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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 163 records · Page 9
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NASA NTRS1972

Longitudinal dynamic stability of a shuttle vehicle.

Analytical study of the longitudinal dynamic stability of a nonrolling, lifting vehicle gliding at hypersonic speeds. The analysis applies to shuttle vehicles designed for operating up to the rim of a planetary atmosphere. A general nondimensional time transformation is introduced to derive a unified second-order linear differential equation for the angle of attack, valid for all types of reentry of a general type of vehicle. The stability of motion is discussed for two fundamental regimes of flight that are based on widely different assumptions. For near ballistic entry along a straight line trajectory, the equation reduces to a confluent hypergeometric equation, the solution of which can be expressed in terms of Whittaker's function. Using a theorem in the theory of stability of differential equations, criteria for damped oscillations are derived. It is shown that the aerodynamic criteria for stability are the same as for the case of ballistic entry. In addition, for each vehicle configuration, and specified planetary atmosphere, there exists an altitude range where the angle of attack frequency is nearly equal to the orbital frequency causing instability in pitch. This resonance instability is due to the ellipticity of the orbit. Criteria for eccentricity instability are derived.

Vinh, N. X.↗
NASA NTRS1971

Stability of uncertain systems

The asymptotic properties of feedback systems are discussed, containing uncertain parameters and subjected to stochastic perturbations. The approach is functional analytic in flavor and thereby avoids the use of Markov techniques and auxiliary Lyapunov functionals characteristic of the existing work in this area. The results are given for the probability distributions of the accessible signals in the system and are proved using the Prohorov theory of the convergence of measures. For general nonlinear systems, a result similar to the small loop-gain theorem of deterministic stability theory is given. Boundedness is a property of the induced distributions of the signals and not the usual notion of boundedness in norm. For the special class of feedback systems formed by the cascade of a white noise, a sector nonlinearity and convolution operator conditions are given to insure the total boundedness of the overall feedback system.

Blankenship, G. L.↗
NASA NTRS1972

Representations of the language recognition problem for a theorem prover

Two representations of the language recognition problem for a theorem prover in first order logic are presented and contrasted. One of the representations is based on the familiar method of generating sentential forms of the language, and the other is based on the Cocke parsing algorithm. An augmented theorem prover is described which permits recognition of recursive languages. The state-transformation method developed by Cordell Green to construct problem solutions in resolution-based systems can be used to obtain the parse tree. In particular, the end-order traversal of the parse tree is derived in one of the representations. An inference system, termed the cycle inference system, is defined which makes it possible for the theorem prover to model the method on which the representation is based. The general applicability of the cycle inference system to state space problems is discussed. Given an unsatisfiable set S, where each clause has at most one positive literal, it is shown that there exists an input proof. The clauses for the two representations satisfy these conditions, as do many state space problems.

Minker, J.↗
DOE OSTI2024

Chiral symmetry and Atiyah-Patodi-Singer index theorem for staggered fermions

We consider the Atiyah-Patodi-Singer (APS) index theorem corresponding to the chiral symmetry of a continuum formulation of staggered fermions called Kähler-Dirac fermions, which have been recently investigated as an ingredient in lattice constructions of chiral gauge theories. We point out that there are two notions of chiral symmetry for Kähler-Dirac fermions, both having a mixed perturbative anomaly with gravity leading to index theorems on closed manifolds. By formulating these theories on a manifold with boundary, we find the APS index theorems corresponding to each of these symmetries, necessary for a complete picture of anomaly inflow, using a recently discovered physics-motivated proof. We comment on a fundamental difference between the nature of these two symmetries by showing that a sensible local, symmetric boundary condition only exists for one of the two symmetries. This sheds light on how these symmetries behave under lattice discretization, and in particular on their use for recent symmetric-mass generation proposals.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

New magnetic symmetries in (d + 2)-dimensional QED

Previous analyses of asymptotic symmetries in QED have shown that the subleading soft photon theorem implies a Ward identity corresponding to a charge generating divergent large gauge transformations on the asymptotic states at null infinity. In this work, we demonstrate that the subleading soft photon theorem is equivalent to a more general Ward identity. The charge corresponding to this Ward identity can be decomposed into an electric piece and a magnetic piece. The electric piece generates the Ward identity that was previously studied, but the magnetic piece is novel, and implies the existence of an additional asymptotic “magnetic” symmetry in QED.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Quantum minimal surfaces from quantum error correction

