Search NASA⌕ Search

SEARCH · Search NASA

Results for “proof”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 397 records · Page 22

Embedding Differential Dynamic Logic in PVS

Differential dynamic logic (dL) is a formal framework for specifying and reasoning about hybrid systems, i.e., dynamical systems that exhibit both continuous and discrete behaviors. These kinds of systems arise in many safety- and mission-critical applications. This paper presents a formalization of dL in the Prototype Verification System (PVS) that includes the semantics of hybrid programs and dL’s proof calculus. The formalization embeds dL into the PVS logic, resulting in a version of dL whose proof calculus is not only formally verified, but is also available for the verification of hybrid programs within PVS itself. This embedding, called Plaidypvs (Properly Assured Implementation of dL for Hybrid Program Verification and Specification), supports standard dL style proofs, but further leverages the capabilities of PVS to allow reasoning about entire classes of hybrid programs. The embedding also allows the user to import the well-established definitions and mathematical theories available in PVS.

PVS↗

Seeing is Believing: Monitoring Future Time Temporal Logic

Runtime monitors for future-time unbounded temporal logics like RVLTL, LTL 3 and FLTL, have double-exponential (2^2^n) worst-case space complexity bounds in size of the input formula. The semantics of these logics require monitors to perform general satisfiability solving for LTL expressions, a well-studied problem whose computational complexity is NP-hard and PSPACE-complete. This paper introduces an unbounded future-time linear temporal logic defined over a lattice. We call our logic an incremental temporal logic as it can be viewed as incrementally constructing proofs about the trace. On this account, we view online runtime monitoring as a decision procedure for proofs systems about incrementally growing traces. We demonstrate that our incremental temporal logic allows monitor construction to void satisfiability solving while still soundly detecting when the property is violated in an online fashion. This enables asymptotic improvements in space complexity. As proof, we provide a procedure to construct monitors that utilize linear space and time in the size of the input formula, while remaining constant in the size of the input stream and suitable for online monitoring. We further demonstrate, through several examples, that our incremental temporal logic is straightforward to adopt and practical for runtime verification.

temporal logic↗

Design and Hardware Progress on a Magnetically-Geared Actuator for Extremely Cold Lunar Environments

Introduction: Under the Motors for Dusty and Extremely Cold Environments (MDECE) Project, NASA Glenn Research Center is developing a magnetically-geared actuator for extremely cold space environments to avoid the wiring and significant efficiency penalty associated with heating grease-lubricated actuators as well as the stringent life and loading constraints imposed by dry film lubricated mechanical gears. The heating penalty can be equivalent to up to a 90% efficiency reduction in permanently shadowed regions on the Moon. This poster or presentation will summarize the progress made over the past 6-12 months on designing the fully-functional actuator and building a proof-of-concept actuator and testing it in an ambient environment. Design Progress: A critical design review was successfully completed at the end of June 2023. This presentation will touch on the key highlights from that review in the areas of electro-magnetic design and optimization, bearing optimization, thermal analysis, structural analysis, and mechanical design and manufacturing. The predicted technical performance measures of the actuator will be mentioned. The team is currently finishing some actions from the review and finalizing the drawing package in preparation for hardware procurement. Hardware Progress: Despite some significant delays in receiving fabricated parts and magnetic subassemblies, progress was made in manufacturing and assembling a proof-of-concept version of both the actuator’s magnetically-geared motor (Fig. 1) and the actuator’s cycloidal-type output magnetic gear stage (Fig. 2) [3]. The presentation will mention key lessons learned to date from the fabrication, assembly, and testing of the proof of concept.

