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A phased-array two-dimensional CPLL array is introduced. The phase dynamics are analyzed and an approximate solution are obtained using the method of continuum phase. By detuning the free-running frequencies of edge elements, linear phase distribution can be achieved among the array. An experimental CPLL array circuit is also shown and tested, proceedings.

We address an important problem in neurophysiology concerning the characterization of coupled neural oscillators from experimental data. The approach employs the formal mathematical description of the dynamics of weakly coupled oscillators by the phase model, and the recently developed methods for identification of directionality of coupling and estimation of coupling delays. We study neuron oscillator models with synaptic coupling and diffusively coupled ensembles of neurons, incorporating time delays in coupling. Results of directionality analysis closely reflect the coupling strength asymmetry. In comparison with the standard cross-correlation analysis, the phase dynamics based time delays estimation provides more accurate estimates of coupling delays

We study the model of a massive inflaton field $\phi$ coupled to another scalar filed $\chi$ with interaction term $g^2\phi^2\chi^2$ for the first stage of preheating. We obtain the the behavior of the phase in terms of the iteration of a simple family of circle maps. When expansion of the universe is taken into account the qualitative behavior of the phase and growth number evolution is reminiscent of the behavior found in the case without expansion., Comment: 4 pages, 4 figures, LaTeX; submitted to the Proceedings of Eleventh Marcel Grossmann Meeting

Synchronization phenomena in coupled circadian oscillators of plant leaves were investigated experimentally using bioluminescence technology for a clock gene. Analyzing the phase of circadian oscillation, the phase-wave propagations and the phase delay caused by the vein network were observed. We describe these phase dynamics using a two-layer model with coupled Stuart-Landau equations. Global synchronization of circadian oscillators in the leaf is also investigated.

We present results from our time dependent model on electro-magnetically induced transparency in a standard Λ configuration. We show that sudden phase jumps in either field leads to transient enhanced absorption for the probe field.

Coherent terahertz (THz) radiations based on intrinsic Josephson junctions (IJJs) from a Bi2Sr2CaCu2O[Formula: see text] (BSCCO) mesa under a bias voltage were observed in 2007. Later on, a novel [Formula: see text] phase kink state was proposed which can explain the key experimental results. However, how to drive the system into the [Formula: see text] phase kink state efficiently still remains an open problem. In this work, we propose several ways to synchronize the system to the [Formula: see text] phase kink state. We start from random and typical regular initial phase configurations. It is found that starting from some initial phase configurations, the system can be driven efficiently into the [Formula: see text] phase kink state. The time spent before entering the [Formula: see text] phase kink states for these initial phase configurations is shorter when the initial phase configuration is further away from the uniform phase configuration.

A model-based robust control approach is proposed that significantly improves imaging bandwidth for the dynamic mode atomic force microscopy. A model for cantilever oscillation amplitude and phase dynamics is derived and used for the control design. In particular, the control design is based on a linearized model and robust H(∞) control theory. This design yields a significant improvement when compared to the conventional proportional-integral designs and verified by experiments.

We demonstrate that a multiple delayed feedback is a powerful tool to control coherence properties of autonomous self-sustained oscillators. We derive the equation for the phase dynamics in presence of noise and delay, and analyze it analytically. In Gaussian approximation a closed set of equations for the frequency and the diffusion constant is obtained. Solutions of these equations are in good agreement with direct numerical simulations.

Modeling and analysis of program behavior are at the foundation of computer system design and optimization. As computer systems become more adaptive, their efficiency increasinsgly depends on program dynamic characteristics. Previous studies have revealed that program runtime execution manifests phase behavior. Recently, methods and tools to analyze and classify program phases have also been developed. However, very few studies have been proposed so far to understand and evaluate program phases from their dynamics and complexity perspectives. In this work, we propose new methods, metrics and frameworks which aim to analyze, quantify, and classify the dynamics and complexity of program phases. Our methods use wavelet techniques to represent program phases at multiresolution scales. The cross-correlation coefficients between phase dynamics observed at different scales are then computed as metrics to quantify phase complexity. We propose to apply wavelet-based multiresolution analysis and data clustering to classify program execution into phases that exhibit similar degree of complexity. Experimental results on SPEC CPU 2000 benchmarks show that the proposed schemes classify complexity-based program phases better than currently used approaches.