We show that complementary state-specific reconstruction of logical (bulk) operators is equivalent to the existence of a quantum minimal surface prescription for physical (boundary) entropies. This significantly generalizes both sides of an equivalence previously shown by Harlow[1]; in particular, we do not require the entanglement wedge to be the same for all states in the code space. In developing this theorem, we construct an emergent bulk geometry for general quantum codes, defining ``areas'' associated to arbitrary logical subsystems, and argue that this definition is ``functionally unique.'' We also formalize a definition of bulk reconstruction that we call ``state-specific product unitary’’ reconstruction. This definition captures the quantum error correction (QEC) properties present in holographic codes and has potential independent interest as a very broad generalization of QEC; it includes most traditional versions of QEC as special cases. Our results extend to approximate codes, and even to the ``non-isometric codes'' that seem to describe the interior of a black hole at late times.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Latent variable Gaussian process models: A rank‐based analysis and an alternative approach

Abstract Gaussian process (GP) models have been extended to emulate expensive computer simulations with both qualitative/categorical and quantitative/continuous variables. Latent variable (LV) GP models, which have been recently developed to map each qualitative variable to some underlying numerical LVs, have strong physics‐based justification and have achieved promising performance. Two versions use LVs in Cartesian (LV‐Car) space and hyperspherical (LV‐sph) space, respectively. Despite their success, the effects of these different LV structures are still poorly understood. This article illuminates this issue with two contributions. First, we develop a theorem on the effect of the ranks of the qualitative factor correlation matrices of mixed‐variable GP models, from which we conclude that the LV‐sph model restricts the interactions between the input variables and thus restricts the types of response surface data with which the model can be consistent. Second, following a rank‐based perspective like in the theorem, we propose a new alternative model named LV‐mix that combines the LV‐based correlation structures from both LV‐Car and LV‐sph models to achieve better model flexibility than them. Through extensive case studies, we show that LV‐mix achieves higher average accuracy compared with the existing two.

Tao, Siyu↗
DOE OSTI2022

Stability of exact solutions of the (2 + 1)-dimensional nonlinear Schrödinger equation with arbitrary nonlinearity parameter κ

In this work, we consider the nonlinear Schrödinger equation (NLSE) in 2+1 dimensions with arbitrary nonlinearity exponent κ in the presence of an external confining potential. Exact solutions to the system are constructed, and their stability as we increase the 'mass' (i.e., the L 2 norm) and the nonlinearity parameter κ is explored. Here we observe both theoretically and numerically that the presence of the confining potential leads to wider domains of stability over the parameter space compared to the unconfined case. Our analysis suggests the existence of a stable regime of solutions for all κ as long as their mass is less than a critical value M*(κ). Furthermore, we find that there are two different critical masses, one corresponding to width perturbations and the other one to translational perturbations. The results of Derrick's theorem are also obtained by studying the small amplitude regime of a four-parameter collective coordinate (4CC) approximation. A numerical stability analysis of the NLSE shows that the instability curve M*(κ) versus κ lies below the two curves found by Derrick's theorem and the 4CC approximation. In the absence of the external potential, κ = 1 demarcates the separation between the blowup regime and the stable regime. In this 4CC approximation, for κ < 1, when the mass is above the critical mass for the translational instability, quite complicated motions of the collective coordinates are possible. Energy conservation prevents the blowup of the solution as well as confines the center of the solution to a finite spatial domain. We call this regime the 'frustrated' blowup regime and give some illustrations. In an appendix, we show how to extend these results to arbitrary initial ground state solution data and arbitrary spatial dimension d.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1988

Inflation in anisotropic scalar-tensor theories

The existence of an inflationary phase in anisotropic Scalar-Tensor Theories is investigated by means of a conformal transformation that allows us to rewrite these theories as gravity minimally coupled to a scalar field with a nontrivial potential. The explicit form of the potential is then used and the No Hair Theorem concludes that there is an inflationary phase in all open or flat anisotropic spacetimes in these theories. Several examples are constructed where the effect becomes manifest.

