Mean Phase Velocity Research Articles

Narrow Width Farley‐Buneman Spectra Above 100 km Altitude

AbstractFor spectra associated with full turbulence the observed mean phase velocity of unstable Farley‐Buneman waves has been found not to exceed the ion‐acoustic speed, cs. This has been attributed to various nonlinear processes. However, weakly turbulent modes are also excited on the edge of the “instability cone.” These modes have to be actual eigenmodes predicted by linear instability theory near‐threshold conditions. Unlike the modes that are associated with strong turbulence, these weakly turbulent modes are affected by the ion drift. This can make the Doppler shift of narrow spectra reach as high as the E × B drift velocity in the upper portion of the unstable layer at small aspect angles. Slow narrow spectra are also predicted nearer the E direction. We have produced a model of the Doppler shift of narrow‐width spectra under various electric field conditions above 100 km altitude. While the fluid dispersion relation is used to clarity the physics, we have also found the eigenmodes from an accepted kinetic dispersion relation. The calculations include a new model of the ion‐acoustic speed based on an empirical model of the electron temperature and of ion frictional heating under strong electric field conditions. The model provides an explanation for various VHF observations of the Doppler shift of narrow spectra that have been called “Type III spectra” and “Type IV spectra” in the existing literature.

Two-attractor chimera and solitary states in a network of nonlocally coupled birhythmic van der Pol oscillators

In this paper, a network of van der Pol oscillators with extended nonlinearity is considered in the context of studies on symmetry-breaking phenomena. The van der Pol oscillator with extended nonlinearity has been widely considered as a model for coherent oscillations in enzyme–substrate systems. The particularity of this model is its multistability known as birhythmicity. Due to this feature of the local dynamics, the coupled dynamics shows a rich variety of symmetry-breaking phenomena, among which peculiar chimera and solitary states involving two types of attractors, namely a large limit cycle and a smaller attractor with quasiperiodic-like oscillations. The units of the main incoherent regions of a pattern of this two-attractor chimera evolve only on the large limit cycle whereas those of the main coherent regions evolve only on the smaller attractor. Also, as a consequence of birhythmicity, the mean phase velocity profile of this chimera pattern shows two levels of frequency, each level corresponding to each attractor. On the other hand, the frequencies of oscillations of the solitary units of the solitary states found there are different from the common frequency of oscillations in the coherent cluster, contrary to the classical solitary states for which all the network units are frequency locked. Interestingly, a phenomenon of coupling-induced birhythmicity is found here: two-attractor patterns emerge in the considered network with monorhythmic local dynamics. This study deepens our understanding of patterns formation in coupled multistable systems.

Climatology of Medium-Scale Traveling Ionospheric Disturbances (MSTIDs) Observed with GPS Networks in the North African Region

We present for the first time the climatology of medium-scale traveling ionospheric disturbances (MSTIDs) by using Global Positioning System (GPS) receiver networks on geomagnetically quiet days (Kp ≤ 3) over the North African region during 2008–2016. The ionospheric Total Electron Content (TEC) were estimated from the dual-frequency GPS measurements, and the TEC perturbations (dTEC) data were derived from the estimated TEC data. We focused on the TEC perturbations (dTEC) associated MSTIDs and statistically analyzed its characteristics, occurrence rate, diurnal and seasonal behavior as well as the interannual dependence. The results show that MSTID is a local and seasonal dependence. The result reveals that occurrence of MSTIDs increases with solar activity. It also shows that MSTIDs predominantly propagates towards the South (equatorward). The MSTIDs event period is (12 ≤ period ≤ 53 min), while the dominant peak-to-peak amplitude is (0.08 ≤ amp ≤ ~ 1.5 dTECU). The study also shows that the amplitude of MSTIDs is higher at the northwest (Lat: ~ 32° N to ~ 38° N, Long: ~ 2° W to ~ 15° W) when compared with northeast (Lat: ~ 28° N to ~ 38° N, Long: ~ 23° E to ~ 40° E), and the disturbance occurrence time is more frequent within the hours of (1200–1600 LT), and (1000—1400 LT) in December solstice at daytime for stations located in the northwest and northeast part of the African region, respectively. While at the nighttime, the MSTIDs also exhibits variability in disturbance occurrence time around (northwest: 2100–0200 LT) and (northeast: 1900-0200 LT) in June solstice, but get extended to March equinox during solar maximum (2014). The mean phase velocity in daytime MSTIDs is higher than the nighttime in every season, except during June solstice.