Histone modifications are central to epigenetic regulation and must be reestablished with each round of DNA replication. Here we describe methods to localize these modifications within mammalian nuclei and to relate them to specific spatiotemporal patterns of DNA replication.

We study the dynamics of an array of Stuart-Landau oscillators with repulsive coupling. Autonomous network with global repulsive coupling settles on one from a continuum of synchronized regimes characterized by zero mean field. Driving this array by an external oscillatory signal produces a nonzero mean field that follows the driving signal even when the oscillators are not locked to the external signal. At sufficiently large amplitude the external signal synchronizes the oscillators and locks the phases of the array oscillations. Application of this system as a beam-forming element of a phase array antenna is considered. The phase dynamics of the oscillator array synchronization is used to reshape the phases of signals received from the phase array antenna and improve its beam pattern characteristics.

The phase difference in coupled chaotic oscillators exhibits a small noiselike fast fluctuation in long-term phase dynamics. The fast fluctuation can cause an error in the measurement of the period of the temporary phase locking state. We discuss why we should filter out the fast fluctuation on determination of periodic phase synchronization.

The advent of high flux femtosecond electron sources provides a new window for observing atomic motions during structural transitions. Studies of ultrafast melting of metals reveal microscopic mechanisms and the full potential of the approach.

Large profile, high price, low efficiency in realization prevent phased array from being broadly used in automobile radar and communication systems, though phased array has high performance. The article puts forward a new kind of shifterless phased array based on coupled oscillators. The article studies the dynamics of nearest-neighbor coupled oscillators after reviewing the principles of electrical beam-scanning. According to the need of beam-scanning the desired solutions of phase dynamics are established. From that, we determine how the accessible parameters of coupled oscillators can be adjusted. The article also determines conditions under which those solutions are stable, i.e., physically realizable. Computer simulations are used to testify the usefulness of the method. Then in the last part of the article a complete transmit-receive scheme for vehicle radar and communication systems is given out.

This paper describes a fully distributed communication timing control method for wireless sensor networks, which exploits the properties of the emergent behavior of coupled phase oscillatory dynamics. Assuming the periodic data communications in massively distributed and locally interacting sensor nodes, a phase oscillatory dynamics is employed to realize a collision free communication timing control. For this purpose, we propose Phase Diffusion Synch- Alliance (PDSA) method, where coordination in repulsive and synchronous actions in the phase dynamics will take an essential role to self-organize a phase difference pattern corresponding to an efficient communication timing pattern in the distributed sensor nodes. We formulate the method and conduct simulations to verify effectiveness of PDSA.

[1] Based on the nonlinear techniques for estimation of coupling between oscillatory systems, we investigate the dynamics of climatic modes characterizing global and the Northern Hemisphere (NH) processes. In particular, indices of the North Atlantic Oscillation (NAO) and El Nino–Southern Oscillation (ENSO) for 1950–2004 are analyzed. The methods based on phase dynamics modeling and nonlinear “Granger causality” are used. We infer that ENSO affects NAO during the last half a century with confidence probability higher than 0.95. The influence is characterized with time delay in the range from a couple of months up to three years and increases during the last decade.

SUMMARY Since thr recent experimental observation of Dose-Einstein condensation in dilutc atomic gases, much interest has been raised about the coherence properties of the condensates Considerable attention has ben devoted to the matter uf the relativr phasp bctween two condensates: hm this phase manifests itself in an interference experiment [I], haw it cm be estnbliihed by measurement, and how it evolves in prespnee of atomic interactionsl2). Rerrritl) it was predicted that the relative phase betwm two condensates should display collopscs and revivals in time due to atomir inierxtioiis. For condcnsates with a rclatwely small number of atoms. of the ordcr of some hundreds, the revirds of thr 7ihar;e cm occur on the 10.'~ time Scale and niight in principle be observed. Howerer up to non a theoretical analysis of irifluence of partrcie lams 011 Lhr pha? dpnmirr B~F missing. Such loss proccs~s. due for example to collisions of rondmsed atonic With the buckgiuund gas or to three-bod! colliaionr. arp nnaruidiiblu in a real experiment and might spoil the cnherenrr prevmring the ubrurvtion of the revivals. IVe dewlop B model to dearrihe thP phase dynamici of the condensates m presence r the asaurnption that the fraction of lost parLicles in II, wc obtain analytical results for thP time depcrldcnce abservables for two nm overlapping and mutually non sueb as tlir nwm beating intensity of the condensates .epresented by the quantity (0'6) (a.herp o (a') and b (6') are the creation iannihilat,ion) operator^ of a particle in the condmsatr A ui B respectively). and the relacive phase probability distrihul ion. We find that. besides the collapses and revirals due to thr Hakiltonian evolution, the rrlvtive phase dependent observable (0'6) expericncps im esponmttal deea)- in time with a rate X given hr the mean total tiumber of luss ewnts per unit oft derohereuce betaren tw condensatcs, is therefore apprommatel inverse lifetiiiiu of a particle in the condensates (whew :T is the total number of atomr). Neverthclcs \ye show that losses do nnt prevent the ObsQrvatiOn of the rrlatise phase rsyivals in condensates with small number of atoms. Finally; se giw a suggestive interimtation of the dramatic cffect of the losses on the rflatii-e phase based on the h1oel.e Carlo wa\p function approach the condensates relative phase in a single !dome Carlo reaiization is shifted br a random amount on tbe order of 7 cosarquently to each mch loss event occurring in the condensates. A few loss prorcsses in a given time interd are then sufficient to smear out the relative phase completely when the average over the stochastic realizacion is taker

