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Testing Surrogate-Based Optimization with the Fortified Branin-Hoo Extended to Four Dimensions

Some popular functions used to test global optimization algorithms have multiple local optima, all with the same value, making them all global optima. It is easy to make them more challenging by fortifying them via adding a localized bump at the location of one of the optima. In previous work the authors illustrated this for the Branin-Hoo function and the popular differential evolution algorithm, showing that the fortified Branin-Hoo required an order of magnitude more function evaluations. This paper examines the effect of fortifying the Branin-Hoo function on surrogate- based optimization, which usually proceeds by adaptive sampling. Two algorithms are considered. The EGO algorithm, which is based on a Gaussian process (GP) and an algorithm based on radial basis functions (RBF). EGO is found to be more frugal in terms of the number of required function evaluations required to identify the correct basin, but it is expensive to run on a desktop, limiting the number of times the runs could be repeated to establish sound statistics on the number of required function evaluations. The RBF algorithm was cheaper to run, providing more sound statistics on performance. A four-dimensional version of the Branin-Hoo function was introduced in order to assess the effect of dimensionality. Furthermore, it was found that the difference between the ordinary function and the fortified one was much more pronounced for the four-dimensional function compared to the two dimensional one.

97 MATHEMATICS AND COMPUTING↗

The use and misuse of statistical analyses

The statistical techniques most often used in space physics include Fourier analysis, linear correlation, auto- and cross-correlation, power spectral density, and superposed epoch analysis. Tests are presented which can evaluate the significance of the results obtained through each of these. Data presented without some form of error analysis are frequently useless, since they offer no way of assessing whether a bump on a spectrum or on a superposed epoch analysis is real or merely a statistical fluctuation. Among many of the published linear correlations, for instance, the uncertainty in the intercept and slope is not given, so that the significance of the fitted parameters cannot be assessed.

Reiff, P. H.↗

Classification image analysis: estimation and statistical inference for two-alternative forced-choice experiments

We consider estimation and statistical hypothesis testing on classification images obtained from the two-alternative forced-choice experimental paradigm. We begin with a probabilistic model of task performance for simple forced-choice detection and discrimination tasks. Particular attention is paid to general linear filter models because these models lead to a direct interpretation of the classification image as an estimate of the filter weights. We then describe an estimation procedure for obtaining classification images from observer data. A number of statistical tests are presented for testing various hypotheses from classification images based on some more compact set of features derived from them. As an example of how the methods we describe can be used, we present a case study investigating detection of a Gaussian bump profile.

Non-NASA Center↗

Simultaneous ROSAT, Ginga, VLA, IUE, and optical observations of the bright quasar H1821+643

Simultaneous optical, UV, and X-ray spectroscopy of the low-redshift high-luminosity QSO H1821+643 is presented in order to examine the connection between the optical UV bump and the soft X-ray excess. The correlation of the short-term variability in the optical/UV and soft X-ray band is examined, and the applicability of the accretion disk models to the simultaneous continuum energy distribution is tested. By fitting the continuum energy distribution with the thin accretion disk model, it was found that bare disk models cannot easily account for the emission in both the UV and the steep excess in the soft X-ray band. The intrinsic X-ray spectrum of H1821+643 exhibited a typical power-law slope above about 0.3 keV, as detected by ROSAT and Ginga. The first detection of H1821+643 in the radio band is reported. This radio-quiet QSO was found to have a substantial radio flux at 20 cm and a typical steep spectral slope.

Kolman, Michiel↗

The binary Cepheid BP Cir - A test of evolutionary tracks

IUE spectra of the system containing the Cepheid BP Cir are used to derive the magnitude difference between the two stars (Delta V = 1.88 +/- 0.3 mag) and the spectral type of the companion (B6.0V). This is the first system yet encountered for which the standard Seaton reddening law is inappropriate. For BP Cir, a stronger 2200-A bump than the standard law is required. However, this does not affect the determination of the temperature of the hot star or the magnitude difference between the two stars, because those use the wavelength regions shorter than 1600 A and longer than 2500 A. The stars are very similar in mass. Possible pulsation in the first overtone mode implies that BP Cir B is evolved beyond the ZAMS but is still in the main sequence band. The best match to BP Cir A and B is with isochrones by Stothers and Chin (1991) with Inglesias and Rogers (1991) opacities and no core convective overshoot and Cepheid pulsation in the first overtone.

