particular, to the dynamics of defects that are necessarily present in realistic striped patterns, such as Rayleigh-Benard convection rolls, observed either experimentally or computationally, and play the crucial role in the overall organization of patterns in extended systems and their long-time evolution. We refer to Newell [1] for a comprehensive overview of the field.

This paper discusses the excitations in a condensed Bose system as manifestations of the dynamics of the phase. It is argued that the standard approach based on spontaneous symmetry breaking is not viable; a superselection rule enforces strict particle conservation. Some recent theoretical results are used to show how the significance of the phase dynamics can be retained without violating the superselection rule.

A holocinematography system based on the copper vapor laser is described where a series of spatially multiplex holograms is recorded in rapid succession (up to 10 kHz).

The phase dynamic equation of motion for a propagating periodic structure is derived in a euclidean invariant manner. The formulation is applied to the generalized Swift-Hohenberg model where the coefficients are complex numbers.

Des equations de champ non lineaires dissipatives derivees de fonctionnelles de potentiel avec minima degeneres sont reduites a un systeme couple d'equations du mouvement des defauts topologiques (dislocations) et de la variable de phase. La theorie est appliquee a l'equation de thermoconvection de Swift-Hohenberg

We perform a linear stability analysis of the priodic crenellated front profiles which provide an amplitude threshold for the cellular instability of a faceted directional solidification front [1]. This analysis assumes that facets are much longer than curved parts of the front (risers). We show that, while the crenellated front is stable as regards phase diffusion, it always has a branch of unstablemodes which are a mixture of amplitude and phase fluctuations. While amplitude variations are primarily controlled by facet kinetics, the lateral riser mobility is limited by the solute diffusion field dynamics Nous faisons une analyse de stabilite lineaire des fronts periodiques creneles qui definissent un seuil d'amplitude pour l'instabilite cellulaire d'un front de solidification directionnelle facette [1]. Nous etudions la limite ou les facettes sont beaucoup plus longues que les parties courbes du front (contremarches). Le front crenele est stable vis-a-vis de la diffusion de phase. Alors que les variations d'amplitude sont essentiellement controlees par la cinetique de facette, la mobilite laterale des contremarches est limitee par la dynamique du champ de diffusion solutale

Spatially small canopy gaps dominated the natural disturbance regime of old-growth spruce–fir forests in the Great Smoky Mountains, North Carolina and Tennessee. New gaps ≤200 m2 in size were formed with a frequency of 0.006 to 0.009/year and the 1- to 10-year age class of these gaps covered an estimated 6 to 17% of the study area (depending on calculation method). Sixty canopy gaps sampled on a 7-ha intensive study site ranged in size from 15 to 150 m2. Although tree replacement patterns in these gaps were unpredictable from gap size and age, the gap event was important in species interactions. The three canopy dominants, Abiesfraseri (Pursh) Poir., Picearubens Sarg., and Betulalutea Michx.f., had unique suites of life history traits. Abies reached high understory densities, but had the highest canopy turnover rate of the three species. Betula was scarce in the understory, but had a crown expansion rate in gaps eight times that of the two conifers. Picea was the longest lived species and appeared to have the best survivorship. Tree replacement models based on advanced regeneration led to the prediction that Abies canopy density would increase and Betula canopy density would decrease, while models based on gap inventories led to opposite conclusions. Data from direct observation of the gap capture process supported the hypothesis that this old-growth stand was near compositional equilibrium and underscored the importance of disturbance effects in community organization.

We study the spatial stability of systems at onset of the temporal intermittent transition to chaos. We show that the phase dynamics during laminar episodes, described as orbits near a saddle-node bifurcation of limit cycles, is second order in time and can lead to propagative behaviour.

Laser induced charge transfer reactions of halogens in rare gas solids and liquids provide a powerful means for the study of condensed phase dynamics. Many-body effects with respect to both electronic and nuclear coordinates, and cooperative interactions with radiation fields, are some of the studied phenomena that are highlighted in this article.The pertinence of these ionic reactions to chemistry in solids is demonstrated in photodissociation studies of molecular halogens in rare gas matrices. The coexistence of both delocalized and localized charge transfer states in solid xenon doped with atomic halogens is presented and dynamical consequences—charge separation, self-trapping and energy storage—are discussed. Static and dynamic solvent effects in liquid phase harpoon reactions are considered. The characterization of cooperative excitations— two-photon, two-electron transitions—in liquid solutions is presented.

