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NASA NTRS1991

Giotto Extended Mission (GEM)

The primary objectives of the Giotto Extended Mission (GEM), are to determine the composition and physical state of the Grigg Skjellerup Comet's nucleus; to determine the processes that govern the composition and distribution of neutral and ionized species in the cometary atmosphere. Giotto consists of a single European Space Agency (ESA) spacecraft that was launched in 1985 from Center Spatial Guyanis in French Guiana on an Ariane launch vehicle. After a successful launch into geostationary orbit and a heliocentric transfer trajectory, the spacecraft successfully encountered Halley's Comet in 1986. One month after encountering Halley's Comet, Mar. 1986, the spacecraft was placed in hibernation in a heliocentric orbit slightly less than 1 AU. Between Feb. and Jul. 1990 the spacecraft was successfully reactivated, checked out, and placed on a trajectory course to intercept comet Grigg Skjellerup. The spacecraft has been in hibernation since Jul. 1990. Information is presented in tabular form in the following areas: coverage goals, Deep Space Network Support, frequency assignments, telemetry, command, and tracking support responsibility.

Wilkins, D. E. B.↗

NASA NTRS2000

A Preview of AMSR: Airborne C-band Microwave Radiometer (ACMR) Observations from SGP99

Although L-band is generally considered ideal for passive microwave sensing of soil moisture, near-future satellite observing systems such as Advanced Mechanically Scanned Radiometer (AMSR) will provide C-band data for several years before any L-band data might become available. The Southern Great Plains'99 (SGP99) Experiment was designed to generate C-band observations suitable for testing and refinement of AMSR-era soil moisture retrieval algorithms. C-band data collected using the Airborne C-band Microwave Radiometer (ACMR), a new high-accuracy NASA/GSFC instrument, clearly demonstrated a strong response to a 9-day drydown event as well as to differences between the northern (cooler & wetter) and southern (warmer & dryer) areas covered by the P-3 flights. For example, the H-polarized brightness temperatures observed during the first three days of the drydown increased up to 50 K in the northern areas. These observations represent a preview of what we can expect from AMSR, albeit at 3-km spatial resolution vs. approximately 60 km for AMSR. Initial results of soil-vegetation microwave modeling will also be presented to estimate the relative contributions of soil physical temperature, canopy physical temperature, soil moisture, and canopy moisture. Significant radio-frequency interference (RFI) was evident during the experiment, and amelioration strategies will be discussed. The net effect of RFI (an upward bias in brightnesses) when averaged over an AMSR footprint is expected to be more subtle.

Kim, Edward↗

DOE OSTI2023

Merging of the superbanana plateau and $\sqrt{v}$ transport regimes in nearly quasisymmetric stellarators

We report alpha particle confinement is one of the most demanding issues for stellarators. It now seems clear that it is possible to design optimized stellarators that confine the background plasma at near tokamak radial transport levels. Moreover, adequate collisionless alpha particle confinement is possible in the core of a highly optimized stellarator. Here, the collisional confinement of barely trapped alphas in an optimized stellarator is considered by accounting for the resonance due to the reversal in direction of the drift within a flux surface and investigating the sensitive role of magnetic shear in keeping this resonance close to the passing boundary in some nearly quasisymmetric stellarator configurations. The treatment relies on a narrow collisional boundary layer formulation that combines the responses of both these resonant pitch angle alphas and the remaining barely trapped alphas. A novel merged regime treatment leads to explicit expressions for the energy diffusivity for both superbanana plateau (or resonant plateau) and $\sqrt{v}$ transport in the large aspect ratio limit for a slowing down tail alpha distribution function, where v is the effective pitch angle scattering collision frequency of the trapped alphas off the background ions. Depending on the details of the optimization scheme and the sign of the magnetic shear, modest magnetic shear can be used to reduce superbanana (or resonant) plateau transport to below the $\sqrt{v}$ transport level. In addition, a quasilinear equation retaining spatial diffusion is derived for a general alpha distribution function that allows the radial alpha transport to modify the distribution so it is no longer isotropic in velocity space.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS2001

Spatial orientation and balance control changes induced by altered gravitoinertial force vectors

