On the direct shock wave problem. a modified theory /final report on bodies with spherical nose/
Modification of mathematical approach to general body problem for investigating direct shock wave problem for bodies with spherical nose
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Modification of mathematical approach to general body problem for investigating direct shock wave problem for bodies with spherical nose
To better characterize seismic hazard, particularly, for induced seismicity, there is an increasing interest in methods to estimate moment magnitude (M w ) for small earthquakes. M w is generally preferred over other magnitude types, but, it is difficult to estimate M w for earthquakes with local magnitude (M L ) <3-3.5, using conventional moment tensor (MT) inversion. The 2020 M ww 5.7 Magna, Utah, seismic sequence provides an opportunity to illustrate and evaluate the value of spectral methods for this purpose. Starting with a high-quality seismic catalog of 2103 earthquakes (M L <5.6), we estimate M w using two independent spectral methods—one based on direct waves, yielding M w,direct , and the other based on coda waves, yielding M w,coda . For the direct-wave method, we present a non-parametric (NP) inversion scheme that solves for apparent geometrical spreading, G(R), and site effects (S), similar to other NP procedures that have been used to calibrate regional M L scales. The NP inversion is constrained using M ws derived from MTs for nine events in the Magna sequence. We recover statistically robust and physically reasonable G(R) and S and compute M w,direct for 635 Magna earthquakes down to M L 0.7. For the coda-wave method, we consider two separate calibration schemes involving previous MT solutions and compute M w,coda for 311 earthquakes down to M L 1.0. For 280 of the events that were processed with both methods—M w,direct and M w,coda —are strongly correlated (r = 0.98), with a mean difference of only 0.05. We compare M w,direct and M w,coda with M L and find reasonably good agreement for M L <3.6 with the theoretically predicted relationship of M w =(2/3)M L +C, in which C is a regional constant. Our results imply that seismic network operators can use spectral-based M w estimates to replace M L estimates for events with M L ≥1.0, and possibly smaller. The main requirement is the existence of a small number of MT solutions for calibration purposes.
Tissues rely on supracellular signals to coordinate their cells over a long range. Two such tissuescale cues are calcium waves and patterns of cell-cell alignment or nematic order. During wound healing, for example, calcium waves propagate across a tissue to guide directed cell migration and reepithelialization. Defects in long-range cell-cell alignment, or nematic orientation, can act to localize morphogenetic events in a tissue. Although these two cues have been considered in isolation, we demonstrate a relationship in epithelial tissue between long-range calcium signaling and the cell’s nematic order: The speed of a wound-induced calcium wave depends monotonically on the angle between the wave vector and cell axis, with maximal wave speed occurring perpendicular to the tissue’s orientation. Including anisotropic di↵usive coupling between cells in a canonical reactiondi↵usion model recapitulates our measured calcium wave dynamics. Our model demonstrates how orientation defects can desynchronize information propagation across a tissue. A calcium wave front is bent around nematic defects, therefore cells the same distance from a wound can receive the calcium signal at di↵erent times. Our work elucidates how spatial patterns in global cell alignment can control collective communication via calcium signaling during development, wound healing, and disease.
Hiss is represented by a field distribution function in order to investigate magnetospheric hiss as a spatially and temporally enduring phenomenon. The study takes into account the whistler mode relationships and the linear and spin motion of the satellite. Hiss signals received on September 23, 1983 by the DE-1 electric and magnetic field antennas are analyzed. A wave normal angle of 60 + or - 5 deg with respect to the local geomagnetic field is found near the geomagnetic equator, and wave normal directions from 30-80 deg with respect to the local geomagnetic field are found away from the equator.
