Estimating the propagation of both reported and undocumented COVID-19 cases in Spain: a panel data frontier approximation of epidemiological models.

We use a stochastic frontier analysis (SFA) approach to model the propagation of the COVID-19 epidemic across geographical areas. The proposed models permit reported and undocumented cases to be estimated, which is important as case counts are overwhelmingly believed to be undercounted. The models can be estimated using only epidemic-type data but are flexible enough to permit these reporting rates to vary across geographical cross-section units of observation. We provide an empirical application of our models to Spanish data corresponding to the initial months of the original outbreak of the virus in early 2020. We find remarkable rates of under-reporting that might explain why the Spanish Government took its time to implement strict mitigation strategies. We also provide insights into the effectiveness of the national and regional lockdown measures and the influence of socio-economic factors in the propagation of the virus.

Near-field acoustical holography and acoustic power analysis of a simulated, highly heated supersonic jet.

Although near-field acoustical holography (NAH) and acoustic intensity analysis have previously been used to investigate the apparent jet noise sources produced by military aircraft, explicit connections to supersonic jet characteristics cannot be made due to a lack of information about the exhaust plume. To begin to bridge this gap and better understand the source information yielded by NAH, the current study instead applies NAH to a virtual measurement of the near-field pressures of a highly heated laboratory-scale supersonic jet generated by large-eddy simulation (LES). The holographic reconstructions of the pressure, particle velocity, and acoustic intensity are found to match the LES-generated acoustic field well and are used to calculate the acoustic power of the jet. The jet's calculated overall acoustic power is compared to the free-stream mechanical power, resulting in an acoustic efficiency of 1.5%. Ray-tracing of the acoustic intensity to the jet centerline generates an axial distribution of the acoustic power origin, showing that almost all the power originates from the supersonic portion of the flow and with the distribution peak upstream of the potential core tip. Holographic reconstruction of the pressures along the nozzle lipline captures the general spectral shape of the LES-generated pressures, though it underestimates the amplitude.

Introduction to the special issue on supersonic jet noise.

This editorial's goals are (1) to highlight a few key developments in supersonic jet and launch vehicle noise research over the past several decades while describing some of the critical modern requirements facing government and industry organizations and (2) to summarize the contributions of the articles in this Supersonic Jet Noise special issue in the context of these developments and requirements.

Translating jet noise measurements to near-field level maps with nearest neighbor bilinear smoothing interpolation.

U.S. Department of Defense hearing conservation and noise limits standards require the definition of safe areas around all objects that emit noise and suggest various methods for characterizing these levels. The protection documents do not describe methods for reducing discrete measurement points into level fields to map safe and hazardous noise areas. For maintainers of high-powered jet aircraft, the suggested 85 dBA level contours that delineate the border between safe and hazardous regions occur at distances that far exceed normal operation positions. Conversion of discrete measurements to modeled levels defined over the entire ground personnel operational area in the aircraft vicinity is required to ensure sufficient protection. Present research offers a method to build a coarse map of grid points with nearest neighbor approximations, and then refines this using bi-linear smoothing. This nearest neighbor bi-linear smoothing approach provides predictions that are sufficiently accurate in cross-validation comparisons to the near-field locations and is the preferred method for the creation of hearing conservation contour level maps.

Somatic cell counts, reproduction indicators, and technical efficiency in milk production: A stochastic frontier analysis for Spanish dairy farms.

Health and reproductive conditions affect milk yields in dairy cows and may lead to differences in technical efficiency across farms. To investigate this, we created a novel panel data set of 197 dairy farms in northern Spain observed over the period 2006-2014 by combining information from 2 different sources and including data on production variables, somatic cell count, and reproduction indicators, as well as a genetic index. We used these data to estimate a stochastic production frontier where the somatic cell count, age at first calving, and calving interval are included as determinants of technical efficiency. Higher somatic cell count, greater age at first calving, and longer calving intervals were found to decrease technical efficiency, translating into significant losses in profits which we quantify through a simulation exercise. We also quantified the effect of genetic selection on profits, taking into account not only its direct effect on productivity but also its indirect effect through reduced technical efficiency due to the effect of genetic selection on the health and reproduction variables.