To better understand the mechanisms of human adaptation to rotating environments, we exposed 19 healthy subjects and 8 vestibular-deficient subjects ("abnormal"; four bilateral and four unilateral lesions) to an interaural centripetal acceleration of 1 g (resultant 45 degrees roll-tilt of 1.4 g) on a 0.8-m-radius centrifuge for periods of 90 min. The subjects sat upright (body z-axis parallel to centrifuge rotation axis) in the dark with head stationary, except during 4 min of every 10 min, when they performed head saccades toward visual targets switched on at 3- to 5-s intervals at random locations (within +/- 30 degrees) in the earth-horizontal plane. Eight of the normal subjects also performed the head saccade protocol in a stationary chair adjusted to a static roll-tilt angle of 45 degrees for 90 min (reproducing the change in orientation but not the magnitude of the gravitoinertial force on the centrifuge). Eye movements, including voluntary saccades directed along perceived earth- and head-referenced planes, were recorded before, during, and immediately after centrifugation. Postural center of pressure (COP) and multisegment body kinematics were also gathered before and within 10 min after centrifugation. Normal subjects overestimated roll-tilt during centrifugation and revealed errors in perception of head-vertical provided by directed saccades. Errors in this perceptual response tended to increase with time and became significant after approximately 30 min. Motion-sickness symptoms caused approximately 25% of normal subjects to limit their head movements during centrifugation and led three normal subjects to stop the test early. Immediately after centrifugation, subjects reported feeling tilted 10 degrees in the opposite direction, which was in agreement with the direction of their earth-referenced directed saccades. Postural COP, segmental body motion amplitude, and hip-sway frequency increased significantly after centrifugation. These postural effects were short-lived, however, with a recovery time of several postural test trials (minutes). There were also asymmetries in the direction of postcentrifugation COP and head tilt which depended on the subject's orientation during the centrifugation adaptation period (left ear or right ear out). The amount of total head movements during centrifugation correlated poorly or inversely with postcentrifugation postural stability, and the most unstable subject made no head movements. There was no decrease in postural stability after static tilt, although these subjects also reported a perceived tilt briefly after return to upright, and they also had COP asymmetries. Abnormal subjects underestimated roll-tilt during centrifugation, and their directed saccades revealed permanent spatial distortions. Bilateral abnormal subjects started out with poor postural control, but showed no postural decrements after centrifugation, while unilateral abnormal subjects had varying degrees of postural decrement, both in their everyday function and as a result of experiencing the centrifugation. In addition, three unilateral, abnormal subjects, who rode twice in opposite orientations, revealed a consistent orthogonal pattern of COP offsets after centrifugation. These results suggest that both orientation and magnitude of the gravitoinertial vector are used by the central nervous system for calibration of multiple orientation systems. A change in the background gravitoinertial force (otolith input) can rapidly initiate postural and perceptual adaptation in several sensorimotor systems, independent of a structured visual surround.

Clinical Trial↗

DOE OSTI2022

Can we use antipredator behavior theory to predict wildlife responses to high-speed vehicles?

Animals seem to rely on antipredator behavior to avoid vehicle collisions. There is an extensive body of antipredator behavior theory that have been used to predict the distance/time animals should escape from predators. These models have also been used to guide empirical research on escape behavior from vehicles. However, little is known as to whether antipredator behavior models are appropriate to apply to an approaching high-speed vehicle scenario. We addressed this gap by (a) providing an overview of the main hypotheses and predictions of different antipredator behavior models via a literature review, (b) exploring whether these models can generate quantitative predictions on escape distance when parameterized with empirical data from the literature, and (c) evaluating their sensitivity to vehicle approach speed using a simulation approach wherein we assessed model performance based on changes in effect size with variations in the slope of the flight initiation distance (FID) vs. approach speed relationship. The slope of the FID vs. approach speed relationship was then related back to three different behavioral rules animals may rely on to avoid approaching threats: the spatial, temporal, or delayed margin of safety. We used literature on birds for goals (b) and (c). Our review considered the following eight models: the economic escape model, Blumstein’s economic escape model, the optimal escape model, the perceptual limit hypothesis, the visual cue model, the flush early and avoid the rush (FEAR) hypothesis, the looming stimulus hypothesis, and the Bayesian model of escape behavior. We were able to generate quantitative predictions about escape distance with the last five models. However, we were only able to assess sensitivity to vehicle approach speed for the last three models. The FEAR hypothesis is most sensitive to high-speed vehicles when the species follows the spatial (FID remains constant as speed increases) and the temporal margin of safety (FID increases with an increase in speed) rules of escape. The looming stimulus effect hypothesis reached small to intermediate levels of sensitivity to high-speed vehicles when a species follows the delayed margin of safety (FID decreases with an increase in speed). The Bayesian optimal escape model reached intermediate levels of sensitivity to approach speed across all escape rules (spatial, temporal, delayed margins of safety) but only for larger (> 1 kg) species, but was not sensitive to speed for smaller species. Overall, no single antipredator behavior model could characterize all different types of escape responses relative to vehicle approach speed but some models showed some levels of sensitivity for certain rules of escape behavior. We derive some applied applications of our findings by suggesting the estimation of critical vehicle approach speeds for managing populations that are especially susceptible to road mortality. Overall, we recommend that new escape behavior models specifically tailored to high-speeds vehicles should be developed to better predict quantitatively the responses of animals to an increase in the frequency of cars, airplanes, drones, etc. they will face in the next decade.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1997

