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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.

This paper introduces an extension of the Internal Model Control algorithm for efficient disturbance rejection. The approach is based on ideas from model based predictive control and diophantine equation derivation. As an illustration of the power of the extension, an example from the process industry is borrowed, namely a drum boiler. The process is challenging for control since it has an integrator and non-minimum phase dynamics. The performance of the proposed extension is compared against nominal IMC design and PID. The simulation results suggest that the proposed algorithm outperforms the other implementations in terms of effective disturbance rejections.

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 consider a $\ensuremath{\varphi}$ Josephson junction, which has a bistable zero-voltage state with the stationary phases $\ensuremath{\psi}=\ifmmode\pm\else\textpm\fi{}\ensuremath{\varphi}$. In the nonzero voltage state the phase ``moves'' viscously along a tilted periodic double-well potential. When the tilting is reduced quasistatically, the phase is retrapped in one of the potential wells. We study the viscous phase dynamics to determine in which well ($\ensuremath{-}\ensuremath{\varphi}$ or $+\ensuremath{\varphi}$) the phase is retrapped for a given damping, when the junction returns from the finite-voltage state back to the zero-voltage state. In the limit of low damping, the $\ensuremath{\varphi}$ Josephson junction exhibits a butterfly effect---extreme sensitivity of the destination well on damping. This leads to an impossibility to predict the destination well.

Pattern recognition invariant against deformation or translation can be performed with dynamic link architecture, which has been proposed by von der Malsburg. Dynamic link is applied to many engineering examples efficiently, but has not been analyzed mathematically. We propose a mathematically tractable model of dynamic link architecture. Our model matches common parts between a template image and a data image. To analyze model mathematically, we derive the phase dynamics from the model equation. We also carry out a computer simulation to verify the mathematical theory.

We propose a new approach for manipulating neural dynamics by using combined TMS (Transcranial magnetic stimulation) – EEG (Electroencephalography) recordings. We demonstrate that we can perturb the phase dynamics of ongoing neural oscillations by TMS. Using the manipulative approach we can investigate (1) state-dependency in frequency-specific network connectivity by analyzing how TMS-evoked phase reset of ongoing activity propagates from one cortical area to the rest of the brain in humans and (2) causal links between the neural dynamics and brain functions. We can causally confirm dynamical and computational models in manipulative manners using this approach.

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.

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.

International audience; Motivated by neuroscience applications, we rigorously derive the phase dynamics of an ensemble of interconnected nonlinear oscillators under the effect of a proportional feedback. We individuate the critical parameters determining the validity of the phase approximation and derive bounds on the accuracy of the latter in reproducing the behavior of the original system. We use these results to study the existence of oscillating phase-locked solutions in the original oscillator model.

In this paper we consider limits of achievable performance for a class of scramjet-powered hypersonic aircraft. A simple 3-DOF model is used to illustrate the main ideas. The vehicle is characterized by unstable and non-minimum phase dynamics. The limitations introduced by the right-half plane zero and actuator saturation on achievable trajectories has been examined. In addition, we examine several vehicle configurations and consider fundamental limitations for the plant and closed loop performance. An optimization methodology that explicitly incorporates performance specifications into the design of vehicle is explored. The advantages of such an approach is illustrated with examples.

In this paper, we propose a framework for generating coordinated periodic movements of robotic systems with external inputs. We developed an adaptive pattern generator model that is composed of a two-factor observation model with a style parameter and phase dynamics with a phase variable. The style parameter controls the spatial patterns of the generated trajectories, and the phase variable controls its temporal profiles. To validate the effectiveness of our proposed method, we applied it to a simulated humanoid model to perform biped walking behaviors coordinated with observed walking patterns and the environment. The robot successfully performed stable biped walking behaviors even when the style of the observed walking pattern and the period were suddenly changed.

We carry out a thorough analysis on a class of cosmological spacetimes which admit three space-like Killing vectors of Bianchi class B and contain electromagnetic fields. Using dynamical system analysis, we show that a family of vacuum plane-wave solutions of the Einstein-Maxwell equations is the stable attractor for expanding universes. Phase dynamics are investigated in detail for particular symmetric models. We integrate the system exactly for some special cases to confirm the qualitative features. Some of the obtained solutions have not been presented previously to the best of our knowledge. Finally, based on those solutions, we discuss the relation between those homogeneous models and perturbations of open FLRW universes. We argue that the vacuum plane-wave modes correspond to a certain long-wavelength limit of electromagnetic perturbations., Revised for publication. 25 pages

In this paper we investigate the regularizing behavior of two-phase Stefan problem near initial Lipschitz data. A description of the regularizing phenomena is given in terms of the corresponding space-time scale.

