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Intrinsic optical signal (IOS) imaging promises a noninvasive method for objective assessment of retinal function. This study demonstrates concurrent optical coherence tomography (OCT) of amplitude-IOS and phase-IOS changes in human photoreceptors. A new procedure for differential-phase-mapping (DPM) is validated to enable depth-resolved phase-IOS imaging. Dynamic OCT revealed rapid amplitude-IOS and phase-IOS changes, which occur almost right away after the stimulus onset. These IOS changes were predominantly observed within the photoreceptor outer segment (OS), particularly two boundaries connecting to the inner segment and retinal pigment epithelium. The comparative analysis supports that both amplitude-IOS and phase-IOS attribute to transient OS morphological change associated with phototransduction activation in retinal photoreceptors. A simulation modeling is proposed to discuss the relationship between the photoreceptor OS length and phase-IOS changes.

When a solute molecule is placed in solution, is it acceptable to presume that its electronic structure is essentially the same as that in the gas phase? In this paper, we address this question from a simulation perspective for the case of the sodium dimer cation (Na

Although Mn-Ga alloys are discussed as novel permanent magnetic materials, there are several drawbacks, including the high price of Ga and the yet too small saturation magnetization to name a few. We used several guidelines to motivate the replacement of Ga by Sn to tackle these issues and explored the phase formation, structural and magnetic properties of a Mn 2.6 Ga 1− x Sn x alloy series. The structure of Sn-rich samples is dominated by the corresponding hexagonal and orthorhombic phases, while the structure of Ga-rich samples shows additional contributions from the tetragonal DO 22 structure. However, formation of the tetragonal phase happens only upon an appropriate annealing procedure. In contrast to the discussion in the literature, our experiments do not hint on the tetragonal DO 22 structure being metastable, but rather indicate the DO 22 structure being an equilibrium phase. In general, the experimentally found phase fractions impact on the magnetic properties and hard magnetic properties are downgraded very rapidly even if only a small amount of Ga is substituted by Sn. This indicates that the DO 22 phase found only in the Ga-rich samples is indeed the one which is most relevant for realization of high magnetic anisotropy.

A transient metal Vanadium dioxide is known to have a coupled structural and electronic transition that can be accessed through light, thermal, or electrical excitation. Ultrafast optical studies of this insulator-to-metal transition indicate that it is mediated by the formation of a transient metallic phase that retains the structure of the original insulating phase. Sood et al. show that a similar sequence occurs when the material is electrically excited with a series of voltage pulses. Using ultrafast electron diffraction, the researchers monitored the structure of a vanadium dioxide sample after excitation and found evidence of a metastable metallic phase that appears during the transition. Science , abc0652, this issue p. 352

Small-signal stability assessment of the three-phase system can be performed using the measured impedances of the load and source. To obtain the dc steady-state operation point, the impedances are measured in the rotating $\boldsymbol{dq}$ -frame, and the phase angle is needed for the coordinate transformation used in both the perturbation injection and the impedance calculation. However, the phase estimation may introduce additional dynamics, affecting the accuracy of impedance measurement. This paper investigates the impact of phase synchronization dynamics on the measured impedance results. It is revealed that the phase variations in the perturbation injection has little effect on the measured impedance, while the phase dynamics introduced in the impedance calculation may have a significant impact. Based on impedance transformation, a new impedance calculation method is proposed, which can reduce the errors caused by the phase dynamics. Finally, the simulation and experiment results verify the accuracy of the analytical results and the effectiveness of the proposed method.

Significance The three spectral types of cone photoreceptors underlie color perception and are largely responsible for inherited and acquired color vision anomalies. In vivo mapping of the trichromatic cone mosaic by imaging provides the most direct and quantitative means to assess the role of photoreceptors in color vision, but remains challenging because cone reflections only weakly differentiate cone types. Here, we show a noninvasive light microscopy modality that reveals the cell’s spectral type, using the optical phase change that arises within the cell when stimulated with light. Our procedure is orders of magnitude faster and more accurate than prior approaches and makes in vivo cone classification promising for a much wider range of color vision applications., Human color vision is achieved by mixing neural signals from cone photoreceptors sensitive to different wavelengths of light. The spatial arrangement and proportion of these spectral types in the retina set fundamental limits on color perception, and abnormal or missing types are responsible for color vision loss. Imaging provides the most direct and quantitative means to study these photoreceptor properties at the cellular scale in the living human retina, but remains challenging. Current methods rely on retinal densitometry to distinguish cone types, a prohibitively slow process. Here, we show that photostimulation-induced optical phase changes occur in cone cells and carry substantial information about spectral type, enabling cones to be differentiated with unprecedented accuracy and efficiency. Moreover, these phase dynamics arise from physiological activity occurring on dramatically different timescales (from milliseconds to seconds) inside the cone outer segment, thus exposing the phototransduction cascade and subsequent downstream effects. We captured these dynamics in cones of subjects with normal color vision and a deuteranope, and at different macular locations by: (i) marrying adaptive optics to phase-sensitive optical coherence tomography to avoid optical blurring of the eye, (ii) acquiring images at high speed that samples phase dynamics at up to 3 KHz, and (iii) localizing phase changes to the cone outer segment, where photoactivation occurs. Our method should have broad appeal for color vision applications in which the underlying neural processing of photoreceptors is sought and for investigations of retinal diseases that affect cone function.