We continue to investigate the possibility that interstellar turbulence is caused by nonlinear interactions among shear Alfven waves. Here, we restrict attention to the symmetric case where the oppositely directed waves carry equal energy fluxes. This precludes application to the solar wind in which the outward flux significantly exceeds the ingoing one. All our detailed calculations are carried out for an incompressible magnetized fluid. In incompressible magnetohydrodynamics (MHD), nonlinear interactions only occur between oppositely direct waves. We present a theory for the strong turbulence of shear Alfven waves. It has the following main characteristics. (1) The inertial-stage energy spectrum exhibits a critical balance between linear wave periods and nonlinear turnover timescales. (2) The 'eddies' are elongated in the direction of the field on small spatial scales; the parallel and perpendicular components of the wave vector, k(sub z) and k(perpendicular) are related by k(sub z) approximately equals k(sub perpendicular to)(exp 2/3) L(exp -1/3), where L is the outer scale of the turbulence. (3) The 'one-dimensional' energy spectrum is proportional to k(sub perpendicular)(exp -5/3)-an anisotropic Kolmogorov energy spectrum. Shear Alfvenic turbulence mixes specific entropy as a passive contaminant. This gives rise to an electron density power spectrum whose form mimics the energy spectrum of the turbulence. Radio wave scattering by these electron density fluctuations produces anisotropic scatter-broadened images. Damping by ion-neutral collisions restricts Alfvenic turbulence to highly ionized regions of the interstellar medium.
For scattering calculations involving nonspherical particles such as ice crystals, we show that the transverse wave condition is not applicable to the refracted electromagnetic wave in the context of geometric optics when absorption is involved. Either the TM wave condition (i.e., where the magnetic field of the refracted wave is transverse with respect to the wave direction) or the TE wave condition (i.e., where the electric field is transverse with respect to the propagating direction of the wave) may be assumed for the refracted wave in an absorbing medium to locally satisfy the electromagnetic boundary condition in the ray tracing calculation. The wave mode assumed for the refracted wave affects both the reflection and refraction coefficients. As a result, a nonunique solution for these coefficients is derived from the electromagnetic boundary condition. In this study we have identified the appropriate solution for the Fresnel reflection/refraction coefficients in light scattering calculation based on the ray tracing technique. We present the 3 x 2 refraction or transmission matrix that completely accounts for the inhomogeneity of the refracted wave in an absorbing medium. Using the Fresnel coefficients for an absorbing medium, we derive an asymptotic solution in an analytical format for the scattering properties of a general polyhedral particle. Numerical results are presented for hexagonal plates and columns with both preferred and random orientations. The asymptotic theory can produce reasonable accuracy in the phase function calculations in the infrared window region (wavelengths near 10 micron) if the particle size (in diameter) is on the order of 40 micron or larger. However, since strong absorption is assumed in the computation of the single-scattering albedo in the asymptotic theory, the single scattering albedo does not change with variation of the particle size. As a result, the asymptotic theory can lead to substantial errors in the computation of single-scattering albedo for small and moderate particle sizes. However, from comparison of the asymptotic results with the FDTD solution, it is expected that a convergence between the FDTD results and the asymptotic theory results can be reached when the particle size approaches 200 micron. We show that the phase function at side-scattering and backscattering angles is insensitive to particle shape if the random orientation condition is assumed. However, if preferred orientations are assumed for particles, the phase function has a strong dependence on scattering azimuthal angle. The single-scattering albedo also shows very strong dependence on the inclination angle of incident radiation with respect to the rotating axis for the preferred particle orientations.
The application of synthetic aperture microwave radar imagery to the measurement of ocean wave direction and wavelength is discussed and an airborne experiment conducted in preparation for the SEASAT-A satellite mission is presented. Models for radar backscattering are examined and it is concluded that the Bragg-Rice model, which represents the ocean surface as a combination of periodic surfaces so that the dominant backscatter matches some portion of the wave spectrum, appears most useful. The experiment was conducted with airborne X-band and L-band synthetic aperture radar (SAR) and data was compared with that obtained from a pitch-and-roll buoy and an instrument package mounted on a sea sled. SAR data was converted to wave spectra and it was found to match data from the buoy, while SAR data on wave direction agrees to within two degrees with the buoy and to within one degree with the sea sled sensors. Wave direction data taken by two real aperture radars is also presented and shown to agree with airborne photographs.
The design, fabrication, and evaluation of a single ended 12 GHz down-converter suitable for use in a low cost satellite ground terminal is described. The mixer uses waveguide, coaxial and MIC (microwave integrated circuit) transmission line components. Theoretical and experimental analyses of several microstrip circuit elements are presented including the traveling wave-directional filter, quarter wave-length proximity directional coupler, low pass filter and the quarterwave band stop filter. The optimum performance achieved for the mixer using a packaged diode was 9.4 db conversion loss and a bandwidth of 275 MHz.