Electrical signal transmission and gap junction regulation in a bone cell network: a cable model for an osteon

A cable model is formulated to estimate the spatial distribution of intracellular electric potential and current, from the cement line to the lumen of an osteon, as the frequency of the loading and the conductance of the gap junction are altered. The model predicts that the characteristic diffusion time for the spread of current along the membrane of the osteocytic processes, 0.03 sec, is nearly the same as the predicted pore pressure relaxation time in Zeng et al. (Annals of Biomedical Engineering. 1994) for the draining of the bone fluid into the osteonal canal. This approximate equality of characteristic times causes the cable to behave as a high-pass, low-pass filter cascade with a maximum in the spectral response for the intracellular potential at approximately 30 Hz. This behavior could be related to the experiments of Rubin and McLeod (Osteoporosis, Academic Press, 1996) which show that live bone appears to be selectively responsive to mechanical loading in a specific frequency range (15-30 Hz) for several species.

NASA Discipline Musculoskeletal↗

NASA NTRS2008

Nonlinear Reduced-Order Analysis with Time-Varying Spatial Loading Distributions

Oscillating shocks acting in combination with high-intensity acoustic loadings present a challenge to the design of resilient hypersonic flight vehicle structures. This paper addresses some features of this loading condition and certain aspects of a nonlinear reduced-order analysis with emphasis on system identification leading to formation of a robust modal basis. The nonlinear dynamic response of a composite structure subject to the simultaneous action of locally strong oscillating pressure gradients and high-intensity acoustic loadings is considered. The reduced-order analysis used in this work has been previously demonstrated to be both computationally efficient and accurate for time-invariant spatial loading distributions, provided that an appropriate modal basis is used. The challenge of the present study is to identify a suitable basis for loadings with time-varying spatial distributions. Using a proper orthogonal decomposition and modal expansion, it is shown that such a basis can be developed. The basis is made more robust by incrementally expanding it to account for changes in the location, frequency and span of the oscillating pressure gradient.

Prezekop, Adam↗

DOE OSTI2020

Response of a charged particle in contact with a chaotic thermostat to an oscillating electric field

A numerical investigation is made of the response of a thermalized charge in contact with a chaotic thermostat to an externally applied, oscillating electric field, with and without a confining magnetic field. This study is based on the recent theoretical development of a chaotic thermostat [G. J. Morales, Phys. Rev. E 99, 062218 (2019)] for which the static properties of a thermalized charge (spatial diffusion and mobilities) were previously established. It is found here that in the unmagnetized case, to extract significant power from the oscillating electric field requires that the oscillatory velocity be larger than the thermal velocity. The spatial diffusion caused by the self-consistent, chaotic fluctuations is shown to be reduced, and even suppressed, by the coherent oscillations. The frequency-dependent mobilities, including cyclotron resonance, are determined, and the nonlinear modifications produced by large electric fields are explored. The value of the mobilities and the modifications to the diffusion coefficient exhibit non-monotonic dependencies on the control parameters.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRSDate not supplied

A Database of CFD-Based Buffet Forcing Functions for Artemis I Structural Response Evaluation

