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Symmetry dilemmas in quantum computing for chemistry: A comprehensive analysis

Symmetry adaptation, universality, and gate efficiency are central but often competing requirements in quantum algorithms for electronic structure and many-body physics. For example, fully symmetry-adapted universal operator pools typically generate long and deep quantum circuits; gate-efficient universal operator pools generally break symmetries; and gate-efficient, fully symmetry-adapted operator pools may not be universal. In this work, we analyze such symmetry dilemmas both theoretically and numerically. On the theory side, we prove that the popular, gate-efficient operator pool consisting of singlet spin-adapted singles and perfect-pairing doubles is not universal when spatial symmetry is enforced. To demonstrate the strengths and weaknesses of the three types of pools, we perform numerical simulations using an adaptive algorithm paired with operator pools that are (i) fully symmetry-adapted and universal, (ii) fully symmetry-adapted and non-universal, and (iii) breaking a single symmetry and universal. Our numerical simulations encompass three physically relevant scenarios in which the target state is (i) the global ground state, (ii) the ground state crossed by a state differing in multiple symmetry properties, and (iii) the ground state crossed by a state differing in a single symmetry property. Our results show when symmetry-breaking but universal pools can be used safely, when enforcing at least one distinguishing symmetry suffices, and when a particular symmetry must be rigorously preserved to avoid variational collapse. Together, the formal and numerical analyses provide a practical guide for designing and benchmarking symmetry-adapted operator pools that balance universality, resource requirements, and robust state targeting in quantum simulations for chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Selection and Assessment of Predictions of the Mars Pathfinder Landing Site

