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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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
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 NTRS2009

PCC Framework for Program-Generators

In this paper, we propose a proof-carrying code framework for program-generators. The enabling technique is abstract parsing, a static string analysis technique, which is used as a component for generating and validating certificates. Our framework provides an efficient solution for certifying program-generators whose safety properties are expressed in terms of the grammar representing the generated program. The fixed-point solution of the analysis is generated and attached with the program-generator on the code producer side. The consumer receives the code with a fixed-point solution and validates that the received fixed point is indeed a fixed point of the received code. This validation can be done in a single pass.

Kong, Soonho↗
DOE OSTI2021

Observations of heteroclinic bifurcations in resistive magnetohydrodynamic simulations of the plasma response to resonant magnetic perturbations

A class of topological magnetic island bifurcations that has not previously been observed in toroidal plasmas is described. Increasing an externally applied three-dimensional magnetic field in resistive magnetohydrodynamic simulations results in the asymmetric elongation of resonant island flux surfaces followed by a sequence of heteroclinic bifurcations. Here, these bifurcations produce new sets of hyperbolic-elliptic fixed points as predicted by the Poincaré-Birkoff fixed point theorem. Field line calculations verify that the new fixed points do not connect to those of the prebifurcated islands as required for heteroclinic bifurcations on a torus with winding numbers composed of common integer factors.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Multichannel Topological Kondo Effect

A Coulomb blockaded M-Majorana island coupled to normal metal leads realizes a novel type of Kondo effect where the effective impurity “spin” transforms under the orthogonal group SO⁡(M). The impurity spin stems from the nonlocal topological ground state degeneracy of the island and thus the effect is known as the topological Kondo effect. We introduce a physically motivated N-channel generalization of the topological Kondo model. Starting from the simplest case N =2, we conjecture a stable intermediate coupling fixed point and evaluate the resulting low-temperature impurity entropy. The impurity entropy indicates that an emergent Fibonacci anyon can be realized in the N =2 model. We also map the case N =2, M =4 to the conventional four-channel Kondo model and find the conductance at the intermediate fixed point. By using the perturbative renormalization group, we also analyze the large-N limit, where the fixed point moves to weak coupling. In the isotropic limit, we find an intermediate stable fixed point, which is stable to “exchange” coupling anisotropies, but unstable to channel anisotropy. We evaluate the fixed point impurity entropy and conductance to obtain experimentally observable signatures of our results. Here, in the large-N limit, we evaluate the full crossover function describing the temperature-dependent conductance.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS2011

Fast Plasma Investigation for MMS: Simulation of the Burst Triggering System

The Magnetospheric Multiscale (MMS) mission will study small-scale reconnection structures and their rapid motions from closely spaced platforms using instruments capable of high angular, energy, and time resolution measurements. To meet these requirements, the Fast Plasma Instrument (FPI) consists of eight (8) identical half top-hat electron sensors and eight (8) identical ion sensors and an Instrument Data Processing Unit (IDPU). The sensors (electron or ion) are grouped into pairs whose 6 degree x 180 degree fields-of-view (FOV) are set 90 degrees apart. Each sensor is equipped with electrostatic aperture steering to allow the sensor to scan a 45 degree x 180 degree fan about the its nominal viewing (0 deflection) direction. Each pair of sensors, known as the Dual Electron Spectrometer (DES) and the Dual Ion Spectrometer (DIS), occupies a quadrant on the MMS spacecraft and the combination of the eight electron/ion sensors, employing aperture steering, image the full-sky every 30-ms (electrons) and 150-ms (ions), respectively. To probe the diffusion regions of reconnection, the highest temporal/spatial resolution mode of FPI results in the DES complement of a given spacecraft generating 6.5-Mb (raised dot) per second of electron data while the DIS generates 1.1-Mb (raised dot) per second of ion data yielding an FPI total data rate of 6.6-Mb (raised dot) per second. The FPI electron/ion data is collected by the IDPU then transmitted to the Central Data Instrument Processor (CIDP) on the spacecraft for science interest ranking. Only data sequences that contain the greatest amount of temporal/spatial structure will be intelligently down-linked by the spacecraft. This requires a data ranking process known as the burst trigger system. The burst trigger system uses pseudo physical quantities to approximate the local plasma environments. As each pseudo quantity will have a different value, a set of two scaling factors is employed for each pseudo term. These pseudo quantities are then combined at the instrument, spacecraft, and observatory level leading to a final ranking of data based on expected scientific interest. Here, we present simulations of the fixed point burst trigger system for the FPI. A variety of data sets based on previous mission data as well as analytical formulations are tested. Comparisons of floating point calculations versus the fixed point hardware simulation are shown. Analysis of the potential sources of error from overflows, quantization, etc. are examined and mitigation methods are presented. Finally a series of calibration curves are presented, showing the expected error in pseudo quantities based solely on the scale parameters chosen and the expected data range. We conclude with a presentation of the current base-lined FPI burst trigger approach.