Time-accurate FUN3D simulations are utilized to estimate buffet-induced unsteady forces experienced by the Space Launch System during the Artemis I (AR01) flight. A set of FUN3D simulations was developed that employed time-accurate mesh translations to simulate the changing velocity and attitude based on the AR01 best estimated trajectory. In these simulations, referred to as accelerating-flow simulations, the freestream Mach number increased from 0.80 to 1.92. Additional time-accurate simulations were obtained at constant freestream Mach number equal to 0.95, 1.18, 1.70, thereby simulating stationary conditions experienced by the flow in a wind-tunnel. On the grounds of favorable comparisons between simulated and flight-measured environments, the FUN3D-based surface pressures were utilized to develop a buffet forcing function (BFF) database. This BFF database was analyzed to characterize the spatial distribution and frequency content of the buffet forces during transonic and supersonic portions of the AR01 flight. The region of interest is located downstream of the forward attachment (FA) hardware between the core stage and the solid rocket boosters where vortex shedding off the FA protuberance produces significant unsteadiness. The analysis reveals that, at transonic and supersonic conditions, buffet forces that are based on constant freestream Mach number data are a good approximation of those based on accelerating-flow simulations.

FUN3D↗

NASA NTRSDate not supplied

A Database of CFD-Based Buffet Forcing Functions for Artemis I Structural Response Evaluation

transonic buffet↗

DOE OSTI2022

The Diurnal Dynamics of Gross Primary Productivity Using Observations From the Advanced Baseline Imager on the Geostationary Operational Environmental Satellite‐R Series at an Oak Savanna Ecosystem

Gross primary productivity (GPP) is the largest flux in the global carbon cycle and satellite-based GPP estimates have long been used to study the trends and interannual variability of GPP. With recent updates to geostationary satellites, we can now explore the diurnal variability of GPP at a comparable spatial resolution to polar-orbiting satellites and at temporal frequencies comparable to eddy covariance (EC) tower sites. We used observations from the Advanced Baseline Imager on the Geostationary Operational Environmental Satellite-R series (GOES-R) to test the ability of subdaily satellite data to capture the shifts in the diurnal course of GPP at an oak savanna EC site in California, USA that is subject to seasonal soil moisture declines. We compared three methods to estimate GPP: (a) a light-use efficiency model, (b) a linear relationship between the product of near-infrared reflectance of vegetation and photosynthetically active radiation (LIN-NIR v P) and EC tower GPP, and (c) a light response curve (LRC-NIR v P) between NIR v P and EC GPP. The LRC-NIR v P achieved the lowest mean absolute error for winter (2 µmol CO 2 m –2 s –1 ), spring (2.51 µmol CO 2 m –2 s –1 ), summer (1.43 µmol CO 2 m –2 s –1 ), and fall (1.35 µmol CO 2 m –2 s –1 ). The ecosystem experienced the largest shift in daily peak GPP in relation to the peak of incoming solar radiation toward the morning hours during the dry summers. The LRC-NIRvP and the light-use efficiency model were in agreement with these patterns of a shift in peak daily GPP toward the morning hours during summer. Our results can help develop diurnal estimates of GPP from geostationary satellites that are sensitive to fluctuating environmental conditions during the day.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS2012

GERMcode: A Stochastic Model for Space Radiation Risk Assessment

A new computer model, the GCR Event-based Risk Model code (GERMcode), was developed to describe biophysical events from high-energy protons and high charge and energy (HZE) particles that have been studied at the NASA Space Radiation Laboratory (NSRL) for the purpose of simulating space radiation biological effects. In the GERMcode, the biophysical description of the passage of HZE particles in tissue and shielding materials is made with a stochastic approach that includes both particle track structure and nuclear interactions. The GERMcode accounts for the major nuclear interaction processes of importance for describing heavy ion beams, including nuclear fragmentation, elastic scattering, and knockout-cascade processes by using the quantum multiple scattering fragmentation (QMSFRG) model. The QMSFRG model has been shown to be in excellent agreement with available experimental data for nuclear fragmentation cross sections. For NSRL applications, the GERMcode evaluates a set of biophysical properties, such as the Poisson distribution of particles or delta-ray hits for a given cellular area and particle dose, the radial dose on tissue, and the frequency distribution of energy deposition in a DNA volume. By utilizing the ProE/Fishbowl ray-tracing analysis, the GERMcode will be used as a bi-directional radiation transport model for future spacecraft shielding analysis in support of Mars mission risk assessments. Recent radiobiological experiments suggest the need for new approaches to risk assessment that include time-dependent biological events due to the signaling times for activation and relaxation of biological processes in cells and tissue. Thus, the tracking of the temporal and spatial distribution of events in tissue is a major goal of the GERMcode in support of the simulation of biological processes important in GCR risk assessments. In order to validate our approach, basic radiobiological responses such as cell survival curves, mutation, chromosomal aberrations, and representative mouse tumor induction curves are implemented into the GERMcode. Extension of these descriptions to other endpoints related to non-targeted effects and biochemical pathway responses will be discussed.

