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At least 1,171 records · Page 65
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NASA NTRS1986

On the polarization of Alpha Orionis

Much of the complex behavior of the polarization observed in the M2 supergiant Alpha Ori can be explained in terms of the combined effects of Rayleigh scattering in the photosphere and scattering by circumstellar dust in the presence of one or more photospheric hot spots. The ad hoc scattering layer of electrons which Schwarz and Clarke employed in their models reported in 1984 can be avoided, eliminating the conflict with the much lower column densities found in other studies of the extended chromosphere of this star. The transfer of polarized continuum radiation in cool model atmospheres has been treated fully. Under conditions of optimal spot area and location on the disk and large temperature differences (up to 1000 K) between the spot and normal photosphere, it is possible to get a net polarization up to about 0.3 percent in the blue in the direct starlight. The effects of spot limb darkening on the polarization of scattered spot light have been evaluated. Narrow-band observations that include molecular bands are encouraged for their diagnostic value.

Doherty, L. R.↗
DOE OSTI2025

New frontiers in wind-wildlife monitoring systems

Effective minimization of negative effects of wind energy on wildlife is an iterative process whereby direct observations of wildlife effects inform and validate mitigation strategies. Yet, the full implementation of this adaptive management has been hindered by a lack of appropriate data. The accurate, high-resolution data required exceeds the capacity of most current monitoring approaches (human observers or monitoring technologies applied in isolation). Current applications of monitoring technologies struggle to harness their full potential by failing to capitalize on opportunities for integration with additional technologies and/or by having limited temporal and spatial resolution. At the emergence of this new frontier of wildlife monitoring, we review the elements of a robust wind-wildlife monitoring system and highlight sensor fusion principles that facilitate effective implementation and integration of multiple monitoring technologies. We also illustrate how sensor fusion solutions can generate high resolution data on collision and displacement effects on terrestrial wildlife across complex spatial and temporal scales.

17 WIND ENERGY↗
DOE OSTI2020

Preliminary Plan for Evaluation of Reactor Pressure Vessel Surveillance Materials from Palisades Nuclear Generating Station

The Palisades Nuclear Generating Station (PNGS), located in Michigan, is owned and operated by Entergy. It is a Combustion Engineering 2-loop pressurized water reactor (PWR) producing 805 MWe (2,565 MWth). The PNGS was built between 1967 and 1970, with approval to operate at full power in 1973; the plant’s original license was due to expire on March 24, 2011. An application for 20-year extension was filed in 2005 with the Nuclear Regulatory Commission and was granted on January 18, 2007. Although the plant was scheduled for decommissioning by 2031, Entergy currently plans to close the PNGS in 2022. The PNGS included in its reactor pressure vessel (RPV) surveillance program a capsule, designated A-60, containing specimens of one of the vessel plates and a weld metal with nickel content of about 1.36 wt% and copper content of about 0.20 wt%. This capsule was irradiated to a fluence of 1.8 x 10 20 n/cm 2 . The capsule was removed from its surveillance position in 1995 and has been resident in the spent fuel pool since that time. The material is also of special interest because of its very high nickel content and because of the potential for development of NiMnSi (nickel-manganese-silicon) precipitates, dubbed “late blooming phases.” The surveillance program also includes a capsule, designated T-150, dedicated specifically for thermal aging, which would provide results for at least 33 effective full power years, which is beyond the current thermal-aging database for such materials. Given that license extensions to 60 years of operation have been approved by the US Nuclear Regulatory Commission for most of the currently operating light water reactors in the United States, and that the first extension to 80 years was recently approved, there exists the probability that some RPVs will reach and possibly exceed a fast neutron fluence (> 1 MeV) of 1 x 10 20 n/cm 2 . This is a fluence regime with no US surveillance data and very little test reactor data, except for the Light Water Reactor Sustainability Program–sponsored University of California Santa Barbara Advanced Test Reactor (ATR) ATR-2 project. Thus, the materials in the A-60 capsule represent a valuable resource for directly exploring the effects of commercial surveillance irradiation on a typical plate and a high-nickel weld with similar materials irradiated in the ATR-2 test reactor project. This report provides background information for the surveillance program, previous results of surveillance materials testing, the preliminary plan for capsule retrieval and disassembly, and the plan for testing and microstructural examination of the mechanical test specimens of these unique materials to assess the features induced by very high irradiation fluence or very long thermal aging time

