Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “HARMONICS”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 415 records · Page 23

Real-Time Observation of Molecular Spinning with Angular High-Harmonic Spectroscopy

We demonstrate an angular high-harmonic spectroscopy method to probe the spinning dynamics of a molecular rotation wave packet in real time. With the excitation of two time-delayed, polarization-skewed pump pulses, the molecular ensemble is impulsively kicked to rotate unidirectionally, which is subsequently irradiated by another delayed probe pulse for high-order harmonic generation (HHG). The spatiotemporal evolution of the molecular rotation wave packet is visualized from the time-dependent angular distributions of the HHG yields and frequency shift measured at various polarization directions and time delays of the probe pulse. Here, the observed frequency shift in HHG is demonstrated to arise from the nonadiabatic effect induced by molecular spinning. Different from the previous spectroscopic and Coulomb explosion imaging techniques, the angular high-harmonic spectroscopy method can reveal additionally the electronic structure and multiple orbitals of the sampled molecule. All the experimental findings are well reproduced by numerical simulations. Further extension of this method would provide a powerful tool for probing complex polyatomic molecules with HHG spectroscopy.

74 ATOMIC AND MOLECULAR PHYSICS↗

Phonon second harmonic generation in NaBr studied by inelastic neutron scattering and computer simulation

The phenomenon of second harmonic generation (SHG) was found for phonons in anharmonic NaBr by inelastic neutron scattering. The temperature dependence of this phonon SHG was measured from 300 K to 650 K. At 300 K the second harmonic (SH) is seen as a high-energy branch around 33 meV, nearly independent of $\overrightarrow{Q}$. The temperature effective potential (TDEP) method and classical molecular dynamics (MD) simulation with machine learning interatomic potential were able to reproduce the SH, and showed that SHG occurs with the flat transverse optical (TO) phonon branch. A classical model of a nonlinear medium explains the intensity and lifetime of the SH, compared to those of the TO modes. Also successful was a quantum model based on the Heisenberg-Langevin equation for interacting phonons coupled to a thermal bath, which also predicts a spectral distribution of the SH. In conclusion, the measured temperature dependence of the intensity of the second harmonic showed that it follows the Planck distribution of a one-phonon quasiparticle, and not two TO phonons.

36 MATERIALS SCIENCE↗

A Multi-Harmonic System Identification Method for Internal Circuit Element Monitoring

Many critical infrastructures depend on the reliability of electronic circuits, whose health depends on the values of internal circuit elements that degrade over time. It is therefore important to estimate the values of internal circuit elements from external measurements and monitor them for changes. The challenge to doing so is that, typically, the internal voltages and currents are not accessible for measurement. Prior work on internal circuit element monitoring uses data obtained from sensors placed inside the circuit or requires additional circuitry to be added to the given system, both of which are undesirable. We propose a new multi-harmonic frequency-domain based system identification method that is non-intrusive. It exploits the latent non-idealities already present in the system, specifically harmonics in the measured input and output signals. We show how sensitivity analysis can be used to both assess the accuracy of the method as well as to optimize the choice of harmonics to use. We use as a motivation and illustrative example the problem of determining the equivalent series resistance and capacitance in a class of dc-link capacitance circuits in Adjustable Speed Drives. We assess the performance of this method using simulations, and establish its validity by experimental results.

Deshpande, Ankit Vivek↗

Harmonic analysis for the characterization and correction of geometric distortion in MRI

