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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.

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

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.

Josephson junctions with weak-links of exotic materials allow the elucidation of the Josephson effect in previously unexplored regimes. Further, such devices offer a direct probe of novel material properties, for example in the search for Majorana fermions. In this work, we report on DC and AC Josephson effect of high-mobility, hexagonal boron nitride (h-BN) encapsulated graphene Josephson junctions. On the application of RF radiation, we measure phase-locked Shapiro steps. An unexpected bistability between $\pm 1$ steps is observed with switching times on the order of seconds. A critical scaling of a bistable state is measured directly from the switching time, allowing for direct comparison to numerical simulations. We show such intermittent chaotic behavior is a consequence of the nonlinear dynamics of the junction and has a sensitive dependence on the current-phase relation. This work draws connections between nonlinear phenomena in dynamical systems and their implications for ongoing condensed matter experiments exploring topology and exotic physics.

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.

In this thesis, comprised of four publications, I investigated phase dynamics of visuomotor control in humans during upright stance in response to an oscillatory visual drive. For this purpose, I applied different versions of a ���moving room��� paradigm in virtual reality while stimulating human participants with anterior-posterior motion of their visual surround and analyzed their bodily responses. Human balance control constitutes a complex interplay of interdependent processes. The main sensory contributors include vision, vestibular input, and proprioception, with a dominant role attributed to vision. The purpose of the balance control system is to keep the body���s center of mass (COM) within a certain spatial range around the current base of support. Ever-changing environmental circumstances along with sensory noise cause the body to permanently sway around its point of equilibrium. Considering this sway, the human body can be modelled as a (multi-link) inverted pendulum. To maintain balance while being exposed to perturbations of the visual environment, humans adjust their sway to counteract the perceived motion of their bodies. Neurodegenerative diseases like Parkinson���s impair balance control and thus are likely to affect these mechanisms. Hence, investigation of bodily responses to a visual drive gives insight into visuomotor control in health and disease. In my first study, I introduced inter-trial phase coherence (ITPC) as a novel method to investigate postural responses to periodical visual stimulation. I found that human participants phase-locked the motion of their center of pressure (COP) to a 3-D dot cloud which oscillated in the anterior-posterior direction. This effect was equally strong for a low frequency of visual stimulation at 0.2 Hz and a high frequency of 1.5 Hz, the latter exceeding the previously assumed frequency range associated with coherent postural sway responses to periodical oscillations of the visual environment (moving room). Moreover, I was able to show that ITPC reliably captured responses in almost all participants, thereby addressing the common problem of inter-subject variability in body sway research. Based on the results of my first study, I concluded phase locking to be an essential feature in human postural control. For the second study, I introduced a mobile and cost-effective setup to apply a visual paradigm consisting of a virtual tunnel which stretched in the anterior-posterior direction and oscillated back and forth at three distinct frequencies (0.2 Hz, 0.8 Hz, and 1.2 Hz). Because tracking of the COP alone neglects crucial information about how COM shifts are arranged across the body, I included additional full-body motion tracking here to evaluate sway of individual body segments. Using a modified measure of phase locking, the phase locking value (PLV), allowed me to find participants phase-locking not only their COP, but also additional segments of their body to the visual drive. While their COP exhibited a strong phase locking to all frequencies of visual stimulation, distribution of phase locking across the body underwent a shift as the frequency of the visual stimulation increased. For the lowest