Low-amplitude Oscillations Research Articles

Enhancing the superplastic deformation capabilities of the Ti-6Al-4V alloy using superimposed oscillations

This study investigates the effect of imposing low frequency, low amplitude oscillations during uniaxial tensile tests on the mechanical behaviour of the Ti-6Al-4V alloy under a typical superplastic temperature of 900 °C. Different material models were used to simulate these tests with the finite element software ABAQUS. A creep strain power model fit through an iterative FEA process yielded a high correlation to the force/displacement and thinning results from uniaxial tensile tests. The developed material models with and without oscillation materials were also used to simulate a free-bulge forming process within the strain rate range of 0.0003 to 0.01 s−1 under constant strain rate testing. Within the domain of the parts formed in this study, the improvement in the forming time ranged from a 120 % reduction at elevated strain rates and reduced part complexity to 520 % in the most complex part geometry.

Canard explosions in turbulent thermo-fluid systems.

A sudden transition to a state of high-amplitude periodic oscillations is catastrophic in a thermo-fluid system. Conventionally, upon varying the control parameter, a sudden transition is observed as an abrupt jump in the amplitude of the fluctuations in these systems. In contrast, we present an experimental discovery of a canard explosion in a turbulent reactive flow system where we observe a continuous bifurcation with a rapid rise in the amplitude of the fluctuations within a narrow range of control parameters. The observed transition is facilitated via a state of bursting, consisting of the epochs of large amplitude periodic oscillations amidst the epochs of low-amplitude periodic oscillations. The amplitude of the bursts is higher than the amplitude of the bursts of an intermittency state in a conventional gradual transition, as reported in turbulent reactive flow systems. During the bursting state, we observe that temperature fluctuations of the exhaust gas vary at a slower time scale in correlation with the amplitude envelope of the bursts. We also present a phenomenological model for thermoacoustic systems to describe the observed canard explosion. Using the model, we explain that the large amplitude bursts occur due to the slow-fast dynamics at the bifurcation regime of the canard explosion.

Dynamics of N-elastically longitudinal coupled rotating pendulums with smooth and discontinuous nonlinearities: Generation of chaotic bursting with many orbits as a solution

The dynamics of a mechanical network, consisting of a certain number (N) of cells, in which each unit cell consists of the irrational coupling of a simple pendulum and inclined mass-spring oscillator, is investigated. The single cell was recently introduced by Ning Han and Qingjie Cao, and it has strong irrational nonlinearity, exhibiting smooth and discontinuous characteristics due to the geometry configuration. The obtained network has a large degree of freedom and consequently has richer dynamics as compared to a single one. The set of discrete equations of this network is found, while the first equation is driven by an external sinusoidal force; the variables here are the angles between the vertical direction and the directions of mass in each unit cell. By using the non-driven version of this set of equations, the equilibrium points are found as well as their stability using the Jacobian matrix. Then, by using the multiple time scale method, the solutions of the set of the network equations are found for weak amplitude oscillations of the system, while the large amplitude solutions are found numerically, showing the ability of the network to transform the shape of some solutions at the input to other forms as the signals evolve in the network. One notices the generation of simple chaotic signals as well as the train of impulse signals. What is important here is the generation of the chaotic bursting with many orbits by the system, which are the simultaneous oscillations around several fixed points. For the case of numerous cells, the system can be used as a waveguide; this is why the set of the equation of the network is reduced to the extended complex Ginzburg Landau (ECGL) equation, with complex nonlinear dispersion and nonlocality terms, using the Tanuiti's reduction perturbation methods. The dissipative dark compacton and peakon as solutions for the ECGL equation are then found. The input-output matching of the network is next investigated via the transfer function of the system near the equilibrium points. The inverse Fourier transform of the transfer function multiplied by the Fourier transform of the input sinusoidal force gives the solution of the network equation for low amplitude oscillations. Finally, the supratransmission condition is studied, leading to the fact that the input sinusoidal signal with frequency nearly inside the forbidden gap zone gradually transforms into the train of chaotic bursting.

Unravelling differential Hes1 dynamics during axis elongation of mouse embryos through single-cell tracking.

