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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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

High critical temperature superconductors (HTS) based devices can have impact in the study of the phase dynamics of Josephson junctions (JJs) thanks to the wide range of junction parameters they offer and to their unconventional properties. Measurements of current-voltage characteristics and of switching current distributions constitute a direct way to classify different regimes of the phase dynamics and of the transport, also in nontrivial case of the moderately damped regime (MDR). MDR is going to be more and more common in JJs with advances in nanopatterning superconductors and synthesizing novel hybrid systems. Distinctive signatures of macroscopic quantum tunneling and of thermal activation in presence of different tunable levels of dissipation have been detected in YBCO grain boundary JJs. Experimental data are supported by Monte Carlo simulations of the phase dynamics, in a wide range of temperatures and dissipation levels. This allows us to quantify dissipation in the MDR and partially reconstruct a phase diagram as guideline for a wide range of moderately damped systems. [ABSTRACT FROM AUTHOR]

A novel structural dynamic model for free standing hybrid riser (FSHR) is established based on the absolute nodal coordinate formulation (ANCF) in the present study. The position and slope coordinates are used in global framework to avoid coordinate transformation, and an accurate geometric relationship is introduced to describe geometric nonlinearity. The current loads on the risers and buoyancy can are simulated by Morrison equation and wake oscillator, respectively. After case validations, the vortex-induced motion (VIM) regimes of the buoyancy can and the phase dynamics of the riser and jumper in a FSHR system, subjected to the ocean current and vessel motion, is numerically investigated. It is found that the VIM of the buoyancy can experiences multiple motion switches among the periodic, quasiperiodic, multiple periodic, transition I and transition II regimes under different vessel motions. The y -motion of the jumper and both x - and y -motions of the riser present the phase trapping phenomenon along the structures. The phase trapping and locking, phase drifting and slipping, and other states are observed for x -motion of the jumper, which form a shape of "fish head" with opening mouth towards lower amplitude or higher period of vessel motion in regime map. • A novel structural dynamic model for FSHR system is established based on the ANCF. • Periodic, quasiperiodic, multiple periodic, transition I and II regimes of VIM are found under different vessel motions. • Three transition and multiple periodic bands are interspersed in the quasiperiodic regime of VIM. • The phase trapping and locking, drifting and slipping, and other states are captured for in-line motion along the jumper. • The phase dynamics of the jumper form a shape of "fish head" in the regime map. [ABSTRACT FROM AUTHOR]

The description of patterns in nonequilibrium systems is a fascinating subject. It becomes somewhat untractable if one insists to keep the original equations in their complete form, as the Oberbeck–Boussinesq equations for instance in Rayleigh–Be´nard convection. Various reduction scheme have been imagined, the ultimate one being the phase picture. I examine a simple version of the phase equation, relevant for systems of travelling rolls or for distributed self-oscillations. The boundary effects limit the ability of this phase to drift freely and yields a well-defined space structure, which can be analyzed in two different limits. [Copyright &y& Elsevier]

A ferromagnetic Josephson junction (JJ) represents a special class of hybrid system where different ordered phases meet and generate novel physics. In this work we report on the transport measurements of underdamped ferromagnetic NbN/GdN/NbN JJs at low temperatures. In these junctions the ferromagnetic insulator gadolinium nitride barrier generates spin-filtering properties and a dominant second harmonic component in the current-phase relation. These features make spin filter junctions quite interesting also in terms of fundamental studies on phase dynamics and dissipation. We discuss the fingerprints of spin filter JJs, through complementary transport measurements, and their implications on the phase dynamics, through standard measurements of switching current distributions. NbN/GdN/NbN JJs, where spin filter properties can be controllably tuned along with the critical current density (J c ), turn to be a very relevant term of reference to understand phase dynamics and dissipation in an enlarged class of JJs, not necessarily falling in the standard tunnel limit characterized by low J c values. [ABSTRACT FROM AUTHOR]

We consider the dynamics of a lattice of phase oscillators with a nearest-neighbor coupling. The clustering hierarchy is described for the case of linear distribution of natural frequencies. We demonstrate that for small couplings prior to the appearance of the first cluster the dynamics is quasi-Hamiltonian: the phase volume is conserved in average, and the spectrum of the Lyapunov exponents is symmetric. We explain this unexpected for a dissipative system phenomenon using the concept of reversibility. We show that for a certain coupling a smooth transition from the quasi-Hamiltonian to the dissipative dynamics occurs, which is a novel type of chaos–chaos transition. [Copyright &y& Elsevier]

Macroscopic oscillations in the brain are involved in various cognitive and physiological processes, yet their precise function is not completely understood. Communication through coherence (CTC) theory proposes that these rhythmic electrical patterns might serve to regulate the information flow between neural populations. Thus, to communicate effectively, neural populations must synchronize their oscillatory activity, ensuring that input volleys from the presynaptic population reach the postsynaptic one at its maximum phase of excitability. We consider an Excitatory–Inhibitory (E–I) network whose macroscopic activity is described by an exact mean-field model. The E–I network receives periodic inputs from either one or two external sources, for which effective communication will not be achieved in the absence of control. We explore strategies based on optimal control theory for phase–amplitude dynamics to design a periodic control that sets the target population in the optimal phase to synchronize its activity with a specific presynaptic input signal and establish communication. The control mechanism resembles the role of a higher cortical area in the context of selective attention. To design the control, we use the phase–amplitude reduction of a limit cycle and leverage recent developments in this field in order to find the most effective control strategy regarding a defined cost function. Furthermore, we present results that guarantee the local controllability of the system close to the limit cycle. • Optimal-control strategies provide controls that suitably adjust the dynamics for enhanced communication. • Controlled synchronization is decisive for effective communication in mean-field models of E–I networks. • Using phase–amplitude description, optimal periodic controls minimally alter the oscillation, while enhance communication. [ABSTRACT FROM AUTHOR]