frequency of 0.2 Hz, participants phase-locked almost their entire body to the stimulus. At higher frequencies, this phase locking shifted towards the lower torso and hip, with subjects almost exclusively phase-locking their hip to the visual drive at the highest frequency of 1.2 Hz. Having introduced a novel and reliable measurement along with a mobile setup, these results allowed me to empirically confirm shifts in postural strategies previously proposed in the literature. In the third study, a collaboration with the neurology department of the Universit��tsklinikum Gie��en und Marburg (UKGM), I used the same setup and paradigm as in the previous study and additionally derived the trajectory of the COM from a weighted combination of certain body segments. The aim was to investigate phase locking of body sway in a group of patients suffering from Parkinson���s disease (PD) to find potential means for an early diagnosis of the illness. For this purpose, I recruited a group of PD patients, an age-matched control group, and a group of young healthy adults. Even though the sway amplitude of PD patients was significantly larger than that of both other groups, they phase-locked their COP and COM in a similar manner as the control groups. However, considering individual body segments, the shift in PLV distribution differed between groups. While young healthy adults, analogous to the participants in the second study, exhibited a shift towards exclusive phase locking of their hips as frequency of the stimulation increased, both PD patients and age-matched controls maintained a rather homogeneous phase locking across their body. This suggested increased body stiffness, although being an effect of age rather than disease. Overall, I concluded that patients of early-to-mid stage PD exhibit impaired motor control, reflected in their increased sway amplitude, but intact visuomotor processing, indicated by their ability to phase-lock the motion of their body to a visual drive. The fourth study, to which I contributed as second author, used experimental data collected from an additional visual condition in the course of the third study. This condition consisted of unpredictable back and forward motion of the simulated tunnel. Here, we investigated the velocity profiles of the COP and COM in response to the unpredictable visual motion and a baseline condition at which the tunnel remained static. We found PD patients to exhibit larger velocities of their COP and COM under both conditions when compared to the control groups. When examining the net increase that unpredictable motion had on the velocity of both parameters, we found a significantly higher increase in COP velocity for both PD patients and age-matched controls, but no increase in COM velocity in any of the groups. These results suggested that all groups successfully maintained their balance under unpredictable visual perturbations, but that PD patients and older adults required more effort to accomplish this task, as reflected by the increased velocity of their COP. Again, these results indicated an effect of age rather than disease on the observed postural responses. In summary, using innovative phase-locking techniques and simultaneously tracking multiple body sway parameters, I was able to provide novel insight into visuomotor control in humans. First, I overcame previous issues of inconsistent sway parameters in groups of participants; Second, I found phase-locking to be an essential feature of visuomotor processing, which also allowed me to empirically confirm previously established theories of postural control; Third, through studies in collaboration with the neurology department of the UKGM, I was able to uncover new aspects of visuomotor processing in Parkinson���s, contributing to a better understanding of the sensorimotor aspects of the disease., Im Rahmen dieser Arbeit, welche sich aus vier experimentellen Studien zusammensetzt, habe ich das Phasenverhalten des menschlichen visuomotorischen Systems w��hrend des aufrechten Stands in Antwort auf visuelle Bewegungsreize untersucht. Hierf��r verwendete ich verschiedene Varianten des ���Moving Room���-Paradigmas, welches ich in virtueller Realit��t (VR) simulierte. W��hrend sich das visuelle Umfeld meiner Proband:innen in unterschiedlicher Weise in anterior-posteriorer (a-p) Richtung bewegte, zeichnete ich die K��rperbewegungen auf, mit denen sie darauf reagierten. Das Halten unseres Gleichgewichts w��hrend des aufrechten Stands bedarf eines komplexen Zusammenspiels vieler