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The change in the phase, from quiescence to surge, may perturb the glacier’s dynamical behavior. To understand these changes through geospatial technique, the fastest moving tidewater Monacobreen Glacier, Svalbard, was studied for the year 2016–2019. It was elucidated that the surge had initiated during 2017–2018 before it the glacier was in quiescence since 2001. Initially, the glacier radar zones, namely percolation refreeze, lower percolation, and clean ice, were identified using the multi-temporal SAR data. These zones were utilized to delineate the equilibrium line altitude, and it was found that it is continuously moving down during surging, unlike the quiescence phase. The accumulation area ratio was always more than 0.67 throughout the analysis. The seasonal change in glacier surface velocity for both the phases was estimated, adapting the most appropriate Offset Tracking approach using the SAR data. The mean velocity over the main trunk was found to vary from 0.5 to 4 m/day. Thereafter, Glen's flow law equation was used to estimate the ice-thickness and found that the glacier has an average thickness range of 216–326 m in quiescence and 136–244 m during the surging. The analysis depicted that the basal shear stresses are increasing with surging, and the viscosity is decreasing. It can be said that the transition of the glacier from quiescent to surging phase has entirely changed its dynamic behavior and characteristics. Further, in the absence of field observations, the geospatial technique may provide reasonable estimates of the glacier’s physical and dynamical parameters.

The study of hyperbolic waves involves various notions which help characterise how these structures evolve. One important facet is the notion of genuine nonlinearity, namely the ability for shocks and rarefactions to form instead of contact discontinuities. In the context of the Whitham modulation equations, this paper demonstrate that a loss of genuine nonlinearity leads to the appearance of a dispersive set of dynamics in the form of the modified Korteweg de-Vries equation governing the evolution of the waves instead. Its form is universal in the sense that its coefficients can be written entirely using linear properties of the underlying waves such as the conservation laws and linear dispersion relation. This insight is applied to two systems of physical interest, one an optical model and the other a stratified hydrodynamics experiment, to demonstrate how it can be used to provide insight into how waves in these systems evolve when genuine nonlinearity is lost.

Using in situ methods to characterize the state of a system during reactions is critical to understanding and improving solvothermal syntheses. This work demonstrates the use of in situ energy-dispersive X-ray diffraction (EDXRD) to investigate the local dynamics during solvothermal formation of Cu4O3 using a general-purpose full-sized laboratory oven. This allows for direct comparison of in situ data with laboratory-based reactions. Using in situ EDXRD, changes in the local amounts of Cu4O3, Cu2O and CuO within approximately 100 × 100 × 700 µm gauge volumes during solvothermal Cu4O3 formation were recorded. Fast conversion between Cu2O and CuO was observed in the solvothermal environment, whereas Cu4O3 was found to be chemically stable against disturbances once formed. The observed differences in local dynamics give further support to the differences in formation mechanisms between Cu4O3 and Cu2O/CuO proposed here.

The phase of low-frequency, rhythmic cortical activity is essential for organizing brain processes because it provides a recurrent temporal frame for information coding. However, the low-frequency cortical phase exhibits great flexibility in response to external influences. Given that brain rhythms have been found to track respiratory inputs, we hypothesized that slow breathing, commonly associated with mental regulation, could reorganize the relationship between these two rhythmic systems through the adjustment of the cortical phase to such a slow train of inputs. Based on simultaneous magnetoencephalography and respiratory measurements, we report that while participants performed paced breathing, slow relative to normal breathing modulated cortical phase activity in the alpha range across widespread brain areas. Such modulation effects were specifically locked to the middle of the inspiration stage and exhibited a well-structured pattern. At the single-subject level, the phase angles underlying the effects became more likely to be diametrically opposed across breaths, indicating unique and consistent phase adjustment to slow inspiratory inputs. Neither cardiac fluctuations nor breathing-unrelated task effects could account for the findings. We suggest that slow-paced inspiration could organize the cortical phase in a regularized phase pattern, revealing a rhythmic but dynamic neural network integrated with different neurophysiological systems through volitional control. NEW & NOTEWORTHY Breathing is more complicated than a simple gas exchange, as it is integrated with numerous cognitive and emotional functions. Controlled slow breathing has often been used to regulate mental processes. This magnetoencephalography study demonstrates that slow-paced relative to normal-paced inspiration could organize the timing of alpha rhythmic activities across breathing cycles in a structured manner over widespread brain areas. Our results reveal how a volitionally controlled change in respiratory behavior could systematically modulate cortical activity.