Phase irregularity: A conceptually simple and efficient approach to characterize electroencephalographic recordings from epilepsy patients.

The severe neurological disorder epilepsy affects almost 1% of the world population. For patients who suffer from pharmacoresistant focal-onset epilepsy, electroencephalographic (EEG) recordings are essential for the localization of the brain area where seizures start. Apart from the visual inspection of the recordings, quantitative EEG signal analysis techniques proved to be useful for this purpose. Among other features, regularity versus irregularity and phase coherence versus phase independence allowed characterizing brain dynamics from the measured EEG signals. Can phase irregularities also characterize brain dynamics? To address this question, we use the univariate coefficient of phase velocity variation, defined as the ratio of phase velocity standard deviation and the mean phase velocity. Beyond that, as a bivariate measure we use the classical mean phase coherence to quantify the degree of phase locking. All phase-based measures are combined with surrogates to test null hypotheses about the dynamics underlying the signals. In the first part of our analysis, we use the Rössler model system to study our approach under controlled conditions. In the second part, we use the Bern-Barcelona EEG database which consists of focal and nonfocal signals extracted from seizure-free recordings. Focal signals are recorded from brain areas where the first seizure EEG signal changes can be detected, and nonfocal signals are recorded from areas that are not involved in the seizure at its onset. Our results show that focal signals have less phase variability and more phase coherence than nonfocal signals. Once combined with surrogates, the mean phase velocity proved to have the highest discriminative power between focal and nonfocal signals. In conclusion, conceptually simple and easy to compute phase-based measures can help to detect features induced by epilepsy from EEG signals. This holds not only for the classical mean phase coherence but even more so for univariate measures of phase irregularity.

Chimera states with coherent domains owning different frequencies in a ring of nonlocally coupled Brusselators

In a chimera state, domains composed of synchronized oscillators coexist with ones composed of desynchronized oscillators. It is a common view that, in a chimera state, oscillators in coherent domains always share the same mean phase velocity. However, recent studies have suggested that oscillators in different coherent domains may have different mean phase velocities. In this work, we study a ring of nonlocally coupled Brusselators. We find a two-frequency chimera state with mixed phase regularities in which Brusselators in adjacent coherent domains oscillate at different velocities. Moreover, Brusselators in coherent domains with higher mean phase velocity are nearly in phase. In contrast, Brusselators in coherent domains with lower mean phase velocity are randomly partitioned into two groups in antiphase. We find that the local mean fields in these two types of coherent domains perform different dynamics. Based on local mean fields, we provide an explanation for the formation of this type of chimera state. Furthermore, the stability diagrams of the two-frequency chimera state with mixed phase regularities are investigated in different parameter planes

Entangled chimeras in nonlocally coupled bicomponent phase oscillators: From synchronous to asynchronous chimeras

Chimera states, a symmetry-breaking spatiotemporal pattern in nonlocally coupled identical dynamical units, have been identified in various systems and generalized to coupled nonidentical oscillators. It has been shown that strong heterogeneity in the frequencies of nonidentical oscillators might be harmful to chimera states. In this work, we consider a ring of nonlocally coupled bicomponent phase oscillators in which two types of oscillators are randomly distributed along the ring: some oscillators with natural frequency ω1 and others with ω2. In this model, the heterogeneity in frequency is measured by frequency mismatch ∣ω1 − ω2∣ between the oscillators in these two subpopulations. We report that the nonlocally coupled bicomponent phase oscillators allow for chimera states no matter how large the frequency mismatch is. The bicomponent oscillators are composed of two chimera states, one supported by oscillators with natural frequency ω1 and the other by oscillators with natural frequency ω2. The two chimera states in two subpopulations are synchronized at weak frequency mismatch, in which the coherent oscillators in them share similar mean phase velocity, and are desynchronized at large frequency mismatch, in which the coherent oscillators in different subpopulations have distinct mean phase velocities. The synchronization-desynchronization transition between chimera states in these two subpopulations is observed with the increase in the frequency mismatch. The observed phenomena are theoretically analyzed by passing to the continuum limit and using the Ott-Antonsen approach.

