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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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Nonlinear susceptibilities for weakly turbulent magnetized plasma: Electromagnetic formalism

This is a companion paper to the previous work [P. H. Yoon, Phys. Plasmas 31, 032309 (2024)] in which the nonlinear susceptibilities of weakly turbulent magnetized plasma are derived under a simplifying assumption of electrostatic interaction. The present paper extends the analysis to a general situation of electromagnetic interaction. The main novelty of the previous and present papers is that by employing the Bessel function addition theorem, the mathematical definitions for the susceptibilities are substantially simplified, a procedure that has not been discussed in the existing literature. In the present paper, a full set of Maxwell’s equations are considered in conjunction with the nonlinear Vlasov equation, which is solved by a perturbative method. The result is a fully general nonlinear susceptibility, given in tensorial form, which is applicable for weakly turbulent magnetized plasmas.

Materials Science↗
DOE OSTI2024

Convexity, Squeezing, and the Elekes-Szabó Theorem

Here, this paper explores the relationship between convexity and sum sets. In particular, we show that elementary number theoretical methods, principally the application of a squeezing principle, can be augmented with the Elekes-Szabó Theorem in order to give new information. Namely, if we let $A \subset \mathbb R$, we prove that there exist $a,a' \in A$ such that\[\left | \frac{(aA+1)^{(2)}(a'A+1)^{(2)}}{(aA+1)^{(2)}(a'A+1)} \right | \gtrsim |A|^{31/12}.\]We are also able to prove that\[\max \{|A+ A-A|, |A^2+A^2-A^2|, |A^3 + A^3 - A^3|\} \gtrsim |A|^{19/12}.\]Both of these bounds are improvements of recent results and takes advantage of computer algebra to tackle some of the computations.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1989

A torus bifurcation theorem with symmetry

Hopf bifurcation in the presence of symmetry, in situations where the normal form equations decouple into phase/amplitude equations is described. A theorem showing that in general such degeneracies are expected to lead to secondary torus bifurcations is proved. By applying this theorem to the case of degenerate Hopf bifurcation with triangular symmetry it is proved that in codimension two there exist regions of parameter space where two branches of asymptotically stable two-tori coexist but where no stable periodic solutions are present. Although a theory was not derived for degenerate Hopf bifurcations in the presence of symmetry, examples are presented that would have to be accounted for by any such general theory.

Vangils, S. A.↗
NASA NTRS2010

A Machine-Checked Proof of A State-Space Construction Algorithm

This paper presents the correctness proof of Saturation, an algorithm for generating state spaces of concurrent systems, implemented in the SMART tool. Unlike the Breadth First Search exploration algorithm, which is easy to understand and formalise, Saturation is a complex algorithm, employing a mutually-recursive pair of procedures that compute a series of non-trivial, nested local fixed points, corresponding to a chaotic fixed point strategy. A pencil-and-paper proof of Saturation exists, but a machine checked proof had never been attempted. The key element of the proof is the characterisation theorem of saturated nodes in decision diagrams, stating that a saturated node represents a set of states encoding a local fixed-point with respect to firing all events affecting only the node s level and levels below. For our purpose, we have employed the Prototype Verification System (PVS) for formalising the Saturation algorithm, its data structures, and for conducting the proofs.

Catano, Nestor↗
NASA NTRS1980

Long-time predictions in nonlinear dynamics

It is known that nonintegrable dynamical systems do not allow precise predictions concerning their behavior for arbitrary long times. The available series solutions are not uniformly convergent according to Poincare's theorem and numerical integrations lose their meaningfulness after the elapse of arbitrary long times. Two approaches are the use of existing global integrals and statistical methods. This paper presents a generalized method along the first approach. As examples long-time predictions in the classical gravitational satellite and planetary problems are treated.

Szebehely, V.↗
DOE OSTI2022

Index Theorems, Generalized Hall Currents, and Topology for Gapless Defect Fermions

In this work, we show how the index of the fermion operator from the Euclidean action can be used to uncover the existence of gapless modes living on defects (such as edges and vortices) in topological insulators and superconductors. The 1-loop Feynman diagram that computes the index reveals an analog of the quantum Hall current flowing on and off the defect—even in systems without conserved currents or chiral anomalies—and makes explicit the interplay between topology in momentum and coordinate space. We provide several explicit examples.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1994

Comparison between Liouville's theorem and observed latitudinal distributions of trapped ions in the plasmapause region