Kim, Myung-Hee Y.↗

DOE OSTI2022

Imaging coherent phonons and precursor dynamics in LaFeAsO with 4D ultrafast electron microscopy

In this work, we used 4D ultrafast electron microscopy (UEM) to directly image femtosecond photoinduced structural dynamics in single-crystal LaFeAsO at initial temperatures of 300 and 100 K, above and below the known structural and magnetic phase-transition temperatures, respectively. With nanometer-picosecond resolution, we resolved an initial (precursor) sigmoidlike response arising from photothermal expansion and lattice reorientation that precedes the onset of propagating coherent acoustic phonons (CAPs). In the specific regions probed, the precursor response at 100 K is shorter than at 300 K ($t$ 0.5;100 K = 11.3ps vs $t$ 0.5;300 K = 17.8ps), and the CAP oscillation frequency is lowered with cooling (ƒ CAP;100 K = 12 GHz vs ƒ CAP;300 K = 21 GHz), correlated to known lattice softening due to the structural phase change. The transient CAP behaviors at 300 K are dispersive, displaying an exponentially decaying phase velocity over the first nanosecond. Further, the CAP symmetry at 300 K matches a first-order antisymmetric shear mode (A 1 ), while at 100 K it is best matched by a mostly nondispersive zero-order symmetric mode (S 0 ). These findings illustrate the sensitivity of UEM imaging to spatially heterogeneous dynamics in the Fe-pnictide materials and more broadly in other quantum materials.

36 MATERIALS SCIENCE↗

NASA NTRS1980

Design concepts for a high-impedance narrow-band 42 GHz power TWT using a fundamental/forward ladder-based circuit

A low-cost, narrowband, millimeter wave space communications TWT design was studied. Cold test interaction structure scale models were investigated and analyses were undertaken to predict the electrical and thermal response of the hypothetical 200 W TWT at 42 GHz and 21 kV beam voltage. An intentionally narrow instantaneous bandwidth (1%, with the possibility of electronic tuning of the center frequency over several percent) was sought with a highly dispersive, high impedance "forward wave' interaction structure based on a ladder (for economy in fabrication) and nonspace harmonic interaction, for a high gain rate and a short, economically focused tube. The "TunneLadder' interaction structure devised combines ladder properties with accommodation for a pencil beam. Except for the impedance and bandwidth, there is much in common with the millimeter wave helix TWTs which provided the ideal of diamond support rods. The benefits of these are enhanced in the TunneLadder case because of spatial separation of beam interception and RF current heating.

Karp, A.↗

DOE OSTI2023

Ultrafast Wavefront Shaping via Space-Time Refraction

A myriad of metasurfaces have been demonstrated that manipulate light by spatially structuring thin optical layers. Manipulation of the optical properties of such layers in both space and time can unlock new physical phenomena and enable new optical devices. Examples include photon acceleration and frequency conversion, which modifies Snell’s relation to a more general, nonreciprocal form. Here, we combine theory and experiment to realize wavefront shaping and frequency conversion on subpicosecond time-scales by inducing space-time refractive index gradients in epsilon-near-zero (ENZ) films with femtosecond light pulses. Furthermore, we experimentally tune wavefront steering by controlling the incident angle of the beams and the pump–probe delay without the need for nanostructure fabrication. As a demonstration of this approach, we leverage the ultrafast, high-bandwidth optical response of transparent oxides in their ENZ wavelength range to create large refractive index gradients and new types of nonreciprocal, ultrafast two-dimensional (2D) optics, including an ultrathin transient lens.