The successful landing of the Mars Pathfinder spacecraft on Mars allows the review of the process of selecting the landing site and assessing predictions made for the site based on Viking and Earth-based data. Selection of the landing site for Mars Pathfinder was a two-phase process. The first phase took place from October 1993 to June 1994 and involved: initial identification of engineering constraints, definition of environmental conditions at the site for spacecraft design, and evaluation of the scientific potential of different landing sites. This phase culminated with the first "Mars Pathfinder Landing Site Workshop", held at the Lunar and Planetary Institute in Houston, Texas on April 18-19, 1994, in which suggested approaches and landing sites were solicited from the entire scientific community. A preliminary site was selected by the project for design purposes in June 1994. The second phase took place from July 1994 to March 1996 and involved: developing criteria for evaluating site safety using images and remote sensing data, testing of the spacecraft and landing subsystems (with design improvements) to establish quantitative engineering constraints on landing site characteristics, evaluating all potential landing sites on Mars, and certification of the site by the project. This phase included a second open workshop, "Mars Pathfinder Landing Site Workshop II: Characteristics of the Ares Vallis Region and Field Trips in the Channeled Scabland, Washington" held in Spokane and Moses Lake September 24-30, 1995 and formal acceptance of the site by NASA Headquarters. Engineering constraints on Pathfinder landing sites were developed from the initial design of the spacecraft and the entry, descent and landing scenario. The site must be within 5 degrees of the subsolar latitude at the time of landing (15N for maximum solar power and flexible communications with Earth. It also must be below 0 km elevation to enable enough time for the parachute to bring the lander to the proper terminal velocity for landing. The entire landing ellipse, which is 70 km by 200 km due to navigational, ephemeris and atmospheric uncertainties, must be free of steep slopes, scarps and obvious hazards in Viking orbiter images, have acceptable radar reflectivity, moderate rock abundances and have little or no dust. Scientific considerations of the Mars Pathfinder payload and mission indicate that analyses of "grab bag" samples at the mouths of outflow channels can offer a first order assessment of a variety of rock types on Mars. Highland sites offer the advantage of in situ analysis of ancient rocks on Mars that record crustal differentiation and the nature of the early environment. Dark gray sites offer the potential of analyzing unweathered and unoxidized materials. Following a general assessment of the safety of different sites, a preliminary selection of a "grab bag" site was made. This site, Ares Vallis, is near the mouth of an outflow channel that may contain ancient Noachian terrain, Hesperian ridged plains, and reworked channel materials. All potential landing sites on Mars that met basic safety criteria were analyzed in detail. Sites (100 by 200 km target ellipses) were considered safe if they were below 0 km elevation, were free of obvious hazards (high relief surface features) in high-resolution (< 50 m/pixel) Viking orbiter images and had acceptable reflectivity and roughness at radar wavelengths, high thermal inertia, moderate rock abundance, low red to violet ratio, and low albedo. Only 4 sites on Mars met all the above criteria, which included 1995 opposition 3.5 cm delay-Doppler radar data. Complete data were evaluated for 7 sites and the Viking landing sites for comparison for all the above criteria as well as crater abundance, hill and mesa abundance, slopes over meter to kilometer scales, low altitude winds (from global circulation models and slopes), the size-frequency distribution of large rocks, as well as rover trafficability and science potential. Discussion of potential hazards at Ares Vallis using a variety of data sets (including radar) at a second open workshop, indicated this site cannot be shown to be any more hazardous than the Viking landing sites. Field trips to the Channeled Scabland and the Ephrata Fan, analogs for Ares Vallis and the landing site, respectively, provided valuable insight into possible geologic processes and potential surface characteristics. Three sites met all the data requirements and safety criteria for landing Pathfinder. Ares Vallis was selected by the project because it appeared acceptably safe (although it appeared to have greater rock abundances than other sites, its elevation was likely the best known) and offered the prospect of analyzing a variety of rock types expected to be deposited by catastrophic floods, which would enable addressing first-order scientific questions such as differentiation of the crust, the development of weathering products, and the nature of the early martian environment and its subsequent evolution. The selection was reviewed by an external board at a number of meetings and accepted, and the site was approved by NASA Headquarters. Data gathered by the Pathfinder lander' and rover provides the opportunity to test the predictions made for the site in the selection process based on remote observations from Earth, orbit, and the surface. The discussion below is taken from Golombek et al. to which the reader is referred for a more complete discussion and a complete list of references, which are omitted here for brevity. Many characteristics of the landing site are consistent with its being shaped and deposited by the Ares and Tiu catastrophic floods. The rocky surface is consistent a depositional plain comprising semi-rounded pebbles, cobbles and tabular boulders (some of which appear imbricated and/or inclined in the direction of flow) that appear similar to depositional plains in terrestrial catastrophic floods. The Twin Peaks appear to be streamlined hills in lander images, which is consistent with interpretations of larger hills in Viking orbiter images of the region that suggest the lander is on the flank of a broad, gentle ridge trending northeast from Twin Peaks. This ridge, which is the rise to the north of the lander, is aligned in the downstream direction from the Ares and Tiu Valles floods, and may be a debris tail deposited in the wake of the Twin Peaks. Channels visible throughout the scene may be a result of late stage drainage. As predicted by delay-Doppler radar measurements and tracking results, the average elevation of the center of the site was about the same as Viking Lander I relative to the 6.1 mbar geoid. The Doppler tracking and two-way ranging estimate for the elevation of the spacecraft is only 45 in lower than the Viking I Lander and within 100 in of that expected, which is within the uncertainties of the measurements. After landing, surface pressures and winds (5-10 m/s) were found to be similar to expectations based on Viking data, although temperatures were about 10 K warmer. The temperature profile below 50 km was also roughly 20 K warmer. As a result, predicted densities were 5% higher near the surface and up to 40% lower at 50 km but within the entry, descent and landing design margins. The populations of craters and small hills and the slopes of the hills measured in high-resolution (38 m/pixel) Viking orbiter images and the radar derived slopes of the landing site are all consistent with observations of these properties in the lander images. A rocky surface was expected from Viking Infra-Red Thermal Mapper (IRTM) observations and comparisons with the Viking landing sites. The observed cumulative fraction of area covered by rocks with diameters greater than 3 cm and heights greater than 0.5 in (potentially hazardous to landing) at Ares is similar to that predicted by IRTM observations and models of Viking lander and Earth analog rock size-frequency distributions. The IRTM prediction postulated an effective thermal inertia of 30 (10(exp -3) cgs units - cal/cubic cm/s(exp 0.5)/K) for the rock population, but we obtain a slightly different effective thermal inertia for the actual rock population. The validity of interpretations of radar echoes prior to landing are supported by a simple radar echo model, an estimate of the reflectivity of the soil from its bulk density, and the fraction of area covered by rocks. In the calculations, the soil produces the quasi-specular echo and the rocks produce the diffuse echo. The derived quasispecular cross section is comparable to the cross-sections and reflectivities reported for 3.5-cm wavelength observations. The model yields a diffuse echo that is modestly larger than the polarized diffuse echo reported for 3.5-cm wavelength observations. At 12.5-cm wavelength, similar rock populations at Ares and the Viking I site were expected because the diffuse echoes are comparable, but the large normal reflectivities suggests that bulk densities of the soils at depth are greater than those at the surface. We also obtain a fine-component inertia near 8.4 which agrees with the fine-component inertia of 8.7 (in 10(exp -3) cgs units) estimated from thermal observations from orbit by the IRTM; for this estimate, we used a bulk thermal inertia of 10.4 for the landing site, an effective thermal inertia near 40 (10(exp -3) cgs units) for the rock population, and a graphical representation of Kieffer's model. Color and albedo data for Ares suggested surfaces of materials at Ares Vallis would be relatively dust free or unweathered prior to landing compared with the materials at the Viking landing sites. This suggestion is supported by the abundance of relatively dark-gray rocks at Ares and their relative rarity at the Viking landing sites, where rocks are commonly coated with bright red dust. Finally, the 40 km long Ephrata Fan of the Channeled Scabland in Washington state, which was deposited where c