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.

The problem of directional coupling detection in ensembles of temporally evolving systems from observed time series is important in diverse fields. A small ensemble of three oscillators is a model of large ensembles which carry important features such as the distinction between direct and indirect influences and, therefore, allows the study of the methods for coupling detection in respect of their ability to distinguish between such influences and, hence, correctly identify directional couplings and provide their appropriate quantitative description. This work considers an ensemble of three exemplary oscillators as a test system to improve the coupling estimation method based on phase dynamics modeling and compare it to the spectral approach called Granger – Geweke spectrum. Possibilities of false conclusions about the structure of couplings are analyzed, sensitivity of both methods and interpretations of coupling characteristics are discussed.

The authors show that neural networks exhibiting noise-induced rhythms, also known as quasi-cycle oscillations, can synchronize through out-of-phase locking depending on the noise intensity and the size of the coupling delay

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

The population and number dynamics of small mammals in the vicinity of the Torey lakes (Southeast Transbaikalia, Russia) were characterized between 2008 and 2017. The monitoring was carried out against the backdrop of the complete drying out of these largest lakes in the region. The stability of the fauna of small mammals was revealed over an 80-year period, although the structure of communities has changed significantly as a result of changes in moistening of the territory. Xerophilous species of mammals had an advantage in the period of studies in the dry climate phase. Correlation analysis showed a possible link between the population dynamics of some common species of small mammals with the precipitation amount of the current and previous years or with the precipitation amount of some spring (in one case, winter) months.

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.

The fragmentation of metals during megaplastic (severe) deformation is described in terms of a two-defect model. The process kinetics has been studied qualitatively. A general expression for the Lyapunov indices, which determine the stability of limiting (stationary) structures, is derived. Critical conditions for controlling parameters are found, and the diagrams that determine the stability of stationary states are constructed.

Objective:We assessed the delay times in the interaction between the autonomic regulatory loop of Heart Rate Variability (HRV) and autonomic regulatory loop of photoplethysmographic waveform variability (PPGV), showing low-frequency oscillations.Material and Methods:In eight healthy subjects aged 25–30 years (3 male, 5 female), we studied at rest (in a supine position) the simultaneously recorded two-hour signals of RR intervals (RRIs) chain and finger photoplethysmogram (PPG). To extract the low-frequency components of RRIs and PPG signal, associated with the low-frequency oscillations in HRV and PPGV with a frequency of about 0.1 Hz, we filtered RRIs and PPG with a bandpass 0.05-0.15 Hz filter. We used a method for the detection of coupling between oscillatory systems, based on the construction of predictive models of instantaneous phase dynamics, for the estimation of delay times in the interaction between the studied regulatory loops.Results:Averaged value of delay time in coupling from the regulatory loop of HRV to the loop of PPGV was 0.9±0.4 seconds (mean ± standard error of the means) and averaged value of delay time in coupling from PPGV to HRV was 4.1±1.1 seconds.Conclusion:Analysis of two-hour experimental time series of healthy subjects revealed the presence of delay times in the interaction between regulatory loops of HRV and PPGV. Estimated delay time in coupling regulatory loops from HRV to PPGV was about one second or even less, while the delay time in coupling from PPGV to HRV was about several seconds. The difference in delay times is explained by the fact that PPGV to HRV response is mediated through the autonomic nervous system (baroreflex), while the HRV to PPGV response is mediated mechanically via cardiac output.