Characterizing distinct components of tactical aircraft noise sources.

Noise from a tactical aircraft can impact operations due to concerns regarding military personnel noise exposure and community annoyance and disturbance. The efficacy of mission planning can increase when the distinct, complex acoustic source mechanisms creating the noise are better understood. For each type of noise, equivalent acoustic source distributions are obtained from a tied-down F-35B operating at various engine conditions using the hybrid method for acoustic source imaging of Padois, Gauthier, and Berry [J. Sound Vib. 333, 6858-6868 (2014)]. The source distributions for the distinct noise types are obtained using different sections of a 71 element, ground-based linear array. Using a subarray close to the nozzle exit plane, source distributions are obtained for fine-scale turbulent mixing noise and broadband shock-associated noise, although grating lobes complicate interpretations at higher frequencies. Results for a subarray spanning the maximum sound region show that the multiple frequency peaks in tactical aircraft noise appear to originate from overlapping source regions. The observation of overlapping spatial extent of competing noise sources is supported by the coherence properties of the source distributions for the different subarrays.

Cumulative noise exposure model for outdoor shooting ranges.

An impulsive noise exposure model for outdoor military shooting ranges was created. The inputs to the model included spatial interpolation of noise exposure metrics measured from a single round of fire from a small-arms ballistic weapon. Energies from this single-shot model were spatially translated and summed to simulate multiple shooters firing multiple rounds based on the equal energy hypothesis for damage risk assessment. A validation measurement was performed, and the uncertainties associated with measurement and modeling were shown to be acceptably low. This model can predict and assess total exposures and protection measures for shooters, instructors, and other range personnel.

Source characterization of full-scale tactical jet noise from phased-array measurements.

Application of phased-array algorithms to acoustic measurements in the vicinity of a high-performance military aircraft yields equivalent source reconstructions over a range of engine conditions. Beamforming techniques for aeroacoustics applications have undergone significant advances over the past decade to account for difficulties that arise when traditional methods are applied to distributed sources such as those found in jet noise. The hybrid method, an inverse method approached via beamforming, is applied to jet noise measured along a 50 element, 30 m linear array to obtain equivalent source distributions. The source distribution extent decreases with increasing frequency or with a decrease in engine condition. A source coherence analysis along the axial dimension of the jet plume reveals that the source coherence lengths scale inversely with increasing engine condition. In addition, a method for extending the array bandwidth to frequencies beyond the spatial Nyquist frequency limit is also implemented. A directivity analysis of the beamforming results reveals that sources near the nozzle radiate to the sideline from a relatively stationary point irrespective of frequency, while the noise source origin of downstream radiating noise varies significantly with frequency.

Partial-field decomposition analysis of full-scale supersonic jet noise using optimized-location virtual references.

Supersonic jet noise reduction efforts benefit from targeted source feature extraction and high-resolution acoustic imaging. Another useful tool for feature extraction is partial field decomposition of sources into independent contributors. Since such decomposition processes are nonunique, care must be taken in the physical interpretation of decomposed partially coherent aeroacoustic fields. The optimized-location virtual reference method (OLVR) is a partial field decomposition designed to extract physically meaningful source and field information through the strategic placement of virtual references within a reconstructed field. The OLVR method is applied here to obtain spatially distinct and ordered partial sources at multiple frequencies of a full-scale, high-performance supersonic jet engine operating at 100% engine power. Partial sources are shown to mimic behaviors of the total source distributions including monotonic growth and decay. Because of finite spatial coherence, multiple partial sources are used to reproduce far-field radiation away from the main lobe, and the number of required sources increases with increasing frequency. An analytical multiwavepacket model is fitted to the partial sources to demonstrate how OLVR partial fields can be leveraged to produce reduced-order models.

Broadband shock-associated noise from a high-performance military aircraft.