Lunar surface↗

Formally Verified ZTA Requirements for OT/ICS Environments with Isabelle/HOL

The clean energy transformation includes the integration of distributed energy resources with the power grid, which has led to a substantial increase in the complexity of power grids infrastructure and the underlying operational technology environment. Power grids infrastructure represents an operational technology environment that has become a system of systems, integrating heterogeneous devices which are both software-and hardware-intensive; as a result, there are increasing demands to exploit advances in the commodity of software-hardware infrastructures to improve energy systems requirements such as cybersecurity and resilience. In such a setting, system requirements at different levels mix, which leads to vulnerabilities and undesirable outcomes. The use of formal methods to characterize and prove system requirements removes ambiguity, increases automation, and provides high levels of assurance and reliability. In this paper, we contribute a methodology and a framework for the system-level verification of zero trust architecture requirements in operational technology environments. We define a formal specification for the core functionalities of operational technology environments, the corresponding invariants, and security proofs. Of particular note is our modular approach for the formal verification of asynchronous interactions in operational technology environments. The formal specification and the proofs have been mechanized using the interactive theorem proving environment Isabelle/HOL.

formal methods↗

Discrete Superconvergence Analysis for Quantum Magnus Algorithms of Unbounded Hamiltonian Simulation

Motivated by various applications, unbounded Hamiltonian simulation has recently garnered great attention. Quantum Magnus algorithms, designed to achieve commutator scaling for time-dependent Hamiltonian simulation, have been found to be particularly efficient for such applications. When applied to unbounded Hamiltonian simulation in the interaction picture, they exhibit an unexpected superconvergence phenomenon. However, existing proofs are limited to the spatially continuous setting and do not extend to discrete spatial discretizations. Here, in this work, we provide the first superconvergence estimate in the fully discrete setting with a finite number of spatial discretization points N, and show that it holds with an error constant uniform in N. The proof is based on the two-parameter symbol class, which, to our knowledge, is applied for the first time in algorithm analysis. The key idea is to establish a semiclassical framework by identifying two parameters through the discretization number and the time step size rescaled by the operator norm, such that the semiclassical uniformity guarantees the uniformity of both. This approach may have broader applications in numerical analysis beyond the specific context of this work.

Borns-Weil, Yonah [University of California, Berke↗

Recent developments in mathematical aspects of relativistic fluids

Abstract We review some recent developments in mathematical aspects of relativistic fluids. The goal is to provide a quick entry point to some research topics of current interest that is accessible to graduate students and researchers from adjacent fields, as well as to researches working on broader aspects of relativistic fluid dynamics interested in its mathematical formalism. Instead of complete proofs, which can be found in the published literature, here we focus on the proofs’ main ideas and key concepts. After an introduction to the relativistic Euler equations, we cover the following topics: a new wave-transport formulation of the relativistic Euler equations tailored to applications; the problem of shock formation for relativistic Euler; rough (i.e., low-regularity) solutions to the relativistic Euler equations; the relativistic Euler equations with a physical vacuum boundary; relativistic fluids with viscosity. We finish with a discussion of open problems and future directions of research.

Disconzi, Marcelo (ORCID:0000000234497778)↗

Degrees of rate control and AutoDiff-driven direct sensitivity analysis in heterogeneous catalysis

Despite the wide application and benefits of the degree of rate control (DRC) analysis, several details remain argued, particularly about the conservation of DRCs at transient (TR) and steady-state (SS) conditions, especially for complex reaction networks. This work argues that previous proofs about the conservation properties of DRCs have been incomplete, and we provide new mathematical proofs at TR and SS conditions. In addition, we use both analytical (automatic differentiation) and numerical (finite difference) approaches to compute DRCs for the case study of ethane hydrogenolysis (EH) over Pt(111). This work confirms that at both TR and SS conditions, the sum of all DRCs, i.e., sum of the degrees of kinetic (DKRC) and thermodynamic rate control (DTRC), is conserved at zero. At SS conditions, the sum of DKRC is conserved at 1 while the sum of DTRC is conserved at −1. In corroboration of previous works, we show that the DTRC for any adsorbate at SS is equal to the product of the species coverage and a constant. In contrast, at TR conditions, the individual sums of both DTRC and DKRC are not conserved and can be any real number, with potential implications for the novel field of dynamic catalysis. Finally, we show that the conventional finite difference (FD) approach, only useful at SS, is prone to inaccuracy and very sensitive to the value of the differential change applied. The optimal differential value also varies significantly with system and rate definition. Consequently, we describe and illustrate in this work the application of the automatic differentiation (AD) approach for the more accurate determination of DRCs at both TR and SS conditions.