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRS2019

Effects of Topography on Tropical Forest Structure Depend on Climate Context

Topography affects abiotic conditions which can influence the structure, function, and dynamics of ecological communities. An increasing number of studies have demonstrated biological consequences of fine-scale topographic heterogeneity but we have a limited understanding of how We merged high-resolution (1 sq. meter) data on topography and canopy height derived from airborne lidar with ground-based data from 15 forest plots in Puerto Rico distributed along a precipitation gradient spanning ca. 800 to 3,500 mm yr(exp -1). Ground-based data included species composition, estimated above-ground biomass (AGB), and two key functional traits (wood density and leaf mass per area, LMA) that reflect resource-use strategies and a trade-off between hydraulic safety and hydraulic efficiency. We used hierarchical Bayesian models to evaluate how the interaction between topography climate is related to metrics of forest structure (i.e., canopy height and AGB), as well as taxonomic and functional alpha- and beta-diversity. Fine-scale topography (characterized with the topographic wetness index, TWI) significantly affected forest structure and the strength (and in some cases direction) of these effects varied across the precipitation gradient. In all plots, canopy height increased with topographic wetness but the effect was much stronger in dry compared to wet forest plots. In dry forest plots, topographically wetter microsites also had higher levels of AGB but in wet forest plots, topographically drier microsites had higher AGB. Fine-scale topography influenced functional composition but had only weak or non-significant effects on taxonomic and functional alpha- and beta-diversity. For instance, community-weighted wood density followed a similar pattern to AGB across plots. We also found a marginally significant association between variation of wood density and topographic heterogeneity that depended on climate context. Synthesis: The effects of fine-scale topographic heterogeneity on tropical forest structure and composition depend on the climate context. Our study demonstrates how a stronger integration of topographic heterogeneity across precipitation gradients could improve estimates of forest structure and biomass, and may provide insight to the ways that topography might mediate species responses to drought and climate change.

Tropical dry forest↗
NASA NTRS2008

Effect of Stepwise Pressure Change on Porosity Evolution during Directional Solidification in Small Cylindrical Channels

Controlled directional solidification experiments were performed in capillary channels, using nitrogen-saturated succinonitrile, to examine the effect of an in-situ stepwise processing pressure increase on an isolated pore evolution. Two experiments were performed using different processing pressure input profiles. The results indicate that a processing pressure increase has a transient effect on pore growth geometry characterized by an initial phase of decreasing pore diameter, followed by a recovery phase of increasing pore diameter. The experimental results also show that processing pressure can be used as a control parameter to either increase or terminate porosity formation. A theoretical model is introduced which indicates that the pore formation process is limited by the diffusion of solute-gas through the melt, and that the observed response toa pressure increase is attributed to the re-equilibration of solute concentration in the melt associated with the increased melt pressure.

Grugel, R.N.↗
DOE OSTI2025

An Experiment with LLMs as Database Design Tutors: Persistent Equity and Fairness Challenges in Online Learning

As large language models (LLMs) continue to evolve, their capacity to replace humans as their surrogates is also improving. As increasing numbers of intelligent tutoring systems (ITSs) are embracing the integration of LLMs for digital tutoring, questions are arising as to how effective they are and if their hallucinatory behaviors diminish their perceived advantages. One critical question that is seldom asked if the availability, plurality, and relative weaknesses in the reasoning process of LLMs are contributing to the much discussed digital divide and equity and fairness in online learning. In this paper, we present an experiment with database design theory assignments and demonstrate that while their capacity to reason logically is improving, LLMs are still prone to serious errors. We demonstrate that in online learning and in the absence of a human instructor, LLMs could introduce inequity in the form of “wrongful” tutoring that could be devastatingly harmful for learners, which we call ignorant bias, in increasingly popular digital learning. We also show that significant challenges remain for STEM subjects, especially for subjects for which sound and free online tutoring systems exist. Based on the set of use cases, we formulate a possible direction for an effective ITS for online database learning classes of the future.