Evans, Nancy R.↗

Ultraviolet interstellar linear polarization. 2: The wavelength dependence

We present new ultraviolet (UV) polarimetry of the well-studied interstellar line of sight toward HD 204827 obtained with the Faint Object Spectrograph on Hubble Space Telescope. HD 204827 is of great interest because the dust along this line of sight has extremely low values of both lambda(sub max) and R(sub V). Its far-UV extinction is very large, reflecting its small R(sub V) value. In addition, we reexamine the entire sample of 14 interstellar lines of sight for which there are now UV polarization data. We find that the previously suggested relationship between lambda(sub max) and the wavelength dependence of the polarization in the UV is strongly supported by the data for this larger sample including HD 204827. Seven stars with lambda(sub max) greater than or equal to 0.54 micron agree well with an extrapolation of the Serkowski relation into the UV while seven stars with lambda(sub max) less than or equal to 0.53 micron show polarization in excess of the Serkowski extrapolation (super-Serkowski). However, the division of the observed lines of sight into Serkowski and super-Serkowski categories is artificial. In fact, the amount of polarization in the UV is correlated with a single parameter, lambda(sub max). This may indicate that there is a mean interstellar polarization law analogous to the mean interstellar extinction law of Cardelli, Calyton, & Mathis which is based on R(sub V). The data are consistent with a linear relationship between 1/lambda(sub max) and rho(UV)/rho(sub max) but more data are needed to define the functional form. We suggest that the Serkowski and super-Serkowski designations be replaced by high and low lambda(sub max) which are more physically descriptive. At the same time, we note that all seven super-Serkowski (low lambda(sub max)) stars lie in a relatively small region of the sky between l(sup II) = 90 deg - 150 deg and b = -5 deg - 15 deg. These stars all lie in or behind a spur of the local Orion spiral arm. Similarly, most of the Serkowski (high lambda(sub max) stars lie in or near the Scorpio-Centaurus OB Association. So lines of sight covering larger areas of the sky are needed to test the universality of the lambda(sub max)/UV polarization relationship. The recent discovery of warm dust near HD 197770 suggests the possibility that a mechanism other than the traditional alignment to the Galactic magnetic field may be invoked to explain its 2175 A polarization bump.

Clayton, Geoffrey C.↗

Recovery of Oxpure 612C-50 Coconut Carbon Particles Using Bump Arrays

Cyanide is used to leach gold from crushed ore (solid matrix) into a gold cyanide solution. The gold is extracted from the cyanide solution by adsorption onto activated carbon. The gold extraction process occurs when the activated coconut carbon is placed into tanks that contain the gold cyanide solution either in a batch process or into a continuous flow circuit. The coconut carbon is then removed from the solution for gold recovery. The use of the mesofluidic separation system (a deterministic lateral displacement system) can significantly reduce costs and waste generated from the process of removing the coconut carbon from the solution. In the coconut carbon recovery process used at many gold mines in Nevada, the gold is attached to carbon particles that are still in the cyanide liquor. The mesofluidic system can rapidly remove the gold bearing carbon particles from the cyanide liquor quickly and with no operating costs. The benefits include: • Reduce operational costs related to filtration and hydro-cyclones • Reduced acid usage for the elution gold stripping phase as only 25% of the fluids will follow the carbon particles to the final express lane when two mesofluidic systems are used in series This alternative particle removal techniques would be advantageous. A promising technique for removing larger particles from slurries is mesofluidic separation, similar to deterministic lateral displacement arrays or “bump” arrays [1] but operates at much larger flow rates. As described by Pease, et al. [2], “Bump arrays in deterministic lateral displacement devices separate large particles from small particles using arrays of staggered posts. Large particles, defined as those with radii larger than the distance between the edge of a post and the stagnation streamline from the next downstream post, must bump toward one side of the device, whereas particles smaller than this distance slalom from entrance to exit without net lateral displacement.” Unlike filters or sieves, the posts in the arrays that cause separation do not block or occlude particle flow but work because particles go around the posts. Unlike hydrocyclones separation, separation is not driven by particle density, because gravitational forces are unimportant to mesofluidic separation. Burns, et al., and Pease, et al., have shown that particles may be separated from complex suspensions, under turbulent flow conditions, and at industrially important flow rates [3-5]. They have also recently shown that mesofluidic devices may be arranged in series to increase separation performance [6]. In this paper, we evaluate the mesofluidic system for the separation of commercial OxPure GR 612 Charred Coconut shell particles as a proof of principle test for the rapid separation using the 1500 micron cut mesofluidic separator. We first describe the experimental system and conditions. We then present the experimental results. [1] Huang, L.R., E.C. Cox, R.H. Austin, J.C. Sturm. 2004. Continuous particle separation through deterministic lateral displacement. Science, 304, 987–990. https://doi.org/10.1126/science.1094567. [2] Pease L.F., J.A. Bamberger, C.A. Burns, and M.J. Minette. 2021. Large Particle Separation from Non-Newtonian Slurries using Bump Arrays. In Proceedings of the ASME 2021 Fluids Engineering Division Summer Meeting FEDSM2021-65904, V003T08A023. New York, New York: ASME. doi:10.1115/FEDSM2021-65904 [3] Burns C.A., T.G. Veldman, J. Serkowski, R.C. Daniel, X.-Y. Yu, M.J. Minette, L.F. Pease. 2021. Mesofluidic separation versus dead-end filtration. Separation and Purification Technology, 254, 117256. https://doi.org/10.1016/j.seppur.2020.117256. [4] Pease L.F., J.E. Serkowski, T.G. Veldman, J. Williams, X.-Y. Yu, M.J. Minette, J.A. Bamberger, C.A. Burns. 2021. Can Bump Arrays Separate Particles from Turbulent Flows?. In Proceedings of the ASME 2021 Fluids Engineering Division Summer Meeting FEDSM2021-67696, V003T08A024. New York, New York: ASME. doi:10.11