The presence of anisotropic plasma distributions, trapped at the Earth's magnetic equator, has consequences for the electric field structure which must exist in equilibrium along the magnetic field line. Data from SCATHA and Dynamics Explorer 1 indicate that the core ion distributions at the magnetic equator can be well described as bi-Maxwellian distributions, with a perpendicular temperature an order of magnitude larger than the parallel temperature. A collisionless model is developed for the variation in plasma parameters, following the forms developed by Whipple (1977). If the core electron anisotropy is low, the resulting electric field of approximately 0.1 microV/m is pointed away from the equator. Under these conditions the self-consistent electric field will not overcome the effects of magnetic trapping. The resulting potential distribution results in a local maximum in total plasma density at the equator. Only when the electron distribution is primarily field-aligned can there be a density minimum at the equator. Comparisons are made between this model and the observed variations in DE 1 plasma parameters with latitude.

Olsen, R. C.↗
DOE OSTI2021

Magnetic properties of alternating Hubbard ladders

We explore the Hubbard Hamiltonian on ladders where the number of sites per rung alternates between two and three. These geometries are bipartite with nonequal or equal number of sites on the two sublattices. Thus they share a key feature of the Hubbard model in a class of lattices which Lieb has shown analytically to exhibit long-range ferrimagnetic order while being amenable to powerful numeric approaches developed for quasi-one-dimensional geometries. The density matrix renormalization group (DMRG) method is used to obtain the groundstate properties, e.g., excitation gaps, charge and spin densities as well as their correlation functions at half filling. We show the existence of long-range ferrimagnetic order in the one-dimensional ladder geometries. Our work provides detailed quantitative results which complement the general theorem of Lieb for generalized bipartite lattices. It also addresses the issue of how the alternation between quasi-long-range order and spin liquid behavior for uniform ladders with odd and even numbers of legs might be affected by a regular alternation pattern.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1989

Simple proof of the concavity of the entropy power with respect to Gaussian noise

A very simple proof of M. H. Costa's result that the entropy power of Xt = X + N (O, tI) is concave in t, is derived as an immediate consequence of an inequality concerning Fisher information. This relationship between Fisher information and entropy is found to be useful for proving the central limit theorem. Thus, one who seeks new entropy inequalities should try first to find new inequalities about Fisher information, or at least to exploit the existing ones in new ways.

Dembo, Amir↗
DOE OSTI2020

Optimal Estimation Retrievals and Their Uncertainties: What Every Atmospheric Scientist Should Know

Remote sensing instruments are heavily used to provide observations for both the operational and research communities. These sensors do not provide direct observations of the desired atmospheric variables, but instead, retrieval algorithms are necessary to convert the indirect observations into the variable of interest. It is critical to be aware of the underlying assumptions made by many retrieval algorithms, including that the retrieval problem is often ill posed and that there are various sources of uncertainty that need to be treated properly. In short, the retrieval challenge is to invert a set of noisy observations to obtain estimates of atmospheric quantities. The problem is often complicated by imperfect forward models, by imperfect prior knowledge, and by the existence of nonunique solutions. Optimal estimation (OE) is a widely used physical retrieval method that combines measurements, prior information, and the corresponding uncertainties based on Bayes’s theorem to find an optimal solution for the atmospheric state. Furthermore, OE also allows the relative contributions of the different sources of error to the uncertainty in the final retrieved atmospheric state to be understood. Here, we provide a novel Python library to illustrate the use of OE for inverse problems in the atmospheric sciences. We introduce two example problems: how to retrieve drop size distribution parameters from radar observations and how to retrieve the temperature profile from ground-based microwave sensors. Using these examples, we discuss common pitfalls, how the various error sources impact the retrieval, and how the quality of the retrieval results can be quantified.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1982

Feedback stabilization and control of linear neutral systems

The first problem treated here is the realization and stabilization of linear neutral systems with discrete delays. It is shown that any autonomous linear neutral system with discrete delays is zero-state equivalent to an abstract linear system over a local ring of operators. Using the abstract model, the basic existence question for neutral realization is then settled. For general infinite dimensional linear systems, there is no precise analog of the finite dimensional state space isomorphism theorem. Because of this, the notion of spectral minimality must be introduced. For the case of single input-single output systems, realizations are obtained that are both minimal and spectrally minimal. Using the Cruz-Hale theory of stable D-operators, conditions are given that ensure that any poles introduced into the realization are strictly contained in the left half plane and indeed are characterized as characteristic values of the D-operator. The problem of the feedback stabilization of neutral systems is then considered using the abstract model. It is shown that, for neutral systems with commensurable delays and a stable D-operator in the sense of Cruz and Hale, Morses theorem (1976) on pole assignment over a PID implies stabilizability in the reachable case.