Complex-valued Hopfield networks which possess the energy function are analyzed. The dynamics of the network with certain forms of an activation function is decomposable into the dynamics of the amplitude and phase of each neuron. Then the phase dynamics is described as a coupled system of phase oscillators with a pair-wise sinusoidal interaction. Therefore its phase synchronization mechanism is useful for the area-wide offset control of the traffic signals. The computer simulations show the effectiveness under the various traffic conditions.

A multiscale approach is used to derive stochastic amplitude and phase dynamics for a canonical noise-sensitive model exhibiting coherence resonance. Explicit expressions for the dependence on noise levels and model type are compared with computational coherence measures.

We measure the phase dynamics and statistics of SOA-based wavelength conversion and XOR operation using linear optical sampling. We elucidate the role of the pattern dependent phase fluctuation in limiting the performance of XOR operation. (2 pages)

Cross-spectral and synchronization analysis of two independent, identical chaotic R\"ossler systems suggest a coupling although there is no interaction. This spuriously detected interaction can either be explained by the absence of mixing or by finite size effects. To decide which alternative holds the phase dynamics is studied by a model of the fluctuations derived from the system's equations. The basic assumption of the model is a diffusive character for the system which corresponds to mixing. Comparison of theoretical properties of the model with empirical properties of the R\"ossler system suggests that the system is mixing but the rate of mixing appears to be rather low.

We measure the velocities of the mean flows that are driven by curved rolls in a pattern formation system. Curved rolls in Faraday waves are generated in experimental cells consisting of channels with varying widths. The mean flow magnitudes are found to scale linearly with roll curvatures and squares of wave amplitudes, agreeing with the prediction from the analysis of phase dynamics expansion. The effects of the mean flows on reducing roll curvatures are also seen.

The relative phase between two uncoupled Bose-Einstein condensates tends to attain a specific value when the phase is measured. This can be done by observing their decay products in interference. We discuss exactly solvable models for this process in cases where competing observation channels drive the phases to different sets of values. We treat the case of two modes which both emit into the input ports of two beam splitters and of a linear or circular chain of modes. In these latter cases, the transitivity of the relative phase becomes an issue.

Focusing on the mechanisms underlying the appearance of phase multistability, the paper examines a variety of phase-locked patterns in the bursting behavior of a model of coupled pancreatic cells. In particular, we show how the number of spikes per train and the proximity of a neighboring equilibrium point can influence the formation of coexisting regimes.

New formulations of active vibration isolation problems for multiple degree-of-freedom (DOF) systems are presented. A position-tracking approach via partial emulation is proposed to take advantage of the natural dynamics of a particular type of actuator: the electrohydraulic actuator. A specific 2DOF system with nonminimum phase dynamics and a noncollocated sensor and actuator pair is chosen to implement this position-tracking approach. Experimental results demonstrate good vibration isolation performance.

We determined the dynamic gain-/phase response of integrated GS-SOAs and analyzed the dependence of switching performance on the switching scheme by using the monolithically integrated GS-MZI.