Chimera States With 2D Deterministic and Random Fractal Connectivity

We study the formation of chimera states in 2D lattices with hierarchical (fractal) connectivity. The dynamics of the nodes follow the Leaky Integrate-and-Fire model and the connectivity has the form of a deterministic or a random Sierpinski carpet. We provide numerical evidence that for deterministic fractal connectivity and small values of the coupling strength, a hierarchical incoherent spot is produced with internal structure influenced by the fractal connectivity scheme. The spot size is similar to the size of the coupling matrix. Stable spots can be formed for symmetric fractal connectivity, while travelling ones are found when the connectivity matrix is asymmetric with respect to the center. For fractal coupling schemes spiral wave chimeras are produced and curious stable patterns are reported, which present triple coexistence of coherent regions, incoherent domains and travelling waves. In all cases, the coherent domains demonstrate the lowest mean phase velocities $\omega$, the incoherent domains show intermediate $\omega$-velocities, while the travelling waves show the highest $\omega$-values. These findings confirm previous studies on symmetric deterministic hierarchical connectivities and extend here to slanted and random fractals.

Solitary states and solitary state chimera in neural networks.

We investigate solitary states and solitary state chimeras in a ring of nonlocally coupled systems represented by FitzHugh-Nagumo neurons in the oscillatory regime. We perform a systematic study of solitary states in this network. In particular, we explore the phase space structure, calculate basins of attraction, analyze the region of existence of solitary states in the system's parameter space, and investigate how the number of solitary nodes in the network depends on the coupling parameters. We report for the first time the occurrence of solitary state chimera in networks of coupled time-continuous neural systems. Our results disclose distinctive features characteristic of solitary states in the FitzHugh-Nagumo model, such as the flat mean phase velocity profile. On the other hand, we show that the mechanism of solitary states' formation in the FitzHugh-Nagumo model similar to chaotic maps and the Kuramoto model with inertia is related to the appearance of bistability in the system for certain values of coupling parameters. This indicates a general, probably a universal desynchronization scenario via solitary states in networks of very different nature.

Ambient noise multimode Rayleigh and Love wave tomography to determine the shear velocity structure above the Groningen gas field

SUMMARYThe Groningen gas field is one of the largest gas fields in Europe. The continuous gas extraction led to an induced seismic activity in the area. In order to monitor the seismic activity and study the gas field many permanent and temporary seismic arrays were deployed. In particular, the extraction of the shear wave velocity model is crucial in seismic hazard assessment. Local S-wave velocity-depth profiles allow us the estimation of a potential amplification due to soft sediments.Ambient seismic noise tomography is an interesting alternative to traditional methods that were used in modelling the S-wave velocity. The ambient noise field consists mostly of surface waves, which are sensitive to the Swave and if inverted, they reveal the corresponding S-wave structures.In this study, we present results of a depth inversion of surface waves obtained from the cross-correlation of 1 month of ambient noise data from four flexible networks located in the Groningen area. Each block consisted of about 400 3-C stations. We compute group velocity maps of Rayleigh and Love waves using a straight-ray surface wave tomography. We also extract clear higher modes of Love and Rayleigh waves.The S-wave velocity model is obtained with a joint inversion of Love and Rayleigh waves using the Neighbourhood Algorithm. In order to improve the depth inversion, we use the mean phase velocity curves and the higher modes of Rayleigh and Love waves. Moreover, we use the depth of the base of the North Sea formation as a hard constraint. This information provides an additional constraint for depth inversion, which reduces the S-wave velocity uncertainties.The final S-wave velocity models reflect the geological structures up to 1 km depth and in perspective can be used in seismic risk modelling.