mesofluidic separation, slurry, bump array↗

Advanced Flip Chips in Extreme Temperature Environments

The use of underfill materials is necessary with flip-chip interconnect technology to redistribute stresses due to mismatching coefficients of thermal expansion (CTEs) between dissimilar materials in the overall assembly. Underfills are formulated using organic polymers and possibly inorganic filler materials. There are a few ways to apply the underfills with flip-chip technology. Traditional capillary-flow underfill materials now possess high flow speed and reduced time to cure, but they still require additional processing steps beyond the typical surface-mount technology (SMT) assembly process. Studies were conducted using underfills in a temperature range of -190 to 85 C, which resulted in an increase of reliability by one to two orders of magnitude. Thermal shock of the flip-chip test articles was designed to induce failures at the interconnect sites (-40 to 100 C). The study on the reliability of flip chips using underfills in the extreme temperature region is of significant value for space applications. This technology is considered as an enabling technology for future space missions. Flip-chip interconnect technology is an advanced electrical interconnection approach where the silicon die or chip is electrically connected, face down, to the substrate by reflowing solder bumps on area-array metallized terminals on the die to matching footprints of solder-wettable pads on the chosen substrate. This advanced flip-chip interconnect technology will significantly improve the performance of high-speed systems, productivity enhancement over manual wire bonding, self-alignment during die joining, low lead inductances, and reduced need for attachment of precious metals. The use of commercially developed no-flow fluxing underfills provides a means of reducing the processing steps employed in the traditional capillary flow methods to enhance SMT compatibility. Reliability of flip chips may be significantly increased by matching/tailoring the CTEs of the substrate material and the silicon die or chip, and also the underfill materials. Advanced packaging interconnects technology such as flip-chip interconnect test boards have been subjected to various extreme temperature ranges that cover military specifications and extreme Mars and asteroid environments. The eventual goal of each process step and the entire process is to produce components with 100 percent interconnect and satisfy the reliability requirements. Underfill materials, in general, may possibly meet demanding end use requirements such as low warpage, low stress, fine pitch, high reliability, and high adhesion.