The intricate dynamics of Hes expression across diverse cell types in the developing vertebrate embryonic tail have remained elusive. To address this, we developed an endogenously tagged Hes1-Achilles mouse line, enabling precise quantification of dynamics at the single-cell resolution across various tissues. Our findings reveal striking disparities in Hes1 dynamics between presomitic mesoderm (PSM) and preneural tube (pre-NT) cells. While pre-NT cells display variable, low-amplitude oscillations, PSM cells exhibit synchronized, high-amplitude oscillations. Upon the induction of differentiation, the oscillation amplitude increases in pre-NT cells. Additionally, our study of Notch inhibition on Hes1 oscillations unveiled distinct responses in PSM and pre-NT cells, corresponding to differential Notch ligand expression dynamics. These findings suggest the involvement of separate mechanisms driving Hes1 oscillations. Thus, Hes1 demonstrates dynamic behaviour across adjacent tissues of the embryonic tail, yet the varying oscillation parameters imply differences in the information that can be transmitted by these dynamics.

Clinical applications of forced oscillation technique (FOT) for diagnosis and management of obstructive lung diseases in children.

Obstructive lung diseases such as bronchial asthma, COPD, and cystic fibrosis are a burden on many patients across the globe. Spirometry is considered the gold standard for diagnosing airflow obstruction, but it can be difficult for pediatric patients to do and requires a lot of effort. As a result, healthcare providers need new, effortless methods to diagnose airway obstructions, particularly in young children and individuals unable to perform the spirometry maneuver. The forced oscillation technique is a modern method requiring only tidal breathing combined with the application of external, source of low-amplitude oscillations to evaluate the respiratory system's response. It might be essential for identifying early respiratory changes caused by smoking, childhood asthma, and may prove more sensitive than spirometry in identifying peripheral airway disturbances or evaluating the long-term success of therapy. This review describes the methodology and the indications for the forced oscillation technique and outlines its relevance in clinical practice.

Understanding the heat release fluctuations and combustion noise characteristics of non-premixed co/counter-swirl syngas flames at MILD conditions

The heat release fluctuations and combustion noise of co/counter-swirl non-premixed syngas (mixture of CO and H2) and air flames at moderate or intense low-oxygen dilution (MILD) conditions has been investigated experimentally using simultaneous OH∗-chemiluminescence (5 kHz) and microphone measurements (50 kHz). Furthermore, the similarities and differences between co and counter-swirl flames are elucidated using proper orthogonal decomposition (POD), spectrogram, and frequency distributions. At a high O2 concentration (21% by volume), noise measurements for both co/counter-swirl flames comprise both high-amplitude periodic and low-amplitude aperiodic oscillations, revealing signatures of intermittency. Interestingly, for periodic oscillations, the global luminosity (Ifluc) obtained from OH∗-chemiluminescence and noise (Pfluc) are found to be in phase, indicating a strong coupling between noise and heat-release rate. Moreover, POD modes indicate that the global heat release fluctuation occurring in the central region of the combustor is the source of these periodic fluctuations. Besides global fluctuation, the heat release region undergoes rotation around the combustor axis with differing frequencies for co and counter-swirl flames. Furthermore, the global fluctuation is found to be prominent for co-swirl flames, while precession motion is more pronounced in counter-swirl flames. When O2 is reduced to 13.13%, the combustion becomes stable, as suggested by low-amplitude aperiodic oscillations in the noise measurement. Heat release of co and counter-swirl flames respond differently to this reduction in O2 concentration. The precession motion remains unaffected for co-swirl flames upon O2 reduction. In contrast, precession motion alters significantly for counter-swirl. Regarding global fluctuations, low oxygen concentration suppresses all periodic fluctuations, mitigates noise, and Pfluc and Ifluc become entirely decoupled for both flames. Hence, the present study demonstrates for the first time the applicability of a low-oxygen dilution strategy in the context of co/counter-swirl flames for decoupling heat release and noise measurements. Furthermore, the study also indicates the varied response of complex co and counter-swirl flames to different oxygen concentrations.