Abstract: We study the phase dynamics of a chain of autonomous, self-sustained, dispersively coupled oscillators. In the quasicontinuum limit the basic discrete model reduces to a Korteveg–de Vries-like equation, but with a nonlinear dispersion. The system supports compactons–solitary waves with a compact support–and kovatons–compact formations of glued together kink–antikink pairs that propagate with a unique speed, but may assume an arbitrary width. We demonstrate that lattice solitary waves, though not exactly compact, have tails which decay at a superexponential rate. They are robust and collide nearly elastically and together with wave sources are the building blocks of the dynamics that emerges from typical initial conditions. In finite lattices, after a long time, the dynamics becomes chaotic. Numerical studies of the complex Ginzburg–Landau lattice show that the non-dispersive coupling causes a damping and deceleration, or growth and acceleration, of compactons. A simple perturbation method is applied to study these effects. [Copyright &y& Elsevier]

• Joule heating phenomenon is incorporated in the AC Josephson effect. • The phase and temperature dynamic states are discussed for various parameters. • Device state diagrams are realized for Josephson weak-link – shunted and unshunted. • A useful thermal model as a guide for the experiments with weak-link-based devices. Superconducting weak-link (WL), behaving like a Josephson junction (JJ), is fundamental to many superconducting devices such as nanoSQUIDs, single-photon detectors, and bolometers. The interplay between unique nonlinear dynamics and inevitable Joule heating in a JJ leads to new characteristics. Here, we report a time-dependent model incorporating thermal effect in the AC Josephson regime for a Josephson WL shunted by a resistor together with an inductor to investigate the dynamics as well as the resulting current-voltage characteristics. We find that the dynamic regime where phase and temperature oscillate simply widens due to a pure resistive shunt. However, a significant inductive time-scale in the shunt loop, competing with the thermal time-scale, introduces high-frequency relaxation oscillations in the dynamic regime. Based on numerical analysis, we present state diagrams for different parameter regimes. Our model is a guide for better controlling the parameters in the experiments of WL-based devices. [ABSTRACT FROM AUTHOR]

Abstract: Large-amplitude oscillations of macroscopic neuronal signals, such as local field potentials and electroencephalography or magnetoencephalography signals, are commonly considered as being generated by a population of mutually synchronized neurons. In a computational study in generic networks of phase oscillators and bursting neurons, however, we show that this common belief may be wrong if the neuronal population receives an external rhythmic input. The latter may stem from another neuronal population or an external, e.g., sensory or electrical, source. In that case the population field potential may be entrained by the rhythmic input, whereas the individual neurons are phase desynchronized both mutually and with their field potential. Intriguingly, the corresponding large-amplitude oscillations of the population mean field are generated by pairwise desynchronized neurons oscillating at frequencies shifted far away from the frequency of the macroscopic field potential. [Copyright &y& Elsevier]

Abstract: Based on the model system undergoing phase separation and chemical reactions, we investigate the dynamics of propagating dissipative waves under external forcing which is periodic both in space and time. A phase diagram for the entrained and non-entrained states under the external forcing is obtained numerically. Theoretical analysis in terms of phase description of the traveling waves is carried out to show that the transition between the entrained and the non-entrained states by changing the external frequency occurs either through a saddle–node bifurcation or through a Hopf bifurcation and that these two bifurcation lines are connected at a Bogdanov–Takens bifurcation point. [Copyright &y& Elsevier]

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

We present experimental results on hydrothermal traveling waves dynamics in long and narrow 1D channels. The onset of primary traveling-wave patterns is briefly presented for different fluid heights and for annular or bounded channels, i.e., within periodic or non-periodic boundary conditions. For periodic boundary conditions, by increasing the control parameter or changing the discrete mean wavenumber of the waves, we produce modulated wave patterns. These patterns range from stable periodic phase-solutions, due to supercritical Eckhaus instability, to spatio-temporal defect-chaos involving traveling holes and/or counter-propagating waves competition, i.e., traveling sources and sinks. The transition from non-linearly saturated Eckhaus modulations to transient pattern breaks by traveling holes and spatio-temporal defects is documented. Our observations are presented in the framework of coupled complex Ginzburg–Landau equations with additional fourth and fifth order terms which account for the reflection symmetry breaking at high wave-amplitude far from onset. The second part of this paper [N. Garnier, A. Chiffaudel, F. Daviaud, Nonlinear dynamics of waves and modulated waves in 1D thermocapillary flows. II. Convective/absolute transitions, Physica D (2003), this issue] extends this study to spatially non-periodic patterns observed in both annular and bounded channel. [Copyright &y& Elsevier]

Local magnetization curves at different times, extracted from high-temporal resolution magneto-optical measurements in Bi2Sr2CaCu2O8+δ, demonstrate the absence of the second magnetization peak (SMP) at short times, its appearance at longer times, and the movement of its onset toward higher induction fields approaching the limit of the thermodynamic order–disorder transition field. We utilize theoretical analysis, based on the Landau–Khalatnikov dynamic equation adopted for the vortex matter order parameter, to simulate the measured time evolution of the SMP. We show that the observed time evolution is a manifestation of a dynamic coexistence of transient-disordered and ordered vortex phases. [Copyright &y& Elsevier]