Results for “AMPLITUDES” — Page 96

NASA NTRS2002

Group Sunspot Numbers: Sunspot Cycle Characteristics

We examine the "Group" sunspot numbers constructed by Hoyt and Schatten to determine their utility in characterizing the solar activity cycle. We compare smoothed monthly Group Sunspot Numbers to Zurich (International) Sunspot Numbers, 10.7-cm radio flux, and total sunspot area. We find that the Zurich numbers follow the 10.7-cm radio flux and total sunspot area measurements slightly better than the Group numbers. We examine several significant characteristics of the sunspot cycle using both Group numbers and Zurich numbers. We find that the "Waldmeier Effect" - the anti-correlation between cycle amplitude and the elapsed time between minimum and maximum of a cycle - is much more apparent in the Zurich numbers. The "Amplitude-Period Effect" the anti-correlation between cycle amplitude and the length of the previous cycle from minimum to minimum - is also much more apparent in the Zurich numbers. The "Amplitude-Minimum Effect" - the correlation between cycle amplitude and the activity level at the previous (onset) minimum is equally apparent in both the Zurich numbers and the Group numbers. The "Even-Odd Effect" - in which odd-numbered cycles are larger than their even-numbered precursors - is somewhat stronger in the Group numbers but with a tighter relationship in the Zurich numbers. The "Secular Trend" - the increase in cycle amplitudes since the Maunder Minimum - is much stronger in Group numbers. After removing this trend we find little evidence for multi-cycle periodicities like the 80 year Gleissberg cycle or the two- and three-cycle periodicities. We also find little evidence for a correlation between the amplitude of a cycle and its period or for a bimodal distribution of cycle periods. We conclude that the Group numbers are most useful for extending the sunspot cycle data further back in time and thereby adding more cycles and improving the statistics. However, the Zurich numbers are more useful for characterizing the on-going levels of solar activity.

Hathaway, D. H.↗

NASA NTRS2003

Effects of broad frequency vibration on cultured osteoblasts

Bone is subjected in vivo to both high amplitude, low frequency strain, incurred by locomotion, and to low amplitude, broad frequency strain. The biological effects of low amplitude, broad frequency strain are poorly understood. To evaluate the effects of low amplitude strains ranging in frequency from 0 to 50 Hz on osteoblastic function, we seeded MC3T3-E1 cells into collagen gels and applied the following loading protocols for 3 min per day for either 3 or 7 days: (1) sinusoidal strain at 3 Hz, with 0-3000 microstrain peak-to-peak followed by 0.33 s resting time, (2) "broad frequency vibration" of low amplitude strain (standard deviation of 300 microstrain) including frequency components from 0 to 50 Hz, and (3) sinusoidal strain combined with broad frequency vibration (S + V). The cells were harvested on day 4 or 8. We found that the S + V stimulation significantly repressed cell proliferation by day 8. Osteocalcin mRNA was up-regulated 2.6-fold after 7 days of S + V stimulation, and MMP-9 mRNA was elevated 1.3-fold after 3 days of vibration alone. Sinusoidal stimulation alone did not affect the cell responses. No differences due to loading were observed in alkaline phosphatase activity and in mRNA levels of type I collagen, osteopontin, connexin 43, MMPs-1A, -3, -13. These results suggest that osteoblasts are more sensitive to low amplitude, broad frequency strain, and this kind of strain could sensitize osteoblasts to high amplitude, low frequency strain. This suggestion implies a potential contribution of stochastic resonance to the mechanical sensitivity of osteoblasts. Copyright 2002 Elsevier Science Ltd.

