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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.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1981

The SIFT computer and its development

Software Implemented Fault Tolerance (SIFT) is an aircraft control computer designed to allow failure probability of less than 10 to the -10th/hour. The system is based on advanced fault-tolerance computing and validation methodology. Since confirmation of reliability by observation is essentially impossible, system reliability is estimated by a Markov model. A mathematical proof is used to justify the validity of the Markov model. System design is represented by a hierarchy of abstract models, and the design proof comprises mathematical proofs that each model is, in fact, an elaboration of the next more abstract model.

Goldberg, J.↗
DOE OSTI2019

Finite Mathematics, Finite Quantum Theory and a Conjecture on the Nature of Time

We first give a rigorous mathematical proof that classical mathematics (involving such notions as infinitely small/large, continuity etc.) is a special degenerate case of finite one in the formal limit when the characteristic p of the field or ring in finite mathematics goes to infinity. We consider a finite quantum theory (FQT) based on finite mathematics and prove that standard continuous quantum theory is a special case of FQT in the formal limit p→∞. The description of states in standard quantum theory contains a big redundancy of elements: the theory is based on real numbers while with any desired accuracy the states can be described by using only integers, i.e. rational and real numbers play only auxiliary role. Therefore, in FQT infinities cannot exist in principle, FQT is based on a more fundamental mathematics than standard quantum theory and the description of states in FQT is much more thrifty than in standard quantum theory. Space and time are purely classical notions and are not present in FQT at all. In the present paper we discuss how classical equations of motions arise as a consequence of the fact that p changes, i.e. p is the evolution parameter. It is shown that there exist scenarios when classical equations of motion for cosmological acceleration and gravity can be formulated exclusively in terms of quantum quantities without using space, time and standard semiclassical approximation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Grid Cyber-Security Strategy in an Attacker-Defender Model

The progression of cyber-attacks on the cyber-physical system is analyzed by the Probabilistic, Learning Attacker, and Dynamic Defender (PLADD) model. Although our research does apply to all cyber-physical systems, we focus on power grid infrastructure. The PLADD model evaluates the effectiveness of moving target defense (MTD) techniques. We consider the power grid attack scenarios in the AND configurations and OR configurations. In addition, we consider, for the first time ever, power grid attack scenarios involving both AND configurations and OR configurations simultaneously. Cyber-security managers can use the strategy introduced in this manuscript to optimize their defense strategies. Specifically, our research provides insight into when to reset access controls (such as passwords, internet protocol addresses, and session keys), to minimize the probability of a successful attack. Our mathematical proof for the OR configuration of multiple PLADD games shows that it is best if all access controls are reset simultaneously. For the AND configuration, our mathematical proof shows that it is best (in terms of minimizing the attacker's average probability of success) that the resets are equally spaced apart. We introduce a novel concept called hierarchical parallel PLADD system to cover additional attack scenarios that require combinations of AND and OR configurations.

97 MATHEMATICS AND COMPUTING↗
NASA NTRSDate not supplied

Applying Formal Methods to Safety-Critical Systems

How do you know a proof is correct? Traditionally, mathematical proofs are socially verified – at least one human, following a set of implicit rules of natural language and logic, determines if the proof is believable. If the proof becomes overly tedious and/or is essential to some safety- or mission-critical application, it becomes necessary to determine the soundness to a higher standard. 'Formal methods' refer to mathematically rigorous techniques and tools that enable specification, design, and verification of hardware and software systems. The specification used in formal methods are statements in a mathematical logic while the formal verifications are deductions in that logic. Formal methods can be difficult or time/resource intensive, but offer a higher level of assurance than standard verification through testing or handwritten proofs. This talk will introduce formal methods, motivated by applications of interest to NASA, including uncrewed aircraft operations in the national airspace, urban air environments, and wildfire areas. The audience will be given a crash course in mechanically verified proofs in the Prototype Verification System (PVS), an interactive theorem prover.