voneinander abh��ngiger Prozesse. Die wichtigsten Sinne, welche uns hierf��r zur Verf��gung stehen, sind unser Sehsinn, die Signale unseres Vestibularorgans (Gleichgewichtssinn) sowie unsere Propriozeption. Hierbei wird unserem Sehsinn eine dominante Rolle zugeschrieben. Die Aufgabe unseres sensomotorischen Systems ist es, unseren K��rperschwerpunkt (engl.: Center Of Mass, COM) in eine situationsabh��ngige Gleichgewichtsposition zu bringen und dort zu halten. Da sich unsere Umwelt fortlaufend ver��ndert und unsere Sinneseindr��cke mit einem Grundrauschen versehen sind, schwankt unser K��rper typischerweise kontinuierlich um diesen Gleichgewichtspunkt. In Bezug auf diese Bewegung kann der menschliche K��rper als umgedrehtes (mehrgliedriges) Pendel aufgefasst werden. Nehmen wir durch St��rungen unseres visuellen Umfelds eine Bewegung unseres K��rpers wahr, so regulieren wir besagtes Schwanken, um der wahrgenommenen Bewegung entgegenzuwirken. Neurodegenerative Krankheiten wie Morbus Parkinson beeintr��chtigen diese Mechanismen und somit einen stabilen aufrechten Stand. Aus diesem Grund erm��glichen Untersuchungen von K��rperbewegungen in Antwort auf visuelle Bewegungsreize Einblicke in die visuomotorische Verarbeitung in gesunden und neuropathologischen Populationen. In meiner ersten Studie f��hrte ich eine neue Methode der Datenanalyse ein, mit welcher ich die Phasenkoh��renz der k��rperlichen Antworten auf oszillatorische visuelle Bewegungsreize zwischen einzelnen Versuchsdurchl��ufen (engl.: Trials) untersuchte (engl.: Inter-trial Phase Coherence, ITPC). Ich fand heraus, dass menschliche Proband:innen die Phase der Bewegung ihres Druckschwerpunktes auf dem Boden (engl.: Center Of Pressure, COP) an den periodischen visuellen Reiz koppelten. Der Stimulus bestand aus einer 3-D Punktewolke, welche in a-p Richtung oszillierte. Diese Kopplung trat sowohl bei einer niedrigen Frequenz der visuellen Oszillation von 0,2 Hz als auch bei einer hohen Frequenz von 1,5 Hz auf. Dabei ��berstiegen die von mir gefundenen Kopplungen an die Frequenz von 1,5 Hz das bisher angenommene Spektrum koh��renter Antworten auf eine periodische Schwingung der Umwelt (���moving room���) bei menschlichen K��rperschwankungen. Ich konnte zeigen, dass ITPC als neue Analysemethode im Kontext von K��rperbewegungen erlaubt, verl��ssliche Antworten bei fast allen Proband:innen nachzuweisen, wodurch es mir zus��tzlich gelang, das in diesem Forschungsfeld g��ngige Problem einer hohen Varianz der Antworten ��ber Proband:innen hinweg zu adressieren. Meine Ergebnisse legen nahe, dass Phasenkopplung einen wichtigen Bestandteil der menschlichen Gleichgewichtskontrolle darstellt. Im Rahmen der zweiten Studie entwickelte ich einen neuen, mobilen und kosteng��nstigen Versuchsaufbau, um visuelle Bewegungsreize in virtueller Realit��t zu pr��sentieren und dabei K��rperbewegungen aufzuzeichnen. Das neue Versuchs-Paradigma bestand hier aus einem virtuellen Tunnel, welcher sich in die a-p Richtung erstreckte. Im Experiment oszillierte der Tunnel mit einer von drei verschiedenen Frequenzen (0,2 Hz; 0,8 Hz; 1,2 Hz) vor und zur��ck. Da ein alleiniges Aufzeichnen des COP unzureichende Informationen dazu liefert, wie Bewegungen des COM realisiert werden, implementierte ich zus��tzlich ein mit dem VR-Setup synchronisiertes video-basiertes Bewegungsmesssystem, welches mir erlaubte, die Bewegungsantworten des gesamten K��rpers aufzuzeichnen. In dieser Studie verwendete ich eine leicht modifizierte Analyse zu Phasenkopplungen, den sogenannten ���Phase-Coupling Value��� (PLV). Mithilfe dieser Analyse fand ich heraus, dass Proband:innen nicht nur die Bewegung ihres COP, sondern auch die Bewegung einzelner K��rpersegmente an die Phase des visuellen Reizes koppelten. W��hrend diese Kopplung im Falle des COP bei allen pr��sentierten Frequenzen deutlich vorhanden war, zeigten die Antworten bestimmter K��rperteile mit steigender Frequenz unterschiedlich starke Kopplungen. Bei der niedrigsten Frequenz von 0,2 Hz koppelten die Proband:innen die Phase der Bewegung ihres nahezu ganzen K��rpers an den visuellen Reiz. Mit steigender Frequenz konzentrierte sich die Phasenkopplung auf den unteren Torso und die H��fte, w��hrend die Proband:innen bei der h��chsten Frequenz von 1,2 Hz beinahe nur noch ausschlie��lich ihre H��ftbewegung an die Phase des Reizes koppelten. Mein neuartiger Versuchsaufbau und die Analysemethode der Phasenkopplung erm��glichten es mir somit, frequenzabh��ngige Bewegungsmuster als Antworten auf die visuellen Reize nachzuweisen, wodurch