Jamil, Hasan M. (ORCID:0000000231243780)↗
DOE OSTI2026

Measuring labor productivity dynamics in U.S. industrial and electric power sectors: a case study (2014–2023)

This study proposes a subsystem methodology for measuring labor productivity in the U.S. industrial and electric power sectors by leveraging public data available between 2014 and 2023. Building on Pasinetti’s framework and subsequent developments, the approach employs Vertically Integrated Sectors (VIS) to account for both direct and indirect productivity effects. The novelty of this work is twofold. First, it enables the estimation of productivity trends over time, providing a robust foundation for empirical analysis. Second, it applies the methodology to a case study of the electric generation sector, highlighting its practical relevance. Using data from the Bureau of Economic Analysis, the Bureau of Labor Statistics, and the Impact Analysis for Planning (IMPLAN) tool, the study reveals significant discrepancies between conventional productivity measures and those derived from the VIS approach. Furthermore, the proposed method aligns with the principles of Integrated Energy Systems by capturing the interrelations among generation, distribution, storage, and consumption. This alignment underscores its utility and applications for energy-related policy and planning. Overall, the findings contribute to more precise labor productivity assessments, supporting informed decision-making and future research. Additionally, the method highlights the importance of considering the whole supply chain, providing interrelated metrics for labor productivity which includes both, direct and indirect effects on the final labor productivity metric. By incorporating intersectoral dependencies, this method offers a more comprehensive and accurate measure of labor productivity compared to traditional metrics.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Predicting Thermal Excursions During in situ Oxidative Regeneration of Packed Bed Catalytic Fast Pyrolysis Catalyst

Ex situ catalytic fast pyrolysis (CFP) uses a secondary reactor to upgrade biomass pyrolysis vapors to stabilized CFP oils with reduced oxygen content. In one configuration, the secondary reactor is operated as a packed-bed swing reactor system which allows coke-deactivated beds to be decarbonized in situ while other beds remain online for vapor upgrading. In situ decarbonization must be done carefully to avoid irreversible deactivation and/or physical degradation of catalyst pellets. Given that packed bed reactors are well known to have poor heat transfer characteristics, this is a critical issue impacting scaleability and commercial viability of the technology. To predict thermal excursions during regeneration, finite element computational models have been built to assist in scaling up oxidative decarbonization of a Pt/TiO2 CFP catalyst (0.5 mm spheres) from a bench scale packed bed with 100 g of catalyst to a pilot scale packed bed with 2 kg of catalyst and internal cooling tubes. Based on transient measurements of outlet temperature and effluent CO2 concentration, and using an assumed coke profile and activation energy, this paper demonstrates that specific combinations of effective thermal conductivity and wall heat transfer coefficient can fit bench scale oxidative regeneration data equally well. For the upscaled 2 kg bed, four bench-scale “best fit” parameter pairs give different predictions for location and magnitude of thermal excursions, with the maximum computed bed temperature gradients ranging from 30 °C cm-1 to as high as 3000 °C cm-1. The larger the fraction of heat removal by conduction through the cooling tubes, the greater the differences between the parameter pairs. The modelling results presented in this paper cast doubt on the industrial viability of the proposed combination of catalyst, bed and regeneration process, and point to the need for alternate reactor designs. However, there is considerable uncertainly in some of the key model parameters. The reliability of model predictions can be increased by adding more temperature measurements at key bed locations, testing additional variations in process conditions, performing careful bed dissections to determine the true coke profile, and perhaps most importantly, directly measuring the effective thermal conductivity of the catalyst pellets.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1998

Replication-deficient adenovirus vector transfer of gfp reporter gene into supraoptic nucleus and subfornical organ neurons