Non-NASA Center↗

NASA NTRS1995

Role of somatosensory and vestibular cues in attenuating visually induced human postural sway

The purpose of this study was to determine the contribution of visual, vestibular, and somatosensory cues to the maintenance of stance in humans. Postural sway was induced by full-field, sinusoidal visual surround rotations about an axis at the level of the ankle joints. The influences of vestibular and somatosensory cues were characterized by comparing postural sway in normal and bilateral vestibular absent subjects in conditions that provided either accurate or inaccurate somatosensory orientation information. In normal subjects, the amplitude of visually induced sway reached a saturation level as stimulus amplitude increased. The saturation amplitude decreased with increasing stimulus frequency. No saturation phenomena were observed in subjects with vestibular loss, implying that vestibular cues were responsible for the saturation phenomenon. For visually induced sways below the saturation level, the stimulus-response curves for both normal subjects and subjects experiencing vestibular loss were nearly identical, implying (1) that normal subjects were not using vestibular information to attenuate their visually induced sway, possibly because sway was below a vestibular-related threshold level, and (2) that subjects with vestibular loss did not utilize visual cues to a greater extent than normal subjects; that is, a fundamental change in visual system "gain" was not used to compensate for a vestibular deficit. An unexpected finding was that the amplitude of body sway induced by visual surround motion could be almost 3 times greater than the amplitude of the visual stimulus in normal subjects and subjects with vestibular loss. This occurred in conditions where somatosensory cues were inaccurate and at low stimulus amplitudes. A control system model of visually induced postural sway was developed to explain this finding. For both subject groups, the amplitude of visually induced sway was smaller by a factor of about 4 in tests where somatosensory cues provided accurate versus inaccurate orientation information. This implied (1) that the subjects experiencing vestibular loss did not utilize somatosensory cues to a greater extent than normal subjects; that is, changes in somatosensory system "gain" were not used to compensate for a vestibular deficit, and (2) that the threshold for the use of vestibular cues in normal subjects was apparently lower in test conditions where somatosensory cues were providing accurate orientation information.

NASA Discipline Neuroscience↗

NASA NTRS2004

Erratum: Evidence That a Deep Meridional Flow Sets the Sunspot Cycle Period

An error was made in entering the data. This changes the results concerning the length of the time lag between the variations in the meridional flow speed and those in the cycle amplitude. The final paragraph on page 667 should read: Finally, we study the relationship between the drift velocities and the amplitudes of the hemisphere/cycles. We compare the drift velocity at the maximum of the cycle to the amplitude of that cycle for that hemisphere. There is a positive (0.5) and significant (95%) correlation between the two. However, an even stronger relationship is found between the drift velocity and the amplitude of the N + 2 cycle. The correlation is stronger (0.7) and more significant (99%), as shown. This relationship is suggestive of a "memory" in the solar cycle, again a property of dynamo models that use meridional circulation. Indeed, the two-cycle lag is precisely the relationship found by Charbonneau & Dikpati. This behavior is, however, more difficult to interpret, and we elaborate on this in the next section. In either case, these correlations only explain part of the variance in cycle amplitude (25% for the current cycle and 50% for the N + 2 cycle). Obviously, other mechanisms, such as variations in the gradient in the rotation rate, also contribute to the cycle amplitude variations. Our investigation of possible connections between drift rates and the amplitudes of the N + 1 and N + 3 cycles gives no significant correlations at these alternative time lags.

Hathaway, David H.↗

NASA NTRS2010

Optimization of Stimulus Characteristics for Vestibular Stochastic Resonance to Improve Balance Function

Stochastic resonance (SR) is a mechanism by which noise can assist and enhance the response of neural systems to relevant sensory signals. Recent studies have shown that applying imperceptible stochastic noise electrical stimulation to the vestibular system significantly improved balance and ocular motor responses. The goal of this study was to optimize the amplitude of the stochastic vestibular signals for balance performance during standing on an unstable surface. Subjects performed a standardized balance task of standing on a block of 10-cm-thick medium-density foam with their eyes closed. Balance performance was measured using a force plate under the foam block and using inertial motion sensors placed on the torso and head segments. Stochastic electrical stimulation was applied to the vestibular system through electrodes placed over the mastoid process. Subjects were tested at seven amplitudes in the 0.01-30Hz frequency range. The root mean square of the signal increased by 30 microamperes for each +/-100 microampere increment in the current range of 0 - +/-700 microampere. Six balance parameters were calculated to characterize the performance of subjects during the baseline and the stimulus periods for all seven amplitudes. Optimal stimulus amplitude was determined as the one at which the ratio of parameters from the stimulus period to the baseline period for any amplitude range was less than that for the no stimulus condition on a minimum of four of six parameters. Results from this study showed that balance performance at the optimal stimulus amplitude showed significant improvement with the application of the vestibular SR stimulation. The amplitude of optimal stimulus for improving balance performance in normal subjects was in the range of +/-100 - +/-300 microamps.