ich bestehende Theorien empirisch belegen konnte. In der dritten Studie, welche als Kollaboration mit der Klinik f��r Neurologie des Unversit��tsklinikums Gie��en und Marburg (UKGM) durchgef��hrt wurde, verwendete ich denselben Versuchsaufbau und das gleiche Paradigma wie in der vorherigen Studie. Zus��tzlich errechnete ich in dieser Studie die Trajektorie des COM als gewichtete Kombination bestimmter K��rpersegmente. Ziel dieser Studie war es, die Phasenkopplung von K��rperschwingungen in einer Gruppe von Parkinson-Patient:innen zu untersuchen, um langfristig dabei mitzuwirken, Methoden f��r eine m��gliche Fr��herkennung der Krankheit zu entwickeln. Zu diesem Zweck untersuchte ich eine Gruppe von Patient:innen, eine Gruppe von gleichaltrigen, gesunden Kontrollproband:innen sowie eine Gruppe von jungen, gesunden Erwachsenen. Patient:innen zeigten eine deutlich erh��hte Amplitude ihrer K��rperbewegungen, koppelten jedoch die Phase ihres COP und auch ihres COM in gleicher Weise an den Stimulus wie beide Kontrollgruppen. Eine Untersuchung der Bewegung einzelner K��rperteile ergab hier jedoch, dass die in der zweiten Studie beschriebenen Bewegungsmuster in Antwort auf h��here Frequenzen in den einzelnen Gruppen unterschiedlich waren. W��hrend die junge Kontrollgruppe, analog zu den Proband:innen meiner zweiten Studie, ihr Bewegungsmuster an die h��heren Frequenzen anpasste bzw. wechselte, behielten sowohl die Patient:innen als auch die gleichaltrige Kontrollgruppe ein eher homogenes Bewegungsmuster bei, auch bei den beiden h��heren Frequenzen des visuellen Reizes. Dies lie�� mich auf eine erh��hte k��rperliche Steifigkeit schlie��en, welche jedoch ein Effekt des Alters und nicht der Krankheit zu sein scheint. Generell folgerte ich aus den Ergebnissen dieser Studie, dass Parkinson-Patient:innen in fr��hen Stadien der Krankheit zwar eine beeintr��chtigte Motorik zeigen, was sich in ihrer erh��hten Bewegungsamplitude widerspiegelt, sie jedoch keine Beeintr��chtigung in ihrer visuomotorischen Verarbeitung aufweisen, da sie prinzipiell noch immer in der Lage sind, die Phase ihrer K��rperbewegung an den visuellen Reiz zu koppeln. In der vierten Studie, in welcher ich als Zweitautor mitwirkte, nutzten wir Daten, welche wir in einem in der dritten Studie zus��tzlich verwendeten Paradigma erhoben hatten. Dieses Paradigma bestand aus einer kontinuierlichen, aber unvorhersehbaren a-p Bewegung des virtuellen Tunnels. Anhand dieser Daten untersuchten wir die Geschwindigkeitsprofile des COP und COM in Antwort auf die unvorhersehbare Bewegung sowie auf eine Kontrollbedingung, w��hrend welcher der Tunnel stillstand. Patient:innen zeigten im Vergleich zu den Kontrollgruppen erh��hte Geschwindigkeiten beider Parameter (COP und COM) unter beiden visuellen Bedingungen. Untersuchungen der Geschwindigkeitserh��hung beider Parameter als Effekt der unvorhersehbaren Bewegung des Tunnels ergaben einen Anstieg der mittleren Geschwindigkeit des COP bei Patient:innen und der gleichaltrigen Kontrollgruppe, jedoch keine Ver��nderung bei der jungen Kontrollgruppe. Die mittlere Geschwindigkeit des COM ��nderte sich bei keiner der Gruppen. Dies lie�� uns schlussfolgern, dass alle Gruppen bei unvorhersehbaren St��rungen ihres visuellen Umfelds in der Lage waren, ihr Gleichgewicht zu halten. Jedoch mussten Patient:innen und ��ltere Kontrollproband:innen hierf��r einen gesteigerten Aufwand betreiben, was sich in der erh��hten mittleren Geschwindigkeit ihres COP zeigte. Die Ergebnisse dieser Studie zeigten erneut einen Alters-, jedoch keinen Krankheits-Effekt. Zusammenfassend kann gesagt werden, dass meine neu in der Forschung zu Stand- und Gangverhalten eingef��hrte Analysemethode der Phasenkopplung sowie das gleichzeitige Aufzeichnen mehrerer Bewegungsparameter es mir erlaubten, neue Erkenntnisse ��ber die visuomotorische Verarbeitung beim Menschen zu gewinnen. Zum einen konnte ich g��ngige Probleme von inkonsistenten Bewegungsantworten innerhalb von untersuchten Personengruppen ��berwinden. Zum anderen konnte ich zeigen, dass Phasenkopplung ein essenzieller Bestandteil der visuomotorischen Verarbeitung zu sein scheint, was mir zus��tzlich erm��glichte, bestehende Theorien der posturalen Kontrolle beim Menschen empirisch zu best��tigen. Zus��tzlich konnte ich durch Studien in Kollaboration mit der Klinik f��r Neurologie des UKGM neue Aspekte der visuomotorischen Verarbeitung bei Morbus Parkinson untersuchen, wodurch ich zu einem besseren Verst��ndnis von sensomotorischen Aspekten der Krankheit beitragen konnte.