The present studies used defined cells of the subfornical organ (SFO) and supraoptic nuclei (SON) as model systems to demonstrate the efficacy of replication-deficient adenovirus (Ad) encoding green fluorescent protein (GFP) for gene transfer. The studies investigated the effects of both direct transfection of the SON and indirect transfection (i.e., via retrograde transport) of SFO neurons. The SON of rats were injected with Ad (2 x 10(6) pfu) and sacrificed 1-7 days later for cell culture of the SON and of the SFO. In the SON, GFP fluorescence was visualized in both neuronal and nonneuronal cells while only neurons in the SFO expressed GFP. Successful in vitro transfection of cultured cells from the SON and SFO was also achieved with Ad (2 x 10(6) to 2 x 10(8) pfu). The expression of GFP in in vitro transfected cells was higher in nonneuronal (approximately 28% in SON and SFO) than neuronal (approximately 4% in SON and 10% in SFO) cells. The expression of GFP was time and viral concentration related. No apparent alterations in cellular morphology of transfected cells were detected and electrophysiological characterization of transfected cells was similar between GFP-expressing and nonexpressing neurons. We conclude that (1) GFP is an effective marker for gene transfer in living SON and SFO cells, (2) Ad infects both neuronal and nonneuronal cells, (3) Ad is taken up by axonal projections from the SON and retrogradely transported to the SFO where it is expressed at detectable levels, and (4) Ad does not adversely affect neuronal viability. These results demonstrate the feasibility of using adenoviral vectors to deliver genes to the SFO-SON axis. Copyright 1998 Academic Press.

NASA Discipline Regulatory Physiology↗
DOE OSTI2022

A High-Throughput MEMS-Based Differential Scanning Calorimeter for Direct Thermal Characterization of Antibodies

Calorimeters, which can be used for rapid thermal characterization of biomolecules, are getting intense attention in drug development. This paper presents a novel MEMS-based differential scanning calorimeter (DSC) for direct thermal characterization of protein samples. The DSC consisted of a pair of temperature sensors made by vanadium oxide (VOx) film with a temperature coefficient of resistivity of –0.025/K at 300 K, a microfluidic device with high thermal insulation (2.8 K/mW), and a Peltier heater for linear temperature scanning. The DSC exhibited high sensitivity (6.1 µV/µW), low noise (0.4 µW), high scanning rate (45 K/min), and low sample consumption volume (0.63 µL). The MEMS DSC was verified by measuring the temperature-induced denaturation of lysozyme at different pH, and then used to study the thermal stability of a monoclonal antibody (mAb), an antigen-binding fragment (Fab), and a dual variable domain immunoglobulin (DVD-Ig) at pH = 6. The results showed that lysozyme is a stable protein in the pH range of 4.0–8.0. The protein stability study revealed that the transition temperatures of the intact Fab fragment, mAb, and DVD proteins were comparable with conformational stability results obtained using conventional commercial DSC. These studies demonstrated that the MEMS DSC is an effective tool for directly understanding the thermal stability of antibodies in a high-throughput and low-cost manner compared to conventional calorimeters.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Arsenic Exposure Causes Global Changes in the Metalloproteome of Escherichia coli

Arsenic is a toxic metalloid with differential biological effects, depending on speciation and concentration. Trivalent arsenic (arsenite, AsIII) is more toxic at lower concentrations than the pentavalent form (arsenate, AsV). In E. coli, the proteins encoded by the arsRBC operon are the major arsenic detoxification mechanism. Our previous transcriptional analyses indicate broad changes in metal uptake and regulation upon arsenic exposure. Currently, it is not known how arsenic exposure impacts the cellular distribution of other metals. This study examines the metalloproteome of E. coli strains with and without the arsRBC operon in response to sublethal doses of AsIII and AsV. Size exclusion chromatography coupled with inductively coupled plasma mass spectrometry (SEC-ICPMS) was used to investigate the distribution of five metals (56Fe, 24Mg, 66Zn, 75As, and 63Cu) in proteins and protein complexes under native conditions. Parallel analysis by SEC-UV-Vis spectroscopy monitored the presence of protein cofactors. Together, these data reveal global changes in the metalloproteome, proteome, protein cofactors, and soluble intracellular metal pools in response to arsenic stress in E. coli. This work brings to light one outcome of metal exposure and suggests that metal toxicity on the cellular level arises from direct and indirect effects.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Magnetic structure and properties of the compositionally complex perovskite (Y 0.2 La 0.2 Pr 0.2 Nd 0.2 Tb 0.2 )MnO 3