Automatic differentiation↗

Determining reference standard strength for neutron-irradiated reduced activation ferritic/martensitic steel F82H by Bayesian method

The deterministic approach widely adopted in the design of structural components relies on systematically defined design limits using empirically determined safety factors. However, this approach is not always appropriate because structures are subjected to a variety of loads in the practical environment, which may result in excessively conservative design limits. In recent years, a more rigorous probabilistic approach that incorporates material strength distributions has become an important solution. In the probabilistic approach, the probability density functions of material strength properties underpin the design criteria. Here, the objective of this study is to identify the density distribution functions that best describe tensile properties of irradiated F82H to define a reference strength for DEMO design. Due to the limited number of existing data, this study specifically employs a Bayesian prediction method based on Monte Carlo simulations to determine a material reference value with statistical reliability and to investigate its effectiveness. For example, the dependence of tensile properties of 300 °C irradiated materials on irradiation damage and the range predicted by 95% Bayesian estimation was evaluated. As a statistical model for the dose dependence of statistical parameters, the normal distribution exhibited a better fit for 0.2% proof strength and tensile strength, whereas the distribution of total elongation data gave comparable reference values for both the normal and Weibull distribution models. Both models gave comparable criteria for the distribution of total elongation data. The Weibull model also gave better results for uniform elongation. The function best describing the model was a logarithmic law for both 0.2% proof strength and tensile strength, while a power law for both total and uniform elongation, which allowed for more comprehensive data prediction of irradiation data with statistical accuracy for DEMO reactor design.

36 MATERIALS SCIENCE↗

Inverse Mapping of the Collision Kernel and Wall Flux Scaling in a Tall Convection‐Cloud Chamber Using Local Sensors and Knowledge‐Informed Deep Learning

Droplet collision–coalescence is a crucial process in cloud physics, but accurately representing this process under different dynamical conditions remains challenging. A proposed future convective‐cloud chamber aims to investigate this key process, but the method for observing it remains unclear, even though it is theoretically established that collision‐coalescence will occur. This study serves as a proof‐of‐concept demonstration of how knowledge‐informed deep learning, combined with measurement data from local sensors in the chamber, can be used to estimate the collision kernels, which determine how the droplet size distribution evolves during collision‐coalescence. In addition to estimating the collision kernel, we also address wall fluxes, another uncertain but important process that acts as a source of heat and moisture in the chamber. Ensemble runs of large‐eddy simulations are conducted by scaling the wall fluxes and the collision kernel, while the measured flow and cloud properties are used as inputs for a neural network. Results indicate that this approach successfully maps the scaling of wall fluxes and the collision kernel with biases of approximately 1% or less relative to the range of the target data. This proof‐of‐concept lays the groundwork for future applications; when the real measurements are available, real sensor data combined with the trained model presented in this work will enable estimation of the actual wall fluxes and collision kernel.

cloud chamber↗

Accelerating science: The usage of commercial clouds in ATLAS Distributed Computing

The ATLAS experiment at CERN is one of the largest scientific machines built to date and will have ever growing computing needs as the Large Hadron Collider collects an increasingly larger volume of data over the next 20 years. ATLAS is conducting R&D projects on Amazon Web Services and Google Cloud as complementary resources for distributed computing, focusing on some of the key features of commercial clouds: lightweight operation, elasticity and availability of multiple chip architectures. The proof of concept phases have concluded with the cloud-native, vendoragnostic integration with the experiment’s data and workload management frameworks. Google Cloud has been used to evaluate elastic batch computing, ramping up ephemeral clusters of up to O(100k) cores to process tasks requiring quick turnaround. Amazon Web Services has been exploited for the successful physics validation of the Athena simulation software on ARM processors. We have also set up an interactive facility for physics analysis allowing endusers to spin up private, on-demand clusters for parallel computing with up to 4 000 cores, or run GPU enabled notebooks and jobs for machine learning applications. The success of the proof of concept phases has led to the extension of the Google Cloud project, where ATLAS will study the total cost of ownership of a production cloud site during 15 months with 10k cores on average, fully integrated with distributed grid computing resources and continue the R&D projects.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Dry Deactivation of Sodium Metal in a Molten LiCl-KCl-CsCl-NaCl System