A dynamic system showing stable rhythmic activity can be represented by the dynamics of phase oscillators. This would provide a useful mathematical framework through which one can understand the system's dynamic properties. A recent study proposed a Bayesian approach capable of extracting the underlying phase dynamics directly from time-series data of a system showing rhythmic activity. Here we extended this method to spike data that otherwise provide only limited phase information. To determine how this method performs with spike data, we applied it to simulated spike data generated by a realistic neuronal network model. We then compared the estimated dynamics obtained based on the spike data with the dynamics theoretically derived from the model. The method successfully extracted the modeled phase dynamics, particularly the interaction function, when the amount of available data was sufficiently large. Furthermore, the method was able to infer synaptic connections based on the estimated interaction function. Thus, the method was found to be applicable to spike data and practical for understanding the dynamic properties of rhythmic neural systems.

By characterizing the phase dynamics in coupled oscillators, we gain insights into the fundamental phenomena of complex systems. The collective dynamics in oscillatory systems are often described by order parameters, which are insufficient for identifying more specific behaviors. To improve this situation, we propose a topological approach that constructs the quantitative features describing the phase evolution of oscillators. Here, the phase data are mapped into a high-dimensional space at each time, and the topological features describing the shape of the data are subsequently extracted from the mapped points. These features are extended to time-variant topological features by adding the evolution time as an extra dimension in the topological feature space. The time-variant features provide crucial insights into the evolution of phase dynamics. Combining these features with the kernel method, we characterize the multi-clustered synchronized dynamics during the early evolution stages. Finally, we demonstrate that our method can qualitatively explain chimera states. The experimental results confirmed the superiority of our method over those based on order parameters, especially when the available data are limited to the early-stage dynamics., 13 pages, 8 figures

Characterizing the complicated flow behaviors arising from high water cut and low velocity oil-water flows is an important problem of significant challenge. We design a high-speed cycle motivation conductance sensor and carry out experiments for measuring the local flow information from different oil-in-water flow patterns. We first use multivariate time-frequency analysis to probe the typical features of three flow patterns from the perspective of energy and frequency. Then we infer complex networks from multi-channel measurements in terms of phase lag index, aiming to uncovering the phase dynamics governing the transition and evolution of different oil-in-water flow patterns. In particular, we employ spectral radius and weighted clustering coefficient entropy to characterize the derived unweighted and weighted networks and the results indicate that our approach yields quantitative insights into the phase dynamics underlying the high water cut and low velocity oil-water flows.

We present a brief discussion of the phase-coherent dynamics of discrete breathers (intrinsic localized modes) in a system of two weakly coupled nonlinear chains and its comparison with periodic tunneling of quantum particles in a double-well potential and with macroscopic quantum tunneling of two weakly linked Bose–Einstein condensates. We consider the dynamics of relative phase of classically-tunneling discrete breathers in two weakly coupled nonlinear chains and show that the dynamics of the relative phase in the π/2 tunneling mode coincides with the experimentally observed dynamics of the relative phase of quantum particles, periodically tunneling in a double-well potential, both for noninteracting and strongly repulsively interacting particles. The observed coincidence demonstrates the correspondence between the dynamics of classical localized excitations in two weakly coupled nonlinear chains and tunneling dynamics of quantum object in the double-well potential. We show that in both π/2 and winding tunneling modes the relative phase experiences periodic jumps by π in the instants of complete depopulation of one of the weakly coupled chains or potential wells. The connection of the observed phase dynamics with the non-quantum uncertainty principle is discussed.

We consider networks of coupled phase oscillators of different complexity: Kuramoto–Daido-type networks, generalized Winfree networks, and hypernetworks with triple interactions. For these setups an inverse problem of reconstruction of the network connections and of the coupling function from the observations of the phase dynamics is addressed. We show how a reconstruction based on the minimization of the squared error can be implemented in all these cases. Examples include random networks with full disorder both in the connections and in the coupling functions, as well as networks where the coupling functions are taken from experimental data of electrochemical oscillators. The method can be directly applied to asynchronous dynamics of units, while in the case of synchrony, additional phase resettings are necessary for reconstruction.