Evidence of Kelvin-Helmholtz and tearing mode instabilities at the magnetopause during space weather events

Introduction: Kelvin-Helmholtz (KH) and tearing mode (TM) instabilities are one of the most important mechanisms of solar wind energy, momentum and plasma transport within the magnetosphere.Methods: To investigate the conditions under which KHTM instabilities occur in the Earth environment it is fundamental to combine simultaneous multipoint in situ measurements and MHD simulations. We analyzed data from the THEMIS and Cluster spacecraft considering two Space Weather (SWE) events starting with an M2.0 flare event (hereafter Case-1) that occurred on 21 June 2015 and the most-intensive flare (X9.3) of solar cycle 24 that occurred on 6 September 2017 (hereafter Case-2).Results: Our analysis utilized a 2D MHD model for incompressible and viscous flow. The results from Case-1 indicate the presence of KH and TM instabilities, suggesting existence of observed low-amplitude oscillations at the nose of the magnetopause. However, the MHD simulations for Case-2 did not show any evidence of KH vortices, but did reveal the presence of “magnetic island” structures during a low-shear condition. The reconnection rate derived from the observations is compared with the computed one in the presence of developed instabilities inside the Earth’s magnetopause.

Low-amplitude Solar-like Oscillations in the K5 V Star ϵ Indi A

We have detected solar-like oscillations in the mid-K-dwarf ϵ Indi A, making it the coolest dwarf to have measured oscillations. The star is noteworthy for harboring a pair of brown dwarf companions and a Jupiter-type planet. We observed ϵ Indi A during two radial velocity campaigns, using the high-resolution spectrographs HARPS (2011) and UVES (2021). Weighting the time series, we computed the power spectra and established the detection of solar-like oscillations with a power excess located at 5265 ± 110 μHz—the highest frequency solar-like oscillations so far measured in any star. The measurement of the center of the power excess allows us to compute a stellar mass of 0.782 ± 0.023 M ⊙ based on scaling relations and a known radius from interferometry. We also determine the amplitude of the peak power and note that there is a slight difference between the two observing campaigns, indicating a varying activity level. Overall, this work confirms that low-amplitude solar-like oscillations can be detected in mid-K-type stars in radial velocity measurements obtained with high-precision spectrographs.

Stability of heavy inclusions in the Earth’s crust

Stability of a heavy inclusion in the Earth’s upper crust is studied by the linear theory method for small perturbations. The presence of such inclusions with an increased density is associated with chemical inhomogeneity or phase transformations. The problem of the stability of a heavy elastic layer above a less dense elastic layer that represents the lower crust and mantle lithosphere is solved. It is shown that such a system is stable: small initial perturbations produce low-amplitude oscillations. The corrections to the oscillation frequency that arise due to the density jump at the boundary between the layers are calculated. The changes in the solution due to the consideration of creep, which is present even in cold geomaterials, are discussed. Creep leads to instability of heavy inclusions in the upper crust. However, because the effective viscosity of the cold upper crust is very high, this instability is of a formal nature, since it develops so slowly that heavy inclusions in the upper crust hardly change their position over a timescale comparable to the age of the Earth.

Mercury records covering the past 90 000 years from lakes Prespa and Ohrid, SE Europe

Abstract. The element mercury (Hg) is a key pollutant, and much insight has been gained by studying the present-day Hg cycle. However, many important processes within this cycle operate on timescales responsive to centennial- to millennial-scale environmental variability, highlighting the importance of also investigating the longer-term Hg records in sedimentary archives. To this end, we here explore the timing, magnitude, and expression of Hg signals retained in sediments over the past ∼ 90 kyr from two lakes, linked by a subterranean karst system: Lake Prespa (Greece, North Macedonia, and Albania) and Lake Ohrid (North Macedonia and Albania). Results suggest that Hg fluctuations are largely independent of variability in common host phases in each lake, and the recorded sedimentary Hg signals show distinct differences first during the Late Pleistocene (Marine Isotope Stages 2–5). The Hg signals in Lake Prespa sediments highlight an abrupt, short-lived peak in Hg accumulation coinciding with local deglaciation. In contrast, Lake Ohrid shows a broader interval with enhanced Hg accumulation and, superimposed, a series of low-amplitude oscillations in Hg concentration peaking during the Last Glacial Maximum, which may result from elevated clastic inputs. Divergent Hg signals are also recorded during the Early and Middle Holocene (Marine Isotope Stage 1). Here, Lake Prespa sediments show a series of large Hg peaks, while Lake Ohrid sediments show a progression to lower Hg values. Since ∼ 3 ka, anthropogenic influences overwhelm local fluxes in both lakes. The lack of coherence in Hg accumulation between the two lakes suggests that, in the absence of an exceptional perturbation, local differences in sediment composition, lake structure, Hg sources, and water balance all influence the local Hg cycle and determine the extent to which Hg signals reflect local- or global-scale environmental changes.