Purpose: Magnetic resonance imaging (MRI) is gaining widespread use in radiation therapy planning, patient setup verification, and real-time guidance of radiation delivery. Successful implementation of these technologies relies on the development of simple and efficient methods to characterize and monitor the geometric distortions arising due to system imperfections and gradient nonlinearities. To this end, the authors present the theory and validation of a novel harmonic approach to the quantification of system-related distortions in MRI. Methods: The theory of spatial encoding in MRI is applied to demonstrate that the 3D distortion vector field (DVF) is given by the solution of a second-order boundary value problem (BVP). This BVP is comprised of Laplace’s equation and a limited measurement of the distortion on the boundary of a specified region of interest (ROI). An analytical series expansion solving this BVP within a spherical ROI is obtained, and a statistical uncertainty analysis is performed to determine how random errors in the boundary measurements propagate to the ROI interior. This series expansion is then evaluated to obtain volumetric DVF mappings that are compared to reference data obtained on a 3 T full-body scanner. This validation is performed within two spheres of 20 cm diameter (one centered at the scanner origin and the other offset +3 cm along each of the transverse directions). Initially, a high-order mapping requiring measurements at 5810 boundary points is used. Then, after exploring the impact of the boundary sampling density and the effect of series truncation, a reduced-order mapping requiring measurements at 302 boundary points is evaluated. Results: The volumetric DVF mappings obtained from the harmonic analysis are in good agreement with the reference data. Following distortion correction using the high-order mapping, the authors estimate a reduction in the mean distortion magnitude from 0.86 to 0.42 mm and from 0.93 to 0.39 mm within the central and offset ROIs, respectively. In addition, the fraction of points with a distortion magnitude greater than 1 mm is reduced from 35.6% to 2.8% and from 40.4% to 1.5%, respectively. Similarly, following correction using the reduced-order mapping, the mean distortion magnitude reduces to 0.45–0.42 mm within the central and offset ROIs, and the fraction of points with a distortion magnitude greater than 1 mm is reduced to 2.8% and 1.5%, respectively. Conclusions: A novel harmonic approach to the characterization of system-related distortions in MRI is presented. This method permits a complete and accurate mapping of the DVF within a specified ROI using a limited measurement of the distortion on the ROI boundary. This technique eliminates the requirement to exhaustively sample the DVF at a dense 3D array of points, thereby permitting the design of simple, inexpensive phantoms that may incorporate additional modules for auxiliary quality assurance objectives.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Shallow-etched thin-film lithium niobate waveguides for highly-efficient second-harmonic generation

High-fidelity periodic poling over long lengths is required for robust, quasi-phase-matched second-harmonic generation using the fundamental, quasi-TE polarized waveguide modes in a thin-film lithium niobate (TFLN) waveguide. Here, a shallow-etched ridge waveguide is fabricated in x-cut magnesium oxide doped TFLN and is poled accurately over 5 mm. The high fidelity of the poling is demonstrated over long lengths using a non-destructive technique of confocal scanning second-harmonic microscopy. We report a second-harmonic conversion efficiency of up to 939 %.W −1 (length-normalized conversion efficiency 3757 %.W −1 .cm −2 ), measured at telecommunications wavelengths. The device demonstrates a narrow spectral linewidth (1 nm) and can be tuned precisely with a tuning characteristic of 0.1 nm/°C, over at least 40 °C without measurable loss of efficiency.

Zhao, Jie (ORCID:0000000306230125)↗

Bright, single helicity, high harmonics driven by mid-infrared bicircular laser fields

High-harmonic generation (HHG) is a unique tabletop light source with femtosecond-to-attosecond pulse duration and tailorable polarization and beam shape. Here, we use counter-rotating femtosecond laser pulses of 0.8 µm and 2.0 μm to extend the photon energy range of circularly polarized high-harmonics and also generate single-helicity HHG spectra. By driving HHG in helium, we produce circularly polarized soft x-ray harmonics beyond 170 eV—the highest photon energy of circularly polarized HHG achieved to date. In an Ar medium, dense spectra at photon energies well beyond the Cooper minimum are generated, with regions composed of a single helicity—consistent with the generation of a train of circularly polarized attosecond pulses. Finally, we show theoretically that circularly polarized HHG photon energies can extend beyond the carbon K edge, extending the range of molecular and materials systems that can be accessed using dynamic HHG chiral spectro-microscopies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Control of second-harmonic generation in all-dielectric intersubband metasurfaces by controlling the polarity of χ (2)

All-dielectric metasurfaces have recently led to a paradigm shift in nonlinear optics as they allow for circumventing the phase matching constraints of bulk crystals and offer high nonlinear conversion efficiencies when normalized by the light-matter interaction volume. Unlike bulk crystals, in all-dielectric metasurfaces nonlinear conversion efficiencies primarily rely on the material nonlinearity, field enhancements, and the modal overlaps, therefore most efforts to date have only focused on utilizing these degrees of freedom. In this work, we demonstrate that for second-harmonic generation in all-dielectric metasurfaces, an additional degree of freedom is the control of the polarity of the nonlinear susceptibility. We demonstrate that semiconductor heterostructures that support resonant nonlinearities based on quantum-engineered intersubband transitions provide this new degree of freedom. We can flip and control the polarity of the nonlinear susceptibility of the dielectric medium along the growth direction and couple it to the Mie-type photonic modes. Here we demonstrate that engineering the χ (2) polarity in the meta-atom enables the control of the second-harmonic radiation pattern and conversion efficiency. Our results therefore open a new direction for engineering and optimizing second-harmonic generation using all-dielectric intersubband nonlinear metasurfaces.

