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Alpha oscillations are modulated in response to visual temporal and spatial cues, However, the neural response to alerting cues is less explored, as is how this response is affected by healthy aging. Using scalp EEG, we examined how visual cortical alpha activity relates to working memory performance. Younger (20-30 years) and older (60-70 years) participants were presented with a visual alerting cue uninformative of the position or size of a lateralized working memory array. Older adults showed longer response times overall, and reduced accuracy when memory load was high. Older adults had less consistent cue-evoked phase resetting than younger adults, which predicted worse performance. Alpha phase prior to memory array presentation predicted response time, but the relationship between phase and response time was weaker in older adults. These results suggest that changes in alpha phase dynamics, especially prior to presentation of task-relevant stimuli, potentially contribute to age-related cognitive decline.

Neural oscillatory dynamics are a candidate mechanism to steer perception of time and temporal rate change. While oscillator models of time perception are strongly supported by behavioral evidence, a direct link to neural oscillations and oscillatory entrainment has not yet been provided. In addition, it has thus far remained unaddressed how context-induced illusory percepts of time are coded for in oscillator models of time perception. To investigate these questions, we used magnetoencephalography and examined the neural oscillatory dynamics that underpin pitch-induced illusory percepts of temporal rate change. Human participants listened to frequency-modulated sounds that varied over time in both modulation rate and pitch, and judged the direction of rate change (decrease vs increase). Our results demonstrate distinct neural mechanisms of rate perception: Modulation rate changes directly affected listeners' rate percept as well as the exact frequency of the neural oscillation. However, pitch-induced illusory rate changes were unrelated to the exact frequency of the neural responses. The rate change illusion was instead linked to changes in neural phase patterns, which allowed for single-trial decoding of percepts. That is, illusory underestimations or overestimations of perceived rate change were tightly coupled to increased intertrial phase coherence and changes in cerebro-acoustic phase lag. The results provide insight on how illusory percepts of time are coded for by neural oscillatory dynamics.

[EN] The microstructure of rubber-modified polystyrene after thermal ageing at 90 °C and multiple extrusion was analyzed by time-domain nuclear magnetic resonance (TD-NMR) in a non-destructive manner. The transverse magnetization decay behaviour observed in TD-NMR was related to the total rubber fraction and its cross-linking density. The data reveal different mechanisms of long-term rubber degradation in high-impact polystyrene (HIPS) during thermo-oxidation and multiple processing: Multiple processing causes a slight increase in the cross-linking density of the rubber phase, without appreciably altering the total amount of rubber fraction. Thermo-oxidation is accompanied by a significant overall decrease of the rubber fraction, an increase of the cross-linking density, and a pronounced increase of the non-crosslinked fraction (chain ends and fragmented segments). The NMR results correlate well with spectroscopic observations and moderately with macroscopic mechanical properties. © 2011 Elsevier Ltd. All rights reserved., The lab support for the NMR studies by Jens Schober and Cornelia Willax is gratefully acknowledged. FV thanks the economical support of the Spanish Ministry of Science and Innovation through the FPU doctoral program.

We experimentally analyze extreme events in a fast (nanosecond) spatially extended oscillatory medium with coherent forcing. We focus on individual events and their emergence in the (spatio-temporally resolved) optical phase dynamics.

One of the most sensitive methods for determining the presence and character of coupling between two oscillators is based on the modeling of their phase dynamics. This method is applicable if the observed oscillations are not synchronous and the length of available time series is no less than 50 characteristic periods. Now it is established that the method can be applied to still shorter time series with a length of 20 to 50 periods, provided that the estimated phase coherence coefficient (measuring the degree of synchronization) does not exceed a certain threshold dependent on the time series length and the frequency detuning. This result expands the possibilities of detecting the coupling between oscillatory systems under conditions of nonstationary signals and deficient data.