Coding for the additive white Gaussian noise (AWGN) channel that also introduces an unknown carrier phase rotation is considered in this work. A simple model that captures the phase dynamics is one, where the unknown carrier phase is considered constant over a block of N symbols, and independent from block to block. In this work, LDPC codes in conjunction with pilot symbols are considered. In particular, a single pilot symbol of specified power is inserted in the beginning of each block of length N, in order to aid the joint estimation and decoding process. As expected, the presence of a pilot symbol implies an inevitable loss in the transmitted power, resulting in a trade-off between the power allocated between the pilots and the coded bits, and the quality of the joint estimation and decoding process.

Two parallel stacks of coupled Josephson junctions (JJs) are investigated to clarify the physics of transitions between the rotating and oscillating states and their effect on the IV-characteristics of the system. The detailed study of phase dynamics and bias dependence of the superconducting and diffusion currents allows one to explain all features of simulated IV-characteristics and demonstrate the correspondence in their behavior. The coupling between JJ in the stacks leads to the branching of IV-characteristics and a decrease in the hysteretic region. The crucial role of the diffusion current in the formation of the IV-characteristic of the parallel stacks of coupled JJs is demonstrated. We discuss the effect of symmetry in a number of junctions in the stacks and show a decrease of the branching in the symmetrical stacks. The observed effects might be useful for development of superconducting electronic devices based on intrinsic JJs.

Purpose: This study aims to assess the phase relationship of prefrontal tissue oxyhemoglobin oscillations using wavelet phase coherence analysis of cerebral Delta [HbO2] signals in cerebral infarction (CI) patients during the resting state. Methods: Continuous recordings of near-infrared spectroscopy signals were obtained from the left and right prefrontal lobes in 21 subjects with CI (Group CI, age: 76.6 ± 8.5 yr) and 21 healthy elderly subjects (Group Healthy, age: 69.0 ± 7.4 yr) during the resting state. The Group CI was further divide into two groups: CI with hypertension and CI without hypertension. The phase synchronization between left and right prefrontal Delta [HbO2] oscillations in four frequency intervals (I, 0.6–2 Hz; II, 0.145–0.6 Hz; III, 0.052–0.145 Hz; and IV, 0.021–0.052 Hz) was analyzed using wavelet phase coherence method. Results: The phase coherences in intervals III and IV were significantly lower in CI with hypertension than in healthy elderly subjects (F = 12.974, p = 0.001 for III and F = 10.073, p = 0.004 for interval IV). The phase coherence of CI without hypertension in interval III was significantly lower than in healthy elderly subjects (F = 9.909, p = 0.004). Also, the phase coherence in interval IV was significantly lower in CI with hypertension than in CI without hypertension (F = 5.665, p = 0.028). Also, the phase agreement in interval IV showed evident difference between Group CI with hypertension and without hypertension. Conclusions: The difference in phase characteristics of prefrontal tissue oxyhemoglobin oscillations between the CI patients and healthy elderly indicates altered phase synchronization. Moreover, the CI combined with hypertension would aggravate this process. This study provides new insight into the phase dynamics of cerebral oxygenation and may be useful in assessing the risk for stroke.

The Higgs field is a complex field that fills all space. Its phase dynamics on a cosmic scale makes the entire universe a superfluid. The energy of this cosmic superfluid can be identified with dark energy, and the fluctuations of the superfluid density lead to dark matter. This is a transcription of a talk as a series of slides, some of which have been combined for reading convenience.

We have investigated variations in the excitability of mammalian cutaneous mechanoreceptor neurons. We focused on the phase dynamics of an action potential relative to a periodic stimulus, showing that the excitability of these sensory neurons has interesting nonstationary oscillations. Using a wavelet analysis, these oscillations were characterized through the depiction of their period as a function of time. It was determined that the induced oscillations are weakly dependent on the stimulus frequency, and that lower temperatures significantly reduce the frequency of the phase response. Our results reveal novel excitability properties in sensory neurons, and, more generally, could prove significant in the deduction of mechanistic attributes underlying the nonstationary excitability in neuronal systems. Since peripheral neurons feed information to the CNS, variable responses observed in higher regions may be generated in part at the site of sensory detection.

We experimentally address long-time dynamics of an artificially curved growth interface in directional solidification. Repetitive cell nucleations are found to appear in a disordered way, but to eventually organize themselves in a coherent way, for long times. This behavior is recovered by simulation of a nonlinear advection-diffusion model for phase dynamics. The existence of a periodic attractor is supported by the derivation of a Lyapunov functional for this model.