42 ENGINEERING↗

Enhancement of harmonic generation by an intense driving laser with high-order waveguide modes in a high-pressure gas-filled hollow waveguide

High-order harmonics have been widely used as reliable tabletop coherent radiation sources recently, but their applications have often been limited by the available pulse energy. Here, we report that by using an overdriven intense laser in a long waveguide with high-pressure gas, phase matching can be achieved in three distinct “regimes”. In the third regime, favorable phase matching is achieved at near-axis positions to enhance harmonic yields. Our results are supported by a full theoretical analysis, and we demonstrate that coupling of the driving laser with the high-order waveguide modes (instead of the fundamental mode used in most prior experiments) is responsible for achieving phase matching. Furthermore, we establish that this phase matching (and harmonic enhancement) is robust, and a scaling relation is derived for the necessary waveguide and gas parameters, allowing our predictions to be tested immediately in any laboratory today.

Li, Baochang [Nanjing University of Science and Te↗

High-speed measurement of rotational anisotropy nonlinear optical harmonic generation using position-sensitive detection

We present a method of performing high-speed rotational anisotropy nonlinear optical harmonic generation experiments at rotational frequencies of several hertz by projecting the harmonic light reflected at different angles from a sample onto a stationary position-sensitive detector. The high rotational speed of the technique, 10 3 to 10 4 times larger than existing methods, permits precise measurements of the crystallographic and electronic symmetries of samples by averaging over low frequency laser-power, beam-pointing, and pulse-width fluctuations. As a result, we demonstrate the sensitivity of our technique by resolving the bulk fourfold rotational symmetry of GaAs about its [001] axis using second-harmonic generation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Single-shot local measurement of terahertz correlated second harmonic generation in laser air plasma filaments

We present a single-shot detection method of terahertz correlated second harmonic generation in plasma-based sources by directly mixing an optical probe into femtosecond laser-induced plasma filaments in air. Furthermore, the single-shot second harmonic trace is obtained by measuring a second harmonic generation on a conventional CCD with a spatiotemporally distorted probe beam. The system shows a spectrometer resolution of 22 fs/pixel on the CCD and a true resolution on the order of the probe pulse duration. With considerable THz peak electric field strength, this formalism can open the door to single-shot THz detection without bandwidth limitations.

47 OTHER INSTRUMENTATION↗

Symmetric second-harmonic generation in sub-wavelength periodically poled thin film lithium niobate

Second-harmonic generation (SHG) extensively employs periodically poled nonlinear crystals through forward quasi-phase-matching to achieve efficient frequency conversion. As poling periods approach sub-micrometers, backward quasi-phase-matching has also been demonstrated, albeit by utilizing pulsed laser drives. The realization of symmetric second-harmonic generation, characterized by counterpropagating pumps, however, has remained elusive despite theoretical predictions. The main challenge lies in achieving strong nonlinear coupling with the poling period below half the wavelength of the second-harmonic light. The recent emergence of high-quality ferroelectric lithium niobate thin films provides an opportunity for achieving precise domain control at submicron dimensions. In this paper, we demonstrate reliable control of ferroelectric domains in a thin film lithium niobate waveguide with a poling period down to 370 nm, thereby realizing highly efficient continuous-wave pumped symmetric SHG. This demonstration not only validates the feasibility of achieving subwavelength periodic poling on waveguides but could also enable submicron ferrolectric domain structures to be leveraged in integrated photonics and nonlinear optics research.

Optics↗

The multi-faceted inverted harmonic oscillator: Chaos and complexity

The harmonic oscillator is the paragon of physical models; conceptually and computationally simple, yet rich enough to teach us about physics on scales that span classical mechanics to quantum field theory. This multifaceted nature extends also to its inverted counterpart, in which the oscillator frequency is analytically continued to pure imaginary values. In this article we probe the inverted harmonic oscillator (IHO) with recently developed quantum chaos diagnostics such as the out-of-time-order correlator (OTOC) and the circuit complexity. In particular, we study the OTOC for the displacement operator of the IHO with and without a non-Gaussian cubic perturbation to explore genuine and quasi scrambling respectively. In addition, we compute the full quantum Lyapunov spectrum for the inverted oscillator, finding a paired structure among the Lyapunov exponents. We also use the Heisenberg group to compute the complexity for the time evolved displacement operator, which displays chaotic behaviour. Finally, we extended our analysis to N-inverted harmonic oscillators to study the behaviour of complexity at the different timescales encoded in dissipation, scrambling and asymptotic regimes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A harmonized protocol to assess the single-cell performance of proton exchange membrane water electrolyzers