An experimental study was performed with the objective of investigating and characterizing a dry technique for deactivation of sodium metal in a molten salt system. The study was performed in three parts. First, proof-of-principle testing of the technique was performed at bench scale. It involved loading and melting tens of grams of clean sodium metal atop a pool of LiCl-KCl-CsCl eutectic at ∼300°C and then adding ammonium chloride particles while mixing. The ammonium chloride reacted with sodium to form sodium chloride and nitrogen/hydrogen off-gases. The sodium chloride assimilated into the salt pool, forming a quaternary salt mixture of LiCl-KCl-CsCl-NaCl. The proof-of-principle testing repeatedly exhibited complete deactivation of the loaded sodium metal. Second, characterization of a LiCl-KCl-CsCl-NaCl system was performed using differential scanning calorimetry to produce a partial phase diagram of LiCl-KCl-CsCl eutectic versus NaCl, which identified the liquidus, solidus, and two-phase regions of the quaternary system. Third, the dry deactivation technique was demonstrated at kg-scale in an inert atmosphere radiological glovebox with sodium metal that was previously separated in the same glovebox from uranium metal in unirradiated blanket elements for the Fermi-1 nuclear reactor. The quaternary salt product at the end of the demonstration was sampled and showed complete deactivation of the sodium metal. Here, in short, this study qualified a technique to completely deactivate batches of sodium metal in the absence of air or water. While this study focused on the deactivation of sodium metal, including bond sodium from unirradiated blanket elements, the technique is applicable to other sources of sodium metal, such as sodium metal from batteries. Furthermore, the technique could also be extended to other alkali metal systems, including lithium, sodium, potassium, rubidium, cesium, and mixtures thereof.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Identifiability and characterization of transmon qutrits through Bayesian experimental design

Robust control of a quantum system is essential to utilize the current noisy quantum hardware to its full potential, such as quantum algorithms. To achieve such a goal, a systematic search for an optimal control for any given experiment is essential. The design of optimal control pulses requires accurate numerical models and, therefore, accurate characterization of the system parameters. We present an online Bayesian approach for quantum characterization of qutrit systems, which automatically and systematically identifies optimal experiments that provide maximum information on the system parameters, thereby greatly reducing the number of experiments that need to be performed on the quantum testbed. Unlike most characterization protocols that provide point-estimates of the parameters, the proposed approach is able to estimate their probability distribution. The applicability of the Bayesian experimental design technique was demonstrated on test problems, where each experiment was defined by a parameterized control pulse. In addition to this, we also present an approach for iterative pulse extension, which is robust under uncertainties in transition frequencies and coherence times, and shot noise, despite being initialized with wide uninformative priors. Furthermore, we provide a mathematical proof of the theoretical identifiability of the model parameters and present conditions on the quantum state under which the parameters are identifiable. The proof and conditions for identifiability are presented for both closed and open quantum systems using the Schrödinger equation and the Lindblad master equation, respectively.

97 MATHEMATICS AND COMPUTING↗

Low-Density Parity-Check Stabilizer Codes as Gapped Quantum Phases: Stability under Graph-Local Perturbations