Серия ОВП-импульсов подземных вод побережья Байкала 20–27 марта 2024 г.: вероятная связь с магнитными бурями

A short (8-day) series of ORP pulses begins with low-amplitude (about 1 mV) oscillations, partially smoothes out, and progresses to deep minima reaching 138 mV. The series differs from the pulses covering the full (30-day) tidal lunar-solar cycle in February–early March 2024. It is suggested that variations in ORP pulses are temporally related to magnetic storms. Also, for generation of powerful ORP pulses, the spring lunar-solar tide is considered as a favorable factor. The March series of pulses is accompanied by decreasing background ORP values. Similar ORP decrease, but without pulses, characterizes the January episodes of earthquakes in the central Baikal Rift System.

Decayless low-amplitude transverse oscillations in short coronal loops as manifestations of driven slow modes

ABSTRACT A recent theoretical study of slow magnetoacoustic oscillations in a curved magnetic slab shows that the principal slow mode causes both dominant longitudinal motions and radial (transverse) kink-like motions of a slab. This modification of wave properties occurs due to the violation of the symmetry of wave motions with respect to the waveguide axis and the slow to fast wave interaction in curved magnetic configurations. In this work, we carry out a comprehensive investigation of the principal slow mode depending on the model parameters. It is shown that the dominance of longitudinal motions in the principal slow mode decreases as both the internal plasma-β and slab aspect ratio increase. The results are used to explain the observed small amplitude decayless transverse oscillations in short coronal loops. In particular, these phenomena are interpreted as direct manifestation of slow mode oscillations in curved coronal loops excited at the footpoints by compressible oscillations of the underlying atmospheric layers. Numerical calculations have shown that the observed velocity range of V = 0.6–5 km s−1 corresponds to radial velocity amplitudes in the principal slow mode, provided that the plasma-β inside the short loops is in the range of βi= 0.3–0.5 and the loop aspect ratio 0.15 ≤ a/R ≤ 0.25. These parameters appear to be typical for low-lying small coronal loops extending from the transition region to the lower corona.

Numerical Simulations of the NREL Phase VI Wind Turbine with Low-Amplitude Sinusoidal Pitch

Currently, most wind turbine performance analyses and simulations are performed assuming constant pitch and yaw angles during each rotation. Nevertheless, induced vibration or rotor imbalance can affect the pitch or yaw angle within each rotation. In this study, the effects of low-amplitude sinusoidal pitch angle oscillations of the blade on the performance of a wind turbine was investigated numerically by comparing it against the baseline (without pitch variations). Large eddy simulations were performed in which the motion of blades was handled by the curvilinear immersed boundary (CURVIB) method. The grid resolution was increased near the moving immersed boundaries using dynamic overset grids to resolve rotating blades. It was found that low-amplitude (up to 3 degrees) sinusoidal oscillations in the pitch angle negligibly affected the mean torque but increased its fluctuations and created distinct features in the wake of the turbine. In fact, the turbine’s mean torque at wind speed of 15 m/s decreases from 1245 N.m to 1223 N.m, while its fluctuation (standard deviation) increases from 2.85 N.m to 7.94 N.m, with a dynamic pitch of 0.5 degrees and frequency of 3.6 Hz.

Propagation of Oscillations in the Indirect Pathway of the Basal Ganglia.