Mulavara, Ajitkumar↗

NASA NTRS2015

Non-Linear Slosh Damping Model Development and Validation

Propellant tank slosh dynamics are typically represented by a mechanical model of spring mass damper. This mechanical model is then included in the equation of motion of the entire vehicle for Guidance, Navigation and Control (GN&C) analysis. For a partially-filled smooth wall propellant tank, the critical damping based on classical empirical correlation is as low as 0.05%. Due to this low value of damping, propellant slosh is potential sources of disturbance critical to the stability of launch and space vehicles. It is postulated that the commonly quoted slosh damping is valid only under the linear regime where the slosh amplitude is small. With the increase of slosh amplitude, the critical damping value should also increase. If this nonlinearity can be verified and validated, the slosh stability margin can be significantly improved, and the level of conservatism maintained in the GN&C analysis can be lessened. The purpose of this study is to explore and to quantify the dependence of slosh damping with slosh amplitude. Accurately predicting the extremely low damping value of a smooth wall tank is very challenging for any Computational Fluid Dynamics (CFD) tool. One must resolve thin boundary layers near the wall and limit numerical damping to minimum. This computational study demonstrates that with proper grid resolution, CFD can indeed accurately predict the low damping physics from smooth walls under the linear regime. Comparisons of extracted damping values with experimental data for different tank sizes show very good agreements. Numerical simulations confirm that slosh damping is indeed a function of slosh amplitude. When slosh amplitude is low, the damping ratio is essentially constant, which is consistent with the empirical correlation. Once the amplitude reaches a critical value, the damping ratio becomes a linearly increasing function of the slosh amplitude. A follow-on experiment validated the developed nonlinear damping relationship. This discovery can lead to significant savings by reducing the number and size of slosh baffles in liquid propellant tanks.

Yang, H. Q.↗

NASA NTRSDate not supplied

Effects of Random Micron-Sized Roughness on Swept-Wing Transition

This study examines the effect of random micron-sized distributed roughness on stationary crossflow instabilities. The roughness parameters are varied by creating nanoparticle coatings of various formulations and applying them to inserts that cover approximately the first 14% of the model. In addition to the baseline configuration (no added roughness, root-mean-square (RMS) ≈ 0.42 𝜇m), panels with RMS roughness values of 4.8 and 8.6 𝜇m were tested, with correlation lengths of 1029 and 385 𝜇m, respectively. Despite the significant roughness levels tested, the transition location was found to be only mildly impacted by the additional roughness, and the roughness panel with lower RMS amplitude caused a larger upstream movement of transition, on average. However, the stationary crossflow amplitudes and wavelength content were found to vary substantially depending on the roughness input. In particular, the panel with higher RMS roughness amplitude resulted in significantly larger amplitudes in the 7.5-9 mm wavelength range at the farthest upstream measurement station, while the lower roughness panel resulted in mildly larger amplitudes at 10 mm and wavelengths larger than 15 mm. Nonlinear Parabolized Stability Equations (PSE) computations were performed to attempt to estimate the initial amplitudes of the stationary crossflow instabilities. Wavelength spectra were matched at the most upstream measurement location, but large discrepancies exist between the predicted and measured growth behavior farther downstream, thus, more work is required to improve confidence in initial amplitude estimates.