During the third intensive observational period of the Surface Wave Dynamics Experiment (SWADE), an aircraft-based experiment was conducted on 5 March 1991 by deploying slow-fall airborne expendable current profilers (AXCPs) and airborne expendable bathythermographs (AXBTs) during a scanning radar altimeter (SRA) flight on the NASA NP-3A research aircraft. As the Gulf Stream (GS) moved into the SWADE domain in late February, maximum upper-layer currents of 1.98 m/s were observed in the core of the baroclinic jet where the vertical current shears were O(10(exp -2)/s). The SRA concurrently measured the sea surface topography, which was transformed into two-dimensional directional wave spectra at 5-6-km intervals along the flight tracks. The wave spectra indicated a local wave field with wavelengths of 40-60 m propagating southward between 120 deg and 180 deg, and a northward-moving swell field from 300 deg to 70 deg associated with significant wave heights of 2-4 m. As the AXCP descended through the upper ocean, the profiler sensed orbital velocity amplitudes of 0.2-0.5 m/s due to low-frequency surface waves. These orbital velocities were isolated by fitting the observed current profiles to the three-layer model based on a monochromatic surface wave, including the steady and current shear terms within each layer. The depth-integrated differences between the observed and modeled velocity profiles were typically less than 3 cm/s. For 17 of the 21 AXCP drop sites, the rms orbital velocity amplitudes, estimated by integrating the wave spectra over direction and frequency, were correlated at a level of 0.61 with those derived from the current profiles. The direction of wave propagation inferred from the AXCP-derived orbital velocities was in the same direction observed by the SRA. These mean wave directions were highly correlated (0.87) and differed only by about 5 deg.
Scanning beam microwave radars were used to measure ocean wave directional spectra from satellites. In principle, surface wave spectral resolution in wave number can be obtained using either short pulse (SP) or dual frequency (DF) techniques; in either case, directional resolution obtains naturally as a consequence of a Bragg-like wave front matching. A four frequency moment characterization of backscatter from the near vertical using physical optics in the high frequency limit was applied to an analysis of the SP and DF measurement techniques. The intrinsic electromagnetic modulation spectrum was to the first order in wave steepness proportional to the large wave directional slope spectrum. Harmonic distortion was small and was a minimum near 10 deg incidence. NonGaussian wave statistics can have an effect comparable to that in the second order of scattering from a normally distributed sea surface. The SP technique is superior to the DF technique in terms of measurement signal to noise ratio and contrast ratio.
The thirty-year non-stationary historical trends in the wave energy climate for United States coastal waters between 1980 and 2009 are investigated using spectral partitioned wave data generated from a WaveWatch III® (version 5.05) hindcast. In addition to historical trends in the omni-directional wave power, frequency and directionally resolved wave power, frequency and directional spreading, and seasonal variability, are examined for the first time, including their geographical distribution. These historical wave energy climate trends are linked to changes to the dominant wave systems and commensurate trends in the historical wind climate. Total wave power trends are consistent with other studies, but the present study identifies regions, and specific frequency and direction bands, where significant wave energy climate changes have occurred. For some regions, changes to wave climate parameters exceeded one-percent annually, more than thirty-percent over the study period. In conclusion, non-stationary trends of this magnitude have significant implications for ocean and coastal engineering projects designed assuming wave climates are stationary and warran
An extensive sonic boom propagation database with low- to normal-intensity booms (overpressures of 0.08 lbf/sq ft to 2.20 lbf/sq ft) was collected for propagation code validation, and initial results and flight research techniques are presented. Several arrays of microphones were used, including a 10 m tall tower to measure shock wave directionality and the effect of height above ground on acoustic level. A sailplane was employed to measure sonic booms above and within the atmospheric turbulent boundary layer, and the sailplane was positioned to intercept the shock waves between the supersonic airplane and the ground sensors. Sailplane and ground-level sonic boom recordings were used to generate atmospheric turbulence filter functions showing excellent agreement with ground measurements. The sonic boom prediction software PCBoom4 was employed as a preflight planning tool using preflight weather data. The measured data of shock wave directionality, arrival time, and overpressure gave excellent agreement with the PCBoom4-calculated results using the measured aircraft and atmospheric data as inputs. C-weighted acoustic levels generally decreased with increasing height above the ground. A-weighted and perceived levels usually were at a minimum for a height where the elevated microphone pressure rise time history was the straightest, which is a result of incident and ground-reflected shock waves interacting.