Large configurational disorder in compositionally complex ceramics can lead to unique functional properties that deviate from traditional rules of alloy mixing. In recent years, compositionally complex oxides (CCOs) have shown intriguing magnetic behavior including long-range order, enhanced magnetic exchange couplings, and mixed phase magnetic structures. This work focuses on how large local spin disorder affects magnetic ordering in a CCO. Specifically, we investigated the A-site alloyed perovskite, (Y 0.2 La 0.2 Pr 0.2 Nd 0.2 Tb 0.2 )MnO 3 , or (5A)MnO 3 , using a combination of bulk magnetometry, synchrotron X-ray diffraction, and temperature-dependent neutron diffraction. The five A-site ions have an average spin and ionic radius nearly equal to that of Nd 3+ ions, which minimizes structural distortions and allows for an understanding of the local spin disorder effects through a direct comparison with NdMnO 3 . Our magnetometry data show that (5A)MnO 3 exhibits two distinct phase transitions associated with the A-site and B-site sublattices, as seen in NdMnO 3 , as well as the presence of domain pinning and exchange bias at low temperature, suggesting a mixed phase magnetic ground state, as seen in other magnetic CCOs. Neutron powder diffraction shows clear long-range antiferromagnetic ordering below 67 K and refines to a Pn'ma' magnetic structure at low temperature, in excellent agreement with the well-studied behavior of NdMnO 3 . The two most notable differences in (5A)MnO 3 magnetism apparent from our data are a slight suppression of the B-site ordering temperature, which is explained by a smaller Mn–O–Mn bond angle in (5A)MnO 3 than NdMnO 3 , and the presence of a magnetic susceptibility transition above the B-site ordering, which could indicate the formation of a cluster glass but requires further study. Finally, this work demonstrates a general method of isolated investigation of size and spin disorder in CCOs and motivates future work using local structure probes to better understand the effects of nanoscale clustering and local spin disorder in magnetic CCOs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1978

Aerodynamic characteristics of a hypersonic research airplane concept having a 70 deg swept double-delta wing at Mach number 0.2

A wind-tunnel of the static longitudinal, lateral and directional stability characteristics of a hypersonic research airplane concept having a 70 deg swept double-delta wing was conducted in the Langley low-turbulence pressure tunnel. The configuration variables included wing planform, tip fins, center fin, and scramjet engine modules. A mach number of 0.2 was investigated over a Reynolds number (based on fuselage length) range of 2,200,000 to 19.75 x 1,000,000 (with a majority of tests at 10.0 x 1,000,000. Tests were conducted through an angle-of-attack range from about -2 deg to 34 deg at angles of sideslip of 0 deg to 5 deg, and at elevon deflection of 0 deg, -5 deg, -10 deg, -15 deg, and -20 deg. The drag coefficient of the integrated scramjet engine appears relatively constant with Reynolds number at the test Mach number of 0.2. Mild pitch-up was exhibited by the models equipped with tip fins. The forward delta, a highly swept forward portion of the wing, was destabilizing. The center fin model has a higher trimmed maximum lift-drag ratio and a wider trim lift and angle-of-attack range than the tip fin model. Both the tip fin models and center fin models exhibited positive dihedral effect and positive directional stability. Roll control was positive for the tip fin model, but yaw due to roll control was unfavorable.

Penland, J. A.↗
DOE OSTI2023

The Dark Energy Survey Year 3 and eBOSS: constraining galaxy intrinsic alignments across luminosity and colour space

