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At least 91 records · Page 5

A proof of the theorem regarding the distribution of lift over the span for minimum induced drag

The proof of the theorem that the elliptical distribution of lift over the span is that which will give rise to the minimum induced drag has been given in a variety of ways, generally speaking too difficult to be readily followed by the graduate of the average good technical school of the present day. In the form of proof this report makes an effort to bring the matter more readily within the grasp of this class of readers.

Durand, W F

Space network scheduling benchmark: A proof-of-concept process for technology transfer

This paper describes a detailed proof-of-concept activity to evaluate flexible scheduling technology as implemented in the Request Oriented Scheduling Engine (ROSE) and applied to Space Network (SN) scheduling. The criteria developed for an operational evaluation of a reusable scheduling system is addressed including a methodology to prove that the proposed system performs at least as well as the current system in function and performance. The improvement of the new technology must be demonstrated and evaluated against the cost of making changes. Finally, there is a need to show significant improvement in SN operational procedures. Successful completion of a proof-of-concept would eventually lead to an operational concept and implementation transition plan, which is outside the scope of this paper. However, a high-fidelity benchmark using actual SN scheduling requests has been designed to test the ROSE scheduling tool. The benchmark evaluation methodology, scheduling data, and preliminary results are described.

Moe, Karen

Axial focusing of impact energy in the Earth's interior: Proof-of-principle tests of a new hypothesis

A causal link between major impact events and global processes would probably require a significant change in the thermal state of the Earth's interior, presumably brought about by coupling of impact energy. One possible mechanism for such energy coupling from the surface to the deep interior would be through focusing due to axial symmetry. Antipodal focusing of surface and body waves from earthquakes is a well-known phenomenon which has previously been exploited by seismologists in studies of the Earth's deep interior. Antipodal focusing from impacts on the Moon, Mercury, and icy satellites has also been invoked by planetary scientists to explain unusual surface features opposite some of the large impact structures on these bodies. For example, 'disrupted' terrains have been observed antipodal to the Caloris impact basis on Mercury and Imbrium Basin on the Moon. Very recently there have been speculations that antipodal focusing of impact energy within the mantle may lead to flood basalt and hotspot activity, but there has not yet been an attempt at a rigorous model. A new hypothesis was proposed and preliminary proof-of-principle tests for the coupling of energy from major impacts to the mantle by axial focusing of seismic waves was performed. Because of the axial symmetry of the explosive source, the phases and amplitudes are dependent only on ray parameter (or takeoff angle) and are independent of azimuthal angle. For a symmetric and homogeneous Earth, all the seismic energy radiated by the impact at a given takeoff angle will be refocused (minus attenuation) on the axis of symmetry, regardless of the number of reflections and refractions it has experienced. Mantle material near the axis of symmetry will experience more strain cycles with much greater amplitude than elsewhere and will therefore experience more irreversible heating. The situation is very different than for a giant earthquake, which in addition to having less energy, has an asymmetric focal mechanism and a larger area. Two independent proof-of-principle approaches were used. The first makes use of seismic simulations, which are being performed with a realistic Earth model to determine the degree of focusing along the axis and to estimate the volume of material, if any, that experiences significant irreversible heating. The second involves two-dimensional hydrodynamic code simulations to determine the stress history, internal energy, and temperature rise as a function of radius along the axis.

Boslough, M. B.

Diagnosing a Failed Proof in Fault-Tolerance: A Disproving Challenge Problem

This paper proposes a challenge problem in disproving. We describe a fault-tolerant distributed protocol designed at NASA for use in a fly-by-wire system for next-generation commercial aircraft. An early design of the protocol contains a subtle bug that is highly unlikely to be caught in fault injection testing. We describe a failed proof of the protocol's correctness in a mechanical theorem prover (PVS) with a complex unfinished proof conjecture. We use a model checking suite (SAL) to generate a concrete counterexample to the unproven conjecture to demonstrate the existence of a bug. However, we argue that the effort required in our approach is too high and propose what conditions a better solution would satisfy. We carefully describe the protocol and bug to provide a challenging but feasible case study for disproving research.

Pike, Lee

A Measure-Theoretic Proof of the Markov Property for Hybrid Systems with Markovian Inputs

The behavior of a general hybrid system in discrete time can be represented by a non-linear difference equation x(k+1) = Fk(x(k), theta(k)), where theta(k) is assumed to be a finite state Markov chain. An important step in the stability analysis of these systems is to establish the Markov property of (x(k), theta(k)). There are, however, no complete proofs of this property which are simple to understand. This paper aims to correct this problem by presenting a complete and explicit proof, which uses only basic measure-theoretical concepts.