Oscillatory signals propagate in the basal ganglia from prototypic neurons in the external globus pallidus (GPe) to their target neurons in the substantia nigra pars reticulata (SNr), internal pallidal segment, and subthalamic nucleus. Neurons in the GPe fire spontaneously, so oscillatory input signals can be encoded as changes in timing of action potentials within an ongoing spike train. When GPe neurons were driven by an oscillatory current in male and female mice, these spike-timing changes produced spike-oscillation coherence over a range of frequencies extending at least to 100 Hz. Using the known kinetics of the GPe→SNr synapse, we calculated the postsynaptic currents that would be generated in SNr neurons from the recorded GPe spike trains. The ongoing synaptic barrage from spontaneous firing, frequency-dependent short-term depression, and stochastic fluctuations at the synapse embed the input oscillation into a noisy sequence of synaptic currents in the SNr. The oscillatory component of the resulting synaptic current must compete with the noisy spontaneous synaptic barrage for control of postsynaptic SNr neurons, which have their own frequency-dependent sensitivities. Despite this, SNr neurons subjected to synaptic conductance changes generated from recorded GPe neuron firing patterns also became coherent with oscillations over a broad range of frequencies. The presynaptic, synaptic, and postsynaptic frequency sensitivities were all dependent on the firing rates of presynaptic and postsynaptic neurons. Firing rate changes, often assumed to be the propagating signal in these circuits, do not encode most oscillation frequencies, but instead determine which signal frequencies propagate effectively and which are suppressed.SIGNIFICANCE STATEMENT Oscillations are present in all the basal ganglia nuclei, include a range of frequencies, and change over the course of learning and behavior. Exaggerated oscillations are a hallmark of basal ganglia pathologies, and each has a specific frequency range. Because of its position as a hub in the basal ganglia circuitry, the globus pallidus is a candidate origin for oscillations propagating between nuclei. We imposed low-amplitude oscillations on individual globus pallidus neurons at specific frequencies and measured the coherence between the oscillation and firing as a function of frequency. We then used these responses to measure the effectiveness of oscillatory propagation to other basal ganglia nuclei. Propagation was effective for oscillation frequencies as high as 100 Hz.

Encoding nonlinear and unsteady aerodynamics of limit cycle oscillations using nonlinear sparse Bayesian learning

This article investigates the applicability of a recently proposed, nonlinear sparse Bayesian learning (NSBL) algorithm to identify and estimate the complex aerodynamics of limit cycle oscillations. NSBL provides a semi-analytical framework for determining the data-optimal sparse model nested within a (potentially) over-parameterized model. This is particularly relevant to nonlinear dynamical systems where modelling approaches involve the use of physics-based and data-driven components. In such cases, the data-driven components, where analytical descriptions of the physical processes are not readily available, are often prone to overfitting, meaning that the empirical aspects of these models will often involve the calibration of an unnecessarily large number of parameters. While an overparameterized model may fit the observed data well, such models may be inadequate for making predictions in regimes that are different from those wherein the data were recorded. In view of this, it is desirable to not only calibrate the model parameters, but also identify the optimal compromise between data fit and model complexity. In this article, we exhibit the optimal model discovery for an aeroelastic system wherein the structural dynamics are well-known and described by a differential equation model, coupled with a semi-empirical aerodynamic model for laminar separation flutter, resulting in low-amplitude limit cycle oscillations (LCO). To illustrate the performance of the algorithm, in this article, we use synthetic data and demonstrate the ability of the algorithm to correctly rediscover the optimal model and model parameters, given a known data-generating model. The synthetic data are generated from a forward simulation of a known differential equation model with parameters selected so as to mimic the dynamics observed in wind-tunnel experiments. Subsequently, we demonstrate the performance of the algorithm for model selection using noisy LCO data from wind tunnel experiments. As there is no ground truth available for the experimental data case, we provide a comparison between NSBL and Bayesian model selection to validate the results, and demonstrate the use of NSBL as an efficient alternative to traditional methods.