Tarn, T. J.↗
NASA NTRS1972

On implicit equations in nonlinear network analysis.

Derivation of conditions for existence of unique solutions to implicit equations of the form y = f(x, u) or x = h(x, u) which are frequently encountered in the analysis of nonlinear networks. The existence of such solutions is demonstrated by applying the principle of contraction mapping and by ascertaining the possibility of a functional inversion according to the Palais (1959) theorem.

Sathe, S. T.↗
DOE OSTI2025

Lie-algebraic classical simulations for quantum computing

The classical simulation of quantum dynamics plays an important role in our understanding of quantum complexity and in the development of quantum technologies. Efficient techniques such as those based on the Gottesman-Knill theorem for Clifford circuits, tensor networks for low entanglement-generating circuits, or Wick's theorem for fermionic Gaussian states have become central tools in quantum computing. In this work, we contribute to this body of knowledge by presenting a framework for classical simulations, dubbed “𝔤-sim”, which is based on the underlying Lie algebraic structure of the dynamical process. When the dimension of the algebra grows at most polynomially in the system size, there exist observables for which the simulation is efficient. Indeed, we show that 𝔤-sim enables new regimes for classical simulations, is able to deal with certain forms of noise in the evolution, as well as can be used to tackle several paradigmatic variational and nonvariational quantum computing tasks. For the former, we perform Lie-algebraic simulations to train and optimize parametrized quantum circuits (thus effectively showing that some variational models can be dequantized), design enhanced parameter initialization strategies, solve tasks of quantum circuit synthesis, and train a quantum-phase classifier. For the latter, we report large-scale noiseless and noisy simulations on benchmark problems. By comparing the limitations of 𝔤-sim and certain Wick's theorem-based simulations, we find that the two methods become inefficient for different types of states or observables, hinting at the existence of distinct, nonequivalent resources for classical simulation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Normal modes, rotational inertia, and thermal fluctuations of trapped ion crystals

The normal modes of a trapped ion crystal are derived using an approach based on the Hermitian properties of the system’s dynamical matrix. This method is equivalent to the standard Bogoliubov method, but for classical systems it is arguably simpler and more general in that canonical coordinates are not necessary. The theory is developed for stable, unstable, and neutrally-stable systems. The method is then applied to ion crystals in a Penning trap. Reduced eigenvalue problems for the case of large applied magnetic field are developed, for which the spectrum breaks into E x B drift modes, axial modes, and cyclotron modes. Thermal fluctuation levels in these modes are analyzed and shown to be consistent with the Bohr-van-Leeuwen theorem, provided that neutrally-stable modes associated with crystal rotations are included in the analysis. An expression for the rotational inertia of the crystal is derived, and a magnetic contribution to this inertia, which dominates in large magnetic fields, is described. An unusual limit is discovered for the special case of spherically-symmetric confinement, in which the rotational inertia does not exist and changes in angular momentum leave the rotation frequency unaffected.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2006

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↗
DOE OSTI2023

Accurate real space iterative reconstruction (RESIRE) algorithm for tomography

Tomography has made a revolutionary impact on the physical, biological and medical sciences. The mathematical foundation of tomography is to reconstruct a three-dimensional (3D) object from a set of two-dimensional (2D) projections. As the number of projections that can be measured from a sample is usually limited by the tolerable radiation dose and/or the geometric constraint on the tilt range, a main challenge in tomography is to achieve the best possible 3D reconstruction from a limited number of projections with noise. Over the years, a number of tomographic reconstruction methods have been developed including direct inversion, real-space, and Fourier-based iterative algorithms. Here, we report the development of a real-space iterative reconstruction (RESIRE) algorithm for accurate tomographic reconstruction. RESIRE iterates between the update of a reconstructed 3D object and the measured projections using a forward and back projection step. The forward projection step is implemented by the Fourier slice theorem or the Radon transform, and the back projection step by a linear transformation. Our numerical and experimental results demonstrate that RESIRE performs more accurate 3D reconstructions than other existing tomographic algorithms, when there are a limited number of projections with noise. Furthermore, RESIRE can be used to reconstruct the 3D structure of extended objects as demonstrated by the determination of the 3D atomic structure of an amorphous Ta thin film. We expect that RESIRE can be widely employed in the tomography applications in different fields. Finally, to make the method accessible to the general user community, the MATLAB source code of RESIRE and all the simulated and experimental data are available at https://zenodo.org/record/7273314.

97 MATHEMATICS AND COMPUTING↗