Ramesham, Rajeshuni↗

Hubble Space Telescope Fine Guidance Sensor Post-Flight Bearing Inspection

Aerospace mechanism engineering success stories often, if not always, consist of overcoming developmental, test and flight anomalies. Many times it is these anomalies that stimulate technology growth and more reliable future systems. However, one must learn from these to achieve an ultimately successful mission. It is not often that a spacecraft engineer is able to inspect hardware that has flown in orbit for several years. However, in February 1997, the Fine Guidance Sensor-1 (FGS-1) was removed from the Hubble Space Telescope (HST) and returned to NASA Goddard Space Flight Center (GSFC) during the second Servicing Mission (SM2). At the time of removal, FGS-1 had nearly 7 years of service and the bearings in the Star Selector Servos (SSS) had accumulated approximately 25 million Coarse Track (CT) cycles. The main reason for its replacement was due to a bearing torque anomaly leading to stalling of the B Star Selector Servo (SSS-B) when reversing direction during a vehicle offset maneuver, referred to herein as a Reversal Bump (RB). The returned HST FGS SSS bearings were disassembled for post-service condition assessment to better understand the actual cause of the torque spikes, identify potential process/design improvements, and provide information for remedial on-orbit operation modifications. The methods and technology utilized for this inspection are not unique to this system and can be adapted to most investigations at varying stages of the mechanism life from development, through testing, to post flight evaluation. The systematic methods used for the HST Fine Guidance Sensor (FGS) SSS and specific findings are the subjects presented in this paper. The lessons learned include the importance of cleanliness and handling for precision instrument bearings and the potential effects from contamination. The paper describes in detail, the analytical techniques used for the SSS and their importance in this investigation. Inspection analytical data and photographs are included throughout the paper.

Pellicciotti, J.↗

Hubble Space Telescope Fine Guidance Sensor Post-Flight Bearing Inspection

Aerospace mechanism engineering success stories often, if not always, consist of overcoming developmental, test and flight anomalies. Many times it is these anomalies that stimulate technology growth and more reliable future systems. However, one must learn from these to achieve an ultimately successful mission. It is not often that a spacecraft engineer is able to inspect hardware that has flown in orbit for several years. However, in February 1997, the Fine Guidance Sensor-I (FGS-1) was removed from the Hubble Space Telescope (HST) and returned to NASA Goddard Space Flight Center (GSFC) during the second Servicing Mission (SM2). At the time of removal, FGS-1 had nearly 7 years of service and the bearings in the Star Selector Servos (SSS) had accumulated approximately 25 million Coarse Track (CT) cycles. The main reason for its replacement was due to a bearing torque anomaly leading to stalling of the B Star Selector Servo (SSS-B) when reversing direction during a vehicle offset maneuver, referred to herein as a Reversal Bump (RB). The returned HST FGS SSS bearings were disassembled for post-service condition assessment to better understand the actual cause of the torque spikes, identify potential process/design improvements, and provide information for remedial on-orbit operation modifications. The methods and technology utilized for this inspection are not unique to this system and can be adapted to most investigation ai varying stages of the mechanism life from development, through testing, io post night evaluation. The systematic methods used for the HST Fine Guidance Sensor (FGS) SSS and specific findings are the subjects presented in this paper. The lessons learned include the importance of cleanliness and handling for precision instrument bearings and the potential effects from contamination. The paper describes in detail, the analytical techniques used for the SSS and their importance in this investigation. Inspection analytical data and photographs are included throughout the paper.

Pellicciotti, Joseph↗

Effect of 3D-printed surface textures on wear mechanism in 3-body abrasion of soil

This study systematically investigates the enhancement of wear resistance in 3D printed surface textures through both experimental and theoretical approaches. Three distinct surface morphologies (Smooth Surface, Surface with uniformly distributed Pits, and Surface with uniformly distributed Bumps) were fabricated using High-Impact Polystyrene, where the meso-scale textures were precisely controlled through the 3D printing process. Wear behavior was evaluated using a 3-body wear tester in an abrasive particle environment, analyzing the influence of surface textures under various operating conditions. Systematic wear tests revealed that optimally designed surface textures achieved a remarkable 77 % reduction in wear compared to the worst-performing sample. The wear mechanisms were comprehensively characterized through weight loss measurements, Scanning Electron Microscopy (SEM), and Energy Dispersive Spectroscopy (EDS) analyses, elucidating the surface morphology changes and their interaction with wear particles. Notably, the study identified how the geometric characteristics of surface textures influence the movement of wear particles and the distribution of contact stresses. Discrete element method simulations corroborated the experimental findings, providing theoretical validation for the enhanced wear resistance of the optimal structure. The high correlation between simulated wear patterns and experimental results validates the reliability of the proposed design methodology. In conclusion, these results demonstrate that 3D printed surface texturing offers a cost-effective and scalable approach to significantly improve wear resistance in engineering applications, presenting a practical alternative to conventional, high-cost surface engineering methods.