The effects of the amplitude nonuniformity of the magnetic field in a betatron on the forced and betatron radial oscillations of electrons during extraction (or discharge toward the target) at the end of the acceleration cycle are examined. The amplitude and phase dynamics of radial betatron oscillations are studied by means of an analog computer.

The hydrodynamics of two-phase liquid—liquid co-current down-flow in a packed column was investigated using adequate tracer techniques. Emphasis was set upon dispersed phase behaviour and hold-up; the choice of a model which accounts for the experimental results obtained has been discussed.

The application of methods drawn from nonlinear and stochastic dynamics to the analysis of cardiovascular time series is reviewed, with particular reference to the identification of changes associated with ageing. The natural variability of the heart rate (HRV) is considered in detail, including the respiratory sinus arrhythmia (RSA) corresponding to modulation of the instantaneous cardiac frequency by the rhythm of respiration. HRV has been intensively studied using traditional spectral analyses, e.g. by Fourier transform or autoregressive methods, and, because of its complexity, has been used as a paradigm for testing several proposed new methods of complexity analysis. These methods are reviewed. The application of time–frequency methods to HRV is considered, including in particular the wavelet transform which can resolve the time-dependent spectral content of HRV. Attention is focused on the cardio-respiratory interaction by introduction of the respiratory frequency variability signal (RFV), which can be acquired simultaneously with HRV by use of a respiratory effort transducer. Current methods for the analysis of interacting oscillators are reviewed and applied to cardio-respiratory data, including those for the quantification of synchronization and direction of coupling. These reveal the effect of ageing on the cardio-respiratory interaction through changes in the mutual modulation of the instantaneous cardiac and respiratory frequencies. Analyses of blood flow signals recorded with laser Doppler flowmetry are reviewed and related to the current understanding of how endothelial-dependent oscillations evolve with age: the inner lining of the vessels (the endothelium) is shown to be of crucial importance to the emerging picture. It is concluded that analyses of the complex and nonlinear dynamics of the cardiovascular system can illuminate the mechanisms of blood circulation, and that the heart, the lungs and the vascular system function as a single entity in dynamical terms. Clear evidence is found for dynamical ageing.

By applying the ‘theory of synchronization’ from the science of complexity to studying the regional regularity of ore formation within the Nanling region of southern China, a characteristic target-pattern regional ore zonality has been discovered. During the early and late Yanshanian epoch (corresponding respectively to the Jurassic and Cretaceous periods), two centers of ore formation emerged successively in the Nanling region; the former is mainly for rare metals (W, Sn, Mo, Bi, Nb) and one rare-earth element (La) and was generated in the Jurassic period; whereas the latter is mainly for base metals (Cu, Pb, Zn, Sb, Hg), noble metals (Au, Ag), and one radioactive element (U) and was generated in the Cretaceous period. Centers of ore formation were brought about by interface dynamics respectively at the Qitianling and Jiuyishan districts in southern Hunan province. The characteristic giant nonlinear target-pattern regional ore zonality was generated by spatio-temporal synchronization process of the Nanling complex metallogenic system. It induced the collective dynamics and cooperative behavior of the system and displayed the configuration of the regional ore zonality. Then dynamical clustering transformed the configuration into rudimentary ordered coherent structures. Phase dynamics eventually defined the spatio-temporal structures of the target-pattern regional ore zonality and determined their localization and distribution. A new methodology for revealing regional ore zonality is developed, which will encourage further investigation of the formation of deep-seated ore resources and the onset of large-scale mineralization.