Barrie, A. C.↗
DOE OSTI2022

Scaling and adiabaticity in a rapidly expanding gluon plasma

In this work we aim to gain qualitative insight on the far-from-equilibrium behavior of the gluon plasma produced in the early stages of a heavy-ion collision. It was recently discovered [1] that the distribution functions of quarks and gluons in QCD effective kinetic theory (EKT) exhibit self-similar “scaling” evolution with time-dependent scaling exponents long before those exponents reach their pre-hydrodynamic fixed-point values. In this work we shed light on the origin of this time-dependent scaling phenomenon in the small-angle approximation to the Boltzmann equation. We first solve the Boltzmann equation numerically and find that time-dependent scaling is a feature of this kinetic theory, and that it captures key qualitative features of the scaling of hard gluons in QCD EKT. We then proceed to study scaling analytically and semi-analytically in this equation. We find that an appropriate momentum rescaling allows the scaling distribution to be identified as the instantaneous ground state of the operator describing the evolution of the distribution function, and the approach to the scaling function is described by the decay of the excited states. That is to say, there is a frame in which the system evolves adiabatically. Furthermore, from the conditions for adiabaticity we can derive evolution equations for the time-dependent scaling exponents. In addition to the known free-streaming and BMSS fixed points, we identify a new “dilute” fixed point when the number density becomes small before hydrodynamization. Corrections to the fixed point exponents in the small-angle approximation agree quantitatively with those found previously in QCD EKT and arise from the evolution of the ratio between hard and soft scales.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Flows into de Sitter space from anisotropic initial conditions: An effective field theory approach

For decades, physicists have analyzed various versions of a “cosmic no-hair” conjecture, to understand under what conditions a spacetime that is initially spatially anisotropic and/or inhomogeneous will flow into an isotropic and homogeneous state. Wald’s theorem, in particular, established that homogeneous but anisotropic spacetimes, if filled with a positive cosmological constant plus additional matter sources that satisfy specific energy conditions, will necessarily flow toward an (isotropic) de Sitter state at late times. Here, in this paper, we study the flow of homogeneous but anisotropic spacetimes toward isotropic states under conditions more general than those to which Wald’s theorem applies. We construct an effective field theory (EFT) treatment for generic “single-clock” systems in anisotropic spacetimes—which are not limited to realizations compatible with scalar-field constructions—and identify fixed points in the resulting phase space. We identify regions of this phase space that flow to isotropic fixed points—including a de Sitter fixed point—even in the absence of a bare cosmological constant, and for matter sources that do not obey the energy conditions required for Wald’s theorem. Such flows into de Sitter reveal the emergence of an effective cosmological constant.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1987

Infrared properties of an anisotropically stirred fluid

A renormalization group is developed for the Navier-Stokes equations driven by an anisotropically correlated random stirring force. The stirring force generates homogeneous turbulence with a preferred direction. The force correlation is the sum of a small anisotropic perturbation and an isotropic correlation chosen, so that the fixed point of renormalization group has a k exp -5/3 energy spectrum. Fixed points for the anisotropic correlation are found near this isotropic fixed point. Two types of anisotropy are analyzed. when the additional stirring is in the plane perpendicular to the preferred direction, the renormalized viscosity is increased. When it is aligned with the preferred direction, the viscosity is decreased. A possible connection with the inverse energy cascade of two-dimensional turbulence is discussed.