We generalize the proof of stability of topological order, due to Bravyi, Hastings, and Michalakis, to stabilizer Hamiltonians corresponding to low-density parity-check (LDPC) codes without the restriction of geometric locality in Euclidean space. We consider Hamiltonians 𝐻 0 defined by ⟦𝑁,𝐾,𝑑⟧ LDPC codes, which obey certain topological quantum order conditions: (i) code distance 𝑑 ≥ 𝑐⁢log (𝑁), implying local indistinguishability of ground states, and (ii) a mild condition on local and global compatibility of ground states—these include good quantum LDPC codes and the toric code on a hyperbolic lattice, among others. We consider stability under weak perturbations that are quasilocal on the interaction graph defined by 𝐻 0 and that can be represented as sums of bounded-norm terms. As long as the local perturbation strength is smaller than a finite constant, we show that the perturbed Hamiltonian has well-defined spectral bands originating from the 𝑂⁡(1) smallest eigenvalues of 𝐻 0 . The band originating from the smallest eigenvalue has 2 𝐾 states, is separated from the rest of the spectrum by a finite energy gap, and has exponentially narrow bandwidth 𝛿 =𝐶⁢𝑁⁢𝑒 −Θ⁡(𝑑) , which is tighter than the best-known bounds even in the Euclidean case. We also obtain that the new ground-state subspace is related to the initial-code subspace by a quasilocal unitary, allowing one to relate their physical properties. Our proof uses an iterative procedure that performs successive rotations to eliminate non-frustration-free terms in the Hamiltonian. Our results extend to quantum Hamiltonians built from classical LDPC codes, which give rise to stable symmetry-breaking phases. These results show that LDPC codes very generally define stable gapped quantum phases, even in the non-Euclidean setting, initiating a systematic study of such phases of matter.

mathematical physics↗

Demystifying Cyberattacks: Potential for Securing Energy Systems With Explainable AI : Preprint

Modernization of energy systems has led to in- creased interactions among multiple critical infrastructures and diverse stakeholders making the challenge of operational decision making more complex and at times beyond cognitive capabilities of human operators. The state-of-the-art machine learning and deep learning approaches show promise of supporting users with complex decision-making challenges, such as those occurring in our rapidly transforming cyber-physical energy systems. However, successful adoption of data-driven decision support technology for critical infrastructure will be dependent on the ability of these technologies to be trustworthy and contextually interpretable. In this paper, we investigate the feasibility of implementing XAI for interpretable detection of cyberattacks in the energy system. Leveraging a proof-of-concept simulation use case of detection of a data falsification attack on a photovoltaic system using XGBoost algorithm, we demonstrate how Local Interpretable Model-Agnostic Explanations (LIME), a flavor XAI approach, can help provide contextual and actionable interpretation of cyberattack detection.

artificial intelligence↗

Feynman diagrams for matter wave interferometry

We introduce a new theoretical framework based on Feynman diagrams to compute phase shifts in matter wave interferometry. The method allows for analytic computation of higher order quantum corrections, beyond the traditional semi-classical approximation. These additional terms depend on the finite size of the initial matter wavefunction and/or have higher order dependence on ℏ. We apply the method to compute the response of matter wave interferometers to power law potentials and potentials with an arbitrary spatial dependence. The analytic expressions are validated by comparing to numerical simulations, and estimates are provided for the scale of the quantum corrections to the phase shift response to the gravitational field of the earth, anharmonic trapping potentials, and gravitational fields from local proof masses. We also find that for certain experimentally feasible parameters, these corrections are large enough to be measured and could lead to systematic errors if they are not mitigated. We find that to first order in a spatially dependent potential, quantum corrections vanish when the initial matter wavepacket has spherical symmetry and the potential satisfies Laplace's equation. We anticipate these quantum corrections will be especially important for trapped matter wave interferometers and for free-space matter wave interferometers in the presence of proof masses. These interferometers are becoming increasingly sensitive tools for mobile inertial sensing, gravity surveying, tests of gravity and its interplay with quantum mechanics, and searches for dark energy.