Pimentel, Luis O.↗
NASA NTRS2001

Automated Theorem Proving in High-Quality Software Design

The amount and complexity of software developed during the last few years has increased tremendously. In particular, programs are being used more and more in embedded systems (from car-brakes to plant-control). Many of these applications are safety-relevant, i.e. a malfunction of hardware or software can cause severe damage or loss. Tremendous risks are typically present in the area of aviation, (nuclear) power plants or (chemical) plant control. Here, even small problems can lead to thousands of casualties and huge financial losses. Large financial risks also exist when computer systems are used in the area of telecommunication (telephone, electronic commerce) or space exploration. Computer applications in this area are not only subject to safety considerations, but also security issues are important. All these systems must be designed and developed to guarantee high quality with respect to safety and security. Even in an industrial setting which is (or at least should be) aware of the high requirements in Software Engineering, many incidents occur. For example, the Warshaw Airbus crash, was caused by an incomplete requirements specification. Uncontrolled reuse of an Ariane 4 software module was the reason for the Ariane 5 disaster. Some recent incidents in the telecommunication area, like illegal "cloning" of smart-cards of D2GSM handies, or the extraction of (secret) passwords from German T-online users show that also in this area serious flaws can happen. Due to the inherent complexity of computer systems, most authors claim that only a rigorous application of formal methods in all stages of the software life cycle can ensure high quality of the software and lead to real safe and secure systems. In this paper, we will have a look, in how far automated theorem proving can contribute to a more widespread application of formal methods and their tools, and what automated theorem provers (ATPs) must provide in order to be useful.

Schumann, Johann↗
NASA NTRS2009

Hyperbolic Orbits and the Planetary Flylby Anomaly

Space probes in the Solar System have experienced unexpected changes in velocity known as the flyby anomaly [1], as well as shifts in acceleration referred to as the Pioneer anomaly [2-4]. In the case of Earth flybys, ESA s Rosetta spacecraft experienced the flyby effect and NASA s Galileo and NEAR satellites did the same, although MESSENGER did not possibly due to a latitudinal property of gravity assists. Measurements indicate that both anomalies exist, and explanations have varied from the unconventional to suggestions that new physics in the form of dark matter might be the cause of both [5]. Although dark matter has been studied for over 30 years, there is as yet no strong experimental evidence supporting it [6]. The existence of dark matter will certainly have a significant impact upon ideas regarding the origin of the Solar System. Hence, the subject is very relevant to planetary science. We will point out here that one of the fundamental problems in science, including planetary physics, is consistency. Using the well-known virial theorem in astrophysics, it will be shown that present-day concepts of orbital mechanics and cosmology are not consistent for reasons having to do with the flyby anomaly. Therefore, the basic solution regarding the anomalies should begin with addressing the inconsistencies first before introducing new physics.

Wilson, T.L.↗
NASA NTRS1975

A Theoretical Investigation of the Input Characteristics of a Rectangular Cavity-Backed Slot Antenna

Equations which represent the magnetic and electric stored energies are derived for an infinite section of rectangular waveguide and a rectangular cavity. These representations which are referred to as being physically observable are obtained by considering the difference in the volume integrals appearing in the complex Poynting theorem. It is shown that the physically observable stored energies are determined by the field components that vanish in a reference plane outside the aperture. These physically observable representations are used to compute the input admittance of a rectangular cavity-backed slot antenna in which a single propagating wave is assumed to exist in the cavity. The slot is excited by a voltage source connected across its center; a sinusoidal distribution is assumed in the slot. Input-admittance calculations are compared with measured data. In addition, input-admittance curves as a function of electrical slot length are presented for several size cavities. For the rectangular cavity backed slot antenna, the quality factor and relative bandwidth were computed independently by using these energy relationships. It is shown that the asymptotic relationship which is usually assumed to exist between the quality bandwidth and the reciprocal of relative bandwidth is equally valid for the rectangular cavity backed slot antenna.

Cockrell, C. R.↗
NASA NTRS1978

Forced oscillations in quadratically damped systems

Bayliss (1975) has studied the question whether in the case of linear differential equations the relationship between the stability of the homogeneous equations and the existence of almost periodic solutions to the inhomogeneous equation is preserved by finite difference approximations. In the current investigation analogous properties are considered for the case in which the damping is quadratic rather than linear. The properties of the considered equation for arbitrary forcing terms are examined and the validity is proved of a theorem concerning the characteristics of the unique solution. By using the Lipschitz continuity of the mapping and the contracting mapping principle, almost periodic solutions can be found for perturbations of the considered equation. Attention is also given to the Lipschitz continuity of the solution operator and the results of numerical tests which have been conducted to test the discussed theory.