Rubinstein, Robert↗
DOE OSTI2026

Towards a Quintic Ginzburg-Landau Description of the (2,7) Minimal Model

We discuss dimensional continuation of the massless scalar field theory with the 𝑖⁢𝜙 5 interaction term. It preserves the so-called 𝒫⁢𝒯 symmetry, which acts by 𝜙 →−𝜙 accompanied by 𝑖 →−𝑖. Below its upper critical dimension 10/3, this theory has interacting infrared fixed points. We argue that the fixed point in 𝑑 = 2 describes the nonunitary minimal conformal model 𝑀⁡(2,7). We identify the operators 𝜙 and 𝜙 2 with the Virasoro primaries 𝜙 1,2 and 𝜙 1,3 , respectively, and 𝑖⁢𝜙 3 with a quasiprimary operator, which is a Virasoro descendant of 𝜙 1,3 . Our identifications appear to be consistent with the operator product expansions and with considerations based on integrability. Using constrained Padé extrapolations, we provide estimates of the critical exponents in 𝑑 = 3. We also comment on possible lattice descriptions of 𝑀⁡(2,7) and discuss RG flows to and from this conformal field theory (CFT). Finally, we conjecture that the minimal models 𝑀⁡(2,2⁢𝑛 +1) are described by the massless scalar field theories with the 𝑖⁢𝜙 2⁢𝑛−1 interaction terms.

Conformal field theory↗
NASA NTRS1989

Terminal attractors in neural networks

A new type of attractor (terminal attractors) for content-addressable memory, associative memory, and pattern recognition in artificial neural networks operating in continuous time is introduced. The idea of a terminal attractor is based upon a violation of the Lipschitz condition at a fixed point. As a result, the fixed point becomes a singular solution which envelopes the family of regular solutions, while each regular solution approaches such an attractor in finite time. It will be shown that terminal attractors can be incorporated into neural networks such that any desired set of these attractors with prescribed basins is provided by an appropriate selection of the synaptic weights. The applications of terminal attractors for content-addressable and associative memories, pattern recognition, self-organization, and for dynamical training are illustrated.

Zak, Michail↗
NASA NTRS1991

Nonlinear response of infinitely long circular cylindrical shells to subharmonic radial loads

The nonlinear response of infinitely long circular cylindrical shells (thin circular rings) in the presence of a two-to-one internal (autoparametric) resonance to a subharmonic excitation of order one-half of the higher mode is analyzed with the multiple-scale method. Four autonomous first-order ordinary differential equations are derived for the modulation of the amplitudes and phases of the interacting models. These modulation equations are used to determine the fixed points and their stability. The fixed points correspond to periodic oscillations of the shell, whereas the limit-cycle solutions of the modulation equations correspond to amplitude and phase-modulated oscillations of the shell. The force response curves exhibit saturation, jumps, and Hopf bifurcation. As excitation frequency changes, all limit cycles deform and lose stability through either pitchfork or cyclic-fold (saddle-node) bifurcations. Some of these saddle-node bifurcations cause a transition to chaos. The pitchfork bifurcations break the symmetry of the limit cycles.

Nayfeh, Ali H.↗
DOE OSTI2021

Perturbative and nonperturbative studies of CFTs with MN global symmetry

Fixed points in three dimensions described by conformal field theories with \ensuremath{M N}_{m,n} = O(m)^n\rtimes S_n M N m , n = O ( m ) n ⋊ S n global symmetry have extensive applications in critical phenomena. Associated experimental data for m=n=2 m = n = 2 suggest the existence of two non-trivial fixed points, while the \varepsilon ε expansion predicts only one, resulting in a puzzling state of affairs. A recent numerical conformal bootstrap study has found two kinks for small values of the parameters m m and n n , with critical exponents in good agreement with experimental determinations in the m=n=2 m = n = 2 case. In this paper we investigate the fate of the corresponding fixed points as we vary the parameters m m and n n . We find that one family of kinks approaches a perturbative limit as m m increases, and using large spin perturbation theory we construct a large m m expansion that fits well with the numerical data. This new expansion, akin to the large N N expansion of critical O(N) O ( N ) models, is compatible with the fixed point found in the \varepsilon ε expansion. For the other family of kinks, we find that it persists only for n=2 n = 2 , where for large m m it approaches a non-perturbative limit with \Delta_\phi\approx 0.75 Δ ϕ ≈ 0.75 . We investigate the spectrum in the case \ensuremath{M N}_{100,2} M N 100 , 2 and find consistency with expectations from the lightcone bootstrap.