Partial synchronous states appear between full synchrony and asynchrony and exhibit many interesting properties. Most frequently, these states are studied within the framework of phase approximation. The latter is used ubiquitously to analyze coupled oscillatory systems. Typically, the phase dynamics description is obtained in the weak coupling limit, i.e., in the first-order in the coupling strength. The extension beyond the first-order represents an unsolved problem and is an active area of research. In this paper, three partially synchronous states are investigated and presented in order of increasing complexity. First, the usage of the phase response curve for the description of macroscopic oscillators is analyzed. To achieve this, the response of the mean-field oscillations in a model of all-to-all coupled limit-cycle oscillators to pulse stimulation is measured. The next part treats a two-group Kuramoto model, where the interaction of one attractive and one repulsive group results in an interesting solitary state, situated between full synchrony and self-consistent partial synchrony. In the last part, the phase dynamics of a relatively simple system of three Stuart-Landau oscillators are extended beyond the weak coupling limit. The resulting model contains triplet terms in the high-order phase approximation, though the structural connections are only pairwise. Finally, the scaling of the new terms with the coupling is analyzed., Comment: 16 pages, 6 figures

Using the previous approach outlined in Ratliff and Bridges (2016, 2015), a novel method is presented to derive the fifth order Kadomtsev–Petviashvili(KP) equation from periodic wavetrains. As a result, the coefficients and criterion for the fifth order KP to emerge take a universal form that can be determined a-priori, relating to the system’s conservation laws and the termination of a Jordan chain. Moreover, the analysis reveals that generically a mixed dispersive term q X X X Y appears within the final phase equation. The theory presented here is complimented by an example from the context of flexural gravity waves in shallow water and a higher order Nonlinear Schrodinger model relevant in plasma physics, demonstrating how the coefficients in this model are determined via elementary calculations.

Increased exposition to blue light may induce many changes in cell behavior and significantly affect the critical characteristics of cells. Here we show that multimodal holographic microscopy (MHM) within advanced image analysis is capable of correctly distinguishing between changes in cell motility, cell dry mass, cell density, and cell death induced by blue light. We focused on the effect of blue light with a wavelength of 485 nm on morphological and dynamical parameters of four cell lines, malignant PC-3, A2780, G361 cell lines, and the benign PNT1A cell line. We used MHM with blue light doses 24 mJ/cm2, 208 mJ/cm2 and two kinds of expositions (500 and 1000 ms) to acquire real-time quantitative phase information about cellular parameters. It has been shown that specific doses of the blue light significantly influence cell motility, cell dry mass and cell density. These changes were often specific for the malignant status of tested cells. Blue light dose 208 mJ/cm2 &times, 1000 ms affected malignant cell motility but did not change the motility of benign cell line PNT1A. This light dose also significantly decreased proliferation activity in all tested cell lines but was not so deleterious for benign cell line PNT1A as for malignant cells. Light dose 208 mJ/cm2 &times, 1000 ms oppositely affected cell mass in A2780 and PC-3 cells and induced different types of cell death in A2780 and G361 cell lines. Cells obtained the least damage on lower doses of light with shorter time of exposition.

In this work, we investigate the dynamics of vortex-induced vibration of an elastically mounted cylinder with very low values of mass and damping. We use two methods to investigate this canonical problem: first we calculate the instantaneous phase between the cylinder motion and the fluid forcing; second we decompose the total hydrodynamic force into drag and lift components that act along and normal to, respectively, the instantaneous effective angle of attack. We focus on the phase dynamics in the large-amplitude–response range, consisting of the initial, upper and lower “branches” of response. The instantaneous phase between the transverse force and displacement shows repeated phase slips separating periods of constant, or continuous-drifting, phase in the second half of the upper branch. The phase between the lift component and displacement shows strong phase locking throughout the large-amplitude range – the average phase varies linearly with the primary frequency – however the modulation of this phase is largest in the second half of the upper branch. These observations suggest that the large-amplitude–response dynamics is driven by two distinct limit cycles – one that is stable over a very small range of reduced velocity at the beginning of the upper branch, and another that consists of the lower branch. The chaotic oscillation between them – the majority of the upper branch – occurs when neither limit cycle is stable. The transition between the upper and lower branches is marked by intermittent switching with epochs of time where different states exist at a constant reduced velocity. These different states are clearly apparent in the phase between the lift and displacement, illustrating the utility of the force decomposition employed. The decomposed force measurements also show that the drag component acts as a damping factor whereas the lift component provides the necessary fluid excitation for free vibration to be sustained.

The liquid-phase processes occurring during fuel droplet combustion are important in deciding the behaviour of the overall combustion process, especially, for the binary fuel droplets. Hence, understanding these processes is essential for explaining the combustion of the binary fuel droplet. However, experimental investigation of such processes is not easily accomplishable due to the very short period of time available for tracking them within the finely small fuel droplet. In the present work, a high speed imaging and subsequent image processing leading to quantitative analysis of the binary fuel droplet combustion including liquid-phase dynamics are performed. Two categories of binary fuels – in which diesel is the base fuel – are prepared and utilized. The first category is biodiesel/diesel and bioethanol/diesel blends, while the second category is the water-in-diesel and diesel-in-water emulsions. Specific optical setup is developed and used for tracking droplet combustion. The resulting magnification of the droplet images is up to 30 times the real size, offering the possibility of droplet interior visualization at high imaging rates up (to 40,000 fps). With the aid of this setup, spatial and temporal tracking of nucleation, bubble formation, puffing, microexplosion, and secondary atomization during the combustion of two adjacent binary fuel droplets are performed. The burning rate constants are evaluated and found to have the same trends as the isolated droplet combustion. However, the ratio of the droplet burning rate constant of the interactive droplet combustion to that of the isolated droplet combustion is higher than unity. This is the same for the nucleation rate within the interacting fuel droplets.