Broadband shock-associated noise (BBSAN) is a prominent noise component from nonideally expanded jets in the forward and sideline directions. BBSAN from laboratory-scale jets has been studied extensively, and spatial trends in BBSAN spectral peak characteristics-frequency, level, and width-have been established. These laboratory-scale trends are compared to those for BBSAN from a tied-down F-35B operated at four engine conditions. While the peak frequency varies as expected, both spatially and across engine condition, the peak level and width do not, pointing to the need for additional research into BBSAN for high-performance military aircraft.

Characterizing acoustic shocks in high-performance jet aircraft flyover noise.

Acoustic shocks have been previously documented in high-amplitude jet noise, including both the near and far fields of military jet aircraft. However, previous investigations into the nature and formation of shocks have historically concentrated on stationary, ground run-up measurements, and previous attempts to connect full-scale ground run-up and flyover measurements have omitted the effect of nonlinear propagation. This paper shows evidence for nonlinear propagation and the presence of acoustic shocks in acoustical measurements of F-35 flyover operations. Pressure waveforms, derivatives, and statistics indicate nonlinear propagation, and the resulting shock formation is significant at high engine powers. Variations due to microphone size, microphone height, and sampling rate are considered, and recommendations for future measurements are made. Metrics indicating nonlinear propagation are shown to be influenced by changes in sampling rate and microphone size, and exhibit less variation due to microphone height.

Military jet noise source imaging using multisource statistically optimized near-field acoustical holography.

The identification of acoustic sources is critical to targeted noise reduction efforts for jets on high-performance tactical aircraft. This paper describes the imaging of acoustic sources from a tactical jet using near-field acoustical holography techniques. The measurement consists of a series of scans over the hologram with a dense microphone array. Partial field decomposition methods are performed to generate coherent holograms. Numerical extrapolation of data beyond the measurement aperture mitigates artifacts near the aperture edges. A multisource equivalent wave model is used that includes the effects of the ground reflection on the measurement. Multisource statistically optimized near-field acoustical holography (M-SONAH) is used to reconstruct apparent source distributions between 20 and 1250 Hz at four engine powers. It is shown that M-SONAH produces accurate field reconstructions for both inward and outward propagation in the region spanned by the physical hologram measurement. Reconstructions across the set of engine powers and frequencies suggests that directivity depends mainly on estimated source location; sources farther downstream radiate at a higher angle relative to the inlet axis. At some frequencies and engine powers, reconstructed fields exhibit multiple radiation lobes originating from overlapped source regions, which is a phenomenon relatively recently reported for full-scale jets.

Multisource statistically optimized near-field acoustical holography.

This paper presents a reduced-order approach to near-field acoustical holography (NAH) that allows the user to account for sound fields generated by multiple spatially separated sources. In this method, an equivalent wave model (EWM) of a given field is formulated to include combinations of planar, cylindrical, spherical, or other elementary wave functions in contrast to an EWM restricted to a single separable coordinate system. This can alleviate the need for higher-order functions, reduce the number of measurements, and decrease error. The statistically optimized near-field acoustical holography (SONAH) algorithm is utilized to perform the NAH projection after the formulation of the multisource EWM. The combined process is called multisource statistically optimized near-field acoustical holography (M-SONAH). This method is used to reconstruct simulated sound fields generated by combinations of a vibrating piston in a sphere and linear arrays of monopole sources. It is shown that M-SONAH can reconstruct near-field pressures in multisource environments with lower errors and fewer measurements than a strictly plane or cylindrical-wave formulation using the same simulated measurement.

Acoustic intensity near a high-powered military jet aircraft.

The spatial variation in vector acoustic intensity has been calculated between 100 and 3000 Hz near a high-performance military aircraft. With one engine of a tethered F-22A Raptor operating at military power, a tetrahedral intensity probe was moved to 27 locations in the geometric near and mid-fields to obtain the frequency-dependent intensity vector field. The angles of the maximum intensity region rotate from aft to sideline with increasing frequency, becoming less directional above 800 Hz. Between 100 and 400 Hz, which are principal radiation frequencies, the ray-traced dominant source region rapidly contracts and moves upstream, approaching nearly constant behavior by 1000 Hz.

Cylindrical acoustical holography applied to full-scale jet noise.