A method for the estimation of the Lyapunov exponent corresponding to enslaved phase dynamics from time series has been proposed. It is valid for both nonautonomous systems demonstrating periodic dynamics in the presence of noise and coupled chaotic oscillators and allows us to estimate precisely enough the value of this Lyapunov exponent in the supercritical region of the control parameters. The main results are illustrated with the help of the examples of the noised circle map, the nonautonomous Van der Pole oscillator in the presence of noise, and coupled chaotic Rössler systems.

Based on a developed and experimentally tested model, self-oscillatory lasing regimes have been studied for a Class A four-frequency gas ring laser with linear coupling of elliptically polarized counter-propagating waves. In the self-oscillatory regime, switching of the intensities, polarization states, and phase differences of the counter-propagating waves is observed, and also a polarization-phase dynamics effect involving displacement of the intensity switching point (with respect to detuning), due to the phase shift as a result of an ellipticity different from zero.

Spiral turbulence observed in Couette-Taylor system has been characterized using the phase diffusion equation suggested by Hegseth et al. [Phys. Rev. Lett. 62, 257 (1989)]. From space-time diagrams, we have measured the diffusion coefficient, the diffusion velocity, and the turbulent spiral pitch.

We analyze neuron-like excitability of a laser with coherent forcing beyond the phase model reduction. Contrary to this oversimplified picture, we find resonant and multipulse excitability, opening novel avenues for complex all-optical operations.

In this paper, we investigate various aspects of electro-magnetically induced transparency (EIT) that are associated with quantum interference. In the first half of this paper, we investigate two cascade schemes and demonstrate two possible absorption pathways in one, which leads to interference, and only one pathway in the other scheme, which does not exhibit EIT. In the second part of this paper, we demonstrate how EIT can be changed into enhanced absorption by changing the phase of either the coupling or probe fields.

The melting of an ultrathin lubricant film is studied at friction between atomically flat surfaces. We take into account fluctuations of lubricant temperature, which are defined by the Ornstein-Uhlenbeck process. Phase diagrams and portraits are calculated for second- and first-order transitions (the melting of an amorphous and that of a crystalline lubricants, respectively). It is shown that, in the former case, a stick-slip friction domain, separating the regions of dry and sliding friction, appears. In the latter case, three domains of stick-slip friction arise, which are characterized by the transitions between dry, metastable and stable sliding friction. The increase in the correlation time of lubricant temperature fluctuations leads to increasing in the rubbing-surface temperature needed for realization of sliding friction. The stationary states, corresponding to dry, stable and metastable sliding friction, are reached as a result of damped oscillations.

The melting of an ultrathin lubricant film at friction between atomically smooth surfaces is studied with allowance for fluctuations of its temperature, which are described by the Ornstein-Uhlenbeck process. The behavior of the most probable types of shear stresses arising in the lubricant is considered, and phase diagrams for second- and first-order phase transformations (the melting of an amorphous lubricant and that of a crystal- line lubricant, respectively) are constructed. It is shown that, in the former case, lubricant temperature fluctua- tions lead to the formation of a stick-slip friction domain separating the domains of dry and sliding friction, which is typical of first-order transitions. In the latter case, three domains of stick-slip friction arise, which mark the transitions between dry friction and metastable and stable sliding friction. As the time of correlation of lubricant temperature fluctuations gets longer, the temperature of rubbing surfaces rises to the point where sliding friction sets in.

This study aims to decrease the gap between invasive high-resolution data acquisition and non-invasive measurement in the animal model under auditory stimuli. We approach this problem by analyzing the degree of shared information between the phase of local field potentials (LFPs) of auditory cortices and the phase of auditory evoked responses (AER) at different frequency domains. It has been extensively illustrated in previous studies that the phase of evoked responses align reliably in presence of a repetitive stimulus. Yet this implies that changes in the instantaneous phase over a series of stimulus presentations must also be mirrored in the laminar activity. To estimate the impact of laminar specific activity on the AER dynamics over a series of acoustic stimulation, we employ an information theoretic approach (mutual information) for quantifying the relevant information encoded in the phase of laminar LFPs and AERs.