Formal Methods↗
NASA NTRSDate not supplied

Intelligent Lemma Selection for Formal Methods Proofs

To help in formally verifying the correctness of various systems, NASA constructs mathematical proofs using the proof assistant PVS (Prototype Verification System). Throughout this effort, NASA has amassed a library of tens of thousands of proven lemmas. While these lemmas can often be applied to new problems, their abundance can make lemma selection a non-trivial task. This project focuses on creating a lemma selector for use in PVS based on existing systems MePo, MaSh, and MeSh, which were written for other proof assistants. An initial benchmark system makes selections based on symbol-level similarity while the final lemma selector is a hybrid system, combining the classical approach used in the benchmark with a machine learning approach which leverages the lemmas' past usage.

Connor T Baumler↗
DOE OSTI2025

Autonomous Operations for Advanced Reactors Utilizing Supervisory Control

Automation is a critical tenet of reactor plant operations as reliance on nuclear energy increases. Nuclear power plants require a large workforce which does not scale with output; that is, the cost per megawatt increases as reactor output becomes smaller. The economic viability of advanced reactors, particularly small modular reactors (SMRs) and microreactors, requires a significantly reduced onsite workforce. The logical solution is establishing a systematic process of elimination of reliance on human operators, and to the extent possible, replacing these actions with automated functions. In this paper, we propose a method for such transformation to establish a robust technical basis to enable transition to autonomy. Our method is based on finite state automata (FSA)—also known as finite state machines (FSMs). Relying on this method allows us to exploit the rich set of mathematical proofs available in the field of regular languages. FSA are one of the mathematical tools to model discrete event systems (DES). These properties are applied to produce an automated startup controller for the Massachusetts Institute of Technology Research Reactor (MITR). The startup procedure is captured in terms of discrete changes from one state to another while an independent supervisory control system directs the sequence of states and alerts a human in the event of an abnormal operation. First, the design and behavior of the MITR rod control system were modeled in Simulink. Then, the startup procedure was applied to the rod control system and the DES performed a startup by procedurally withdrawing rods to the subcritical position. The simulation also stops rod motion in response to an uncontrollable event and restarts rod motion once the event has been cleared.

46 - INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AN↗
DOE OSTI2021

Proof that Combining the Forced-collision and DXTRAN Monte Carlo Variance-reduction Techniques is Fair

This report provides mathematical proof that the MCNP DXTRAN (also known in other codes as forced-flight) and forced-collision variance-reduction techniques do not bias the expected value of Monte Carlo simulation estimates when combined. Proof is also provided that the techniques are unbiased when used independently. To prove that the techniques are unbiased, this report derives the first History Score Moment Equation (HSME) for non-multiplying media employing only forced collisions, only DXTRAN, and then both the variance-reduction techniques combined, as defined next. The HSMEs are found by forming the History Score Probability Density Functions (HSPDFs) and then taking the first score moment. Following its derivation, each HSME with a variance-reduction technique employed is reduced to the HSME for an analog simulation. Because the HSME represents the expected contribution to estimators in the simulation, reducing the HSME with variance reduction to the analog HSME shows that the simulation is unbiased despite the variance-reduction technique considered in the HSME. Analysis regarding higher-score moments of each technique is the subject of prior work and is not addressed herein. Throughout this work, the phase space p is defined to be the particle position x, direction-of-flight unit vector $\hat{Ω}$, energy E, and statistical weight w, $$p ≡ (x; \hat{Ω}; E; w).$$ A reduced phase-space excluding the statistical weight of the particle, $$r ≡ (x; \hat{Ω}; E),$$ is also used.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

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↗
NASA NTRS2004

A Generic Software Safety Document Generator

Formal certification is based on the idea that a mathematical proof of some property of a piece of software can be regarded as a certificate of correctness which, in principle, can be subjected to external scrutiny. In practice, however, proofs themselves are unlikely to be of much interest to engineers. Nevertheless, it is possible to use the information obtained from a mathematical analysis of software to produce a detailed textual justification of correctness. In this paper, we describe an approach to generating textual explanations from automatically generated proofs of program safety, where the proofs are of compliance with an explicit safety policy that can be varied. Key to this is tracing proof obligations back to the program, and we describe a tool which implements this to certify code auto-generated by AutoBayes and AutoFilter, program synthesis systems under development at the NASA Ames Research Center. Our approach is a step towards combining formal certification with traditional certification methods.