Analyzing Conditions for the Occurrence of the Voice of the Sea on the Basis of Infrasound Measurements

Conditions for the occurrence of the “voice of the sea” within the infrasonic range are studied and its parameters are determined from measurements performed in the waters of the Black Sea (2011 and 2016) and the Sea of Okhotsk (2017). Different parameters (mean correlations, acoustic-arrival spectra, directions, and phase velocities) of high-frequency infrasounds (1–10 Hz) recorded during the 2011 and 2016 experiments carried out in Katsiveli (Crimea) are compared. Wind conditions over the Black Sea waters and the conditions of propagation of acoustic waves along the direction of their arrivals during these measurements have been studied in detail. In both cases, atmospheric vortices are observed in the direction of infrasound arrivals, which cause the wind to change its direction over the sea surface. The interaction between two oppositely directed atmospheric vortices (according to data obtained in 2011) and a vortex observed to the west of the recording point (according to data obtained in 2016) result in the generation of infrasounds. The generation of microbaroms and the voice of the sea due to wind-direction variations, which cause the nonlinear interaction of surface waves propagating in opposite directions and the formation of their 2nd harmonics in the form of standing surface waves, is discussed. The most probable regions of infrasound generation are determined from an analysis of the profiles of wind velocity and direction along the path of infrasound arrivals and acoustic-pressure fields calculated using the parabolic-equation method according to the $${{C}_{{{\text{eff}}}}}$$ profiles in the direction of infrasound propagation. In both cases, these regions coincide with zones in which the wind velocity had dropped to zero and the wind direction had reversed. The infrasound within a microbarom frequency range of 0.2–0.3 Hz and the (higher frequency) sea voice with a mean frequency of 5.5 Hz, which were simultaneously recorded from the same direction, are given as an example.

Synchronization patterns in LIF neuron networks: merging nonlocal and diagonal connectivity

The effects of nonlocal and reflecting connectivities have been previously investigated in coupled Leaky Integrate-and-Fire (LIF) elements, which assimilate the exchange of electrical signals between neurons. In this work, we investigate the effect of diagonal coupling inspired by findings in brain neuron connectivity. Multi-chimera states are reported both for the simple diagonal and combined nonlocal–diagonal connectivities, and we determine the range of optimal parameter regions where chimera states appear. Overall, the measures of coherence indicate that as the coupling range increases (below all-to-all coupling) the emergence of chimera states is favored and the mean phase velocity deviations between coherent and incoherent regions become more prominent. A number of novel synchronization phenomena are induced as a result of the combined connectivity. We record that for coupling strengths σ 1. In the intermediate regime, σ ~ 1, the oscillators have common mean phase velocity (i.e., are frequency-locked) but different phases (i.e., they are phase-asynchronous). Solitary states are recorded for small values of the coupling strength, which grow into chimera states as the coupling strength increases. We determine parameter values where the combined effects of nonlocal and diagonal coupling generate chimera states with two different levels of synchronous domains mediated by asynchronous regions.

Combination of dispersion curves from MASW measurements

Multichannel analysis of surface waves (MASW) is a seismic exploration method for determination of near-surface shear wave velocity profiles based on analysis of horizontally travelling Rayleigh waves. This paper aims to propose a methodology and recommendations for combining dispersion data from several multichannel records. The dispersion curves are added up within logarithmically spaced wavelength intervals and the uncertainty of the mean phase velocity estimates is evaluated by using classical statistics and the bootstrap. The results indicate that combining multiple dispersion curves, which have been gathered by receiver spreads of different lengths (but with the same midpoint), can increase the investigation depth of the survey, improve its resolution at shallow depth and overall improve the reliability of the results as compared to the use of a single record. Moreover, the uncertainty of the combined mean dispersion curve can be determined and further used to present the shear wave velocity profile with upper and lower boundaries.