The “Guttenberg” positive δ13C excursion (GICE) interval of Latest Sandbian–early Katian (Late Ordovician) spans ca. 1.2 Myr in Asian reference sections

The boundary between the Sandbian and Katian stages of the Late Ordovician is directly followed by the onset of the Guttenberg positive isotope carbon excursion (GICE), which is potentially a means to aid in global correlation of this stage boundary. The sedimentary record of the GICE in mid-continent North American sections often spans only a few meters and has been estimated to span <400 kyr. In contrast, a major sustained positive excursion that has been considered equivalent to the GICE spans over 100 m within some other sections in North America and in the Qilang Formation of the Tarim Basin in northwest China. In addition to enhancing the carbon-isotope records of this expanded record of the GICE, we applied cyclostratigraphy analysis to detailed natural-gamma logging from the Dawangou section, Tarim Basin, which is the auxiliary GSSP for the Sandbian Stage, and from the nearby Sishichang section. The average proportion of carbonate to marl in the outer shelf facies of these sections exhibits cycles of ca. 30 m. Superimposed on these large-scale cycles are ca. 1.5-m oscillations. We interpret these cycles as a sedimentary record of long-eccentricity (405 kyr) and precession cycles. Three secondary low-amplitude oscillations in δ13C are superimposed on the broad GICE plateau and are in phase with the long-eccentricity cycles. The astronomical-tuned sedimentary stratigraphy of these sections implies that the main GICE interval has a duration of ca. 1.2 Myr, with an uncertainty of ca. 200 kyr depending upon how the onset and termination of the GICE is defined. Similar secondary peaks in δ13C on the main GICE excursion reported from other regions have been termed G1, G2 and G3. In the Dawangou section, the estimated placement of the Sandbian-Katian stage boundary is midway between G1 and G2. The GICE record in the composite δ13C stratigraphy from the Cincinnati region of Ohio-Kentucky exhibits an initial “Logana” positive excursion followed by a “Macedonia” positive excursion, and we suggest that these are correlative to the G2 and G3 secondary peaks on the broad GICE as identified in Asia. In both the Tarim region and in the Cincinnati composite, these two secondary peaks in δ13C occur during intervals of greater clay content relative to carbonate. If verified, this astronomically tuned reference scale of the δ13C modulations will enable high-resolution global correlation of biozones and other events near the Sandbian-Katian stage boundary and during the Early Katian.

Mitigation of limit cycle oscillations in a turbulent thermoacoustic system via delayed acoustic self-feedback.

We report the occurrence of amplitude death (AD) of limit cycle oscillations in a bluff body stabilized turbulent combustor through delayed acoustic self-feedback. Such feedback control is achieved by coupling the acoustic field of the combustor to itself through a single coupling tube attached near the anti-node position of the acoustic standing wave. We observe that the amplitude and dominant frequency of the limit cycle oscillations gradually decrease as the length of the coupling tube is increased. Complete suppression (AD) of these oscillations is observed when the length of the coupling tube is nearly 3 / 8 times the wavelength of the fundamental acoustic mode of the combustor. Meanwhile, as we approach this state of amplitude death, the dynamical behavior of acoustic pressure changes from the state of limit cycle oscillations to low-amplitude chaotic oscillations via intermittency. We also study the change in the nature of the coupling between the unsteady flame dynamics and the acoustic field as the length of the coupling tube is increased. We find that the temporal synchrony between these oscillations changes from the state of synchronized periodicity to desynchronized aperiodicity through intermittent synchronization. Furthermore, we reveal that the application of delayed acoustic self-feedback with optimum feedback parameters completely disrupts the positive feedback loop between hydrodynamic, acoustic, and heat release rate fluctuations present in the combustor during thermoacoustic instability, thus mitigating instability. We anticipate this method to be a viable and cost-effective option to mitigate thermoacoustic oscillations in turbulent combustion systems used in practical propulsion and power systems.

Mean-field model of synchronization for open-loop, swirl controlled thermoacoustic system.