Golombek, M. P.↗

The impact of flying qualities on helicopter operational agility

Flying qualities standards are formally set to ensure safe flight and therefore reflect minimum, rather than optimum, requirements. Agility is a flying quality but relates to operations at high, if not maximum, performance. While the quality metrics and test procedures for flying, as covered for example in ADS33C, may provide an adequate structure to encompass agility, they do not currently address flight at high performance. This is also true in the fixed-wing world and a current concern in both communities is the absence of substantiated agility criteria and possible conflicts between flying qualities and high performance. AGARD is sponsoring a working group (WG19) title 'Operational Agility' that deals with these and a range of related issues. This paper is condensed from contributions by the three authors to WG19, relating to flying qualities. Novel perspectives on the subject are presented including the agility factor, that quantifies performance margins in flying qualities terms; a new parameter, based on maneuver acceleration is introduced as a potential candidate for defining upper limits to flying qualities. Finally, a probabilistic analysis of pilot handling qualities ratings is presented that suggests a powerful relationship between inherent airframe flying qualities and operational agility.

Padfield, Gareth D.↗

Magnetic exchange interactions in binuclear and tetranuclear iron(III) complexes described by spin‐flip DFT and Heisenberg effective Hamiltonians

Abstract Low‐energy spectra of single‐molecule magnets (SMMs) are often described by Heisenberg Hamiltonians. Within this formalism, exchange interactions between magnetic centers determine the ground‐state multiplicity and energy separation between the ground and excited states. In this contribution, we extract exchange coupling constants ( J ) for a set of iron (III) binuclear and tetranuclear complexes from all‐electron calculations using non‐collinear spin‐flip time‐dependent density functional theory (NC‐SF‐TDDFT). For 12 binuclear complexes with J ‐values ranging from −6 to −132 cm −1 , our benchmark calculations using the short‐range hybrid ω PBEh functional and 6‐31G(d,p) basis set agree well with the experimentally derived values (mean absolute error of 4.7 cm −1 ). For the tetranuclear SMMs, the computed J constants are within 6 cm −1 from the experimentally derived values. We explore the range of applicability of the Heisenberg model by analyzing bonding patterns in these Fe(III) complexes using natural orbitals (NO), their occupations, and the number of effectively unpaired electrons. The results illustrate the efficiency of the spin‐flip protocol for computing the exchange couplings and the utility of the NO analysis in assessing the validity of effective spin Hamiltonians.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Fault tolerant system performance modeling

With the proliferation of complex digital systems on aircraft, the need to accurately predict system performance early in the system design cycle becomes imperative. In the past, system designers have relied on ad hoc methods for evaluating performance issues. This has produced systems that have not always worked as originally intended. To alleviate these design deficiencies, formal methods, with supporting tools, must be adhered to during the system design process. The use of performance modeling tools is becoming widely accepted as a way to address timing considerations of system design. An additional incentive for the use of these tools is that they allow the system architect to analyze system component interactions (i.e., bus contention, contention of functions for a processing site, and system repair activity on application performance). This inherent flexibility can result in an explicit specification of the system architecture. This paper addresses a method that supports performance modeling of fault tolerant systems using a discrete event simulation tool. An additional focus is on lessons learned from analyzing these classes of problems. The methodology and supporting work provide system architects with the capability to specify candidate architectures and accurately predict their performance in the early stages of design, where changes to system design is most cost effective. The work has been supported under NASA contract NAS1-18099. Integrated Airframe Propulsion Control System Architecture (IAPSA II). This contract addresses methodology, analysis, and detailed design of integrated control system architectures suitable for high-performance aircraft of the 1990's.