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.

We have studied the phase properties of initially coherent light interacting with two identical two-level atoms using the Hermitian phase operator of Pegg and Barnett. The results show that, in a certain initial state of the atoms, the field would, to a certain extent, preserve its order in phase, even for a long interaction time with the two atoms.

Previous studies of the phase properties of optical linear amplifiers and attenuators have been restricted to situations where the effect on the phase of single-mode light is found to be diffusive. In this paper we give an analysis of phase-sensitive linear amplification and attenuation in the weak-field regime that clearly reveals a non-diffusive effect on the phase. Indeed we show that a weak field which has initially a uniform phase probability density can inherit non-random phase properties from both phase-sensitive attenuators and amplifiers. In contrast, we find that phase-insensitive amplifiers and attenuators have merely a diffusive effect on the phase of the light.

In a directional viscous fingering experiment, a phase diffusion behavior of the regular array of cells is demonstrated. At constant wave number, the evolution of the phase diffusion coefficient D with the parameter of the instability \ensuremath{\epsilon} is reported. This coefficient D is found to decrease at low \ensuremath{\epsilon} values in agreement with the presence of an Eckhaus instability, but to increase strongly at large \ensuremath{\epsilon} values. This unusual increase of D is also present in the analytical and numerical study of two coupled amplitude equations for the modes k and 2k. The phase diffusion coefficient is found to diverge at the threshold of the parity-breaking bifurcation.

The phase jump dynamics in a photosensitive Belousov-Zhabotinsky reaction has been studied. It was found that an initially inhomogeneous phase distribution evolved to a homogeneous one, so that the phase at phase-lag points rises to the value at phase-lead points. A steep phase distribution was shown to become smoother in the course of time, inducing a dephasing wave which restores the system to a uniform phase. Applications of photosensitive chemical reactions to image processing (image storage, inversing, contouring) are discussed

We analyze the phase properties of a strong cavity field interacting with an ensemble of initially excited N two-level atoms. Using the Pegg-Barnett phase formalism [Phys. Rev. A 39, 1665 (1989)], we calculate the phase probability distribution as well as the phase variance. The phase probability density exhibits a (N+1)-peak structure at the initial stages of the evolution. The phase variance is used to illustrate the progressive randomization of the phase on the long-time evolution. The difference in the phase dynamics for the N even and the N odd case is pointed out.

Phase models are a powerful method to quantify the coupled dynamics of nonlinear oscillators from measured data. We use two phase modeling methods to quantify the dynamics of pairs of coupled electrochemical oscillators, based on the phases of the two oscillators independently and the phase difference, respectively. We discuss the benefits of the two-dimensional approach relative to the one-dimensional approach using phase difference. We quantify the dependence of the coupling functions on the coupling magnitude and coupling time delay. We show differences in synchronization predictions of the two models using a toy model. We show that the two-dimensional approach reveals behavior not detected by the one-dimensional model in a driven experimental oscillator. This approach is broadly applicable to quantify interactions between nonlinear oscillators, especially where intrinsic oscillator sensitivity and coupling evolve with time.

Alpha-frequency band (8-14 Hz) oscillations are among the most salient phenomena in human electroencephalography (EEG) recordings and yet their functional roles have remained unclear. Much of research on alpha oscillations in human EEG has focused on peri-stimulus amplitude dynamics, which phenomenologically support an idea of alpha oscillations being negatively correlated with local cortical excitability and having a role in the suppression of task-irrelevant neuronal processing. This kind of an inhibitory role for alpha oscillations is also supported by several functional magnetic resonance imaging (fMRI) and trans-cranial magnetic stimulation (TMS) studies. Nevertheless, investigations of local and inter-areal alpha phase dynamics suggest that the alpha-frequency band rhythmicity may play a role also in active task-relevant neuronal processing. These data imply that inter-areal alpha phase synchronization could support attentional, executive, and contextual functions. In this review, we outline evidence supporting different views on the roles of alpha oscillations in cortical networks and unresolved issues that should be addressed to resolve or reconcile these apparently contrasting hypotheses.

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 experimentally investigate the phase dynamics of laser networks with homogenous time-delayed mutual coupling and establish the fundamental rules that govern their state of synchronization. We identified a specific substructure that imposes its synchronization state on the entire network and show that for any coupling configuration the network forms at most two synchronized clusters. Our results indicate that the synchronization state of the network is a nonlocal phenomenon and cannot be deduced by decomposing the network into smaller substructures, each with its individual synchronization state.