Tejada, Arturo

Post-Correlation Processing for the VLBI2010 Proof-of-Concept System

For the past three years, the MIT Haystack Observatory and the broadband team have been developing a proof-of-concept broadband geodetic VLBI microwave (2-12 GHz) receiver. Also on-going at Haystack is the development of post-correlation processing needed to extract the geodetic observables. Using this processing, the first fully-phase-calibrated geodetic fringes have been produced from observations conducted with the proof-of-concept system. The results we present show that the phase-calibrated phase residuals from four 512 MHz bands spanning 2 GHz have an RMS phase variation of 8deg which corresponds to a delay uncertainty of 12 ps.

Beaudoin, Christopher

Querying Proofs (Work in Progress)

We motivate and introduce the basis for a query language designed for inspecting electronic representations of proofs. We argue that there is much to learn from large proofs beyond their validity, and that a dedicated query language can provide a principled way of implementing a family of useful operations.

Aspinall, David

Correctness Proof of a Self-Stabilizing Distributed Clock Synchronization Protocol for Arbitrary Digraphs

This report presents a deductive proof of a self-stabilizing distributed clock synchronization protocol. It is focused on the distributed clock synchronization of an arbitrary, non-partitioned digraph ranging from fully connected to 1-connected networks of nodes while allowing for differences in the network elements. This protocol does not rely on assumptions about the initial state of the system, and no central clock or a centrally generated signal, pulse, or message is used. Nodes are anonymous, i.e., they do not have unique identities. There is no theoretical limit on the maximum number of participating nodes. The only constraint on the behavior of the node is that the interactions with other nodes are restricted to defined links and interfaces. We present a deductive proof of the correctness of the protocol as it applies to the networks with unidirectional and bidirectional links. We also confirm the claims of determinism and linear convergence.

Malekpour, Mahyar R.

External Vision Systems (XVS) Proof-of-Concept Flight Test Evaluation

NASA's Fundamental Aeronautics Program, High Speed Project is performing research, development, test and evaluation of flight deck and related technologies to support future low-boom, supersonic configurations (without forward-facing windows) by use of an eXternal Vision System (XVS). The challenge of XVS is to determine a combination of sensor and display technologies which can provide an equivalent level of safety and performance to that provided by forward-facing windows in today's aircraft. This flight test was conducted with the goal of obtaining performance data on see-and-avoid and see-to-follow traffic using a proof-of-concept XVS design in actual flight conditions. Six data collection flights were flown in four traffic scenarios against two different sized participating traffic aircraft. This test utilized a 3x1 array of High Definition (HD) cameras, with a fixed forward field-of-view, mounted on NASA Langley's UC-12 test aircraft. Test scenarios, with participating NASA aircraft serving as traffic, were presented to two evaluation pilots per flight - one using the proof-of-concept (POC) XVS and the other looking out the forward windows. The camera images were presented on the XVS display in the aft cabin with Head-Up Display (HUD)-like flight symbology overlaying the real-time imagery. The test generated XVS performance data, including comparisons to natural vision, and post-run subjective acceptability data were also collected. This paper discusses the flight test activities, its operational challenges, and summarizes the findings to date.

Shelton, Kevin J.

Modeling of proof mass self-gravity field for the Laser Interferometry Space Antenna (LISA)

This paper describes the development of the self-gravity modeling tool used to predict and control the motion of one of the proof masses of the orbiting LISA gravitational wave detector. LISA is a space-borne gravitational wave detector, which is formed by three spacecraft orbiting the Sun and forming the vertices of an equilateral triangle with a side of 5 million km in length. Requirements on the forces and moments, and the force gradients and moment gradients, applied to the proof mass exist. This paper computes these quantities analytically, so that gravitational balancing considerations can now be done effectively.

Quadrelli, Marco B.

CHP-PRA: Sensorimotor Countermeasures Proof of Concept

The capabilities included in Crew Health and Performance (CHP) systems are designed to keep the crew healthy, happy, and productive. In doing so, the CHP system allows reductions in human related risks to be realized. All human missions, though particularly future Artemis and Mars missions, have constraints on the mass and volume allocated to the CHP system. Thus, trades must be made on how to best buy down risk while still meeting other requirements. Understanding how different CHP capabilities influence medical, performance, and long-term health risks is key to making informed choices among these trades. To address this, an integrated CHP Probabilistic Risk Assessment (PRA) model is being developed. Much like how IMPACT is designed to allow medical resource trades informed by medical risks, CHP PRA will enable analogous trades in human system risks across all CHP functions and capabilities. There are 29 Human System Risk Board (HSRB) risk areas to consider for model implementation. This effort focused solely on the implementation of countermeasures associated with sensorimotor risk. The framework and lessons learned from this proof of concept will benefit the implementation of other risks and countermeasures. Astronauts experience sensorimotor changes when entering or exiting a microgravity environment. While most sensorimotor issues are resolved within a few days, they pose a serious risk to crew health and performance during the adaptation period. This adaptation period aligns with gravity transitions and key mission phases where the crew members may be required to complete challenging tasks ideally with an undisturbed sensorimotor system. Countermeasures such as training or pharmaceuticals can be used to mitigate risk. This effort began by identifying physiological changes to the sensorimotor system that could lead to functional performance decrements or medical conditions and potential countermeasures, so that the overall effect of sensorimotor disturbance on human risk could be captured. We then selected example countermeasures, mapped relationships between countermeasures and outcomes, and used results from existing sensorimotor investigations to define the relationship between a sensorimotor countermeasure and subsequent performance of a sensorimotor-affected task. Specifically, using shuttle landing performance data, we compared the use or absence of inflight training capabilities to yield a relative performance change that can be applied to the prediction of the risk associated with manual control performance in future missions, as depicted in the figure. This sensorimotor proof of concept demonstrates how HRP research information can be transformed into quantifiable relationships to describe changes in HSRB medical and performance risks.