Asymptotic AFM amplitude-phase dynamics is a powerful modeling tool for the development of AFM control systems and applications. We explain the model and demonstrate simple practical examples that can be easily programmed and analyzed using simulation tools such as Control and Simulation Loop (National Instruments) or Simulink (Mathworks). We first introduce asymptotic AFM models, then formulate their mathematical properties relevant to AFM, and provide examples of simulation for Hertz and Lennard-Jones tip-sample interaction forces. Material of this paper can be used to study and practice AFM dynamics in simulation, as well as for design of AFM model-based control modes and applications.

We investigate nonlinear phase dynamics of an ideal kink mode, induced by E × B flow. Here the phase is the cross phase (θ c) between perturbed stream function of velocity ( ϕ ˜ ) and magnetic field ( ψ ˜ ), i.e. θ c = θ ϕ − θ ψ . A dimensionless parameter, analogous to the Richardson number, R i = 16 γ kink 2 / ω ˆ E 2 (γ kink: the normalized growth rate of the pure kink mode; ω ˆ E : normalized E × B shearing rate) is defined to measure the competition between phase pinning by the current density and phase detuning by the flow shear. When R i > 1, θ c is locked to a fixed value, corresponding to the conventional eigenmode solution. When R i ≤ 1, θ c enters a phase slipping or oscillating state, corresponding to a nonmodal solution. The nonlinear phase dynamics method provides a more intuitive explanation of the complex dynamical behavior of the kink mode in the presence of E × B shear flow.

Under consideration is the system of partial differential equations describing the dynamics of a two-phase medium. Exact partially invariant solutions of rank 1 and defect 1 of this system are obtained with respect to some four-dimensional subalgebras. The phenomenon of collapse (an instantaneous source) in a two-phase medium is described.

The problem of interval estimation of the time delay of the coupling between oscillatory systems from observed time series is considered. It is shown that the known asymptotic estimates based on the empirical model in the form of a system of first-order phase oscillators and the maximum likelihood formalism can lead to false inferences of the value of the time delay in two typical situations: 1) nonlinear low-dimensional systems whose phases are well-determined but, as a result of significant amplitude fluctuations, the phase approximation is insufficient for describing the dynamics and 2) systems whose phases are defined not quite well because of too large amplitude fluctuations. A method for empirical diagnostics of problematic situations and its modification (coarse estimation) providing a low probability of false inferences in these situation are proposed. The efficiency of the diagnostic criterion and coarse estimation suggested is demonstrated on reference systems with different dynamic properties (linear stochastic oscillators, van der Pol oscillators, and Ressler and Lorenz chaotic systems).

First order phase reduced model is a good approximation of the dynamics of forced nonlinear oscillators near its limit cycle. The phase evolution is determined by the unforced frequency, the forcing term, and the phase response curve (PRC). Such models arise in biological oscillations such as in circadian rhythm, neural signaling, heart beat, etc. This technical note focuses on the phase regulation of the circadian rhythm using light intensity as the input. Though the model is simple, the circle topology of the state space needs to be carefully addressed. The most common entrainment method is to use a periodic input, such as in our daily light-dark cycle. We obtain the complete stable entrainment condition based on the entraiment input and the PRC. Motivated by the jet-lag problem, we also consider the minimum time entrainment control to achieve a specified phase shift. Application of the Pontryagin Minimum Principle leads to an efficient solution strategy for the optimal control, without solving the two-point boundary value problem. The optimal control may be further represented as a feedback control law based on the current and desired phases. Our analysis allows the answer to questions such as: When traveling from New York to Paris, is it faster to use light to shift the phase forward by 6 hours or delay the phase by 18 hours? The answer is somewhat counter-intuitive—delaying by 18 hours requires less time. The general answer depends on the light intensity level and the shape of the PRC. PRCs for human and Drosophila from the literature are used to illustrate the results.