Open-loop control is known to be an effective strategy for controlling self-excited periodic oscillations, known as thermoacoustic instability, in turbulent combustors. Here, we present experimental observations and a synchronization model for the suppression of thermoacoustic instability achieved by rotating the otherwise static swirler in a lab-scale turbulent combustor. Starting with the state of thermoacoustic instability in the combustor, we find that a progressive increase in the swirler rotation rate leads to a transition from the state of limit cycle oscillations to the low-amplitude aperiodic oscillations through a state of intermittency. To model such a transition while also quantifying the underlying synchronization characteristics, we extend the model of Dutta et al. [Phys. Rev. E 99, 032215 (2019)] by introducing a feedback between the ensemble of phase oscillators and the acoustic. The coupling strength in the model is determined by considering the effect of the acoustic and swirl frequencies. The link between the model and experimental results is quantitatively established by implementing an optimization algorithm for model parameter estimation. We show that the model is capable of replicating the bifurcation characteristics, nonlinear features of time series, probability density function, and amplitude spectrum of acoustic pressure and heat release rate fluctuations at various dynamical states observed during the transition to the state of suppression. Most importantly, we discuss the flame dynamics and demonstrate that the model without any spatial inputs qualitatively captures the characteristics of the spatiotemporal synchronization between the local heat release rate fluctuations and the acoustic pressure that underpins a transition to the state of suppression. As a result, the model emerges as a powerful tool for explaining and controlling instabilities in thermoacoustic and other extended fluid dynamical systems, where spatiotemporal interactions lead to rich dynamical phenomena.

A Mean-Field Firing-Rate Model for the Suprachiasmatic Nucleus

We present a mean-field formalism for modeling firing-rate statistics of brain regions whose neurons exhibit atypical firing patterns and heterogeneous electrophysiological properties. We apply the formalism to the suprachiasmatic nucleus (SCN)—the human circadian pacemaker—whose neurons can intrinsically exhibit depolarized low-amplitude membrane oscillations (DLAMOs), depolarization block (DB), and standard action potential firing at different times of day. Further, gamma-aminobutyric acid reversal potentials and molecular circadian phases of SCN neurons, among other properties, vary across the network and/or slowly over time. Our formalism consists of a system of integro-differential equations describing the time evolution of the mean and standard deviation of synaptic conductances across the network. Electrophysiological properties of SCN neurons are incorporated by computing responses to synaptic conductance inputs of a Hodgkin–Huxley-type SCN neuron model that exhibits DLAMOs and DB. Such responses are then averaged over distributions of relevant quantities and included in the differential equations. Results suggest mechanisms by which physiologically relevant changes to firing activities may arise, highlighting means by which the amplitude of firing rates may shrink, the standard deviation of firing rates may grow, and by which a mid-day dip in firing rates may appear. For instance, results show that a large spread in circadian phases across SCN neurons reduces the size of oscillations in SCN network firing activity across the 24-hour day, identifying a mechanism by which heterogeneities in neuron electrophysiology could influence circadian rhythms.

On the possibility of rogue wave generation based on the dynamics of modified Burridge-Knopoff model of earthquake fault

In this study we propose a modified Burridge‐Knopoff model of earthquake fault, in which two tectonic plates are strongly coupled by nonlinear springs. By minimizing the effects of the veloci‐ ty‐weakening stick‐slip friction force between the masses and the moving surface, and in the limit of low amplitude oscillations; the system exhibits both stick‐slip and damped oscillatory motions as the values of some parameters are varied. Such motions usually characterize the dynamics of an earthquake fault, even though it is not always felt because of the low amplitude of vibrations. However when enough stress builds up in the subduction zones to overcome the frictional forces between tectonic plates, the oceanic rocks suddenly slip and there is violent release of energy at the epicentre. This outburst of energy simply signifies the generation of a very large amplitude and localized nonlinear wave. Such wave profile exactly fits the Peregrine solution of the damped/ forced nonlinear Schrodinger amplitude equation, derived from the modified one‐dimensional Burridge‐Knopoff equation of motion. In the regime of minimal or no frictional forces, these mon‐ ster waves suddenly appear and disappear without traces as shown by the numerical investigations. Our results strongly suggest that rogue waves emanates from the dynamics of nonlinearly coupled tectonic plates in subduction zones. This is further complemented by the fact that these giant waves were initially observed in Pacific and Atlantic oceans, which play hosts to the world’s largest oceanic subduction zones.