A new method is proposed for the investigation of transitions from synchronous dynamics of coupled oscillators to asynchronous regimes attained upon synchronization breakage by a sequence of short phase resetting pulses. The possibility to use the proposed method for determining the coefficient of coupling between interacting systems from an analysis of the signals generated by these systems is considered.

The formation of spatially repetitive structures along the growth axis of a developing embryo is a common theme in developmental biology. Here we apply the novel flow-distributed oscillator (FDO) mechanism of wave pattern formation to the problem of axial segmentation in general and to somitogenesis in particular. We argue that the conditions for formation of FDO waves are satisfied during somitogenesis in the chick and mouse and that the waves of gene expression observed in these species arise from phase dynamics in a growing oscillatory medium. We substantiate this claim by showing that the FDO mechanism allows the waves to be mimicked by an inorganic experiment and that it predicts a wavelength that coincides with that observed experimentally. To see whether the FDO mechanism is compatible with other aspects of somitogenesis, we construct an FDO-based model of somitogenesis and successfully test it against a number of experimental observations, including the effect of heat shock. Our analysis provides a rigorous physical basis for the hypothesis that the phase dynamics of a segmental clock controls important stages of segmentation during somitogenesis in the chick and mouse as well as in other organisms that undergo segmentation during their axial growth.

In the quasi-one-dimensional mixed-stack organic charge-transfer complex, TTF-CA, photoirradiation is known to trigger transitions between the neutral and ionic phases. Here we use a one-dimensional extended Peierls–Hubbard model with alternating potentials and calculate the mean-field dynamics of charge density coupled with that of lattice displacements. We show qualitative differences between the photoinduced ionic-to-neutral and neutral-to-ionic transitions, which are consistent with recent experimental findings. That is, the ionic-to-neutral transition proceeds cooperatively, characterized by threshold behavior, while the neutral-to-ionic transition proceeds uncooperatively, characterized by linear behavior. The threshold absorption in the former depends on the strength or the duration of the pulse. The coherence during the transition dynamics is also different between the two transitions. In the ionic-to-neutral transition, a clear interference effect is observed as a function of the interval when the pulse is spilt into two.

A vector equation of motion in the Lagrangian frame of reference is rearranged into a set of two scalar equations to determine the relative-velocity magnitude of a particle and its direction. The resulting system, written in terms of the Lame coefficients, is solved jointly with continuum equations of motion in the Eulerian frame of reference. The method is exemplified by the flow of a heterogeneous mixture between permeable parallel walls and the flow of a heterogeneous non-Newtonian fluid over the surface of a sedimentation centrifuge rotor.

Driven mean-field threshold systems demonstrate complex observable space-time patterns of behavior that are difficult to understand or predict without knowledge of the underlying dynamics, which are typically unobservable. Here we describe a new method based on phase dynamics techniques to analyze and forecast the space-time patterns of activity in these systems. Application to earthquake data from a typical, seismically active region shows that the method holds considerable promise for forecasting the temporal occurrence of the largest future events. We demonstrate the power of our technique via an application to the difficult problem of earthquake forecasting in southern California.

Transient phase dynamics, synchronization and desynchronization which are stimulus-locked (i.e. tightly time-locked to a repetitively administered stimulus) are studied in two coupled phase oscillators in the presence of noise. The presented method makes it possible to detect such processes in numerical and experimental signals. The time resolution is enormous, since it is only restricted by the sampling rate. Stochastic stimulus locking of the phases or the n:m phase difference at a particular time t relative to stimulus onset is defined by the presence of one or more prominent peaks in the cross-trial distribution of the phases or the n:m phase difference at time t relative to stimulus onset in an ensemble of post-stimulus responses. Unlike the presented approach, both triggered averaging (where an ensemble of post-stimulus responses is simply averaged) and cross-trial cross correlation (CTCC) lead to severe misinterpretations: The oscillators' coupling may cause a transient anti-phase clustering of the post-stimulus responses. Triggered averaging cannot distinguish such a response decorrelation from a mean amplitude decrease of the single responses. CTCC not only depends on the oscillators' phase difference but also on their phases and, thus, inevitably displays "artificial" oscillations that are not related to synchronization or desynchronization.