Summary A description in terms of phase and amplitude variables is given for nonlinear oscillators subject to white Gaussian noise described by Ito stochastic differential equations. The stochastic differential equations derived for the amplitude and the phase are rigorous, and their validity is not limited to the weak noise limit. It is shown that if Floquet vectors are used, then in the neighborhood of a limit cycle the phase variable coincides with the asymptotic phase defined through isochrons. Two techniques for the analysis of the phase and amplitude equations are discussed, that is, asymptotic expansion method and a phase reduction procedure based on projection operators technique. Formulas for the expected angular frequency, expected oscillation amplitude, and amplitude variance are derived using Ito calculus. Copyright © 2016 John Wiley & Sons, Ltd.

International audience; To describe all possible injection locking configurations of spin torque nano-oscillators (STNO), previous analytical descriptions are extended by introducing the most general form of the driving force: ℱ ∝ +. We provide the expressions of the corresponding forcing functions ℱ for the six basic conservative and dissipative forcing torques (~ × and ~ × × with = , ,), and demonstrate at the example of a uniform in-plane magnetized STNO, that the general case (| | | |) as well as special cases, can occur depending on: (i) the nature of the forcing torque, (ii) the direction with respect to the equilibrium direction, (iii) the harmonic order and (iv) the operation point (dc current). These relations provide a straightforward means to analyze more complex forcing torques such as a rotating field or the superposition of damping-like and field-like spin transfer torques. Besides the phase properties we also address in detail the power properties of the injection locked state for which two new parameters are introduced: the locking power range and the power angle. They can provide important complementary information on the driving forces from experiment. The general description presented here is not limited to STNOs and is valid for any non-isochronous auto-oscillator driven by an elliptical forcing of conservative or dissipative nature.

We show that the analog of the geometric phase for non-Hermitian coupled waveguides with $\mathcal{PT}$ symmetry and at least one periodically varying parameter can be purely imaginary, is hence no longer a true phase and instead a real multiplier, and will consequently result in the amplification of Floquet sidebands in the system. The sideband peaks seen in the spectrum of the system's eigenstates after evolution along the waveguides can be directly mapped to the spectrum of the derivative of the geometric function. The sidebands are magnified (becoming virtually unstable) as the exceptional point of the system is approached, and nonadiabatic effects begin to appear. Because the system cannot evolve adiabatically in the vicinity of the exceptional point, $\mathcal{PT}$ symmetry will be observed breaking earlier than theoretically predicted.

A theoretical formalism is developed to simultaneously solve equation of motion of the magnetizations in two ferromagnets and the spin-pumping induced spin transport equation. Based on the formalism, a coupled motion of the magnetizations in a self-oscillation state is studied. The spin pumping is found to induce an in-phase synchronization of the magnetizations for the oscillation around the easy axis. For an out-of-plane self-oscillation around the hard axis, on the other hand, the spin pumping leads to an in-phase synchronization in a small current region, whereas an antiphase synchronization is excited in a large current region. An analytical theory based on the phase equation reveals that the phase difference between the magnetizations in a steady state depends on the oscillation direction, clockwise or counterclockwise, of the magnetizations., 11 pages, 7 figures, published

The bifurcation of plane waves to localised structures is investigated in the Dysthe equation, which incorporates the effects of mean flow and wave steepening. Through the use of phase modulation techniques, it is demonstrated that such occurrences may be described using a Korteweg - de Vries (KdV) equation. The solitary wave solutions of this system form a qualitative prototype for the bifurcating dynamics, and the role of mean flow and steepening is then made clear through how they enter the amplitude and width of these solitary waves. Additionally, higher order phase dynamics are investigated, leading to increased nonlinear regimes which in turn have a more profound impact on how the plane waves transform under defects in the phase., Comment: 23 pages, 14 figures

We present a theoretical and numerical study of Fourier space triad phase dynamics in one-dimensional stochastically forced Burgers equation at Reynolds number $\mathrm{Re} \approx 2.7 \times 10^4$. We demonstrate that Fourier triad phases over the inertial range display a collective behaviour characterised by intermittent periods of synchronisation and alignment, reminiscent of Kuramoto model (Kuramoto 1984) and directly related to collisions of shocks in physical space. These periods of synchronisation favour efficient energy fluxes across the inertial range towards small scales, resulting in strong bursts of dissipation and enhanced coherence of Fourier energy spectrum. The fast time scale of the onset of synchronisation relegates energy dynamics to a passive role: this is further examined using a reduced system with the Fourier amplitudes fixed in time -- a phase-only model. We show that intermittent triad phase dynamics persists without amplitude evolution and we broadly recover many of the characteristics of the full Burgers system. In addition, for both full Burgers and phase-only systems the physical space velocity statistics reveals that triad phase alignment is directly related to the non-Gaussian statistics typically associated with structure-function intermittency in turbulent systems., Comment: Accepted for publication in Journal of Fluid Mechanics