We study numerically the effects of noise and periodic forcings on cluster synchronization in a chain of Van der Pol oscillators. We generalize the notion of effective synchronization to the case of a spatially extended system. It is shown that the structure of synchronized clusters can be effectively controlled by applying local external forcings. The effect of amplitude relations on the phase dynamics is also explored.

Pattern selection and stability in polymeric fluid convection are studied in the framework of amplitude equations derived in the vicinity of oscillatory instability. These are complex Ginzburg-Landau equations, and their coefficients, as computed from the underlying Navier-Stokes equations, are such that the selected patterns correspond to standing waves. The phase dynamics of these waves is derived and may be described by coupled equations of the Kuramoto-Sivashinsky type.

The slow dynamics of nearly stationary patterns in a FitzHugh-Nagumo model are studied using a phase dynamics approach. A Cross-Newell phase equation describing slow and weak modulations of periodic stationary solutions is derived. The derivation applies to the bistable, excitable, and the Turing unstable regimes. In the bistable case stability thresholds are obtained for the Eckhaus and the zigzag instabilities and for the transition to traveling waves. Neutral stability curves demonstrate the destabilization of stationary planar patterns at low wavenumbers to zigzag and traveling modes. Numerical solutions of the model system support the theoretical findings.

Interactions between limbs play an essential role in the formation of coherent macroscopic configurations during the bimanual performance of rhythmic movements. To uncover possible cortical aspects of these interactions, we study the relation between magneto-encephalographic signals and behavioral data during polyrhythmic tapping. In general, an explicit description of the relevant couplings requires a reliable quantification of phenomena like frequency and phase locking. Therefore, we first discuss a new cross-spectral measure that allows for the determination of frequency-locked areas in spatio-temporal signals. Subsequently, we estimate the corresponding generalized phase dynamics based on a system of two non-linearly coupled self-sustaining oscillators. The implications of these results for quantitative estimates of the functional coupling between hands/cortical areas in terms of distinct regimes of phase locking are discussed.

We investigate the relative phase coherence properties and the occurrence of demixing instabilities for two mutually interacting and time evolving Bose-Einstein condensates in traps. Our treatment naturally includes the additional decoherence effect due to fluctuations in the total number of particles. Analytical results are presented for the breathe-together solution, an extension of previously known scaling solution to the case of a binary mixture of condensates. When the three coupling constants describing the elastic interactions among the atoms in the two states are close to each other, a dramatic increase of the phase coherence time is predicted. Numerical results are presented for the parameters of the recent JILA experiments., 19 pages, 3 figures, final version of the paper

Study of weakly non-linear dynamics of a reaction–super-diffusion system near a Hopf bifurcation by means of fractional analogues of complex Ginzburg-Landau and Kuramoto-Sivashinsky equations is presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

In the absence of losses the phase of a Bose-Einstein condensate undergoes collapses and revivals in time due to elastic atomic interactions. As experiments necessarily involve inelastic collisions, we develop a model to describe the phase dynamics of the condensates in presence of collisional losses. We find that a few inelastic processes are sufficient to damp the revivals of the phase. For this reason the observability of phase revivals for present experimental conditions is limited to condensates with a few hundreds of atoms., 24 pages, 9 figures. submitted to European Journal of Physics D

The phase dynamics of a closed 0‐π junction is investigated. Such a system can be realized, for example, in a small d(x2−y2)‐wave superconductor embedded in a conventional s‐wave superconducting matrix. The Hamiltonian of the system is derived. We prove that the system can be mapped on a quantum two‐level system when the system size is small enough.

The Sixth Conference on Molecular Reaction Dynamics in Condensed Matter was held Feb. 28 - Mar 3 at the Hotel La Casa del Camino in Laguna Beach, CA, sponsored by AFOSR and UC Irvine, and organized by D. Dlott and A. Apkarian. There were 39 attendees, including professors, graduate students, postdoctoral fellows, technical staff members from national laboratories and a representative from AFOSR. 34 talks were presented. There were 21 invited talks (50 minutes with discussion) and 9 contributed talks (25 minutes with discussion). Lively discussion continued until the wee hours. The conference website is: http://dlottgroup.scs.uiuc.edu/moldyn/. Symposia on the following topics were presented: (1) New frontiers; (2) Multidimensional spectroscopy; (3) Condensed phase dynamics; (4) Chemical reaction dynamics; and (5) Confined molecules: clusters and droplets.

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.