boundary-layer transition↗

NASA NTRSDate not supplied

Effects of Random Micron-Sized Roughness on Swept-Wing Transition

This study examines the effect of random micron-sized distributed roughness on stationary crossflow instabilities. The roughness parameters are varied by creating nanoparticle coatings of various formulations and applying them to inserts that cover approximately the first 14% of the model. In addition to the baseline configuration (no added roughness, root-mean-square (RMS) ≈ 0.42 𝜇m), panels with RMS roughness values of 4.8 and 8.6 𝜇m were tested, with correlation lengths of 1029 and 385 𝜇m, respectively. Despite the significant roughness levels tested, the transition location was found to be only mildly impacted by the additional roughness, and the roughness panel with lower RMS amplitude caused a larger upstream movement of transition, on average. However, the stationary crossflow amplitudes and wavelength content were found to vary substantially depending on the roughness input. In particular, the panel with higher RMS roughness amplitude resulted in significantly larger amplitudes in the 7.5-9 mm wavelength range at the farthest upstream measurement station, while the lower roughness panel resulted in mildly larger amplitudes at 10 mm and wavelengths larger than 15 mm. Nonlinear Parabolized Stability Equations (PSE) computations were performed to attempt to estimate the initial amplitudes of the stationary crossflow instabilities. Wavelength spectra were matched at the most upstream measurement location, but large discrepancies exist between the predicted and measured growth behavior farther downstream, thus, more work is required to improve confidence in initial amplitude estimates.

boundary-layer transition↗

NASA NTRSDate not supplied

Effects of Random Micron-Sized Roughness on Swept-Wing Transition

This study examines the effect of random micron-sized distributed roughness on stationary crossflow instabilities. The roughness parameters are varied by creating nanoparticle coatings of various formulations and applying them to inserts that cover approximately the first 14% of the model. In addition to the baseline configuration (no added roughness, root-mean-square (RMS) ≈ 0.42 𝜇m), panels with RMS roughness values of 4.8 and 8.6 𝜇m were tested, with correlation lengths of 1029 and 385 𝜇m, respectively. Despite the significant roughness levels tested, the transition location was found to be only mildly impacted by the additional roughness, and the roughness panel with lower RMS amplitude caused a larger upstream movement of transition, on average. However, the stationary crossflow amplitudes and wavelength content were found to vary substantially depending on the roughness input. In particular, the panel with higher RMS roughness amplitude resulted in significantly larger amplitudes in the 7.5-9 mm wavelength range at the farthest upstream measurement station, while the lower roughness panel resulted in mildly larger amplitudes at 10 mm and wavelengths larger than 15 mm. Nonlinear Parabolized Stability Equations (PSE) computations were performed to attempt to estimate the initial amplitudes of the stationary crossflow instabilities. Wavelength spectra were matched at the most upstream measurement location, but large discrepancies exist between the predicted and measured growth behavior farther downstream, thus, more work is required to improve confidence in initial amplitude estimates.

boundary-layer transition↗

DOE OSTI2018

Large-Signal Impedance Modeling of Three-Phase Voltage Source Converters: Preprint

Resonance problems have become a major hurdle in the large-scale grid integration of renewable energy. It is important to be able to predict the amplitude of resonance-induced distortions for the protection and control design of power electronic converters. We recently presented an impedance-based approach for the prediction of resonance amplitude. It was shown that the impedance response of a converter starts changing with the amplitude of resonance; this blocks the amplitude growth beyond a certain point where the converter forms a limit cycle mode of sustained oscillations. The large-signal impedance of a converter captures the change in its impedance response with the resonance amplitude, and it can be used to predict the resonance amplitude under different operation conditions. This paper presents large-signal sequence impedance modeling for three-phase voltage source converters (VSC) with dq-current control and PLL. Modeling challenges encountered in the absence of the small-signal approximation are addressed by a) leveraging the dominating influence of hard non-linearities such as pulse-width modulation saturation and limiters over soft non-linearities in shaping the converter large-signal behavior and b) modeling the large-signal gain of hard non-linearities using appropriate describing functions. Developed large-signal impedance models are validated using numerical simulations. Measurements of the large-signal impedance responses of a commercial 1-MW VSC-based inverter are also presented to experimentally demonstrate the effects of the injected perturbation amplitude on impedance response as predicted by the developed model.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2013