Collective synchronous motion of the phases is introduced in a model for the stochastic passive advection-diffusion of a scalar with external forcing. The model for the phase coupling dynamics follows the well known Kuramoto model paradigm of limit-cycle oscillators. The natural frequencies in the Kuramoto model are assumed to obey a given scale dependence through a dispersion relation of the drift-wave form $-\beta\frac{k}{1+k^2}$, where $\beta$ is a constant representing the typical strength of the gradient. The present aim is to study the importance of collective phase dynamics on the characteristic time evolution of the fluctuation energy and the formation of coherent structures. Our results show that the assumption of a fully stochastic phase state of turbulence is more relevant for high values of $\beta$, where we find that the energy spectrum follows a $k^{-7/2}$ scaling. Whereas for lower $\beta$ there is a significant difference between a-synchronised and synchronised phase states, and one could expect the formation of coherent modulations in the latter case., Comment: Accepted for publication in Physics of Plasmas

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

A geometric-based methodology that was recently proposed provides a systematic controller design approach for controlling remote vibration at multiple points using only a restricted number of sensors and actuators. Valuable physical insight into the existence of control solutions for vibration attenuation at multiple locations is retained with this approach in contrast to alternatives, such as $\mathcal {H}_{2}$ and $\mathcal {H}_{\infty }$ methods. A drawback of the existing geometric design approach is that the controller implementation for the broadband case incorporates an inverted local control path transfer function. When the sensor and actuator are noncollocated or when there is significant latency or phase lag in the system, the local control path model will have nonminimum phase characteristics. Therefore, the resulting controller for this situation will itself be unstable due to the inclusion of an inverted nonminimum phase transfer function. In this brief paper, a systematic procedure is presented, which extends the previous work and which yields both a stable and stabilizing controller without requiring a minimum phase control path assumption. Furthermore, robustness against control spillover at out-of-band frequencies is incorporated within this modified design procedure without deteriorating controller performance within the design bandwidth. The detailed control design procedure is illustrated using a simulated beam vibration problem. Finally, the design approach is experimentally validated using a test rig that replicates the problem of vibration transmission in rotary propulsion systems.

In this work, the mode analysis technique of complex networks nonlinear selfoscillatory vortex-based spin-torque nano-oscillattors (STNOs) with nonidentity and nonisochrony is developed. We construct adjacency matrices of different type of networks and calculate the normal modes. After the calculation of normal modes we shift to truncated equations for slowly varying amplitudes and phases in the normal coordinates using generalized quasi-Hamiltonian approach. Finally, we present the phase dynamics based on the Kuramotoapproach and compare different networks to the ability of synchronization.

International audience; We report on successful 10 Gb/s transmission of a message hidden in a chaotic optical phase over more than 100 km of an installed fiber optic network. This represents the best performance to date for so-called optical chaos communication, a physical layer oriented optical data encryption technique. Such performances was achieved through the use of a recently developed electro-optic nonlinear delay phase dynamics, inspired from differential phase modulation techniques. The setup appears as a superior alternative to the most popular architectures, i.e., the ones involving laser rate equations subjected to delayed feedback. It is compatible with standard dispersion compensation techniques and optical amplification, as shown by two field experiments over installed fiber optic networks.

International audience; We demonstrate experimentally how nonlinear optical phase dynamics can be generated with an electro-optic delay oscillator. The presented architecture consists of a linear phase modulator, followed by a delay line, and a differential phase-shift keying demodulator (DPSK-d). The latter represents the nonlinear element of the oscillator effecting a nonlinear transformation. This nonlinearity is considered as nonlocal in time since it is ruled by an intrinsic differential delay, which is significantly greater than the typical phase variations. To study the effect of this specific nonlinearity, we characterize the dynamics in terms of the dependence of the relevant feedback gain parameter. Our results reveal the occurrence of regular GHz oscillations (approximately half of the DPSK-d free spectral range), as well as a pronounced broadband phase-chaotic dynamics. Beyond this, the observed dynamical phenomena offer potential for applications in the field of microwave photonics and, in particular, for the realization of novel chaos communication systems. High quality and broadband phase-chaos synchronization is also reported with an emitter-receiver pair of the setup

We investigate theoretically and experimentally the detrimental e ect of ber dispersion on the synchroniza- tion of an optoelectronic phase chaos cryptosystem. We evaluate the root-mean square synchronization error and the cancellation spectra between the emitter and the re- ceiver in order to characterize the quality of the optical ber communication link. These two indicators explicitly show in temporal and spectral domain how ber dispersion does negatively a ect the phase chaos cancellation at the re- ceiver stage. We demonstrate that the dispersion manage- ment techniques used in conventional optical ber networks, such as dispersion-compensating modules/ bers or disper- sion shifted bers, are also e cient to strongly reduce the detrimental e ects of ber propagation in phase chaos com- munications. This compatibility therefore opens the way to a successful integration of more than 10-Gb/s phase chaos communications systems in existing networks, even when the ber link spans over more than 100 km.