Three-dimensional chimera patterns in networks of spiking neuron oscillators.

We study the stable spatiotemporal patterns that arise in a three-dimensional (3D) network of neuron oscillators, whose dynamics is described by the leaky integrate-and-fire (LIF) model. More specifically, we investigate the form of the chimera states induced by a 3D coupling matrix with nonlocal topology. The observed patterns are in many cases direct generalizations of the corresponding two-dimensional (2D) patterns, e.g., spheres, layers, and cylinder grids. We also find cylindrical and "cross-layered" chimeras that do not have an equivalent in 2D systems. Quantitative measures are calculated, such as the ratio of synchronized and unsynchronized neurons as a function of the coupling range, the mean phase velocities, and the distribution of neurons in mean phase velocities. Based on these measures, the chimeras are categorized in two families. The first family of patterns is observed for weaker coupling and exhibits higher mean phase velocities for the unsynchronized areas of the network. The opposite holds for the second family, where the unsynchronized areas have lower mean phase velocities. The various measures demonstrate discontinuities, indicating criticality as the parameters cross from the first family of patterns to the second.

Cross-Correlation of Station-to-Station Free Surface Elevation Time Series for Breaking Water Waves

Free surface elevation time series of breaking water waves were measured in a laboratory flume. This was done in order to analyze changes in wave characteristics as the waves propagated from deep water to the shore. A pair of parallel- wire capacitive wave gages was used to simultaneously measure free surface elevations at different positions along the flume. One gage was kept fixed near the wave generator to provide a reference while the other was moved in steps of 0.1 m in the vicinity of the break point. Data from these two wave gages measured at the same time constitute station-to-station free surface elevation time series. Fast Fourier Transform (FFT) based cross-correlation techniques were employed to determine the time lag between each pair of the time series. The time lag was used to compute the phase shift between the reference wave gage and that at various points along the flume. Phase differences between two points spaced 0.1 m apart were used to calculate local mean wave phase velocity for a point that lies in the middle. Results show that moving from deep water to shallow water, the measured mean phase velocity decreases almost linearly from about 1.75 m/s to about 1.50 m/s at the break point. Just after the break point, wave phase velocity abruptly increases to a maximum value of 1.87 m/s observed at a position 30 cm downstream of the break point. Thereafter, the phase velocity decreases, reaching a minimum of about 1.30 m/s.

Anisotropic Tomography Around La Réunion Island From Rayleigh Waves

AbstractIn the western Indian Ocean, the Réunion hot spot is one of the most active volcanoes on Earth. Temporal interactions between ridges and plumes have shaped the structure of the zone. This study investigates the mantle structure using data from the Réunion Hotspot and Upper Mantle‐Réunions Unterer Mantel (RHUM‐RUM) project, which significantly increased the seismic coverage of the western part of the Indian Ocean. For more than 1 year, 57 ocean bottom seismometer stations and 23 temporary land stations were deployed over this area. For each earthquake station path, the Rayleigh wave fundamental mode phase velocities were measured for the periods from 30 s to 300 s and group velocities for the period from 16 s to 250 s. A three‐dimensional model of the shear velocity in the upper mantle was built in two steps. First, the path mean phase and group velocities were inverted, to obtain regionalized velocity maps for each separate period. Then, all of the phase and group velocity maps were combined and inverted at each grid point, to obtain the local S wave velocity as a function of depth, using a transdimensional inversion scheme. The three‐dimensional anisotropic S wave velocity model has resolution down to 300 km in depth. The tomographic model and surface tectonics are correlated down to ∼100 km in depth. Starting at 50 km in depth, a slow velocity anomaly beneath Rodrigues Ridge and the east‐west orientation of the azimuthal anisotropy show a connection between Réunion upwelling and the Central Indian Ridge. The slow velocity signature beneath La Réunion is connected at greater depths (150–300 km) with a large slow velocity zone beneath the entire Mascarene Basin. This develops along a northeast direction, following the general motion direction of the African Plate. These observations indicate nonisotropic spreading of hot plume material and dominant horizontal flow in the upper mantle beneath this area.