3-body abrasion↗

Real-time processor for staring receivers

The design, fabrication, and testing of a state-of-the-art, high-throughput on-focal plane IR-image signal processor is described. The processing functions performed are frame differencing and thresholding. The final focal plane array will consist of a 128 x 128-pixel platinum-silicide detector bump-mounted to an on-chip CCD multiplexer. The processor is in a 128-channel parallel-pipeline format. Each channel consists of a pixel regenerator (charge differencer), 128-pixel frame store CCD memory, pixel differencer, second pixel regenerator, thresholder (analog comparator), and digital latch. Four parallel analog outputs and four parallel digital outputs are included. The digital outputs provide a bit map of the image. All analog clock signals (128 KHz, 256 KHz, and 5 MHz) are generated by on-chip TTL-input clock drivers. TTL clock driver inputs are generated off-chip. The technology is low-temperature surface and buried channel CCD/CMOS/indium bump. The design goal was 8-bit resolution at 77 K and 1000 frames/s. Applications include point- or extended-target motion detection with thresholding. Design trade-offs and enhancements (such as on-chip detector gain compensation and a simple window processor) are discussed.

Hanzal, Brian↗

Spline-Based Smoothing of Airfoil Curvatures

Constrained fitting for airfoil curvature smoothing (CFACS) is a splinebased method of interpolating airfoil surface coordinates (and, concomitantly, airfoil thicknesses) between specified discrete design points so as to obtain smoothing of surface-curvature profiles in addition to basic smoothing of surfaces. CFACS was developed in recognition of the fact that the performance of a transonic airfoil is directly related to both the curvature profile and the smoothness of the airfoil surface. Older methods of interpolation of airfoil surfaces involve various compromises between smoothing of surfaces and exact fitting of surfaces to specified discrete design points. While some of the older methods take curvature profiles into account, they nevertheless sometimes yield unfavorable results, including curvature oscillations near end points and substantial deviations from desired leading-edge shapes. In CFACS as in most of the older methods, one seeks a compromise between smoothing and exact fitting. Unlike in the older methods, the airfoil surface is modified as little as possible from its original specified form and, instead, is smoothed in such a way that the curvature profile becomes a smooth fit of the curvature profile of the original airfoil specification. CFACS involves a combination of rigorous mathematical modeling and knowledge-based heuristics. Rigorous mathematical formulation provides assurance of removal of undesirable curvature oscillations with minimum modification of the airfoil geometry. Knowledge-based heuristics bridge the gap between theory and designers best practices. In CFACS, one of the measures of the deviation of an airfoil surface from smoothness is the sum of squares of the jumps in the third derivatives of a cubicspline interpolation of the airfoil data. This measure is incorporated into a formulation for minimizing an overall deviation- from-smoothness measure of the airfoil data within a specified fitting error tolerance. CFACS has been extensively tested on a number of supercritical airfoil data sets generated by inverse design and optimization computer programs. All of the smoothing results show that CFACS is able to generate unbiased smooth fits of curvature profiles, trading small modifications of geometry for increasing curvature smoothness by eliminating curvature oscillations and bumps (see figure).

Li, W.↗

Progress on the International Space Station - We're Part Way up the Mountain

The first phase of the International Space Station construction has been completed, and research has begun. Russian, U.S., and Canadian hardware is on orbit, and Italian logistics modules have visited often. With the delivery of the U.S. Laboratory, Destiny, significant research capability is in place, and dozens of U.S. and Russian experiments have been conducted. Crew members have been on orbit continuously since November 2000. Several "bumps in the road" have occurred along the way, and each has been systematically overcome. Enormous amounts of hardware and software are being developed by the International Space Station partners and participants around the world and are largely on schedule for launch. Significant progress has been made in the testing of completed elements at launch sites in the United States and Kazakhstan. Over 250,000 kilograms of flight hardware have been delivered to the Kennedy Space Center and integrated testing of several elements wired together has progressed extremely well. Mission control centers are fully functioning in Houston, Moscow, and Canada, and operations centers Darmstadt, Tsukuba, Turino, and Huntsville will be going on line as they are required. Extensive coordination efforts continue among the space agencies of the five partners and two participants, involving 16 nations. All of them continue to face their own challenges and have achieved significant successes. This paper will discuss the contributions of the International Space Station partners and participants, their accomplished milestones, and upcoming events. The International Space Station program, the largest and most complicated peacetime project in history, has progressed part way up the mountain, and the partners are continuing their journey to the top. The International Space Station (ISS) is unprecedented in its technological, engineering, and management complexity, and is one of the largest international collaborations ever undertaken. The ISS is a dramatic example of the ability of nations to work together as a team toward common goals and dreams. The challenges encountered and overcome by the international ISS team have been likened to climbing a mountain. Construction of the ISS has progressed rapidly in the past year. ISS is now a functioning microgravity laboratory in space hosting a permanent human presence, prompting the characterization that we are "part way up the mountain, and the team continues its climb."