For αβ>−1, stable time periodic solutions A(X,T)=AqeiqX+iωqT are the locally preferred planform for the complex Ginzburg–Landau equation ∂ T A=A+(1+iα)∂ X 2 A−(1+iβ)A|A| 2 . In order to describe the spatial global behavior, an evolution equation for the local wave number q can be derived formally. The local wave number q satisfies approximately a conservation law ∂τq=∂ξh(q). It is the purpose of this paper to explain the extent to which the conservation law is valid by proving estimates for this formal approximation.

The simplified models of neural networks based on biophysical Hodgkin–Huxley neurons are studied with a focus on coherent-phase dynamics. In our approach, each neuron is considered as a nonlinear oscillator, and collective dynamics of a mesoscopic network of neural oscillators are studied using the methods of nonlinear dynamics. We explore the mechanisms for synchrony, clustering and their breakup in the synaptic parameter space and discuss implications to temporal aspects of neural-information processing.

In this paper we extendthe results of Frankel andKiemel ( SIAM J. Appl. Math ,5 3 (1993), pp. 1436-1446) to a network of slowly coupledoscillators. First, we use Malkin's theorem to derive a canonical phase model that describes synchronization properties of a slowly coupled network. Then, we illustrate the result using slowly coupledoscillators (1) near And ronov-Hopf bifurcations, (2) near saddle-node on invariant circle bifurcations, and (3) near relaxation oscillations. We compare andcontrast synchronization properties of slowly andweakly coupledoscillators.

The ultrafast optically-heterodyne-detected optical Kerr effect (OHD-OKE) is established as a relatively simple tool for recording the ultrafast dynamics of liquids with high temporal resolution and excellent signal-to-noise ratios. The principles and practice of the OHD-OKE method are outlined. Its application in recording the dynamics of several molecular liquids is described. The data are discussed in terms of the underlying microscopic molecular motions. Orientational motion--both librational and diffusive--is responsible for a significant fraction of the dynamics. Other potential contributions are discussed, but these are less readily assigned. The application of OHD-OKE measurements in interpreting ultrafast studies of the optical dynamics of solutions is discussed. Finally the extension of OHD-OKE methods to record the dynamics of more complex, heterogeneous, media is described.

We construct a theory of dynamical behavior in intrinsic Josephson junction stacks with multigap superconducting layers. The theory predicts the existence of two kinds of phase modes, one of which is the Josephson-plasma mode and other of which is the Leggett’s mode. We discuss a cooperative phenomena induced by inter-band Josephson coupling in addition to capacitive and inductive couplings between the superconducting layers.

We study theoretically the non linear polarization dynamics of Vertical-Cavity Surface-Emitting Lasers in the presence of an external cavity providing delayed optical feedback and cross polarization re-injection. We show that far from the laser threshold, the dynamics remains confined close to the equatorial plane of a Stokes sphere of a given radius and we reduce the dynamics to a dynamical system composed of two phases: the orientation phase of the quasi-linear polarization and the optical phase of the field. We explore the complex modal structure given by the double feedback configuration and recovers as particular cases the Lang-Kobayashi modes and the modes founds by Giudici et al. [1]. We also re-interpret the square waves switching dynamics as phase kinks.

We apply retrospective cost adaptive control (RCAC) to a linearized aircraft dynamics with an unknown transition to nonminimum-phase (NMP) dynamics. In prior work, RCAC was used for command-following with unknown NMP zeros. In this work we extend those results to command following for cases where the dynamics transition from minimum-phase to NMP. We use system identification techniques to identify the NMP zero, and use this information in RCAC. We consider both full-state feedback and output feedback, and in both cases we follow step commands with transitioning dynamics. We first consider the case where RCAC is unaware of the change and NMP zero identification is unavailable to RCAC. We then assume that NMP zero information is available to RCAC from system identification.