Optical chaos communications met intensive research efforts during the last 10 years [1,2], resulting in 2004 in a field experiment in the metropolitan optical network of Athens [3]. Current efforts are now concentrating on device oriented architectures, in order to improve reliability, efficiency, and security. Among the few competitive approaches developed in the literature, the electro-optic one showed first its strong potential in terms of bit rate and decoding quality [4]. However, it was suffering from a few drawbacks in terms of technological complexity, due to the intensity superposition condition required by the mixing between the binary intensity message and the chaotic optical intensity carrier.

We demonstrate in numerical experiments that estimators of strength and directionality of coupling between oscillators based on modeling of their phase dynamics [D.A. Smirnov and B.P. Bezruchko, Phys. Rev. E 68, 046209 (2003)] are widely applicable. Namely, although the expressions for the estimators and their confidence bands are derived for linear uncoupled oscillators under the influence of independent sources of Gaussian white noise, they turn out to allow reliable characterization of coupling from relatively short time series for different properties of noise, significant phase nonlinearity of the oscillators, and non-vanishing coupling between them. We apply the estimators to analyze a two-channel human intracranial epileptic electroencephalogram (EEG) recording with the purpose of epileptic focus localization., Comment: 22 pages, 7 figures, the paper is to be published in Chaos, 2005, vol.15, issue 2, see http://chaos.aip.org/

We study a simple model of a massive inflaton field $\phi$ coupled to another scalar filed $\chi$ with interaction term $g^2\phi^2\chi^2$. We use the theory developed by Kofman {\em et al.} (Phys. Rev. D {\bf 56} (1997) 3258 [arXiv:hep-ph/9704452])for the first stage of preheating to give a full description of the dynamics of the $\chi$ field modes, including the behaviour of the phase, in terms of the iteration of a simple family of circle maps. The parameters of this family of maps are a function of time when expansion of the universe is taken into account. With this more detailed description, we obtain a systematic study of the efficiency of particle production as a function of the inflaton field and coupling parameters, and we find that for $g \lesssim 3 \times 10^{-4}$ the broad resonance ceases during the first stage of preheating., Comment: 14 pages, 12 figures, accepted for publication in Phys. Rev. D. Correct Figure 9, results unchanged. Added references and corrected misprints/misspellings

This paper investigates the linear and non-linear instabilities during evaporation of liquid layers and droplets by means of two-phase 3D direct numerical simulations. The interface is open to the atmosphere under the consideration that vapour diffusion is the rate- limiting mechanism for evaporation. In both configurations, the vapour-liquid interface is prone to travelling thermal instabilities, i.e., hydrothermal waves (HTWs), due to the presence of temperature gradients along the interface. We have already shown in our recent work 7 that under saturated conditions (negligible evaporation) the HTWs additionally give rise to interface deformations of similar features, i.e., physical waves. We have also demonstrated 8 that phase change plays a dual role through its effect on these instabilities: the latent energy required during the evaporation process tends to inhibit the HTWs while the accompanying level reduction enhances the physical waves by minimizing the role of gravity. The dynamics of the gas phase are also discussed. We have also established that the HTW-induced convective patterns in the gas along with the travelling nature of the instabilities have a significant impact on the local evaporation flux and the vapour distribution above the interface. The Marangoni effect plays a major role in the vapour distribution generating a vacuum effect in the warm region and vapour accumulations at the cold boundary capable of inverting the phase change, i.e., the capillary flow can lead to local condensation. These results provide evidence of the inefficiencies of the traditional phase change models based on pure vapour diffusion to capture the dynamics of thermocapillary flows. To conclude, we also present results of a parallel investigation focusing on three-dimensional phenomena on evaporating sessile drops placed on heated substrates.

Aim of the study is to apply the analysis of phase dynamics to investigation of the coupling patterns between heart rate variability, respiration and peripheral circulation in healthy subjects at rest and after moderate physical exercises. Material and Methods ― 30-minutes electrocardiogram (ECG), photoplethysmogram (PPG) and respiration records were obtained from healthy subjects aged 22±2 (mean ± standard deviation) before and after active Martine Kushelevsky test (20 squats in 30 seconds). The coherence function was estimated between all the signals from each subject, and the phase dynamics modeling was used to detect the directional coupling in high-frequency (HF; 0.14-0.40 Hz) and low-frequency ranges (LF; 0.04-0.14 Hz). Results ― At rest (before the physical activity) no statistically significant couplings were detected between the HF rhythms of respiration and heart rate (RR intervals). For the HF rhythms in respiration and PPG, the influence respirationPPG was detected. No couplings were detected between the LF rhythms. After the moderate physical exercise, predominant direction of the influence was RR intervals  PPG in the LF range and both RR intervals  respiration and PPG  respiration in the HF range. The influence PPG  respiration was delayed by several seconds. Conclusion ― adaptation to the moderate physical activity has led to the decrease in the overall coherence and changes in patterns of directional coupling between the LF and HF rhythms in respiration, heart rate and peripheral circulation. The obtained results confirm nonlinearity and complexity of the coupling patterns in cardiovascular system.