ABSTRACT We present direct constraints on galaxy intrinsic alignments (IAs) using the Dark Energy Survey Year 3 (DES Y3), the Extended Baryon Oscillation Spectroscopic Survey (eBOSS), and its precursor, the Baryon Oscillation Spectroscopic Survey (BOSS). Our measurements incorporate photometric red sequence (redMaGiC) galaxies from DES with median redshift z ∼ 0.2–1.0, luminous red galaxies from eBOSS at z ∼ 0.8, and also an SDSS-III BOSS CMASS sample at z ∼ 0.5. We measure two-point IA correlations, which we fit using a model that includes lensing, magnification, and photometric redshift error. Fitting on scales 6 Mpc h−1 < rp < 70 Mpc h−1, we make a detection of IAs in each sample, at 5σ–22σ (assuming a simple one-parameter model for IAs). Using these red samples, we measure the IA–luminosity relation. Our results are statistically consistent with previous results, but offer a significant improvement in constraining power, particularly at low luminosity. With this improved precision, we see detectable dependence on colour between broadly defined red samples. It is likely that a more sophisticated approach than a binary red/blue split, which jointly considers colour and luminosity dependence in the IA signal, will be needed in future. We also compare the various signal components at the best-fitting point in parameter space for each sample, and find that magnification and lensing contribute $\sim 2\!-\!18~{{\ \rm per\ cent}}$ of the total signal. As precision continues to improve, it will certainly be necessary to account for these effects in future direct IA measurements. Finally, we make equivalent measurements on a sample of emission-line galaxies from eBOSS at z ∼ 0.8. We constrain the non-linear alignment amplitude to be $A_1=0.07^{+0.32}_{-0.42}$ (|A1| < 0.78 at 95 per cent CL).

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Three-dimensional reconstruction of implosion stagnation in laser direct drive on OMEGA

Multidimensional effects on hot-spot formation must be considered to better understand the current limits on the performance of direct-drive inertial confinement fusion experiments on OMEGA with cryogenically layered solid deuterium–tritium targets. A comprehensive reconstruction effort has been established at the Laboratory for Laser Energetics to infer hot-spot and shell conditions at stagnation from a large collection of x-ray, neutron, and particle detectors along multiple lines of sight. Several time-gated and time-integrated x-ray imagers are being used to record the shape of the hot-spot plasma. A 3D hot-spot x-ray emission tomography technique has been developed to infer low-mode drive asymmetries from the hot-spot shape. A suite of neutron diagnostics is used to provide measurements of hot-spot flow velocity, ion temperature, and areal density. Here, the information obtained from the x-ray and neutron detectors will be combined into a coherent model of the shape of the hot spot and shell assembly.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1972

Radiant heat transfer between nongray directional surfaces.

Real surface property effects on local and overall heat transfer are studied for a simple system of interacting opaque surfaces. Wavelength, temperature and directional dependence of surface properties is included in the analysis for equal and unequal temperature specularly reflecting surfaces. Tungsten is employed as a representative metal and Roberts' model is used to describe the wavelength and temperature dependence of its optical parameters. The relationships of electromagnetic theory are employed to describe the directional dependence of spectral properties. Numerical results establish that gray direction independent property analysis adequately predicts the general trends of real surface analysis. The results also establish that spectral and temperature dependence of surface properties influences radiant heat transfer to a greater degree than does directional dependence of properties. Property models which adequately account for the nongray character of engineering surfaces while neglecting directional dependence of properties can provide heat transfer results of acceptable engineering accuracy.

Fischer, W. D.↗
NASA NTRS1979

Gust alleviation using direct turbulence measurements

The research reported upon in this paper describes an effective method of gust alleviation using direct measurements of atmospheric turbulence to drive the aircraft control surfaces in a way that attempts to directly counter or cancel those forces and moments produced on the aircraft by gusts. The method yields a feedforward or open loop control law, simple to mechanize and relatively insensitive to changes in flight condition. When applied directly, the resulting control law effectively gust-alleviates in the low frequency phugoid and short period range but has a tendency to amplify structural mode vehicle motions due to the phase lag of the actuators. A method of design based upon the use of a diagonal or Jordan form of the equations of motion enables the designer to avoid this problem of structural mode excitation.

Rynaski, E. G.↗
NASA NTRS1992

Convective and morphological instabilities during crystal growth: Effect of gravity modulation

During directional solidification of a binary alloy at constant velocity in the vertical direction, morphological and convective instabilities may occur due to the temperature and solute gradients associated with the solidification process. The effect of time-periodic modulation (vibration) is studied by considering a vertical gravitational acceleration which is sinusoidal in time. The conditions for the onset of solutal convection are calculated numerically, employing two distinct computational procedures based on Floquet theory. In general, a stable state can be destabilized by modulation and an unstable state can be stabilized. In the limit of high frequency modulation, the method of averaging and multiple-scale asymptotic analysis can be used to simplify the calculations.

Coreill, S. R.↗