Denney, Ewen↗
DOE OSTI2024

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↗
NASA NTRS2009

Assurance Cases for Proofs as Evidence

Proof-carrying code (PCC) provides a 'gold standard' for establishing formal and objective confidence in program behavior. However, in order to extend the benefits of PCC - and other formal certification techniques - to realistic systems, we must establish the correspondence of a mathematical proof of a program's semantics and its actual behavior. In this paper, we argue that assurance cases are an effective means of establishing such a correspondence. To this end, we present an assurance case pattern for arguing that a proof is free from various proof hazards. We also instantiate this pattern for a proof-based mechanism to provide evidence about a generic medical device software.

Chaki, Sagar↗
NASA NTRS2016

The Mathematics of Dispatchability Revisited

Dispatchability is an important property for the efficient execution of temporal plans where the temporal constraints are represented as a Simple Temporal Network (STN). It has been shown that every STN may be reformulated as a dispatchable STN, and dispatchability ensures that the temporal constraints need only be satisfied locally during execution. Recently it has also been shown that Simple Temporal Networks with Uncertainty, augmented with wait edges, are Dynamically Controllable provided every projection is dispatchable. Thus, the dispatchability property has both theoretical and practical interest. One thing that hampers further work in this area is the underdeveloped theory. The existing definitions are expressed in terms of algorithms, and are less suitable for mathematical proofs. In this paper, we develop a new formal theory of dispatchability in terms of execution sequences. We exploit this to prove a characterization of dispatchability involving the structural properties of the STN graph. This facilitates the potential application of the theory to uncertainty reasoning.

control↗
NASA NTRS1987

A generalized procedure for constructing an upwind based TVD scheme

A generalized formulation for constructing second- and higher-order accurate TVD (total variation diminishing) schemes is presented. A given scheme is made TVD by limiting antidiffusive flux differences with some linear functions, so-called limiters. The general idea of the formulation and its mathematical proof of Harten's TVD conditions is shown by applying the Lax-Wendroff method to scalar nonlinear equations and a constant-coefficient system of conservation laws. For the system of equations, several definitions are derived for the argument used in the limiter function and present their performance in numerical experiments. The formulation is extended to the nonlinear system. It is demonstrated that the present procedure can easily convert existing central or upwind, and second- or higher-order differencing schemes to preserve monotonicity and yield physically admissible solutions. The formulation is simple mathematically as well as numerically; both matrix-vector multiplication and Riemann solver are avoided. Although the notion of TVD is based on the initial value problem, application to the steady Euler equations of the formulation is also made.

Liou, Meng-Sing↗
NASA NTRS1987

A generalized procedure for constructing an upwind-based TVD scheme

A generalized formulation for constructing second- and higher-order accurate TVD (total variation diminishing) schemes is presented. A given scheme is made TVD by limiting antidiffusive flux differences with some nonlinear functions, so-called limiters. The general idea of the formulation and its mathematical proof of Harten's TVD conditions is shown by applying the Lax-Wendroff method to a scalar nonlinear equation and constant-coefficient system of conservation laws. For the system of equations, several definitions are derived for the argument used in the limiter function and present their performance to numerical experiments. Then the formulation is formally extended to the nonlinear system of equations. It is demonstrated that use of the present procedure allows easy conversion of existing central or upwind, and second- or higher-order differencing schemes so as to preserve monotonicity and to yield physically admissible solutions. The formulation is simple mathematically as well as numerically; neither matrix-vector multiplication nor Riemann solver is required. Roughly twice as much computational effort is needed as compared to conventional scheme. Although the notion of TVD is based on the initial value problem, application to the steady Euler equations of the formulation is also made. Numerical examples including various ranges of problems show both time- and spatial-accuracy in comparison with exact solutions.