Adaptive dynamical networks appear in various real-word systems. One of the simplest phenomenological models for investigating basic properties of adaptive networks is the system of coupled phase oscillators with adaptive couplings. In this paper, we investigate the dynamics of this system. We extend recent results on the appearance of hierarchical frequency-multi-clusters by investigating the effect of the time-scale separation. We show that the slow adaptation in comparison with the fast phase dynamics is necessary for the emergence of the multi-clusters and their stability. Additionally, we study the role of double antipodal clusters, which appear to be unstable for all considered parameter values. We show that such states can be observed for a relatively long time, i.e., they are metastable. A geometrical explanation for such an effect is based on the emergence of a heteroclinic orbit., 16 pages, 8 figures

We develop a technique for the multivariate data analysis of perturbed self-sustained oscillators. The approach is based on the reconstruction of the phase dynamics model from observations and on a subsequent exploration of this model. For the system, driven by several inputs, we suggest a dynamical disentanglement procedure, allowing us to reconstruct the variability of the system's output that is due to a particular observed input, or, alternatively, to reconstruct the variability which is caused by all the inputs except for the observed one. We focus on the application of the method to the vagal component of the heart rate variability caused by a respiratory influence. We develop an algorithm that extracts purely respiratory-related variability, using a respiratory trace and times of R-peaks in the electrocardiogram. The algorithm can be applied to other systems where the observed bivariate data can be represented as a point process and a slow continuous signal, e.g. for the analysis of neuronal spiking., Comment: 10 pages, 8 figures

Synchronization occurs in many natural and technological systems, from cardiac pacemaker cells to coupled lasers. In the synchronized state, the individual cells or lasers coordinate the timing of their oscillations, but they do not move through space. A complementary form of self-organization occurs among swarming insects, flocking birds, or schooling fish; now the individuals move through space, but without conspicuously altering their internal states. Here we explore systems in which both synchronization and swarming occur together. Specifically, we consider oscillators whose phase dynamics and spatial dynamics are coupled. We call them swarmalators, to highlight their dual character. A case study of a generalized Kuramoto model predicts five collective states as possible long-term modes of organization. These states may be observable in groups of sperm, Japanese tree frogs, colloidal suspensions of magnetic particles, and other biological and physical systems in which self-assembly and synchronization interact., Collective self-organized behavior can be observed in a variety of systems such as colloids and microswimmers. Here O’Keeffe et al. propose a model of oscillators which move in space and tend to synchronize with neighboring oscillators and outline five types of collective self-organized states.

A minimal model of nonlinear phase dynamics in drift waves is shown to support phase bore solutions. Coupled nonlinear equations for amplitude, phase, and zonal flow are derived for the Hasegawa-Mima system and specialized to the case of spatiotemporally constant amplitude. In that limit, phase curvature (finite second derivative of the phase with respect to the radius) alone generates propagating shear flows. The phase field evolves nonlinearly by a competition between phase steepening and dispersion. The analytical solution of the model reveals that the phase bore solutions so obtained realize the concept of a phase slip in a concrete dynamical model of drift wave dynamics. The implications for phase turbulence are discussed.

We perform experiments and phase model simulations with a ring network of oscillatory electrochemical reactions to explore the effect of random connections and non-isochronocity of the interactions on the pattern formation. A few additional links facilitate the emergence of the fully synchronized state. With larger non-isochronicity, complex rotating waves or persistent irregular phase dynamics can derail the convergence to global synchronization. The observed long transients of irregular phase dynamics exemplify the possibility of a sudden onset of hyper synchronous behavior without any external stimulus or network reorganization., Comment: 4 pages main text and 4 pages supplemental material

Overall descriptors of the information (determinicity) and entropy (uncertainty) content of complex molecular states are reexamined. These resultant concepts combine the classical (probability) contributions of Fisher and Shannon, and the relevant nonclassical supplements due to the state phase/current. The information-theoretic principles determining equilibria in molecules and their fragments are explored and the nonadditive part of the global entropy is advocated as a descriptor of the classical index of the quantum entanglement of molecular subsystems. Affinities associated with the probability and phase fluxes are identified and the criterion of vanishing overall information-source is shown to identify the system stationary electronic states. The production of resultant density of the gradient-information is expressed in terms of the conjugate affinities (forces, perturbations) and fluxes (currents, responses). The Schrodinger dynamics of probability and phase components of molecular electronic states is used to determine the temporal evolution of the overall gradient information and complex entropy. The global sources of the resultant information/entropy descriptors are shown to be of purely nonclassical origin, thus identically vanishing in real electronic states, e.g., the nondegenerate ground state of a molecule.