The harmonization of testing protocols for proton exchange membrane (PEM) electrolyzers is essential for ensuring accurate and reliable performance assessments and accelerating the development of hydrogen production technologies. This protocol provides a structured approach to PEM electrolyzer setup and testing, incorporating key considerations for test station design and single-cell characterization techniques. Polarization curves and electrochemical impedance spectroscopy (EIS) are detailed, along with best practices from academic and industry research groups to enhance data accuracy and comparability. By addressing material variability and harmonizing testing methodologies, this framework enables more precise evaluations of membrane electrode assemblies and electrolyzer components. Harmonized protocols not only streamline development efforts but also foster collaboration across institutions, ultimately supporting the commercialization of hydrogen solutions through improved stack efficiency and durability.

08 HYDROGEN↗

Nonlinear Effects in Three-minute Oscillations of the Solar Chromosphere. I. An Analytical Nonlinear Solution and Detection of the Second Harmonic

The vertical propagation of nonlinear acoustic waves in an isothermal atmosphere is considered. A new analytical solution that describes a finite-amplitude wave of an arbitrary wavelength is obtained. Although the short- and long-wavelength limits were previously considered separately, the new solution describes both limiting cases within a common framework and provides a straightforward way of interpolating between the two limits. Physical features of the nonlinear waves in the chromosphere are described, including the dispersive nature of low-frequency waves, the steepening of the wave profile, and the influence of the gravitational field on wavefront breaking and shock formation. The analytical results suggest that observations of three-minute oscillations in the solar chromosphere may reveal the basic nonlinear effect of oscillations with combination frequencies, superposed on the normal oscillations of the system. Explicit expressions for a second-harmonic signal and the ratio of its amplitude to the fundamental harmonic amplitude are derived. Observational evidence of the second harmonic, obtained with the Fast Imaging Solar Spectrograph, installed at the 1.6 m New Solar Telescope of the Big Bear Observatory, is presented. The presented data are based on the time variations of velocity determined from the Na i D{sub 2} and H α lines.