Discrete event simulation↗

Reduced-Order Blade Mistuning Analysis Techniques Developed for the Robust Design of Engine Rotors

The primary objective of this research program is to develop vibration analysis tools, design tools, and design strategies to significantly improve the safety and robustness of turbine engine rotors. Bladed disks in turbine engines always feature small, random blade-to-blade differences, or mistuning. Mistuning can lead to a dramatic increase in blade forced-response amplitudes and stresses. Ultimately, this results in high-cycle fatigue, which is a major safety and cost concern. In this research program, the necessary steps will be taken to transform a state-of-the-art vibration analysis tool, the Turbo-Reduce forced-response prediction code, into an effective design tool by enhancing and extending the underlying modeling and analysis methods. Furthermore, novel techniques will be developed to assess the safety of a given design. In particular, a procedure will be established for using eigenfrequency curve veerings to identify "danger zones" in the operating conditions--ranges of rotational speeds and engine orders in which there is a great risk that the rotor blades will suffer high stresses. This work also will aid statistical studies of the forced response by reducing the necessary number of simulations. Finally, new strategies for improving the design of rotors will be pursued. Several methods will be investigated, including the use of intentional mistuning patterns to mitigate the harmful effects of random mistuning, and the modification of disk stiffness to avoid reaching critical values of interblade coupling in the desired operating range. Recent research progress is summarized in the following paragraphs. First, significant progress was made in the development of the component mode mistuning (CMM) and static mode compensation (SMC) methods for reduced-order modeling of mistuned bladed disks (see the following figure). The CMM method has been formalized and extended to allow a general treatment of mistuning. In addition, CMM allows individual mode mistuning, which accounts for the realistic effects of local variations in blade properties that lead to different mistuning values for different mode types (e.g., mistuning of the first torsion mode versus the second flexural mode). The accuracy and efficiency of the CMM method and the corresponding Turbo-Reduce code were validated for an example finite element model of a bladed disk.

Min, James B.↗

An approach to verification and validation of a reliable multicasting protocol: Extended Abstract

This paper describes the process of implementing a complex communications protocol that provides reliable delivery of data in multicast-capable, packet-switching telecommunication networks. The protocol, called the Reliable Multicasting Protocol (RMP), was developed incrementally using a combination of formal and informal techniques in an attempt to ensure the correctness of its implementation. Our development process involved three concurrent activities: (1) the initial construction and incremental enhancement of a formal state model of the protocol machine; (2) the initial coding and incremental enhancement of the implementation; and (3) model-based testing of iterative implementations of the protocol. These activities were carried out by two separate teams: a design team and a V&V team. The design team built the first version of RMP with limited functionality to handle only nominal requirements of data delivery. This initial version did not handle off-nominal cases such as network partitions or site failures. Meanwhile, the V&V team concurrently developed a formal model of the requirements using a variant of SCR-based state tables. Based on these requirements tables, the V&V team developed test cases to exercise the implementation. In a series of iterative steps, the design team added new functionality to the implementation while the V&V team kept the state model in fidelity with the implementation. This was done by generating test cases based on suspected errant or off-nominal behaviors predicted by the current model. If the execution of a test in the model and implementation agreed, then the test either found a potential problem or verified a required behavior. However, if the execution of a test was different in the model and implementation, then the differences helped identify inconsistencies between the model and implementation. In either case, the dialogue between both teams drove the co-evolution of the model and implementation. We have found that this interactive, iterative approach to development allows software designers to focus on delivery of nominal functionality while the V&V team can focus on analysis of off nominal cases. Testing serves as the vehicle for keeping the model and implementation in fidelity with each other. This paper describes (1) our experiences in developing our process model; and (2) three example problems found during the development of RMP. Although RMP has provided our research effort with a rich set of test cases, it also has practical applications within NASA. For example, RMP is being considered for use in the NASA EOSDIS project due to its significant performance benefits in applications that need to replicate large amounts of data to many network sites.