We explore identical R\"ossler systems organized into two equally-sized groups, among which differing positive and negative in- and out-coupling strengths are allowed. Patterns of distinctly synchronized phase dynamics are observed, which coexist with chaotically evolving amplitudes. In particular, we report the emergence of traveling phase waves, i.e. states in which the oscillators settle on a new rhythm different from their own. We further elucidate our findings through phase-coupled R\"ossler systems, establishing a connection with the Kuramoto model. Together with the study of noise effects, our results suggest a promising new avenue towards the coexistence of chaotic, noisy and regular collective dynamics., Comment: 5 pages, 4 figures and Supplemental Material

Multidimensional ultrafast spectroscopies are one of the premier tools to investigate condensed phase dynamics of biological, chemical and functional nanomaterial systems. As they reach maturity, the variety of frequency domains that can be explored has vastly increased, with experimental techniques capable of correlating excitation and emission frequencies from the terahertz through to the ultraviolet. Some of the most recent innovations also include extreme cross-peak spectroscopies that directly correlate the dynamics of electronic and vibrational states. This review article summarizes the key technological advances that have permitted these recent advances, and the insights gained from new multidimensional spectroscopic probes.

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.

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

Water is often viewed as a collection of monomers interacting electrostatically with each other. We compare the water proton momentum distributions from recent neutron scattering data with those calculated from two electronic structure-based models. We find that below 500 K these electrostatic models, one based on a multipole expansion, which includes the polarizability of the monomers, are not able to even qualitatively account for the sizable vibrational zero-point contribution to the enthalpy of vaporization. This discrepancy is evidence that the change in the proton well upon solvation cannot be entirely explained by electrostatic effects alone, but requires correlations of the electronic states on the molecules involved in the hydrogen bonds to produce the observed softening of the well.

We use Metropolis Monte Carlo and umbrella sampling to calculate the free energies of interaction of two methane molecules and their charged derivatives in cylindrical water-filled pores. Confinement strongly alters the interactions between the nonpolar solutes, and completely eliminates the solvent separated minimum (SSM) that is seen in bulk water. The free energy profiles show that the methane molecules are either in contact or at separations corresponding to the diameter and the length of the cylindrical pore. Analytic calculations that estimate the entropy of the solutes, which are solvated at the pore surface, qualitatively explain the shape of the free energy profiles. Adding charges of opposite sign and magnitude $0.4e$ or $e$ (where $e$ is the electronic charge) to the methane molecules decreases their tendency for surface solvation and restores the SSM. We show that confinement induced ion-pair formation occurs whenever $l_B/D \sim O(1)$, where $l_B$ is the Bjerrum length, and $D$ is the pore diameter. The extent of stabilization of the SSM increases with ion charge density as long as $l_B/D < 1$. In pores with $D \le 1.2$ nm, in which the water is strongly layered, increasing the charge magnitude from $0.4e$ to $e$ reduces the stability of the SSM. As a result, ion-pair formation which occurs with negligible probability in the bulk, is promoted. In larger diameter pores that can accomodate a complete hydration layer around the solutes, the stability of the SSM is enhanced., 23 pages, 8 figures. To be published in The Journal of Chemical Physics

By defining a spatially varying replica overlap parameter for a supercooled liquid referenced to an ensemble of fiducial liquid state configurations, we explicitly construct a constrained replica free energy functional that maps directly onto an Ising Hamiltonian with both random fields and random interactions whose statistics depend on the liquid structure. Renormalization group results for random magnets when combined with these statistics for the Lennard-Jones glass suggest that discontinuous replica symmetry breaking would occur if a liquid with short range interactions could be equilibrated at a sufficiently low temperature where its mean field configurational entropy would vanish, even though the system strictly retains a finite configurational entropy.

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 evaluate exactly the statistical integral for an inhomogeneous one-dimensional counterion-only Coulomb gas between two charged boundaries and from this compute the effective interaction, or disjoining pressure, between the bounding surfaces. Our exact results are compared with the limiting cases of weak and strong coupling which are the same for 1D and 3D systems. For systems with a large number of counterions it is found that the weak coupling (mean-field) approximation for the disjoining pressure works perfectly and that fluctuations around the mean-field in 1D are much smaller than in 3D. In the case of few counterions it works less well and strong coupling approximation performs much better as it takes into account properly the discreteness of the counterion charges., Comment: 16 pages RevTex, 1 .eps figure

The two-dimensional vibrational response of the disordered strongly fluctuating OH exciton band in liquid water is investigated using a new simulation protocol. The direct nonlinear exciton propagation generalizes the nonlinear exciton equations to include nonadiabatic time dependent Hamiltonian and transition dipole fluctuations. The excitonic picture is retained and the large cancellation between Liouville pathways is built-in from the outset. The sensitivity of the photon echo and double-quantum-coherence techniques to frequency fluctuations, molecular reorientation, intermolecular coupling, and the two-exciton coherence is investigated. The photon echo is particularly sensitive to the frequency fluctuations and molecular reorientation, whereas the double-quantum coherence provides a unique probe for intermolecular couplings and two-exciton coherence.