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.

We will review concepts, theory and experimental results on whether and in which conditions a quantum system, governed by a single macroscopic degree of freedom interacting with its environment, can tunnel out of a metastable state. The macroscopic quantum tunneling (MQT) experiments discussed in this chapter demonstrate that \(\varphi \) is indeed a quantum variable. Differently from the tunneling of a microscopic entity, coupling to the environment plays a major role in the macroscopic analog, and can be so strong that the motion in the classically accessible region is highly damped.

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.

Superconductivity exhibits elegant macroscopic quantum coherence in such a way that the many-body physics can be understood in a one-body way, described by the superconducting phase, and its quantum conjugate variable, the charge. When two superconductors are connected to each other through a tunnel junction, the charge tunneling can be controlled by the phase difference φ, leading to many interesting phenomena. For decades, because of the robustness of phase coherence in large junctions, a simple classical approach by modeling the system by a damped pendulum to the problem is successful and overwhelmed.(Tinkham 1996) However, as the sub-micro fabrication techniques had emerged in the 1990’s, ultra small junctions were found exhibiting stronger quantum fluctuations in phase due to charging effect, which cannot be overlooked. For exploring the novel phenomena in the opposite limit, people have made devices with robust charging effect. These phenomena can be well understood by treating the charge tunneling as a noncoherent perturbation to the quantum states described by charge. However, in the case when the Josephson energy and charging energy are competing, neither approach gives a satisfactory description. One of the attempts is to include the coherent nature in the charge tunneling processes by introducing a phase correlation function in time, which quantifies the robustness of the phase coherence.(Ingold & Nazarov 1991) The correlation function, which has been studied in many other fields, has a universal relation to the dissipation of the system, called fluctuation-dissipation theorem. Taken in this sense, dissipation is an important controlling parameter in the phase coherence robustness. If the environment impedance of the junction is much smaller than the quantum resistance (for Cooper pairs) RQ=h/4e2, the phase fluctuation is strongly damped, leading to pronounced phase coherence.(Devoret, Esteve et al. 1990) Indeed, why the classical model is so successful? The pioneer work done by Cadeira and Leggett(Caldeira & Leggett 1983) has pointed out that the environment impedance plays an important role. Their work stimulated many studies in dissipation-driven phase transitions in various systems including Josephson junctions.(Leggett, Chakravarty et al. 1987; Schon & Zaikin 1990) In this article, we will focus on the responses of Josephson junctions under microwave irradiation. Theoretically the phenomenon can be explained by the phase dynamics under an ac driving. In section 2, we will start from a classical picture by considering a Langevin

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.