In this work, a Lattice-Boltzmann-Method (LBM) model for simulating hysteresis in a proton exchange membrane (PEMFC) electrode is presented. One of the main challenges hindering study of the cathode catalyst layer (CCL) in PEMFCs is the lack of understanding of two-phase transport and how it affects electrochemical performance. Researchers have typically used high level approximations that oversimplify the microstructure of the CCL—these are known as macrohomogenous models. However, as the field has progressed, the flaws in these idealizations are being revealed, especially in areas of improving our understanding of flooding as well as catalyst layer hysteresis. Previously, the microstructure details needed to build an accurate mesoscale model have eluded researchers; however, with advances in tomography and focused-ion-beam scanning-electron-microscopy (FIB-SEM), creating these representations has become possible. Using LBM with these representations, the difficult problem of catalyst layer capillary hysteresis can be examined. In two-phase capillary hysteresis, both the equilibrium saturation position as well as absolute value depends on the wetting history. Based on the models, it is ascertained that at lower capillary numbers, the liquid begins to undergo capillary fingering – only above a capillary pressure of 5 MPa, a regime change into stable displacement is observed. As capillary fingering does not lead to uniform removal of liquid, the prediction is that because high capillary pressures are needed to change to the regime of stable displacement, wicking will not be an effective means of water removal. Figure 1

In this work, the scaling behavior of the sleep process is evaluated by using detrended fluctuation analysis based on wavelets. The analysis is carried out from arrivals of short and recurrent cortical events called A-phases, which in turn build up the Cyclic Alternating Pattern phenomenon, and are classified in three types: A1, A2 and A3. In this study, 61 sleep recordings corresponding to healthy, nocturnal frontal lobe epilepsy patients and sleep-state misperception subjects, were analyzed. From the A-phase annotations, the onsets were extracted and a binary sequence with one second resolution was generated. An item in the sequence has a value of one if an A-phase onset occurs in the corresponding window, and a value of zero otherwise. In addition, we consider other different temporal resolutions from 2[Formula: see text]s to 256[Formula: see text]s. Furthermore, the same analysis was carried out for sequences obtained from the different types of A-phases and their combinations. The results of the numerical analysis showed a relationship between the time resolutions and the scaling exponents; specifically, for higher time resolutions a white noise behavior is observed, whereas for lower time resolutions a behavior towards to [Formula: see text]-noise is exhibited. Statistical differences among groups were observed by applying various wavelet functions from the Daubechies family and choosing the appropriate sequence of A-phase onsets. This scaling analysis allows the characterization of the free-scale dynamic of the sleep process that is specific for each sleep condition. The scaling exponent could be useful as a diagnosis parameter in clinics when sleep macrostructure does not offer enough information.

This chapter discusses chemical reactions in solution; first, how solvents modify the potential energy surface of the reacting molecules and second, the role of diffusion. As a first approximation, solvent effects are described by models where the solvent is represented by a dielectric continuum, focusing on the Onsager reaction-field model for solvation of polar molecules. The reactants of bimolecular reactions are brought into contact by diffusion, and the interplay between diffusion and chemical reaction that determines the overall reaction rate is described. The solution to Fick’s second law of diffusion, including a term describing bimolecular reaction, is discussed. The limits of diffusion control and activation control, respectively, are identified. It concludes with a stochastic description of diffusion and chemical reaction based on the Fokker–Planck equation, which includes the diffusion of particles interacting via a potential U(r).

A method for estimating the characteristics of the delayed coupling between the oscillatory systems, which is based on the empirical simulation of the phase dynamics with allowance for the phase-noise correlatedness, is proposed. The method efficiency is illustrated FOR the standard stochastic and chaotic oscillators in numerical experiments. Using this method for analyzing climatic time series, we confirm the presence of the delayed influence of the El Nino Southern oscillation on the North Atlantic Oscillation.

The phase dynamics of two parallel connected stacks of intrinsic Josephson junctions (JJs) in high temperature superconductors is numerically investigated. The calculations are based on the system of nonlinear differential equations obtained within the CCJJ + DC model, which allows one to determine the general current-voltage characteristic of the system, as well as each individual stack. The processes with increasing and decreasing base currents are studied. The features in the behavior of the current in each stack of the system due to the switching between the states with rotating and oscillating phases are analyzed.