36 MATERIALS SCIENCE↗

NASA NTRS2012

Phase Coupling in Langmuir Wave Packets: Evidence for Four Wave Interactions in Solar Type III Radio Bursts

The four wave interaction process, known as the oscillating two stream instability (OTSI) is considered as one of the mechanisms responsible for stabilizing the electron beams associated with solar type III radio bursts. It has been reported that (1) an intense localized Langmuir wave packet associated with a type III burst contains the spectral characteristics of the OTSI: (a) a resonant peak at the local electron plasma frequency, f(sub pe), (b) a Stokes peak at a frequency slightly lower than f(sub pe), (c) anti-Stokes peak at a frequency slightly higher than f(sub pe), and (d) a low frequency enhancement below a few hundred Hz, (2) the frequencies and wave numbers of these spectral components satisfy the resonance conditions of the OTSI, and (3) the peak intensity of the wave packet is well above the thresholds for the OTSI as well as spatial collapse of envelope solitons. Here, for the first time, applying the trispectral analysis on this wave packet, we show that the tricoherence, which measures the degree of coherent four-wave coupling amongst the observed spectral components exhibits a peak. This provides an additional evidence for the OTSI and related spatial collapse of Langmuir envelope solitons in type III burst sources.

Thejappa, G.↗

NASA NTRS2001

Modeling Modern Methane Emissions from Natural Wetlands: Model Description and Results - 1

Methane is an important greenhouse gas which contributes about 22 percent to the present greenhouse effect. Natural wetlands currently constitute the biggest methane source and were the major source in preindustrial times. Wetland emissions depend highly on the climate, i.e., on soil temperature and water table. To investigate the response of methane emissions from natural wetlands to climate variations, a process-based model that derives methane emissions from natural wetlands as a function of soil temperature, water table, and net primary productivity is used. For its application on the global scale, global data sets for all model parameters are generated. In addition, a simple hydrologic model is developed in order to simulate the position of the water table in wetlands. The hydrologic model is tested against data from different wetland sites, and the sensitivity of the hydrologic model to changes in precipitation is examined. The global methane hydrology model constitutes a tool to study temporal and spatial variations in methane emissions from natural wetlands. The model is applied using high-frequency atmospheric forcing fields from European Center for Medium-range Weather Forecasts (ECMWF) re-analyses of the period from 1982 to 1993. We calculate global annual methane emissions from wetlands to be 260 teragrams per year. Twenty-five percent of these methane emissions originate from wetlands north of 30 degrees North Latitude. Only 60 percent of the produced methane is emitted, while the rest is re-oxidized. A comparison of zonal integrals of simulated global wetland emissions and results obtained by an inverse modeling approach shows good agreement. In a test with data from two wetlands the seasonality of simulated and observed methane emissions agrees well.

Biogeochemical processes↗

NASA NTRS1991

Potential vorticity index

Based on the European Center For Medium Range Weather Forecasting (ECMWF) First Global Atmospheric Research Program Global Experiment (FGGE) IIIb data set in the 1978 to 1979 winter, a potential vorticity (PV) index was defined as a measure of the zonally averaged, mid-latitude PV gradient on the 300 K isentropic surface in the Northern Hemisphere. The evolution of that index and its relation to teleconnection patterns of 500 mb geopotential height anomaly are studied. The results of the temporal and spatial variation of blocking and cyclogenesis in the 1978 to 1979 winter and its relation to global and local PV gradients were obtained. Complex empirical orthogonal function (EOF) analyses were performed, using the same FGGE data set for the 1978 to 1979 winter, for a representative high latitude band and mid latitude band geopotential height anomalies at 500 mb, phi sub h, phi sub m, and PV gradient at 300 K, delta(Q), at each longitude for the three month period. The focus of current research is the following: (1) to perform Fourier analyses for the first three EOF's of phi sub h, phi sub m, and delta(Q) at given latitude bands, and to find the dominant wavenumbers and frequencies which are responsible for these EOF's; (2) to compare the results from EOF and Fourier analyses which will be used to explore the relations of blocking and cyclogensis with local and global PV gradients; and (3) to study the time dependence of the local PV gradients and relate it to the PV index vacillation cycles observed in the PV index cycle.

Barcilon, Albert↗