Two-frequency chimera state in a ring of nonlocally coupled Brusselators.

Chimera states, which consist of coexisting domains of spatially coherent and incoherent dynamics, have been intensively investigated in the past decade. In this work, we report a special chimera state, 2-frequency chimera state, in one-dimensional ring of nonlocally coupled Brusselators. In a 2-frequency chimera state, there exist two types of coherent domains and oscillators in different types of coherent domains have different mean phase velocities. We present the stability diagram of 2-frequency chimera state and study the transition between the 2-frequency chimera state and an ordinary 2-cluster chimera state.

Chimeras in leaky integrate-and-fire neural networks: effects of reflecting connectivities

The effects of nonlocal and reflecting connectivity are investigated in coupled Leaky Integrate-and-Fire (LIF) elements, which assimilate the exchange of electrical signals between neurons. Earlier investigations have demonstrated that non-local and hierarchical network connectivity often induces complex synchronization patterns and chimera states in systems of coupled oscillators. In the LIF system we show that if the elements are non-locally linked with positive diffusive coupling in a ring architecture the system splits into a number of alternating domains. Half of these domains contain elements, whose potential stays near the threshold, while they are interrupted by active domains, where the elements perform regular LIF oscillations. The active domains move around the ring with constant velocity, depending on the system parameters. The idea of introducing reflecting non-local coupling in LIF networks originates from signal exchange between neurons residing in the two hemispheres in the brain. We show evidence that this connectivity induces novel complex spatial and temporal structures: for relatively extensive ranges of parameter values the system splits in two coexisting domains, one domain where all elements stay near-threshold and one where incoherent states develop with multileveled mean phase velocity distribution.

Basin stability for chimera states

Chimera states, namely complex spatiotemporal patterns that consist of coexisting domains of spatially coherent and incoherent dynamics, are investigated in a network of coupled identical oscillators. These intriguing spatiotemporal patterns were first reported in nonlocally coupled phase oscillators, and it was shown that such mixed type behavior occurs only for specific initial conditions in nonlocally and globally coupled networks. The influence of initial conditions on chimera states has remained a fundamental problem since their discovery. In this report, we investigate the robustness of chimera states together with incoherent and coherent states in dependence on the initial conditions. For this, we use the basin stability method which is related to the volume of the basin of attraction, and we consider nonlocally and globally coupled time-delayed Mackey-Glass oscillators as example. Previously, it was shown that the existence of chimera states can be characterized by mean phase velocity and a statistical measure, such as the strength of incoherence, by using well prepared initial conditions. Here we show further how the coexistence of different dynamical states can be identified and quantified by means of the basin stability measure over a wide range of the parameter space.

Chimera states and the interplay between initial conditions and non-local coupling.

Chimera states are complex spatio-temporal patterns that consist of coexisting domains of coherent and incoherent dynamics. We study chimera states in a network of non-locally coupled Stuart-Landau oscillators. We investigate the impact of initial conditions in combination with non-local coupling. Based on an analytical argument, we show how the coupling phase and the coupling strength are linked to the occurrence of chimera states, flipped profiles of the mean phase velocity, and the transition from a phase- to an amplitude-mediated chimera state.

Chimera states in bursting neurons.

We study the existence of chimera states in pulse-coupled networks of bursting Hindmarsh-Rose neurons with nonlocal, global, and local (nearest neighbor) couplings. Through a linear stability analysis, we discuss the behavior of the stability function in the incoherent (i.e., disorder), coherent, chimera, and multichimera states. Surprisingly, we find that chimera and multichimera states occur even using local nearest neighbor interaction in a network of identical bursting neurons alone. This is in contrast with the existence of chimera states in populations of nonlocally or globally coupled oscillators. A chemical synaptic coupling function is used which plays a key role in the emergence of chimera states in bursting neurons. The existence of chimera, multichimera, coherent, and disordered states is confirmed by means of the recently introduced statistical measures and mean phase velocity.