Callahan, John R.↗

Fisher for complements: extracting cosmology and neutrino mass from the counts-in-cells PDF

In this work, we comprehensively analyse the cosmology dependence of counts-in-cells statistics. Furthermore, we focus on the shape of the one-point probability distribution function (PDF) of the matter density field at mildly non-linear scales. Based on large-deviation statistics, we parametrize the cosmology dependence of the matter PDF in terms of the linear power spectrum, the growth factor, the spherical collapse dynamics, and the non-linear variance. We extend our formalism to include massive neutrinos, finding that the total matter PDF is highly sensitive to the total neutrino mass Mν and can disentangle it from the clustering amplitude σ 8 . Additionally, using more than a million PDFs extracted from the Quijote simulations, we determine the response of the matter PDF to changing parameters in the νΛCDM model and successfully cross-validate the theoretical model and the simulation measurements. We present the first νΛCDM Fisher forecast for the matter PDF at multiple scales and redshifts, and its combination with the matter power spectrum. We establish that the matter PDF and the matter power spectrum are highly complementary at mildly non-linear scales. The matter PDF is particularly powerful for constraining the matter density Ωm, clustering amplitude σ 8 and the total neutrino mass Mν. Adding the mildly non-linear matter PDF to the mildly non-linear matter power spectrum improves constraints on Ω m by a factor of 5 and σ 8 by a factor of 2 when considering the three lowest redshifts. In our joint analysis of the matter PDF and matter power spectrum at three redshifts, the total neutrino mass is constrained to better than 0.01 eV with a total volume of 6 (Gpc h -1 ) 3 . We discuss how density-split statistics can be used to translate those encouraging results for the matter PDF into realistic observables in galaxy surveys.

79 ASTRONOMY AND ASTROPHYSICS↗

Analytically Derived Piezoelectric Ejecta Data Transformations, with Implications for Claims of Experimentally Observed Self-Similarity

Building upon a previously documented analytic formalism, we derive a set of data transformations that relate piezoelectrically inferred time-dependent ejecta masses, dynamical ejecta cloud densities, and "radiographic" ejecta cloud density distributions. These transformation rules are derived rigorously, with careful attention to the assumption of instant ejecta production which is inherent in the piezoelectric mass inference procedure. Some of these relationships have not appeared previously in the literature, including solutions for the unique ejecta velocity distribution and radiographic ejecta cloud density distribution consistent with the instant-production assumption for a given piezoelectrically inferred mass dataset. In deriving the latter, we prove that—again subject to the ubiquitous instant-creation assumption—measurements at a single sensor are sufficient to determine properties of the ejecta cloud everywhere at all times. Other data transformation relationships have appeared in the literature without a rigorous derivation, or have been stated in forms that obscure the key mathematical relationships. We apply these results to arguments for self-similar ejecta cloud evolution, thereby deriving mathematical expressions by which claims of self-similarity may be examined. We prove that one analysis used in the literature to claim experimental evidence of a short ejecta production timescale—and consequently of self-similar cloud evolution—in fact places no constraint the ejecta production interval and therefore does not support the associated conclusion. We also provide a potentially useful uniqueness proof.

30 DIRECT ENERGY CONVERSION↗

Patterns in Crew-Initiated Photography of Earth from ISS - Is Earth Observation a Salutogenic Experience?

To provide for the well-being of crewmembers on future exploration missions, understanding how space station crewmembers handle the inherently stressful isolation and confinement during long-duration missions is important. A recent retrospective survey of previously flown astronauts found that the most commonly reported psychologically enriching aspects of spaceflight had to do with their Perceptions of Earth. Crewmembers onboard the International Space Station (ISS) photograph Earth through the station windows. Some of these photographs are in response to requests from scientists on the ground through the Crew Earth Observations (CEO) payload. Other photographs taken by crewmembers have not been in response to these formal requests. The automatically recorded data from the camera provides a dataset that can be used to test hypotheses about factors correlated with self-initiated crewmember photography. The present study used objective in-flight data to corroborate the previous questionnaire finding and to further investigate the nature of voluntary Earth-Observation activity. We examined the distribution of photographs with respect to time, crew, and subject matter. We also determined whether the frequency fluctuated in conjunction with major mission events such as vehicle dockings, and extra-vehicular activities (EVAs, or spacewalks), relative to the norm for the relevant crew. We also examined the influence of geographic and temporal patterns on frequency of Earth photography activities. We tested the hypotheses that there would be peak photography intensity over locations of personal interest, and on weekends. From December 2001 through October 2005 (Expeditions 4-11) crewmembers took 144,180 photographs of Earth with time and date automatically recorded by the camera. Of the time-stamped photographs, 84.5% were crew-initiated, and not in response to CEO requests. Preliminary analysis indicated some phasing in patterns of photography during the course of a mission (significant quadratic and trimodal models). There was also a small but significant increase in photo activity on the weekends. In contrast, fewer photos were taken during major station events and for a period of time immediately preceding those events. Data on photography patterns presented here represent a relatively objective group-level measure of Earth observing activities on ISS. Crew Earth Observations offers a self-initiated positive activity that may be important in salutogenesis (maintenance of well-being) of astronauts on long-duration missions. Consideration should be given to developing substitute activities for crewmembers in future exploration missions where there will not be the opportunity to look at Earth, such as on long-duration transits to Mars.