79 ASTRONOMY AND ASTROPHYSICS↗

HarDWR - Harmonized Water Rights Records

A dataset within the Harmonized Database of Western U.S. Water Rights (HarDWR). For a detailed description of the database, please see the meta-record v2.0. Changelog v2.0 - Recalculated based on data sourced from WestDAAT - Changed using a Site ID column to identify unique records to using aa combination of Site ID and Allocation ID - Removed the Water Management Area (WMA) column from the harmonized records. The replacement is a separate file which stores the relationship between allocations and WMAs. This allows for allocations to contribute to water right amounts to multiple WMAs during the subsequent cumulative process. - Added a column describing a water rights legal status - Added "Unspecified" was a water source category - Added an acre-foot (AF) column - Added a column for the classification of the right's owner v1.02 - Added a .RData file to the dataset as a convenience for anyone exploring our code. This is an internal file, and the one referenced in analysis scripts as the data objects are already in R data objects. v1.01 - Updated the names of each file with an ID number less than 3 digits to include leading 0s v1.0 - Initial public release Description Here we present an updated database of Western U.S. water right records. This database provides consistent unique identifiers for each water right record, and a consistent categorization scheme that puts each water right record into one of seven broad use categories. These data were instrumental in conducting a study of the multi-sector dynamics of inter-sectoral water allocation changes though water markets (Grogan et al., *in review*). Specifically, the data were formatted for use as input to a process-based hydrologic model, Water Balance Model (WBM), with a water rights module (Grogan et al., *in review*). While this specific study motivated the development of the database presented here, water management in the U.S. West is a rich area of study (e.g., Anderson and Woosly, 2005; Tidwell, 2014; Null and Prudencio, 2016; Carney et al., 2021) so releasing this database publicly with documentation and usage notes will enable other researchers to do further work on water management in the U.S. West. We produced the water rights database presented here in four main steps: (1) data collection, (2) data quality control, (3) data harmonization, and (4) generation of cumulative water rights curves. Each of steps (1)-(3) had to be completed in order to produce (4), the final product that was used in the modeling exercise in Grogan et al. (*in review*). All data in each step is associated with a spatial unit called a Water Management Area (WMA), which is the unit of water right administration utilized by the state in which the right came from. Steps (2) and (3) required use to make assumptions and interpretation, and to remove records from the raw data collection. We describe each of these assumptions and interpretations below so that other researchers can choose to implement alternative assumptions an interpretation as fits their research aims. Motivation for Changing Data Sources The most significant change has been a switch from collecting the raw water rights directly from each state to using the water rights records presented in WestDAAT, a product of the Water Data Exchange (WaDE) Program under the Western States Water Council (WSWC). One of the main reasons for this is that each state of interest is a member of the WSWC, meaning that WaDE is partially funded by these states, as well as many universities. As WestDAAT is also a database with consistent categorization, it has allowed us to spend less time on data collection and quality control and more time on answering research questions. This has included records from water right sources we had previously not known about when creating v1.0 of this database. The only major downside to utilizing the WestDAAT records as our raw data is that further updates are tied to when WestDAAT is updated, as some states update their public water right records daily. However, as our focus is on cumulative water amounts at the regional scale, it is unlikely most records updates would have a significant effect on our results. The structure of WestDAAT led to several important changes to how HarWR is formatted. The most significant change is that WaDE has calculated a field known as `SiteUUID`, which is a unique identifier for the Point of Diversion (POD), or where the water is drawn from. This separate from `AllocationNativeID`, which is the identifier for the allocation of water, or the amount of water associated with the water right. It should be noted that it is possible for a single site to have multiple allocations associated with it and for an allocation to be able to be extracted from multiple sites. The site-allocation structure has allowed us to adapt a more consistent, and hopefully more realistic, approach in organizing the water right records than we had with HarDWR v1.0. This was incredibly helpful as the raw data from many states had multiple water uses within a single field within a single row of their raw data, and it was not always clear if the first water use was the most important, or simply first alphabetically. WestDAAT has already addressed this data quality issue. Furthermore, with v1.0, when there were multiple records with the same water right ID, we selected the largest volume or flow amount and disregarded the rest. As WestDAAT was already a common structure for disparate data formats, we were better able to identify sites with multiple allocations and, perhaps more importantly, allocations with multiple sites. This is particularly helpful when an allocation has sites which cross WMA boundaries, instead of just assigning the full water amount to a single WMA we are now able to divide the amount of water between the number of relevant WMAs. As it is now possible to identify allocations with water used in multiple WMAs, it is no longer practical to store this information within a single column. Instead the stAllocationToWMATab.csv file was created, which is an allocation by WMA matrix containing the percent Place of Use area overlap with each WMA. We then use this percentage to divide the allocation's flow amount between the given WMAs during the cumulation process to hopefully provide more realistic totals of water use in each area. However, not every state provides areas of water use, so like HarDWR v1.0, a hierarchical decision tree was used to assign each allocation to a WMA. First, if a WMA could be identified based on the allocation ID, then that WMA was used; typically, when available, this applied to the entire state and no further steps were needed. Second was the spatial analysis of Place of Use to WMAs. Third was a spatial analysis of the POD locations to WMAs, with the assumption that allocation's POD is within the WMA it should belong to; if an allocation still had multiple WMAs based on its POD locations, then the allocation's flow amount would be divided equally between all WMAs. The fourth, and final, process was to include water allocations which spatially fell outside of the state WMA boundaries. This could be due to several reasons, such as coordinate errors / imprecision in the POD location, imprecision in the WMA boundaries, or rights attached with features, such as a reservoir, which crosses state boundaries. To include these records, we decided for any POD which was within one kilometer of the state's edge would be assigned to the nearest WMA. Other Changes WestDAAT has Allowed In addition to a more nuanced and consistent method of assigning water right's data to WMAs, there are other benefits gained from using the WestDAAT dataset. Among those is a consistent categorization of a water right's legal status. In HarDWR v1.0, legal status was effectively ignored, which led to many valid concerns about the quality of the database related to the amounts of water the rights allowed to be claimed. The main issue was that rights with legal status' such as "application withdrawn", "non-active", or "cancelled" were included within HarDWR v1.0. These, and other water rights status' which were deemed to not be in use have been removed from this version of the database. Another major change has been the addition of the "unspecified water source category. This is water that can come from either surface water or groundwater, or the source of which is unknown. The addition of this source category brings the total number of categories to three. Due to reviewer feedback, we decided to add the acre-foot (AF) column so that the data may be more applicable to a wider audience. We added the ownerClassification column so that the data may be more applicable to a wider audience. File Descriptions The dataset is a series of various files organized by state sub-directories. In addition, each file begins with the state's name, in case the file is separate from its sub-directory for some reason. After the state name is the text which describes the contents of the file. Here is each file described in detail. Note that st is a placeholder for the state's name. stFullRecords_HarmonizedRights.csv: A file of the complete water records for each state. The column headers for each of this type of file are: state - The name of the state to which the allocations belong to. FIPS - The two digit numeric state ID code. siteID - The site location ID for POD locations. A site may have multiple allocations, which are the actual amount of water which can be drawn. In a simplified hypothetical, a farm stead may have an allocation for "irrigation" and an allocation for "domestic" water use, but the water is drawn from the same pumping equipment. It should be noted that many of the site ID appear to have been added by WaDE, and therefore may not be recognized by a given state's water rights database. allocationID - The allocation ID for the water right. For most states this is the water right ID, and what is recommended to use should a right be looked up on a given state's water rights database. The water amounts associated with these IDs tend to be finer scaled than those associated with siteID. It should be noted that some allocations may be extracted from multiple sites, particularly for larger Places of Use. ownerClassification - A classification of the types of owners for water rights. The most common is `Private` which incorporates a wide range of entities. Several classifications would be grouped into a government category, most of which are for the U.S. Federal Government. These allocations could be listed as "Federal", "United States of America", or as the names of any number of federal agencies. The last major grouping of entities is for "Native American"s. priorityDate - The date we use as the water right priority date for our modeling analysis. This is the legal priority date when it is available. However, for some rights, specifically from California and New Mexico, we used a pseudo priority date (e.g. well completion date or start of well drilling date) when a legal priority date was not available. The most questionable dates come from New Mexico, where the only date associated with certain water right records was the date the allocation was recorded in the database. As the allocation record creation tended to be within a few months of the filing of the application of the water right, from manually double checking the water rights, and our analysis focuses on aggregating water rights on the timescale of years, we determined it was acceptable to use such dates to include as many records as possible. primaryBeneficialUse - From the numerous state water use categories, WaDE categorized them into 21 categories WestDAAT. This column is the original WaDE category for the primary water use at the PoD site. allocationBeneficialUse - From the numerous state water use categories, WaDE categorized them into 21 categories for WestDAAT. This column is the original WaDE category