Glick, Jonah [Northwestern U.; Fermilab] (ORCID:00↗

Fungal elemental profiling unleashed through rapid laser-induced breakdown spectroscopy (LIBS)

ABSTRACT Elemental profiling of fungal species as a phenotyping tool is an understudied topic and is typically performed to examine plant tissue or non-biological materials. Traditional analytical techniques such as inductively coupled plasma–optical emission spectroscopy (ICP-OES) and inductively coupled plasma–mass spectrometry (ICP-MS) have been used to identify elemental profiles of fungi; however, these techniques can be cumbersome due to the difficulty of preparing samples. Additionally, the instruments used for these techniques can be expensive to procure and operate. Laser-induced breakdown spectroscopy (LIBS) is an alternative elemental analytical technique—one that is sensitive across the periodic table, easy to use on various sample types, and is cost-effective in both procurement and operation. LIBS has not been used on axenic filamentous fungal isolates grown in substrate media. In this work, as a proof of concept, we used LIBS on two genetically distinct fungal species grown on a nutrient-rich and nutrient-poor substrate media to determine whether robust elemental profiles can be detected and whether differences between the fungal isolates can be identified. Our results demonstrate a distinct correlation between fungal species and their elemental profile, regardless of the substrate media, as the same strains shared a similar uptake of carbon, zinc, phosphorus, manganese, and magnesium, which could play a vital role in their survival and propagation. Independently, each fungal species exhibited a unique elemental profile. This work demonstrates a unique and valuable approach to rapidly phenotype fungi through optical spectroscopy, and this approach can be critical in understanding these fungi's behavior and interactions with the environment. IMPORTANCE Historically, ionomics, the elemental profiling of an organism or materials, has been used to understand the elemental composition in waste materials to identify and recycle heavy metals or rare earth elements, identify the soil composition in space exploration on the moon or Mars, or understand human disorders or disease. To our knowledge, ionomic profiling of microbes, particularly fungi, has not been investigated to answer applied and fundamental biological questions. The reason is that current ionomic analytical techniques can be laborious in sample preparation, fail to measure all potential elements accurately, are cost-prohibitive, or provide inconsistent results across replications. In our previous efforts, we explored whether laser-induced breakdown spectroscopy (LIBS) could be used in determining the elemental profiles of poplar tissue, which was successful. In this proof-of-concept endeavor, we undertook a transdisciplinary effort between applied and fundamental mycology and elemental analytical techniques to address the biological question of how LIBS can used for fungi grown axenically in a nutrient-rich and nutrient-poor environment.

59 BASIC BIOLOGICAL SCIENCES↗

Two-Stage Distributionally Robust Conic Linear Programming over 1-Wasserstein Balls

Here, this paper studies two-stage distributionally robust conic linear programming under constraint uncertainty over type-1 Wasserstein balls. We present optimality conditions for the dual of the worst-case expectation problem, which characterizes worst-case uncertain parameters for its inner maximization problem. This condition offers an alternative proof, a counterexample, and an extension to previous works. Additionally, the condition highlights the potential advantage of a specific distance metric for out-of-sample performance, as exemplified in a numerical study on a facility location problem with demand uncertainty. Furthermore, cutting-plane-based algorithms, equipped with a unified scenario generation framework, are proposed for addressing both unbounded support and second-stage dual feasible regions, with a finite convergence proof under less stringent assumptions.

Wasserstein↗

Data for A Generalized Platform for Artificial Intelligence-powered Autonomous Protein Engineering

Proteins are the molecular machines of life with numerous applications in energy, health, and sustainability. However, engineering proteins with desired functions for practical applications remains slow, expensive, and specialist-dependent. Here we report a generally applicable platform for autonomous enzyme engineering that integrates machine learning and large language models with biofoundry automation to eliminate the need for human intervention, judgement, and domain expertise. Requiring only an input protein sequence and a quantifiable way to measure fitness, this automated platform can be applied to engineer a wide array of proteins. As a proof of concept, we engineer Arabidopsis thaliana halide methyltransferase (AtHMT) for a 90-foldimprovement in substrate preference and 16-fold improvement in ethyl-transferase activity, along with developing a Yersinia mollaretii phytase (YmPhytase) variant with 26-fold improvement in activity at neutral pH. This is accomplished in four rounds over 4 weeks, while requiring construction and characterization of fewer than 500 variants for each enzyme. This platform for autonomous experimentation paves the way for rapid advancements across diverse industries, from medicine and biotechnology to renewable energy and sustainable chemistry.

AI/ML↗