Bayliss, A.↗
DOE OSTI2026

Analytical small-signal stability analysis of low-inertia power system frequency response considering secondary frequency regulation

Modern power systems are increasingly vulnerable to frequency instability as inverter-based resources (IBRs) replace synchronous machines and reduce system rotational inertia. Existing small-signal frequency stability assessment methods are either computationally intensive, relying on simulation-driven approaches, or lack analytical stability regions that explicitly account for secondary frequency response (SFR). This paper introduces new analytical frameworks that enable evaluation small-signal frequency stability while explicitly incorporating tunable IBR and SFR parameters. Using Kharitonov’s theorem with an overbounding approach, explicit small-signal stability criteria are derived. In addition, based on Białas’ criterion and Hurwitz matrix, analytical stability regions are established to reveal feasible design spaces for SFR and IBR parameters tuning. Extensive Matlab/Simulink-based simulations validate the accuracy and computational efficiency of the proposed methods, demonstrating that coordinated tuning of SFR and IBR parameters can substantially enhance system resilience. By bridging analytical rigor with practical tunability, this work provides an analytical framework for assessing small-signal frequency stability in low-inertia grids, supporting the real-time, scalable, and resilient operation of sustainable power systems.

14 SOLAR ENERGY↗
DOE OSTI2022

MIONet: Learning Multiple-Input Operators via Tensor Product

As an emerging paradigm in scientific machine learning, neural operators aim to learn operators, via neural networks, that map between infinite-dimensional function spaces. Several neural operators have been recently developed. However, all the existing neural operators are only designed to learn operators defined on a single Banach space; i.e., the input of the operator is a single function. Here, for the first time, we study the operator regression via neural networks for multiple-input operators defined on the product of Banach spaces. We first prove a universal approximation theorem of continuous multiple-input operators. We also provide a detailed theoretical analysis including the approximation error, which provides guidance for the design of the network architecture. Based on our theory and a low-rank approximation, we propose a novel neural operator, MIONet, to learn multiple-input operators. MIONet consists of several branch nets for encoding the input functions and a trunk net for encoding the domain of the output function. Here, we demonstrate that MIONet can learn solution operators involving systems governed by ordinary and partial differential equations. In our computational examples, we also show that we can endow MIONet with prior knowledge of the underlying system, such as linearity and periodicity, to further improve accuracy.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1987

The field-aligned flow approximation for electrons within layers possessing a normal mass flux - A corollary to the deHoffmann-Teller theorem

In this paper, an approximate extension of the deHoffmann-Teller (1950) theorem for electrons within layers possessing a normal mass flux is derived. It is shown that the deHoffmann-Teller frame electron bulk velocity is nearly parallel to the magnetic field everywhere through those one-dimensional time-stationary layers which possess a normal mass flux, even though electric field perpendicular to the magnetic field exists throughout such layers. Examples of layers of this class are the fast and slow shocks as well as rotational discontinuities.

Scudder, J. D.↗
NASA NTRS1975

Random coding strategies for minimum entropy

This paper proves that there exists a fixed random coding strategy for block coding a memoryless information source to achieve the absolute epsilon entropy of the source. That is, the strategy can be chosen independent of the block length. The principal new tool is an easy result on the semicontinuity of the relative entropy functional of one probability distribution with respect to another. The theorem generalizes a result from rate-distortion theory to the 'zero-infinity' case.

Posner, E. C.↗
DOE OSTI2024

Efficient Unitary Designs from Random Sums and Permutations

A unitary k-design is an ensemble of unitaries that matches the first k moments of the Haar measure. In this work, we provide two efficient constructions of k-designs on n-qubits using new random matrix theory techniques. Our first construction is based on exponentiating sums of random i.i.d. Hermitian matrices and uses O(k2n2)-many gates. In the spirit of central limit theorems, we show that this random sum approximates the Gaussian Unitary Ensemble (GUE). We then show that the product of just two exponentiated GUE matrices is already approximately Haar random. Our second construction is based on products of exponentiated sums of random permutations and uses Õ(k poly (n)) many gates. The k dependence is optimal (up to polylogarithmic factors) and is inherited from the efficiency of existing k-wise independent permutations. Furthermore, replacing random permutations with quantum-secure pseudorandom permutations (PRPs), we also obtain a pseudorandom unitary (PRU) ensemble that is secure under nonadaptive queries. A central feature of both proofs is a new connection between the polynomial method in quantum query complexity and the large-dimension (N) expansion in random matrix theory. In particular, the first construction uses the polynomial method to control high moments of certain random matrix ensembles without requiring delicate Weingarten calculations. In doing so, we define and solve a moment problem on the unit circle, asking whether a finite number of equally weighted points can reproduce a given set of moments. In our second construction, the key step is to exhibit an orthonormal basis for irreducible representations of the partition algebra that has a low-degree large-N expansion. This allows us to show that the distinguishing probability is a low-degree rational polynomial of the dimension N.

algebra↗