DNA supercoils are generated in genome regulation processes such as transcription and replication and provide mechanical feedback to such processes. Under tension, a DNA supercoil can present a coexistence state of plectonemic and stretched phases. Experiments have revealed the dynamic behaviors of plectonemes, e.g., diffusion, nucleation, and hopping. To represent these dynamics with conformational changes, we demonstrated first the fast dynamics on the DNA to reach torque equilibrium within the plectonemic and stretched phases, and then identified the two-phase boundaries as collective slow variables to describe the essential dynamics. According to the timescale separation demonstrated here, we developed a two-phase model on the dynamics of DNA supercoiling, which can capture physiologically relevant events across timescales of several orders of magnitudes. In this model, we systematically characterized the slow dynamics between the two phases and compared the numerical results with those from the DNA polymer physics-based worm-like chain model. The supercoiling dynamics, including the nucleation, diffusion, and hopping of plectonemes, have been well represented and reproduced, using the two-phase dynamic model, at trivial computational costs. Our current developments, therefore, can be implemented to explore multiscale physical mechanisms of the DNA supercoiling-dependent physiological processes.

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

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.

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.

In this study, we investigate the role of stochastic parametric noise on the phase dynamics and the frequency characteristics of a vortex induced vibration (VIV) system, in the framework of synchronisation theory. In-phase, arbitrary-phase and anti-phase synchronisations exist during pre lock-in, lock-in and post lock-in regimes of the deterministic system, respectively. However the noise induced phase dynamics is found to be considerably different from the corresponding deterministic scenario and is largely dependent on the intensity of noise. Stochastic noise alters the conventional route to instability and is seen to induce new dynamical states such as Noise Induced Intermittency (NII) and quasi-periodicity in the structural response. It is also observed that noise triggers additional system frequencies in both structural and flow responses albeit not the same way. The birth of new dynamical states is strongly linked with these frequency characteristics of the structural and the flow oscillators. Phase can characterise the overall dynamics of coupled oscillators systematically and in the present study relative phase has been exploited in a stochastic framework in terms of both averaged and instantaneous quantities. The stochastic VIV system manifests asynchronous and synchronous phase dynamics as well as regions of phase slips during the transition boundaries of stochastic bifurcations. These are quantitatively and qualitatively monitored through phase coherence values in the desired parametric ranges.

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

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.

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.

We consider a singular phase field system located in a smooth bounded domain. In the entropy balance equation appears a logarithmic nonlinearity. The second equation of the system, deduced from a balance law for the microscopic forces that are responsible for the phase transition process, is perturbed by an additional term involving a possibly nonlocal maximal monotone operator and arising from a class of sliding mode control problems. We prove existence and uniqueness of the solution for this resulting highly nonlinear system. Moreover, under further assumptions, the longtime behavior of the solution is investigated.

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.

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

This article presents the phase dynamics of an inline long Josephson junction in voltage state under the influence of constant external magnetic field. Fractional calculus approach is used to model the evolution of the phase difference between the macroscopic wave functions of the two superconductors across the junction. The governing non-linear partial differential equation is then solved using finite difference-finite element schemes. Other quantities of interest like Josephson current density and voltage across the junction are also computed. The effects of various parameters in the model on phase difference,Josephson current density and voltage are analyzed graphically with the help of numerical simulations.

We report the exact phase dynamics of Manakov bright and dark vector solitons in an inhomogeneous optical system by means of a variable coefficient coupled nonlinear Schr\"odinger equation. To investigate the phase dynamics, we have modified the Manakov system with a relation between two modes of propagation, that are obtained by the Hirota bilinear method. The importance of the phase study in soliton interaction is revealed by asymptotic analysis of two-soliton solutions. In contrast with the Manakov bright soliton, the time-dependent dark vector soliton exhibits a gradual phase shift due to the blackness factor. The various inhomogeneous effects on the soliton phase are investigated, with a particular emphasis on nonlinear tunneling. The intensity and corresponding phase of the tunneling soliton either forms a peak or valley and retains its shape after tunneling. Unlike the bright counterpart, the gain or loss term significantly affects the phase of the dark soliton. Apart from the study of soliton intensity, the phase profile of bright and dark vector solitons and its dynamical features are also explored. As the study is not limited to intensity description, the present study could serve as a reference for the future studies on multisolitons phase dynamics in photonics and related fields.

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

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

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

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.