Robinson, Julie A.↗

Impact of Numerical Hydrodynamics in Turbulent Mixing Transition Simulations

Underresolved simulations are unavoidable in high Reynolds (Re) and Mach (Ma) number turbulent flow applications at scale. Implicit large-Eddy simulation (ILES) often becomes the effective strategy to capture the dominating effects of convectively driven flow instabilities. We evaluate the impact of three distinct numerical strategies in simulations of transition and turbulence decay with ILES: the Harten–Lax–van Leer (HLL) Riemann solver applying Strang splitting and a Lagrange-plus-Remap formalism to solve the directional sweep—denoted split; the Harten–Lax–Van Leer-Contact (HLLC) Riemann solver using a directionally unsplit strategy and parabolic reconstruction—denoted unsplit; and the HLLC Riemann solver using unsplit and a low-Ma correction (LMC)—denoted unsplit*. Three case studies are considered: (1) a shock tube problem prototyping shock-driven turbulent mixing, (2) the Taylor–Green Vortex (TGV) prototyping transition to turbulence, and, (3) an homogeneous isotropic turbulence (HIT) case, focusing on the impact of discretization on transition and decay from fixed well-characterized initial conditions. Significantly more accurate predictions are provided by the unsplit schemes, in particular, when augmented with the LMC. For given resolution, only the unsplit schemes predict the turbulent mixing transition after reshock observed in the shock tube experiments. Relevant comparisons of ILES based on Euler and Navier–Stokes equations addressing potential occurrence of low-Re regimes in the applications are presented. Unsplit schemes are instrumental in allowing to capture the spatial development of the TGV flow and its validation at prescribed Re with significantly less resolution. HIT analysis confirms higher simulated turbulence Re and increased small-scale content associated with the unsplit discretizations.

74 ATOMIC AND MOLECULAR PHYSICS↗

3-D Surface Depression Profiling Using High Frequency Focused Air-Coupled Ultrasonic Pulses

Surface topography is an important variable in the performance of many industrial components and is normally measured with diamond-tip profilometry over a small area or using optical scattering methods for larger area measurement. This article shows quantitative surface topography profiles as obtained using only high-frequency focused air-coupled ultrasonic pulses. The profiles were obtained using a profiling system developed by NASA Glenn Research Center and Sonix, Inc (via a formal cooperative agreement). (The air transducers are available as off-the-shelf items from several companies.) The method is simple and reproducible because it relies mainly on knowledge and constancy of the sound velocity through the air. The air transducer is scanned across the surface and sends pulses to the sample surface where they are reflected back from the surface along the same path as the incident wave. Time-of-flight images of the sample surface are acquired and converted to depth/surface profile images using the simple relation (d = V*t/2) between distance (d), time-of-flight (t), and the velocity of sound in air (V). The system has the ability to resolve surface depression variations as small as 25 microns, is useable over a 1.4 mm vertical depth range, and can profile large areas only limited by the scan limits of the particular ultrasonic system. (Best-case depth resolution is 0.25 microns which may be achievable with improved isolation from vibration and air currents.) The method using an optimized configuration is reasonably rapid and has all quantitative analysis facilities on-line including 2-D and 3-D visualization capability, extreme value filtering (for faulty data), and leveling capability. Air-coupled surface profilometry is applicable to plate-like and curved samples. In this article, results are shown for several proof-of-concept samples, plastic samples burned in microgravity on the STS-54 space shuttle mission, and a partially-coated cylindrical ceramic composite sample. Impressive results were obtained for all samples when compared with diamond-tip profiles and measurements from micrometers. The method is completely nondestructive, noninvasive, non-contact and does not require light-reflective surfaces.