We present a brief summary of the results of Charters et al. [1] where a simple model of a massive inflation field ϕ coupled to another scalar filed χ with interaction term g 2ϕ2χ2 for the first stage of preheating, and we give a full description of the dynamics of the χ field modes, including the behaviour of the phase, in terms of the iteration of a simple family of circle maps.

Improving the frequency precision by synchronizing a lattice of oscillators is studied in the phase reduction limit. For the most commonly studied case of purely dissipative phase coupling (the Kuramoto model) I confirm that the frequency precision of N oscillators perturbed by independent noise sources is improved by a factor N as expected from simple averaging arguments. In the presence of reactive coupling, such as will typically be the case for non-dissipatively coupled oscillators based on high-Q resonators, the synchronized state consists of target like waves radiating from a local source which is a region of higher frequency oscillators. In this state all the oscillators evolve with the same frequency, however I show that the improvement of the frequency precision is independent of N for large N, but instead depends on the disorder and reflects the dependence of the frequency of the synchronized state on just those oscillators in the source region of the waves., Comment: 18 pages, 8 figures; clarified wording of text and added references

The discovery of High Critical Temperature Superconductors (HTS) generated great activity to develop dc Superconductive Quantum Interference Devices (SQUIDs), with operating temperatures up to the boiling point of liquid nitrogen, 77. K.It was immediately apparent that small-scale devices, like SQUIDs, would require the development of thin-film techniques and novel Josephson junction's fabrication technologies. At present, grain-boundary junctions are the most widely used in SQUIDs. However, their properties are strongly affected by the d-wave symmetry of the order parameter. As a consequence the static and dynamic properties of HTS SQUIDs can be profoundly modified. The d-wave symmetry also offers the possibility to design π-SQUIDs showing a complementary behavior in magnetic field, compared to conventional ones, as well as dc SQUIDs with a double well potential. In this chapter the new Josephson phenomenology of HTS SQUIDs is derived, compared with experimental data available in literature, and discussed in view of future novel applications. © 2011 Woodhead Publishing Limited All rights reserved.

Physico-chemical systems driven away from thermal equilibrium usually undergo various types of instabilities leading to the formation of spatio-temporal patterns on macroscopic time and space scales. In two-dimensional geometries, patterns of different symmetries may be simultaneously stable. We study here the phase stability of hexagonal planforms in the framework of amplitude equations and reduced dynamical models close to the instability points.

Hodgkin-Huxley model neurons coupled by weak excitatory interactions are studied by a phase reduction technique. All the information about the coupling between the neurons and their synchronization is then contained in an effective interaction between their phases. One shows analytically that an excitatory coupling can result in an effective inhibition between the neurons reducing their firing rates. Systems of two neurons exhibit bistability and out-of-phase locking. It is suggested that these features may have significant consequences for networks.

Arrays of coupled oscillators can be used for power-combining at microwave and millimeter-wave frequencies, and have been successfully demonstrated with a variety of devices. Such arrays have also recently been mode-locked for pulse generation, and can be configured for phase-shifterless beam scanning. The nonlinear theory of coupled oscillator phase dynamics depends crucially on the parameters describing the coupled between oscillators. Methods for experimental characterization of these parameters are described here, and simple models which reproduce the measurements quite well are developed. The models apply to radiative coupling and the effects of external reflectors which are sometimes used for stabilization. The theory is verified with a two-oscillator system. >

We have proposed and investigated a model of drying colloidal suspension drop placed onto a horizontal substrate in which the sol to gel phase transition occurs. The temporal evolution of volume fraction of the solute and the gel phase dynamics were obtained from numerical simulations. Our model takes into account the fact that some physical quantities are dependent on volume fraction of the colloidal particles., Submitted to IJMPB

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.

We report measurements on the phase dynamics of a detuned single mode laser which has in the past shown correspondence to the complex Lorenz equation. The corresponding ranges of periodic pulsing, of detuned chaos and of windows within the chaotic domain are investigated.

In this paper we present an electronic system designed to emulate neural networks. Two major restrictions are assumed: discrete synapses (+1,0,−1) and threshold-type neurons. Drawbacks given by restrictions are solved with a more complex learning algorithm that maps real valued configurations for synapses into bipolar ones. The central unit of the system is an ASIC designed in accordance with a new sequential dynamics, which is faster and with better recall characteristics. As a result, the system designed has a fast recall phase and a large number of neurons. A handwritten OCR system is being designed.

We consider a three-component model of an active medium where local oscillations are coupled to a slowly propagating field. Using the Kuramoto approximation of phase dynamics, we show that this uniform medium can support steady autonomous pacemakers. These were patterns spontaneously emerge from the background of uniform bulk oscillations and are stable with respect to small perturbations.