On the exact evaluation of spin networks

We introduce a fully coherent spin network amplitude whose expansion generates all SU(2) spin networks associated with a given graph. We then give an explicit evaluation of this amplitude for an arbitrary graph. We show how this coherent amplitude can be obtained from the specialization of a generating functional obtained by the contraction of parametrized intertwiners à la Schwinger. We finally give the explicit evaluation of this generating functional for arbitrary graphs.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2026

Large deformations of Tr(Φ 3 ) and the world at infinity

The amplitudes of the non-linear sigma model can be obtained from those of Tr(Φ 3 ) theory by sending the kinematic (Mandelstam) variables to infinity in a certain direction. In this paper we characterize the behavior of Tr(Φ 3 ) amplitudes under a general class of large kinematic shifts called g-vector shifts. The objects that live in this world at infinity retain certain key amplitude-like properties, most notably factorization, and admit descriptions in terms of polytopes, but they are not generally amplitudes of any cognizable theory. We identify particular g-vector shifts that lead at infinity to mixed amplitudes involving two pions and any number of scalars, allowing us to provide polytopal descriptions of these amplitudes.

effective field theories↗

DOE OSTI2017

Heptagons from the Steinmann cluster bootstrap

We reformulate the heptagon cluster bootstrap to take advantage of the Steinmann relations, which require certain double discontinuities of any amplitude to vanish. These constraints vastly reduce the number of functions needed to bootstrap seven-point amplitudes in planar $ \mathcal{N} $ = 4 supersymmetric Yang-Mills theory, making higher-loop contributions to these amplitudes more computationally accessible. In particular, dual superconformal symmetry and well-defined collinear limits suffice to determine uniquely the symbols of the three-loop NMHV and four-loop MHV seven-point amplitudes. We also show that at three loops, relaxing the dual superconformal $\bar{Q}$ relations and imposing dihedral symmetry (and for NMHV the absence of spurious poles) leaves only a single ambiguity in the heptagon amplitudes. These results point to a strong tension between the collinear properties of the amplitudes and the Steinmann relations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2015

Simple recursion relations for general field theories

On-shell methods offer an alternative definition of quantum field theory at tree-level, replacing Feynman diagrams with recursion relations and interaction vertices with a handful of seed scattering amplitudes. In this paper we determine the simplest recursion relations needed to construct a general four-dimensional quantum field theory of massless particles. For this purpose we define a covering space of recursion relations which naturally generalizes all existing constructions, including those of BCFW and Risager. The validity of each recursion relation hinges on the large momentum behavior of an n-point scattering amplitude under an m-line momentum shift, which we determine solely from dimensional analysis, Lorentz invariance, and locality. We show that all amplitudes in a renormalizable theory are 5-line constructible. Amplitudes are 3-line constructible if an external particle carries spin or if the scalars in the theory carry equal charge under a global or gauge symmetry. Remarkably, this implies the 3-line constructibility of all gauge theories with fermions and complex scalars in arbitrary representations, all supersymmetric theories, and the standard model. Moreover, all amplitudes in non-renormalizable theories without derivative interactions are constructible; with derivative interactions, a subset of amplitudes is constructible. We illustrate our results with examples from both renormalizable and non-renormalizable theories. In conclusion, our study demonstrates both the power and limitations of recursion relations as a self-contained formulation of quantum field theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2016

All orders results for self-crossing Wilson loops mimicking double parton scattering