The moderately damped regime (MDR) in a Josephson junction (JJ) is quite distinct from the well-known case of underdamped systems and quite common in devices characterized by low critical currents. Measurements of switching current distribution (SCD) are a direct way of discriminating the phase dynamics and the transport also in nontrivial cases of moderate damping. MDR is going to be more and more common with advances in nanopatterning superconductors and in materials science finalized to build hybrid devices. We report on measurements of SCDs, both in the thermal and quantum regime, on moderately damped NbN/MgO/NbN JJs. A transition from the Thermal Activation (TA) regime to Macroscopic Quantum Tunnelling (MQT) occurs at about 90 mK, while above 1.6 K a phase diffusive dynamics is clearly observed. The combined analysis of these regimes through numerical simulations allowed us to extract the fundamental parameters, which completely characterize the phase dynamics of such moderately damped JJs.

We have studied the phase dynamics in an oscillatory chemical system (Belousov−Zhabotinsky reaction). The phase distribution and isophase lines in the 2D phase space were reconstructed. The dynamic...

We discuss the phase dynamics in the system of a set of nonlinear coupled oscillators. We find a direct and simple geometric method to observe the geometric phase for this system, and it provides a possibility for the experimental measurements.

We study the nonlinear phase equation for propagating patterns. We investigate the transition from a propagating localized pattern to a space-filling spatiotemporally disordered pattern and discuss in detail to what extent there are propagating localized states that breathe in time periodically, quasiperiodically, and chaotically. Differences and similarities to the phenomena occurring for the quintic complex Ginzburg-Landau equation are elucidated. We also discuss for which experimentally accessible systems one could observe the phenomena described.

The idea of phase dynamics originally considered for regular non-equilibrium patterns is applied to irregular patterns. In the dissipation-dominated regime, a slow modulation of irregular pattern is shown to decay in time according to the diffusion law. Possible relevance of this result for the ultra-slow diffusion modes observed in glass-forming systems is discussed. In this connection we speculate about a possibility of appearance of some sorts of soft structures resembling quasi-periodic microcrystalline states in glass-forming systems.

Based on neurophysiological evidence, studies modeling human locomotion system have shown that a bipedal walking is generated by mutual entrainments between the oscillatory activities of a central pattern generator (CPG) and a Body. The walking model could well reproduce human walking. However, it has been also shown that time delay in the sensorimotor loop destabilizes mutual entrainments, which leads a failure to walk. Recently, theoretical studies have discovered a phenomenon in which a CPG can induce the phase of its oscillatory activity to shift forward according to time delay. This self-organized phenomenon overcoming time delay is called “flexible-phase locking”. Then, theoretical studies have hypothesized that one of the essential mechanisms to yield of flexible-phase locking is a stable limit cycle of CPG activity. This study demonstrates the hypothesis in walking models through computer simulation by replacing the CPG model with the one having different oscillation properties.

A time dependent thermal model for a superconducting constriction based weak-link (WL) is discussed for investigating the deterministic dynamics of its temperature and phase. A new dynamic regime is found where a non-zero voltage exists across the WL and its temperature stabilizes between the bath temperature and superconductor's critical temperature. This regime exists over a limited bias current range and gives rise to a new hysteretic regime in current-voltage characteristics. We also discuss the effect of fluctuations on the current-voltage characteristics and experimental implications of this dynamic regime., Comment: 7 pages, 4 figures; revised on 25 Nov 2014

The objective of the present paper is the modeling and analysis of the dynamics of macrophages and certain growth factors in the inflammatory phase, the first one of the wound healing process. It is the phase where there exists a major difference between diabetic and non-diabetic wound healing, an effect that we will consider in this paper Supported by grants MTM2011-27739-C04-01 (Spain) and 2009SGR345 (Catalonia). Supported by FAPESP 2008/55516-3 and CAPES/DGU 238/11 (Brazil). Supported by grants MTM2011-27739-C04-03 (Spain) and 2009SGR345 (Catalonia)

An unusual bifurcation sequence exhibited in a recently proposed nonlinear delay electro-optic phase dynamics setup, is explored both experimentally and analytically. Strong agreements indicate that well-controlled dynamical complexity can be usefull in many emerging applications.