The 36-gigahertz surface contour radar and the airborne oceanographic lidar were used in the SIR-B underflight mission off the coast of Chile in October 1984. The two systems and some of their wave-measurement capabilities are described. The surface contour radar can determine the directional wave spectrum and eliminate the 180-degree ambiguity in wave propagation direction that is inherent in some other techniques such as stereophotography and the radar ocean wave spectrometer. The Airborne Oceanographic Lidar can acquire profile data on the waves and produce a spectrum that is close to the nondirectional ocean-wave spectrum for ground tracks parallel to the wave propagation direction.
The SCR was asked to participate in the Frontal Air-Sea Interaction Experiment (FASINEX) to provide directional wave spectra. The NASA P-3 carrying the SCR, the Radar Ocean Wave Spectrometer, and the Airborne Oceanographic Lidar was one of five aircrafts and two ocean research ships participating in this coordinated study of the air sea interaction in the vicinity of a sea surface temperature front near 28 deg N, 70 deg W. Analysis of data from the February 1986 experiment is still ongoing, but results already submitted for publication strengthen the hypothesis that off-nadir radar backscatter is closely correlated to wind stress. The SCR provided valuable information on the directional wave spectrum and its spatial variation.
SUMMARY Robustness of source parameter estimates is a fundamental issue in understanding the relationships between small and large events; however, it is difficult to assess how much of the variability of the source parameters can be attributed to the physical source characteristics or to the uncertainties of the methods and data used to estimate the values. In this study, we apply the coda method by Mayeda et al. using the coda calibration tool (CCT), a freely available Java-based code (https://github.com/LLNL/coda-calibration-tool) to obtain a regional calibration for Central Italy for estimating stable source parameters. We demonstrate the power of the coda technique in this region and show that it provides the same robustness in source parameter estimation as a data-driven methodology [generalized inversion technique (GIT)], but with much fewer calibration events and stations. The Central Italy region is ideal for both GIT and coda approaches as it is characterized by high-quality data, including recent well-recorded seismic sequences such as L'Aquila (2009) and Amatrice–Norcia–Visso (2016–2017). This allows us to apply data-driven methods such as GIT and coda-based methods that require few, but high-quality data. The data set for GIT analysis includes ∼5000 earthquakes and more than 600 stations, while for coda analysis we used a small subset of 39 events spanning 3.5 < Mw < 6.33 and 14 well-distributed broad-band stations. For the common calibration events, as well as an additional 247 events (∼1.7 < Mw < ∼5.0) not used in either calibration, we find excellent agreement between GIT-derived and CCT-derived source spectra. This confirms the ability of the coda approach to obtain stable source parameters even with few calibration events and stations. Even reducing the coda calibration data set by 75 per cent, we found no appreciable degradation in performance. This validation of the coda calibration approach over a broad range of event size demonstrates that this procedure, once extended to other regions, represents a powerful tool for future routine applications to homogeneously evaluate robust source parameters on a national scale. Furthermore, the coda calibration procedure can homogenize the Mw estimates for small and large events without the necessity of introducing any conversion scale between narrow-band measures such as local magnitude (ML) and Mw, which has been shown to introduce significant bias.
A major achievement of the F-24 experiment on OGO 6 was a verification of the theory of the polarization of proton whistlers. As predicted, the electron whistler was found to be right-hand polarized and the proton whistler left hand polarized. The transition from right- to left-hand polarization was found to occur very rapidly. Thus it appears that the experimental technique may allow great accuracy in the measurement of the cross-over frequency, a frequency that provides information on the ionic composition of the ionosphere.
The properties of directional discontinuities occurring in selected periods of interplanetary magnetic field data are investigated. Microscale fluctuations in these selected periods have previously been identified as being predominantly Alfvenic on time scales ranging from 5 min to a few hours. We argue that the majority of directional discontinuities in such periods are rotational and outwardly propagating.
A preliminary assessment has been made of the capability of the Seasat synthetic aperture radar to detect ocean waves. Comparison with surface and aircraft measurements from five passes of the satellite over the Gulf of Alaska indicates agreement to within about 15 percent in wavelength and about 25 deg in wave direction. These results apply to waves 100 to 250 meters in length, propagating in a direction predominantly across the satellite track, in sea states with significant wave height in a range of 2 to 3.5 meters.