Modeling and interpreting (partial) synchronous neural activity can be a challenge. We illustrate this by deriving the phase dynamics of two seminal neural mass models: the Wilson-Cowan firing rate model and the voltage-based Freeman model. We established that the phase dynamics of these models differed qualitatively due to an attractive coupling in the first and a repulsive coupling in the latter. Using empirical structural connectivity matrices, we determined that the two dynamics cover the functional connectivity observed in resting state activity. We further searched for two pivotal dynamical features that have been reported in many experimental studies: (1) a partial phase synchrony with a possibility of a transition towards either a desynchronized or a (fully) synchronized state; (2) long-term autocorrelations indicative of a scale-free temporal dynamics of phase synchronization. Only the Freeman phase model exhibited scale-free behavior. Its repulsive coupling, however, let the individual phases disperse and did not allow for a transition into a synchronized state. The Wilson-Cowan phase model, by contrast, could switch into a (partially) synchronized state, but it did not generate long-term correlations although being located close to the onset of synchronization, i.e. in its critical regime. That is, the phase-reduced models can display one of the two dynamical features, but not both. We would like to thank Mark Woolrich for his contribution to data acquisition and analysis and the fruitful discussion about interpretation of our findings. We received the following funding: GD, RT: ERC Advanced Grant: DYSTRUCTURE (n. 295129), GD: Spanish Research Project PSI2013-42091-P, Human Brain Project, and FP7-ICT BrainScales (269921). MLK: ERC Consolidator Grant CAREGIVING (n. 615539) and Center for Music in the Brain/Danish National Research Foundation (DNRF117). AD, BP: H2020-MSA-ITN COSMOS (n. 642563).

We discuss the long-wavelength, low-frequency excitations of non- equilibrium systems with a helical structure as observed in spiral vortex flow in the Taylor instability in long cylinders. We find that a single-phase equation can give rise to a propagating mode, a situation unknown from hydrodynamics in local thermodynamic equilibrium.

Flow field effects on pattern forming instabilities are studied in the framework of amplitude equations and phase dynamics. In thin horizontal fluid layers, it is shown that the vertical profile of imposed fluid velocity fields induces anisotropy effects which determine the selection and stability properties of spatiotemporal patterns associated with Turing and Hopf bifurcations. In deformed metals, the role of plastic flows in the formation of dislocation microstructures is discussed.

The length dynamics both of microtubule-associated protein (MAP)-rich and MAP-depleted bovine brain microtubules were examined at polymer mass steady state. In both preparations, the microtubules exhibited length redistributions shortly after polymer mass steady state was attained. With time, however, both populations relaxed to a state in which no further changes in length distributions could be detected. Shearing the microtubules or diluting the microtubule suspensions transiently increased the extent to which microtubule length redistributions occurred, but again the microtubules relaxed to a state in which changes in the polymer length distributions were not detected. Under steady-state conditions of constant polymer mass and stable microtubule length distribution, both MAP-rich and MAP-depleted microtubules exhibited behavior consistent with treadmilling. MAPs strongly suppressed the magnitude of length redistributions and the steady-state treadmilling rates. These data indicate that the inherent tendency of microtubules in vitro is to relax to a steady state in which net changes in the microtubule length distributions are zero. If the basis of the observed length redistributions is the spontaneous loss and regain of GTP-tubulin ("GTP caps") at microtubule ends, then in order to account for stable length distributions the microtubule ends must reside in the capped state far longer than in the uncapped state, and uncapped microtubule ends must be rapidly recapped. The data suggest that microtubules in cells may have an inherent tendency to remain in the polymerized state, and that microtubule disassembly must be induced actively.

We present the nonlinear phase equations describing the stability of a one-dimensional periodic pattern, with mean flow effect due to Galilean invariance. We show that the phase dynamics is second order in time, and could lead to an oscillatory instability of the pattern.

We present dynamic equations for the slow macroscopic variables of the wavy vortex state. The static solutions explain in a qualitative way recent experimental results of Ahlers et al. on the variation of the vortex diameter throughout the cell. In addition, we predict the existence of a pair of propagating or overdamped normal modes (depending on the wave vector of the disturbance) formed by the slow variables.

The equation of motion for the slow time dependence of convective rolls due to long-wavelength inhomogeneities is shown to have a singular dependence on the wave vector of the disturbance. Consequences for the skew varicose instability and the wave-number selection principle in textures of curved rolls suggested by Pomeau and Manneville are discussed.

Discussion du comportement a basse frequence de systemes proches de l'equilibre thermodynamique, qui forment des diagrammes a variation spatiale dus a des contraintes ou a des champs externes. On montre que dans ces systemes, la «phase» peut se propager, c'est-a-dire que l'equation dynamique pour la variable lente est du 2eme ordre dans le temps