Loop-level scattering amplitudes for massless particles have singularities in regions where tree amplitudes are perfectly smooth. For example, a 2 → 4 gluon scattering process has a singularity in which each incoming gluon splits into a pair of gluons, followed by a pair of 2 → 2 collisions between the gluon pairs. This singularity mimics double parton scattering because it occurs when the transverse momentum of a pair of outgoing gluons vanishes. The singularity is logarithmic at fixed order in perturbation theory. We exploit the duality between scattering amplitudes and polygonal Wilson loops to study six-point amplitudes in this limit to high loop order in planar N = 4 super-Yang-Mills theory. The singular configuration corresponds to the limit in which a hexagonal Wilson loop develops a self-crossing. The singular terms are governed by an evolution equation, in which the hexagon mixes into a pair of boxes; the mixing back is suppressed in the planar (large N c) limit. Because the kinematic dependence of the box Wilson loops is dictated by (dual) conformal invariance, the complete kinematic dependence of the singular terms for the self-crossing hexagon on the one nonsingular variable is determined to all loop orders. The complete logarithmic dependence on the singular variable can be obtained through nine loops, up to a couple of constants, using a correspondence with the multi-Regge limit. As a byproduct, we obtain a simple formula for the leading logs to all loop orders. Furthermore, we also show that, although the MHV six-gluon amplitude is singular, remarkably, the transcendental functions entering the non-MHV amplitude are finite in the same limit, at least through four loops.

1/N expansion scattering amplitudes↗

DOE OSTI2025

All loop scattering for all multiplicity

We study the recently introduced curve integral formalism that defines a new family of formulas for the scattering amplitudes of the colored scalar trϕ 3 theory. We find that the curve integral manifests a very surprising fact about these amplitudes: the dependence on the number of particles, n, and the loop order, L, is effectively decoupled in these formulas. We derive the curve integrals at tree-level for all n. We then show that, for higher loop-order, it suffices to study the curve integrals for L-loop tadpole-like amplitudes, which have just one particle per color trace-factor. By combining these tadpole-like formulas with the tree-level results, we find formulas for the all n amplitudes at L loops. We illustrate this result by giving explicit curve integrals for all the amplitudes in the theory, including the non-planar amplitudes, through to two loops, for all n.

1/N Expansion↗

DOE OSTI2014

Plasma wakefields driven by an incoherent combination of laser pulses: A path towards high-average power laser-plasma accelerators

The wakefield generated in a plasma by incoherently combining a large number of low energy laser pulses (i.e., without constraining the pulse phases) is studied analytically and by means of fully self-consistent particle-in-cell simulations. The structure of the wakefield has been characterized and its amplitude compared with the amplitude of the wake generated by a single (coherent) laser pulse. We show that, in spite of the incoherent nature of the wakefield within the volume occupied by the laser pulses, behind this region, the structure of the wakefield can be regular with an amplitude comparable or equal to that obtained from a single pulse with the same energy. Wake generation requires that the incoherent structures in the laser energy density produced by the combined pulses exist on a time scale short compared to the plasma period. Incoherent combination of multiple laser pulses may enable a technologically simpler path to high-repetition rate, high-average power laser-plasma accelerators, and associated applications.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2014

Thermal vibration of a rectangular single-layered graphene sheet with quantum effects

The thermal vibration of a rectangular single-layered graphene sheet is investigated by using a rectangular nonlocal elastic plate model with quantum effects taken into account when the law of energy equipartition is unreliable. The relation between the temperature and the Root of Mean Squared (RMS) amplitude of vibration at any point of the rectangular single-layered graphene sheet in simply supported case is derived first from the rectangular nonlocal elastic plate model with the strain gradient of the second order taken into consideration so as to characterize the effect of microstructure of the graphene sheet. Then, the RMS amplitude of thermal vibration of a rectangular single-layered graphene sheet simply supported on an elastic foundation is derived. The study shows that the RMS amplitude of the rectangular single-layered graphene sheet predicted from the quantum theory is lower than that predicted from the law of energy equipartition. The maximal relative difference of RMS amplitude of thermal vibration appears at the sheet corners. The microstructure of the graphene sheet has a little effect on the thermal vibrations of lower modes, but exhibits an obvious effect on the thermal vibrations of higher modes. The quantum effect is more important for the thermal vibration of higher modes in the case of smaller sides and lower temperature. The relative difference of maximal RMS amplitude of thermal vibration of a rectangular single-layered graphene sheet decreases monotonically with an increase of temperature. The absolute difference of maximal RMS amplitude of thermal vibration of a rectangular single-layered graphene sheet increases slowly with the rising of Winkler foundation modulus.

77 NANOSCIENCE AND NANOTECHNOLOGY↗