Fortenberry, Lindy↗

Testing the AGN paradigm; Proceedings of the 2nd Annual Topical Astrophysics Conference, Univ. of Maryland, College Park, Oct. 14-16, 1991

The present volume on testing the AGN paradigm discusses black holes, accretion disks, high-energy continuum jets, AGN geometry, and the broad-line region. Attention is given to the search for black holes in galaxy nuclei, the structure of M32 at red wavelengths, testing the AGN paradigm for the Milky Way, and relativistic fluid flows in the magnetized Schwarzschild spacetime. Topics addressed include orbital models for the periodic X-ray flares of NGC 6814, observational evidence for thin AGN disks, X-ray Fe line studies, and the role of the UV bump in line emission. Also discussed are signatures of black hole accretion disks, rapid variability in AGN and accretion disk hot spots, relativistic jets in AGN, and the radiation field in astrophysical jets.

Holt, Stephen S.↗

Weak bump quasars

Research into the optical, ultraviolet and infrared continuum emission from quasars and their host galaxies was carried out. The main results were the discovery of quasars with unusually weak infrared emission and the construction of a quantitative estimate of the dispersion in quasar continuum properties. One of the major uncertainties in the measurement of quasar continuum strength is the contribution to the continuum of the quasar host galaxy as a function of wavelength. Continuum templates were constructed for different types of host galaxy and individual estimates made of the decomposed quasar and host continua based on existing observations of the target quasars. The results are that host galaxy contamination is worse than previously suspected, and some apparent weak bump quasars are really normal quasars with strong host galaxies. However, the existence of true weak bump quasars such as PHL 909 was confirmed. The study of the link between the bump strength and other wavebands was continued by comparing with IRAS data. There is evidence that excess far infrared radiation is correlated with weaker ultraviolet bumps. This argues against an orientation effect and implies a probable link with the host galaxy environment, for instance the presence of a luminous starburst. However, the evidence still favors the idea that reddening is not important in those objects with ultraviolet weak bumps. The same work has led to the discovery of a class of infrared weak quasars. Pushing another part of the envelope of quasar continuum parameter space, the IR-weak quasars have implications for understanding the effects of reddening internal to the quasars, the reality of ultraviolet turnovers, and may allow further tests of the Phinney dust model for the IR continuum. They will also be important objects for studying the claimed IR to x-ray continuum correlation.

Wilkes, B. J.↗

A bootstrap approach to bump hunting

An important question in cluster analysis and pattern recognition is the determination of the number of clusters into which a given population should be divided. Frequently, particularly when certain specific clustering methods are being used, the number of clusters is taken to be equal to the number of modes, or local maxima, in the probability density function underlying the given data set. The use of kernal density estimates in mode estimation is discussed. The test statistic to be used is defined and a bootstrap technique for assessing significance is given. An illustrative application is followed by an examination of the asymptotic behavior of the test statistic.

Silverman, B. W.↗

The case for antiparticles in the extragalactic cosmic radiation

The presence of an excess of low-energy antiprotons in the primary cosmic radiation has given rise to several possible explanations, some of which involve exotic processes such as mini-black holes and extragalactic antiparticles. The latter possibility is considered, and it is shown that there are interesting implications for the cosmic radiation at higher energies. Indeed, it may be possible to account for a previously puzzling feature of the cosmic ray spectrum (a 'bump' in the range between 10 to the 14th and 10 to the 15th eV) by hypothesizing a primary extragalactic origin for the bulk of the observed cosmic ray antiprotons, although such an explanation is not unique. In this model, most of the cosmic rays above 10 to the 15th eV are extragalactic. A method of testing this hypothesis experimentally is described.

Stecker, F. W.↗