Collisions lead to the collapse and revival of the interference fringes between two atomic Bose–Einstein condensates. We study the collapses and revivals of the relative phase between the condensates for two different initial states. One state invokes Bose–broken symmetry allowing us to write the wavefunction as a superposition of total number (of both condensates) states whereas the other does not.

Even though synchronization in autonomous systems has been observed for over three centuries, reports of systematic experimental studies on synchronized oscillators are limited. Here, we report on observations of internal synchronization in coupled silicon micromechanical oscillators associated with a reduction in the relative phase random walk that is modulated by the magnitude of the reactive coupling force between the oscillators. Additionally, for the first time, a significant improvement in the frequency stability of synchronized micromechanical oscillators is reported. The concept presented here is scalable and could be suitably engineered to establish the basis for a new class of highly precise miniaturized clocks and frequency references.

We generalize our recent approach to reconstruction of phase dynamics of coupled oscillators from data [B. Kralemann et al., Phys. Rev. E, 77, 066205 (2008)] to cover the case of small networks of coupled periodic units. Starting from the multivariate time series, we first reconstruct genuine phases and then obtain the coupling functions in terms of these phases. The partial norms of these coupling functions quantify directed coupling between oscillators. We illustrate the method by different network motifs for three coupled oscillators and for random networks of five and nine units. We also discuss nonlinear effects in coupling., Comment: 6 pages, 5 figures, 27 references

We systematically develop a technique for reconstructing the phase dynamics equations for coupled oscillators from data. For autonomous oscillators and for two interacting oscillators we demonstrate how phase estimates obtained from general scalar observables can be transformed to genuine phases. This allows us to obtain an invariant description of the phase dynamics in terms of the genuine, observable-independent phases. We discuss the importance of this transformation for characterization of strength and directionality of interaction from bivariate data. Moreover, we demonstrate that natural (autonomous) frequencies of oscillators can be recovered if several observations of coupled systems at different, yet unknown coupling strengths are available. We illustrate our method by several numerical examples and apply it to a human electrocardiogram and to a physical experiment with coupled metronomes.

We propose a natural two-speed model for the phase dynamics of Si(111) 7x7 phase transition to high-temperature unreconstructed phase. We formulate the phase dynamics by using phase-field method and adaptive mesh refinement. Our simulated results show that a 7x7 island decays with its shape kept unchanged, and its area decay rate is shown to be a constant increasing with its initial area. Low-energy electron microscopy experiments concerned are explained, which confirms that the dimer chains and corner holes are broken first in the transition, and then the stacking fault is remedied slowly. This phase-field method is a reliable approach to phase dynamics of surface phase transitions.

By means of an electron hole rate equation model we explain the phase dynamics of a quantum dot semiconductor optical amplifier and the appearance of different decay times observed in pump and probe experiments. The ultrafast hole relaxation leads to a first ultrafast recovery of the gain, followed by electron relaxation and, in the nanosecond timescale, radiative and non-radiative recombinations. The phase dynamics is slower and is affected by thermal redistribution of carriers within the dot. We explain the ultrafast response of quantum dot amplifiers as an effect of hole escape and recombination without the need to assume Auger processes.

We develop an effective description of noise-induced oscillations based on deterministic phase dynamics. The phase equation is constructed to exhibit correct frequency and distribution density of noise-induced oscillations. In the simplest one-dimensional case the effective phase equation is obtained analytically, whereas for more complex situations a simple method of data processing is suggested. As an application an effective coupling function is constructed that quantitatively describes periodically forced noise-induced oscillations., This paper has been withdrawn by the author due to errors in Fig. 3 and faulty conclusions drawn from Fig. 4

Time-resolved gain and phase dynamics of an InAs/InGaAsP/InP quantum-dot semiconductor optical amplifier are investigated. The recovery is dominated by an ultrafast component (~1 ps), indicating strongly that the gain medium is genuinely dot-like in character.