Roth, Don J.↗

Constraining the Physical Properties of Stellar Coronal Mass Ejections with Coronal Dimming: Application to Far-ultraviolet Data of є Eridani

Coronal mass ejections (CMEs) are a prominent contributor to solar system space weather and might have impacted the Sun's early angular momentum evolution. A signal diagnostic of CMEs on the Sun is coronal dimming: a drop in coronal emission, tied to the mass of the CME, that is the direct result of removing emitting plasma from the corona. We present the results of a coronal dimming analysis of Fe XII 1349 Å and Fe XXI 1354 Å emission from ϵ Eridani ( ϵ Eri), a young K2 dwarf, with archival far-ultraviolet observations by the Hubble Space Telescope's Cosmic Origins Spectrograph. Following a flare in 2015 February, ϵ Eri's Fe XXI emission declined by 81 ± 5%. Although enticing, a scant 3.8 minutes of preflare observations allows for the possibility that the Fe XXI decline was the decay of an earlier, unseen flare. Dimming nondetections following each of three prominent flares constrain the possible mass of ejected Fe XII-emitting (1 MK) plasma to less than a few × 10 15 g. This implies that CMEs ejecting this much or more 1 MK plasma occur less than a few times per day on ϵ Eri. On the Sun, 10 15 g CMEs occur once every few days. For Eri, the mass-loss rate due to CME-ejected 1 MK plasma could be < 0.6 Ṁ Ꙩ well below the star's estimated 30 Ṁ Ꙩ mass-loss rate (wind + CMEs). The order-of-magnitude formalism we developed for these mass estimates can be broadly applied to coronal dimming observations of any star.

Stellar coronal mass ejections↗

Experimental philosophy leading to a small scale digital data base of the conterminous United States for designing experiments with remotely sensed data

Research using satellite remotely sensed data, even within any single scientific discipline, often lacked a unifying principle or strategy with which to plan or integrate studies conducted over an area so large that exhaustive examination is infeasible, e.g., the U.S.A. However, such a series of studies would seem to be at the heart of what makes satellite remote sensing unique, that is the ability to select for study from among remotely sensed data sets distributed widely over the U.S., over time, where the resources do not exist to examine all of them. Using this philosophical underpinning and the concept of a unifying principle, an operational procedure for developing a sampling strategy and formal testable hypotheses was constructed. The procedure is applicable across disciplines, when the investigator restates the research question in symbolic form, i.e., quantifies it. The procedure is set within the statistical framework of general linear models. The dependent variable is any arbitrary function of remotely sensed data and the independent variables are values or levels of factors which represent regional climatic conditions and/or properties of the Earth's surface. These factors are operationally defined as maps from the U.S. National Atlas (U.S.G.S., 1970). Eighty-five maps from the National Atlas, representing climatic and surface attributes, were automated by point counting at an effective resolution of one observation every 17.6 km (11 miles) yielding 22,505 observations per map. The maps were registered to one another in a two step procedure producing a coarse, then fine scale registration. After registration, the maps were iteratively checked for errors using manual and automated procedures. The error free maps were annotated with identification and legend information and then stored as card images, one map to a file. A sampling design will be accomplished through a regionalization analysis of the National Atlas data base (presently being conducted). From this analysis a map of homogeneous regions of the U.S.A. will be created and samples (LANDSAT scenes) assigned by region.

Labovitz, M. L.↗

Analytic and Computational Perspectives of Multi-Scale Theory for Homogeneous, Laminated Composite, and Sandwich Beams and Plates

This paper reviews the theoretical foundation and computational mechanics aspects of the recently developed shear-deformation theory, called the Refined Zigzag Theory (RZT). The theory is based on a multi-scale formalism in which an equivalent single-layer plate theory is refined with a robust set of zigzag local layer displacements that are free of the usual deficiencies found in common plate theories with zigzag kinematics. In the RZT, first-order shear-deformation plate theory is used as the equivalent single-layer plate theory, which represents the overall response characteristics. Local piecewise-linear zigzag displacements are used to provide corrections to these overall response characteristics that are associated with the plate heterogeneity and the relative stiffnesses of the layers. The theory does not rely on shear correction factors and is equally accurate for homogeneous, laminated composite, and sandwich beams and plates. Regardless of the number of material layers, the theory maintains only seven kinematic unknowns that describe the membrane, bending, and transverse shear plate-deformation modes. Derived from the virtual work principle, RZT is well-suited for developing computationally efficient, C0-continuous finite elements; formulations of several RZT-based elements are highlighted. The theory and its finite elements provide a unified and reliable computational platform for the analysis and design of high-performance load-bearing aerospace structures.