Near-field acoustical holography methods are used to predict sound radiation from an engine installed on a high-performance military fighter aircraft. Cylindrical holography techniques are an efficient approach to measure the large and complex sound fields produced by full-scale jets. It is shown that a ground-based, one-dimensional array of microphones can be used in conjunction with a cylindrical wave function field representation to provide a holographic reconstruction of the radiated sound field at low frequencies. In the current work, partial field decomposition methods and numerical extrapolation of data beyond the boundaries of the hologram aperture are required prior to holographic projection. Predicted jet noise source distributions and directionality are shown for four frequencies between 63 and 250 Hz. It is shown that the source distribution narrows and moves upstream, and that radiation directionality shifts toward the forward direction, with increasing frequency. A double-lobe feature of full-scale jet radiation is also demonstrated.

Similarity spectra analysis of high-performance jet aircraft noise.

Noise measured in the vicinity of an F-22A Raptor has been compared to similarity spectra found previously to represent mixing noise from large-scale and fine-scale turbulent structures in laboratory-scale jet plumes. Comparisons have been made for three engine conditions using ground-based sideline microphones, which covered a large angular aperture. Even though the nozzle geometry is complex and the jet is nonideally expanded, the similarity spectra do agree with large portions of the measured spectra. Toward the sideline, the fine-scale similarity spectrum is used, while the large-scale similarity spectrum provides a good fit to the area of maximum radiation. Combinations of the two similarity spectra are shown to match the data in between those regions. Surprisingly, a combination of the two is also shown to match the data at the farthest aft angle. However, at high frequencies the degree of congruity between the similarity and the measured spectra changes with engine condition and angle. At the higher engine conditions, there is a systematically shallower measured high-frequency slope, with the largest discrepancy occurring in the regions of maximum radiation.

Near-field shock formation in noise propagation from a high-power jet aircraft.

Noise measurements near the F-35A Joint Strike Fighter at military power are analyzed via spatial maps of overall and band pressure levels and skewness. Relative constancy of the pressure waveform skewness reveals that waveform asymmetry, characteristic of supersonic jets, is a source phenomenon originating farther upstream than the maximum overall level. Conversely, growth of the skewness of the time derivative with distance indicates that acoustic shocks largely form through the course of near-field propagation and are not generated explicitly by a source mechanism. These results potentially counter previous arguments that jet "crackle" is a source phenomenon.

On autocorrelation analysis of jet noise.

Meaningful use of the autocorrelation in jet noise analysis is examined. The effect of peak frequency on the autocorrelation function width is removed through a temporal scaling prior to making comparisons between measurements or drawing conclusions about source characteristics. In addition, a Hilbert transform-based autocorrelation envelope helps to define consistent characteristic time scales. Application of these processes to correlation functions based on large and fine-scale similarity spectra reveal that the large-scale noise radiation from an F-22A deviates from the similarity spectrum model.

Sound power and acoustic efficiency of an installed GE F404 jet engine.

Classical jet noise theory indicates that radiated sound power is proportional to the jet velocity raised to the eighth and third powers for subsonic and supersonic jets, respectively. To connect full-scale measurements with classical jet noise theory, this letter presents sound power and acoustic efficiency values for an installed GE-F404 engine. When subsonic, the change in sound power follows the eighth-power law, and the sound power change approximately follows the third-power law at supersonic conditions, with an acoustic efficiency of ∼0.5-0.6%. However, the OAPWL increase from subsonic to supersonic jet velocities is greater than would be predicted.

Reserve capacity of public and private hospitals in response to demand uncertainty.

A feature of hospitals is that they face uncertain demand for the services they offer. To cover fluctuations in demand, they need to maintain reserve service capacity in the form of beds, equipment, personnel, etc. to minimize the probability of excess queuing or turning away patients, creating a trade-off between reserve service capacity and economic costs. Using a simple theoretical framework, we show how the reserve capacity established depends on institutional characteristics that can affect the objective of the hospital. In particular, we show that private and public hospitals may provide different levels of reserve capacity. In an empirical application using a panel data set of Spanish hospitals over the period 1996-2006, we model reserve service capacity using a distance frontier approach. Our results show that private hospitals generally react to a lesser extent to demand uncertainty than public hospitals.