74 ATOMIC AND MOLECULAR PHYSICS↗
NASA NTRS1944

Detail Calculations of the Estimated Shift in Stick-Fixed Neutral Point Due to the Windmilling Propeller and to the Fuselage of the Republic XF-12 Airplane

Detail calculations are presented of the shifts in stick-fixed neutral point of the Republic XF-12 airplane due to the windmilling propellers and to the fuselage. The results of these calculations differ somewhat from those previously made for this airplane by Republic Aviation Corporation personnel under the direction of Langley flight division personnel. Due to these differences the neutral point for the airplane is predicted to be 37.8 percent mean aerodynamic chord, instead of 40.8 percent mean aerodynamic chord as previously reported.

White, M. D.↗
DOE OSTI2023

Spontaneous breaking of finite group symmetries at all temperatures

We study conformal field theories with finite group symmetries with spontaneous symmetry breaking (SSB) phases which persist at all temperatures. We work with two \lambda \phi^4 λ ϕ 4 theories coupled through their mass terms. The two \lambda \phi^4 λ ϕ 4 theories are chosen to preserve either the cubic symmetry group, or the tetrahedral symmetry group. A one-loop calculation in the 4-\epsilon 4 − ϵ expansion shows that there exist infinitely many fixed points that can host an all temperature SSB phase. An analysis of the renormalization group (RG) stability matrix of these fixed points, reveals that their spectrum contains at least three relevant operators. In other words, these fixed points are tetracritical points.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Fast explicit solutions for neutrino-electron scattering: Explicit asymptotic methods

Here, we present results of explicit asymptotic approximations applied to neutrino-electron scattering in a representative model of neutrino population evolution under conditions characteristic of core-collapse supernova explosions or binary neutron star mergers. It is shown that this approach provides stable solutions of these stiff systems of equations, with accuracy and time stepping comparable to that for standard implicit treatments such as backward Euler, fixed point iteration, and Anderson-accelerated fixed point iteration. Because each time step can be computed more rapidly with the explicit asymptotic approximation than with implicit methods, this suggests that algebraically stabilized explicit integration methods could be used to compute neutrino evolution coupled to hydrodynamics more efficiently in stellar explosions and mergers than the methods currently in use.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Stability analysis of a one-dimensional multiphysics model of a molten salt fast reactor

Reactor designs with a fast neutron spectrum have recently moved into the research focus for possible Generation IV reactor concepts - a representative of which is the molten salt fast reactor (MSFR). In order to assess the safety and reliability of this reactor concept, it is necessary to obtain knowledge of the system behaviour. An important part of this research concerns the dynamical stability of the MSFR. Research regarding the MSFR stability so far has either been using linearized models for stability criteria or only been examining certain transients at fixed parameter values. This work delivers a comprehensive stability analysis for a non-linearized MSFR model, and a wide range of values for all relevant parameters. For this purpose, a one-dimensional MSFR model was set up, taking neutron kinetics and thermal hydraulics in the form of a system of differential equations into account. The stability of this model was investigated by means of the numerical tool MATCONT, which was used to monitor the evolution of a so-called fixed-point solution, here referring to the steady state at operating conditions of the system, while system parameters got varied. The MATCONT analyses showed no loss of stability for any of the considered parameter variations and no solutions that might co-exist in parallel with the steady-state fixed-point solution. Therefore these results indicate a stable fixed point to which all solution transients converge, making the considered MSFR model insusceptible to deviations from the equilibrium. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