The tear film is a dynamic multilayered structure. The interactions and the interfacial dynamics between the layers that occur during a blink cycle must be such that they allow for maintenance of a stable tear film. Attempts to understand these dynamics have been limited by the techniques and biomarkers used. Quantum dots (qdots) offer a new potential to monitor the dynamics of the tear film layers in vivo without the drawbacks of previously used methodologies. Indium phosphide–gallium qdots were used to differentially assess the dynamics of the lipid and aqueous layers of the tear film in real time. In the aqueous, qdots dispersed to form a stable local region that was swept away into the upper and lower menisci during a blink. They did not redisperse onto the ocular surface but were progressively removed from the menisci through the puncta. Some of these qdots adhered to the mucin layer on the ocular surface in a meshlike pattern and remained there for five to six blinks before they were removed. The organic qdots dispersed quickly but patchily over the whole outer surface of the tear film. They also strongly marked both eyelid margins and slowly dispersed onto the skin and eyelashes and not through the puncta. Some were trapped in the menisci as blobs that rolled along the meniscus. These data support the view of a distinct three-layered tear film: an inner mucin layer attached to the epithelial cells, a fluid aqueous layer, and an outer viscoelastic lipid layer. From the Clinical Editor Indium galium posphide quantum qdots were used to differentially assess the tear film in real time. These data support the view of a distinct three layered tear film: an inner mucin layer attached to the epithelial cells; a fluid aqueous layer; and an outer viscoelastic lipid layer.

In this paper a control configuration for inverse-response processes is presented. It results in a Smith-type predictor scheme that aims to put the non-minimum phase dynamics out of the feedback loop. The design is carried out analytically by solving an H ∞ weighted optimization problem assuming a second order stable process with one positive zero. The performance of the proposed control configuration is compared by simulation with two different approaches to show its applicability.

A crucial insight into handwriting dynamics is embodied in the idea that stable, robust handwriting movements correspond to attractors of an oscillatory dynamical system. We present a phase dynamic model of visuomotor performance involved in copying simple oriented lines. Our studies on human performance in copying oriented lines revealed a systematic error pattern in orientation of drawn lines, i.e., lines at certain orientation are drawn more accurately than at other values. Furthermore, human subjects exhibit "flips" in direction at certain characteristic orientations. It is argued that this flipping behavior has its roots in the fact that copying process is inherently ambiguous-a line of given orientation may be drawn in two different (mutually opposite) directions producing the same end result. The systematic error patterns seen in human copying performance is probably a result of the attempt of our visuomotor system to cope with this ambiguity and still be able to produce accurate copying movements. The proposed nonlinear phase-dynamic model explains the experimentally observed copying error pattern and also the flipping behavior with remarkable accuracy. � 2009 Springer-Verlag.

We study the relationship between synchronization and the rate with which information is exchanged between nodes in a spatio-temporal network that describes the dynamics of classical particles under a substrate Remoissenet-Peyrard potential. We also show how phase and complete synchronization can be detected in this network. The difficulty in detecting phase synchronization in such a network appears due to the highly non-coherent character of the particle dynamics which unables a proper definition of the phase dynamics. The difficulty in detecting complete synchronization appears due to the spatio character of the potential which results in an asymptotic state highly dependent on the initial state., to appear in PRAMANA

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.

We have studied phase dynamics in EIT. We observed how the transmission decreases and recovers when the phase of the optical field changes abruptly. The result can be used for the fast control of EIT.

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.

Objective This study examines the utility of new measures of event-related spatio-temporal waves in the EEG as a marker of ADHD, previously shown to be closely related to the P3 ERP in an adult sample. Methods Wave activity in the EEG was assessed during both an auditory Oddball and a visual continuous performance task (CPT) for an ADHD group ranging in age from 6 to 18 years and comprising mostly Combined and Inattentive subtypes, and for an age and gender matched control group. Results The ADHD subjects had less wave activity at low frequencies (∼1 Hz) during both tasks. For auditory Oddball targets, this effect was shown to be related to smaller P3 ERP amplitudes. During CPT, the ∼1 Hz wave activity in the ADHD subjects was inversely related to clinical and behavioral measures of hyperactivity and impulsivity. CPT wave activity at ∼1 Hz was seen to “normalise” following treatment with stimulant medication. Conclusions The results identify a deficit in low frequency wave activity as a new marker for ADHD associated with levels of hyperactivity and impulsivity. Significance The marker is evident across a range of tasks and may be specific to ADHD. While lower ∼1 Hz activity partly accounts for reduced P3 ERPs in ADHD, the effect also arises for tasks that do not elicit a P3. Deficits in behavioral inhibition are hypothesized to arise from underlying dysregulation of cortical inhibition.