Liou, Meng-Sing↗
DOE OSTI2025

Boundary Corrections for Kernel Approximation to Differential Operators

The kernel-based approach to operator approximation for partial differential equations has been shown to be unconditionally stable for linear PDEs and numerically exhibit unconditional stability for non-linear PDEs. These methods have the same computational cost as an explicit finite difference scheme but can exhibit order reduction at boundaries. In previous work on periodic domains, order reduction was addressed, yielding high-order accuracy. The issue addressed in this work is the elimination of order reduction of the kernel-based approach for a more general set of boundary conditions. Further, we consider the case of both first and second order operators. To demonstrate the theory, we provide not only the mathematical proofs but also experimental results by applying various boundary conditions to different types of equations. The results agree with the theory, demonstrating a systematic path to high order for kernel-based methods on bounded domains.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

The second-generation Shifted Boundary Method and its numerical analysis

Recently, the Shifted Boundary Method (SBM) was proposed within the class of unfitted (or immersed, or embedded) finite element methods. By reformulating the original boundary value problem over a surrogate (approximate) computational domain, the SBM avoids integration over cut cells and the associated problematic issues regarding numerical stability and matrix conditioning. Accuracy is maintained by modifying the original boundary conditions using Taylor expansions. Hence the name of the method, that shifts the location and values of the boundary conditions. In this article, we present enhanced variational SBM formulations for the Poisson and Stokes problems with improved flexibility and robustness. These simplified variational forms allow to relax some of the assumptions required by the mathematical proofs of stability and convergence of earlier implementations. First, we show that these new SBM implementations can be proved asymptotically stable and convergent even without the rather restrictive assumption that the inner product between the normals to the true and surrogate boundaries is positive. Second, we show that it is not necessary to introduce a stabilization term involving the tangential derivatives of the solution at Dirichlet boundaries, therefore avoiding the calibration of an additional stabilization parameter. Finally, we prove enhanced L 2 -estimates without the cumbersome assumption – of earlier proofs – that the surrogate domain is convex. Instead we rely on a conventional assumption that the boundary of the true domain is smooth, which can also be replaced by requiring convexity of the true domain. The aforementioned improvements open the way to a more general and efficient implementation of the Shifted Boundary Method, particularly in complex three-dimensional geometries. We complement these theoretical developments with numerical experiments in two and three dimensions.

42 ENGINEERING↗
DOE OSTI2018

Review of Authentication Strategies and Trends for Distributed Energy Resources (DERs)

In this study we review literature on machine to machine (M2M) authentication and encryption pertaining to communication with grid-attached power inverters. We regard security recommendations from NIST, constrained device recommendations from CoAP, as well as influences from the existing markets. We will not focus on passwordless or multifactor schemes of user authentication, the handover/roaming authentication of mobile systems, or the group authentication of WiMAX/LTE communications. The de-facto standards for authentication and encryption are certificate-based public key cryptography and AES, respectively. While certificate-based public key cryptography is widely adopted, certificate management is seen as an Achilles heel of public key infrastructure (PKI). State of the art authentication system research includes work on certificateless authentication; however, much work in the areas of privacy preservation, efficient or lightweight systems continue to be based in public key methods. We will see efforts such as bilinear pairing, aggregate message authentication codes, one-time signatures, and Merkle trees surface and resurface with improved authentication approaches. Though research continues to produce new encryption schemes, AES prevails as a viable choice, as it can be implemented across a variety of resource constrained devices. Other lightweight encryption algorithms often employ the same fundamental addition-rotation-xor operations as AES while achieving higher efficiency, but at steep tradeoffs to security. Despite mathematical proofs of the security of cryptographic algorithms, in practice the greatest weaknesses continue to be incurred during implementation. Security researchers will find edge cases and bugs that allow unintentional behavior. In the following sections, accepted methodologies of authentication and encryption are discussed. Due diligence for securing M2M communications requires consideration during planning, design, implementation and product lifetime, as opposed to a set-it and forget-it policy. Best practices can be gleaned from published successes and failures, with no single end-all, be-all detailed solution.

97 MATHEMATICS AND COMPUTING↗