Tessler, Alexander↗

A Decision-Relevant Factor-Fixing Framework: Application to Uncertainty Analysis of a High-Dimensional Water Quality Model

Factor Fixing (FF) is a common method for reducing the number of model parameters to lower computational cost. FF typically starts with distinguishing the insensitive parameters from the sensitive and pursues uncertainty quantification (UQ) on the resulting reduced-order model, fixing each insensitive parameter at a fixed value. There is a need, however, to expand such a common approach to consider the effects of decision choices in the FF-UQ procedure on metrics of interest. Therefore, to guide the use of FF and increase confidence in the resulting dimension-reduced model, we propose a new adaptive framework consisting of four principles: (a) re-parameterize the model first to reduce obvious non-identifiable parameter combinations, (b) focus on decision relevance especially with respect to errors in quantities of interest (QoI), (c) conduct adaptive evaluation and robustness assessment of errors in the QoI across FF choices as sample size increases, and (d) reconsider whether fixing is warranted. The framework is demonstrated on a spatially-distributed water quality model. The error in estimates of QoI caused by FF can be estimated using a Polynomial Chaos Expansion (PCE) surrogate model. Built with 70 model runs, the surrogate is computationally inexpensive to evaluate and can provide global sensitivity indices for free. For the selected catchment, just two factors may provide an acceptably accurate estimate of model uncertainty in the average annual load of Total Suspended Solids (TSS), suggesting that reducing the uncertainty in these two parameters is a priority for future work before undertaking further formal uncertainty quantification.

54 ENVIRONMENTAL SCIENCES↗

Nearest neighbour distributions: New statistical measures for cosmological clustering

ABSTRACT The use of summary statistics beyond the two-point correlation function to analyse the non-Gaussian clustering on small scales, and thereby, increasing the sensitivity to the underlying cosmological parameters, is an active field of research in cosmology. In this paper, we explore a set of new summary statistics – the k-Nearest Neighbour Cumulative Distribution Functions (kNN-CDF). This is the empirical cumulative distribution function of distances from a set of volume-filling, Poisson distributed random points to the k-nearest data points, and is sensitive to all connected N-point correlations in the data. The kNN-CDF can be used to measure counts in cell, void probability distributions, and higher N-point correlation functions, all using the same formalism exploiting fast searches with spatial tree data structures. We demonstrate how it can be computed efficiently from various data sets – both discrete points, and the generalization for continuous fields. We use data from a large suite of N-body simulations to explore the sensitivity of this new statistic to various cosmological parameters, compared to the two-point correlation function, while using the same range of scales. We demonstrate that the use of kNN-CDF improves the constraints on the cosmological parameters by more than a factor of 2 when applied to the clustering of dark matter in the range of scales between 10 and $40\, h^{-1}\, {\rm Mpc}$. We also show that relative improvement is even greater when applied on the same scales to the clustering of haloes in the simulations at a fixed number density, both in real space, as well as in redshift space. Since the kNN-CDF are sensitive to all higher order connected correlation functions in the data, the gains over traditional two-point analyses are expected to grow as progressively smaller scales are included in the analysis of cosmological data, provided the higher order correlation functions are sensitive to cosmology on the scales of interest.

79 ASTRONOMY AND ASTROPHYSICS↗

Analytic and Computational Perspectives of Multi-Scale Theory for Homogeneous, Laminated Composite, and Sandwich Beams and Plates

This paper reviews the theoretical foundation and computational mechanics aspects of the recently developed shear-deformation theory, called the Refined Zigzag Theory (RZT). The theory is based on a multi-scale formalism in which an equivalent single-layer plate theory is refined with a robust set of zigzag local layer displacements that are free of the usual deficiencies found in common plate theories with zigzag kinematics. In the RZT, first-order shear-deformation plate theory is used as the equivalent single-layer plate theory, which represents the overall response characteristics. Local piecewise-linear zigzag displacements are used to provide corrections to these overall response characteristics that are associated with the plate heterogeneity and the relative stiffnesses of the layers. The theory does not rely on shear correction factors and is equally accurate for homogeneous, laminated composite, and sandwich beams and plates. Regardless of the number of material layers, the theory maintains only seven kinematic unknowns that describe the membrane, bending, and transverse shear plate-deformation modes. Derived from the virtual work principle, RZT is well-suited for developing computationally efficient, C(sup 0)-continuous finite elements; formulations of several RZT-based elements are highlighted. The theory and its finite element approximations thus provide a unified and reliable computational platform for the analysis and design of high-performance load-bearing aerospace structures.

Tessler, Alexander↗