Caroline R Austin

Proof-of-Concept for a Long-Term Health Metric to Quantify End of Mission Health Status in Astronauts

NASA has long used Probabilistic Risk Assessment (PRA) when high-stakes decisions need to be made about complex systems. For spaceflight medical risk, the Human Research Program’s Medical Extensible Dynamic Probabilistic Risk Assessment Tool (MEDPRAT) is a significant step towards robustly quantifying the risk to crew health during exploration missions. However, there remains a significant gap in the ability to comprehensively characterize and assess risk across the disparate functionalities and capabilities which comprise the entire Crew Health and Performance (CHP) system. To fill this gap, the Crew Health and Performance – Probabilistic Risk Assessment (CHP-PRA) project aims to perform risk characterization for the CHP system by assessing performance risk in addition to medical risk. This effort also includes quantifying Long-Term Health (LTH) risk in addition to in-mission risk outcomes within the CHP-PRA results. LTH risk encompasses the timeframe from immediately post-flight, through the rest of an astronaut’s career, through retirement, and until death. A proof-of-concept LTH risk metric is based on medical condition end-state, as defined by the Evidence Library, capturing the spaceflight specific medical impacts persisting into post-flight[1]. Condition outcomes in the Evidence Library progress through three Clinical Phases (CP): the diagnostic phase (CP1), the treatment/convalescent phase (CP2), and the end-state phase (CP3) which represents the detrimental effects of the condition after the crew member has recovered to the maximal extent. Each CP has an associated Task Impairment (TI), defined as the degree of crew incapacity due to experiencing the condition, and is quantified with a 0-1 range. Conditions with an associated CP3 (e.g. Sepsis, Traumatic Hypovolemic Shock, Sudden Cardiac Arrest, etc.) typically have serious consequences that can cause an astronaut to be fully or partially debilitated throughout the remainder of the mission. Consequently, the Cumulative CP3 TI End-of-Mission Health Status Metric is developed by CHP-PRA to quantify the cumulative effects of all conditions which progressed to the CP3 state throughout the entirety of the mission. Hence, this End-of-Mission Health Status Metric attempts to serve as an indicator of an astronaut’s health state at the time of landing. The severity of the lingering effects of in-mission medical events are dependent on mission activities and the level of available in-mission medical care. This allows the associated cumulative TI metric to be used in comparison with the crew’s end of mission health status for different levels of in-mission resources. This presentation provides the strategy for using CP3 as an LTH metric component, as well as a proof-of-concept demonstration of LTH risk characterization using this component.

long term health

On the completeness of contraction map proof method for holographic entropy inequalities

The contraction map proof method is the commonly used method to prove holographic entropy inequalities. Existence of a contraction map corresponding to a holographic entropy inequality is a sufficient condition for its validity. But is it also necessary? In this note, we answer that question in affirmative for all linear holographic entropy inequalities with rational coefficients. We show that the pre-image of a non-contraction map is not a hypercube, but a proper cubical subgraph, and show that this manifests as alterations to the geodesic structure in the bulk, which leads to the violation of inequalities by holographic geometries obeying the RT formula.

97 MATHEMATICS AND COMPUTING

Active control of laser beam pointing for the Zettawatt-Equivalent Ultrashort pulse laser System: a proof-of-principle study with 16-inch optics

We present a proof-of-principle study of active beam-pointing control for the Zettawatt-Equivalent Ultrashort pulse laser System (ZEUS) using a piezo-actuated 16-inch mirror. To the best of our knowledge, this is the largest actively controlled mirror reported in a high-power laser system. A simple proportional feedback control was implemented based on a field-programmable gate array, which reduced the standard deviation of beam-pointing fluctuations by 91% to 0.075 μrad in the horizontal direction and by 78% to 0.25 μrad in the vertical direction. We also demonstrated the elimination of long-term pointing jitter caused by temperature drift using the same apparatus.