Economics↗

The physical librations of the moon, including higher harmonic effects

The equations of the physical libration of the moon are developed using a representation of the earth-moon orbit as a Kepler ellipse referred to the lunar equator and expanding the lunar potential in terms of these Kepler elements. The Improved Lunar Ephemeris is used to calculate solar perturbations, and a linear integration of all effects arising from lunar gravitational harmonics through the fourth degree is performed. Aside from unobservable constant offsets of the principal axes, the main effects of the higher harmonics on longitude are: 10-sec six-yearly (argument omega), 1.2-sec three-yearly, 0.5-sec annual, and 0.1-sec monthly; on pole direction they are on the order of 0.5-sec six-yearly and 1.0-sec monthly. The higher harmonics must hence be taken into account in analyzing ranging data of 10 cm accuracy.

Kaula, W. M.↗

Type III solar radio bursts and the fundamental-harmonic hypothesis

The observational evidence is reviewed for the occurrence of type III solar radio bursts in pairs with frequency ratio two to one. We show that the observations can be explained under the hypothesis that there is a tendency for a type III burst to be followed by a second burst within approximately one second. This explanation leads to fewer difficulties than the hypothesis that type III bursts occur in pairs, one member being emitted at the fundamental of the local coronal plasma frequency, the other at its second harmonic. We conclude that in general, type III bursts are emitted at the second harmonic of the plasma frequency and that type III theories should account for this and only under very special circumstances (which are rare) for the emission at the fundamental and the second harmonic.

Rosenberg, H.↗

Disjoint design spaces in the optimization of harmonically excited structures

The paper deals with a method of optimizing harmonically or dynamically excited structures which removes the frequency constraint (that specifies that the structure's first natural frequency of vibration must be greater than the excitation frequency), replaces the displacement constraint by an inequality constraint on the allowable stress and applies finite element approximations to the continuous one-dimensional structures. When the problem is posed in this manner, the feasible design space is disconnected or 'disjoint'. An attempt is made to explain this disjointness by studying the optimal design of a thin-walled cantilevered rod subjected to steady, simple harmonic torsional excitation. The finite element method is applied to the optimization of a harmonically excited structure with an arbitrary number of design variables, with the disjointness of the design space, a complicating factor.

Johnson, E. H.↗