A two-dimensional D-shaped cylinder and heaving foil were mounted in tandem and used to simulate the main body and tail, respectively, of a natural swimmer. Thrust/drag measurements of the force on the foil and particle image velocimetry measurements of the flow downstream of the swimming system were conducted at a Reynolds number of about $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}10^4$ in a water channel with a constant free stream current speed. Two main sets of measurements were conducted: one set with the swimming system locked at a fixed streamwise location in the water channel as the heave frequency of the foil was varied; the other set with the system freely swimming to a desired set-point position from different upstream and downstream locations. When the freely swimming system reached and maintained its set-point position, so that its swimming speed matched that of the current, the oscillation frequency of the heaving foil corresponded to a Strouhal number of 0.36. Phase portraits of the measured thrust/drag forces reveal limit cycle oscillations for all swimming cases studied, which suggests that self-regulation drives the selection of this Strouhal number. No coupling was observed between the vortices shed by the D-shaped cylinder and the self-selected frequency of the heaving foil during free swimming. An examination of the ratio of the phase-locking indices for the input heaving motion of the foil and the coupled fluidic thrust/drag response reveals that it approaches a value of 0.5 over time when the freely swimming system is released from rest and allowed to achieve steady-state cruising. The jet produced by the freely swimming foil was inclined at an angle of approximately $4^\circ $ with respect to the direction of the mean flow.

We formulate a theory for the collective phase description of globally coupled noisy limit-cycle oscillators exhibiting macroscopic rhythms. Collective phase equations describing such macroscopic rhythms are derived by means of a two-step phase reduction. The collective phase sensitivity and collective phase coupling functions, which quantitatively characterize the macroscopic rhythms, are illustrated using three representative models of limit-cycle oscillators. As an important result of the theory, we demonstrate noise-induced anti-phase synchronization between macroscopic rhythms by direct numerical simulations of the three models., Comment: 19 pages, 11 figures

Phase dynamics of disordered Josephson junction ladders (JJLs) driven by external currents which are spatially and temporally modulated is studied using a numerical simulation based on a random field XY model. This model is considered theoretically as an effective model of JJLs with structural disorder in a magnetic field. The spatiotemporal modulation of external currents causes peculiar dynamical effects of phases in the system under certain conditions, such as the directed motion of phases and the mode-locking in the absence of dc currents. We clarify the details of effects of the spatiotemporal modulation on the phase dynamics.

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.

Light is the primary signal that calibrates circadian neural circuits and thus coordinates daily physiological and behavioral rhythms with solar entrainment cues. Drosophila and mammalian circadian circuits consist of diverse populations of cellular oscillators that exhibit a wide range of dynamic light responses, periods, phases, and degrees of synchrony. How heterogeneous circadian circuits can generate robust physiological rhythms while remaining flexible enough to respond to synchronizing stimuli has long remained enigmatic. Cryptochrome is a short-wavelength photoreceptor that is endogenously expressed in approximately half of Drosophila circadian neurons. In a previous study, physiological light response was measured using real-time bioluminescence recordings in Drosophila whole-brain explants, which remain intrinsically light-sensitive. Here we apply analysis of real-time bioluminescence experimental data to show detailed dynamic ensemble representations of whole circadian circuit light entrainment at single neuron resolution. Organotypic whole-brain explants were either maintained in constant darkness (DD) for 6 days or exposed to a phase-advancing light pulse on the second day. We find that stronger circadian oscillators support robust overall circuit rhythmicity in DD, whereas weaker oscillators can be pushed toward transient desynchrony and damped amplitude to facilitate a new state of phase-shifted network synchrony. Additionally, we use mathematical modeling to examine how a network composed of distinct oscillator types can give rise to complex dynamic signatures in DD conditions and in response to simulated light pulses. Simulations suggest that complementary coupling mechanisms and a combination of strong and weak oscillators may enable a robust yet flexible circadian network that promotes both synchrony and entrainment. A more complete understanding of how the properties of oscillators and their signaling mechanisms facilitate their distinct roles in light entrainment may allow us to direct and augment the circadian system to speed recovery from jet lag, shift work, and seasonal affective disorder.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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