laser pointing control

A Proof of the Asymptotic Variance of Path Length Estimators for Single-Collision Monte Carlo Source Iteration in the Thick Diffusion Limit

Here, we prove a theorem relating the variance of path length estimators for single-collision Monte Carlo source iteration to a parameter that becomes infinitesimally small in an important physical regime arising in radiative transfer. In our usage, “single-collision Monte Carlo source iteration” refers to Monte Carlo Boltzmann transport methods in which each Monte Carlo particle history includes no more than a single collision, and the physics of multiple scattering is modeled by lagging the scattering source term and iterating until this term converges. Our theorem can be used to construct variance reduction techniques which improve the order of the estimator variance. This enables calculations that would otherwise require impractically large sample sizes to achieve practical estimator uncertainties. We believe this is the first postulation of a theorem relating estimator variance to a limiting case parameter for single-collision Monte Carlo source iteration, and the first proof of such a theorem. We illustrate the theorem’s value with an example in which the authors of a transport method used the theorem to design a variance reduction technique that improved the uncertainty of their solution by a factor of about 500 for a proxy problem from radiative transfer that contains both optically-thick and optically-thin material.

Mathematics and Computing

Full Scale HEPA Filter Encapsulation in Ultra-High-Performance Grout - Proof of Concept

The Hanford Tank Waste Treatment and Immobilization Plant (WTP) currently being constructed to treat radioactive waste, includes vitrification facilities for both the high-level waste (HLW) and low activity waste (LAW) fractions. Operation of the WTP will produce contaminated high-efficiency particulate air filters (HEPA), as part of the solid secondary waste (SSW) stream. The HEPA filters receive off-gas from the vessel vent header and primary off-gas treatment system in LAW Facility and remove particulate contaminants including 99 Tc and 129 I salts. The current disposal method for HEPA filters is encapsulation in metal containers using cementitious material (CM) and disposal in the Integrated Disposal Facility (IDF). Results from the 2017 IDF Performance Assessment (PA) WRPS (2018) demonstrated that while compliance is maintained for the 1000 year compliance period mandated by DOE O 435.1 and its accompanying manual, release of constituents from the HEPA filters result in exceedance of the performance objective imposed as the groundwater regulatory limit at later times. For example, at about 1500 years post-closure, solid secondary waste (SSW), including HEPA filters is predicted to become a dominant contributor to 99 Tc release and over the 10,000-year sensitivity analysis period, SSW is the dominant contributor of 129 I release to the groundwater. The estimated release could potentially be reduced if the HEPA filters are not compacted and waste containers could be distributed throughout a large space, thereby diluting the contaminant release. Additionally, a better cementitious material could be used to encapsulate the HEPA filters. One alternative method for disposal of contaminated HEPA filters is encapsulation of the filters in ultra high-performance grout (UHPG). UHPG is a variation of ultra-high-performance concrete (UHPC) is commonly used in the prestressed concrete industry for large structural members. Recent studies of UHPG show it has excellent properties for containing radionuclides such as 99 Tc and 129 I Nichols and Kaplan (2021). This report presents the results of the first attempt to encapsulate a clean, full-size HEPA filter in UHPG and evaluate the effectiveness of the immobilization process and final waste form. A full-scale proof-of-concept simulated waste form was prepared by encapsulating a HEPA filter in a 110-gallon stainless steel (SS) drum using UHPG. A change from Type I/II PC to Type 1L PLC was made after American Rock Products informed the team that they would no longer be using Type I/II by the end of 2024 and the northwest was phasing out Type I/II PC overall. Type I/II PC used in previous studies of UHPG for encapsulation (Nichols and Kaplan 2021). After the UHPG was cured both the scaled mockup and the full-scale simulated waste forms were sectioned for visual examination. UHPG completely encapsulated the filters and bonded to the external surfaces of materials comprising the filters. No cracks were observed in the sectioned waste forms.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W

A Proof for the Unbiased Nature of Range-Doppler Measurements in Coarse-Resolution Dechirp-on-Receive Feedback Synthetic Aperture Radar Navigation

In feedback synthetic aperture radar (SAR) navigation, observables extracted from SAR range-Doppler images correct position and velocity errors accumulated within an associated navigation system. Unlike most other sensors, which produce measurements without input from a navigation system, SARs require a prior estimate of the radar’s position and velocity to adjust the radar’s matched filter during range-Doppler image formation. Consequently, it is possible for position and velocity errors within a navigation system to manifest as additional errors (biases) in the range-Doppler measurement observables. Prior work has not tackled this possibility in the context of feedback SAR navigation with a dechirp-on-receive radar. This paper offers a proof demonstrating that range-Doppler observables extracted from coarse-resolution vertical SAR images formed with a dechirp-on-receive radar may be safely modeled as unbiased measurements of the radar’s true position and velocity despite the presence of moderate navigation errors.

dechirp-on-receive