Search NASA⌕ Search

SEARCH · Search NASA

Results for “Number theory”

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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS1978

Using dynamo theory to predict the sunspot number during solar cycle 21

On physical grounds it is suggested that the polar field strength of the sun near a solar minimum is closely related to the solar activity of the following cycle. Four methods of estimating the polar magnetic field strength of the sun near solar minimum are employed to provide an estimate of the yearly mean sunspot number of cycle 21 at solar maximum of 140 + or - 20. This estimate may be considered a first-order attempt to predict the cycle activity using one parameter of physical importance based upon dynamo theory.

Schatten, K. H.↗
NASA NTRS1975

A model for generation of bow-shock-associated upstream waves

A model is proposed for the generation of upstream hydromagnetic waves by proton beams reflected at the earth's bow shock. It is assumed that the reflection process can produce some gyrophase bunching of the protons, thus creating a gyrophase disturbance that propagates with the beam as it streams back along interplanetary field lines. This leads to the production of driven hydromagnetic waves in the left-hand mode. The resulting theory predicts a wave amplitude, frequency, and polarization in the solar wind rest frame. The amplitude depends on the fraction of protons assumed to be phase coherent in their gyromotion and on the plasma beta, beam velocity, temperatures, and the Alfven Mach number. The theory also predicts the Doppler-shifted frequencies and the apparent sense of polarization that would be observed in satellite measurement frames.

Fredricks, R. W.↗
DOE OSTI2022

Complex saddles and Euclidean wormholes in the Lorentzian path integral

We study complex saddles of the Lorentzian path integral for 4D axion gravity and its dual description in terms of a 3-form flux, which include the Giddings-Strominger Euclidean wormhole. Transition amplitudes are computed using the Lorentzian path integral and with the help of Picard-Lefschetz theory. The number and nature of saddles is shown to qualitatively change in the presence of a bilocal operator that could arise, for example, as a result of considering higher-topology transitions. We also analyze the stability of the Giddings-Strominger wormhole in the 3-form picture, where we find that it represents a perturbatively stable Euclidean saddle of the gravitational path integral. This calls into question the ultimate fate of such solutions in an ultraviolet-complete theory of quantum gravity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Two-photon above-threshold ionization of helium

Multiphoton ionization provides a clear window into the nature of electron correlations in the helium atom. In the present study, the final-state energy range extends up to the region near the N = 2 and N = 3 ionization thresholds, where two-photon ionization proceeds via continuum intermediate states above the lowest threshold. Our calculations are performed using multichannel quantum defect theory (MQDT) and the streamlined R-matrix method. The sum and integration over all intermediate states in the two-photon ionization amplitude is evaluated using the inhomogeneous R-matrix method developed by Robicheaux and Gao. The seamless connection of that method with MQDT allows us to present high-resolution spectra of the final-state Rydberg resonances. Our analysis classifies the resonances above the N = 2 threshold in terms of their group theory quantum numbers. Furthermore, their dominant decay channels are found to obey the previously conjectured propensity rule far more weakly for these even-parity states than was observed for the odd-parity states relevant to single-photon ionization.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2025

Research in Theoretical Particle Physics: Neutrino Masses and The Origin of CP-Violation

The main goal of this project was to investigate the theories of neutrino masses at the low scale and the origin of CP-violation in physics beyond the Standard Model. The origin of neutrino masses is one of the most pressing issues in particle physics. In this proposal, we investigated the theories for neutrino masses based on local total lepton number. In these theories anomaly cancellation predicts the existence of extra fermions with lepton number, and one of them is a good dark matter (DM) candidate. The cosmological constraints on the DM relic density implies that the lepton number symmetry breaking scale must be below the multi-TeV scale. Therefore, one can hope to test the origin of neutrino masses in current or future experiments. We investigated in great detail the anomaly cancellation in these gauge theories, study the different mechanisms for neutrino masses, study the predictions for direct and indirect dark matter experiments. Since these theories predict new sources of CP violation, we investigated the predictions for the electric dipole moments (EDM). The Higgs decays and the different signatures at the Large Hadron Collider were investigated in great detail. Finally, we studied the possible baryogenesis mechanisms in these theories in agreement with the EDM, DM and collider constraints. The origin of CP violation in the Standard Model is unknown. In this proposal, we investigated the simplest mechanisms for spontaneous CP-violation to explain the CP-violation in the CKM matrix and the value of the QCD vacuum angle. We discussed the Nelson-Barr mechanism in gauge theories predicting vector-like quarks from anomaly cancellation such as theories for local baryon number. We discussed the Bento-Branco-Parada mechanism in gauge theories to explain the CP-Violation in the CKM matrix. We will investigate models with two Higgs doublets in the context of the minimal theory for quark-lepton unification. We will show the non-decoupling effects in the Higgs sector, the main constraints coming from flavour violating processes when the Yukawa couplings are related by the gauge symmetry in theories for quark-lepton unification. We will investigate the predictions for electric dipole moments in these theories. The possibility to have successful baryogenesis was investigated. Finally, we investigated the relation between CP-violation in the quark and leptonic sectors. The future results from these studies could help us to understand two main issues in physics beyond the Standard Model: The Origin of Neutrino Masses and CP-violation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Constraining $\mathcal{f(R)}$ gravity with a $\mathcal{k}$-cut cosmic shear analysis of the Hyper Suprime-Cam first-year data

Here, using Subaru Hyper Suprime-Cam (HSC) year 1 data, we perform the first k-cut cosmic shear analysis constraining both Λ CDM and f(R) Hu-Sawicki modified gravity. To generate the f(R) cosmic shear theory vector, we use the matter power spectrum emulator trained on COLA (COmoving Lagrangian Acceleration) simulations [Phys. Rev. D 103, 123525 (2021)]. The k-cut method is used to significantly down-weight sensitivity to small scale (k > 1h Mpc -1 ) modes in the matter power spectrum where the emulator is less accurate, while simultaneously ensuring our results are robust to baryonic feedback model uncertainty. We have also developed a test to ensure that the effects of poorly modeled small scales are nulled as intended. For Λ CDM we find S 8 =σ 8 (Ω m /0.3) 0.5 =0.789$^{+0.039}_{-0.022}$, while the constraints on the f(R) modified gravity parameters are prior dominated. In the future, the k-cut method could be used to constrain a large number of theories of gravity where computational limitations make it infeasible to model the matter power spectrum down to extremely small scales.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Mode spectrum characteristics and onset of the low-shear MHD stability regime

Equilibria with extended regions of weak magnetic shear, including some tokamak scenarios and stellarators, can be susceptible to pressure-driven internal MHD instabilities even though there is no mode rational surface in the plasma. Nonresonant modes, in particular, can have properties that are unattractive for confinement, including displacing substantial volumes of the plasma and leading to more efficient pressure gradient flattening in the nonlinear regime. The onset and linear properties of the low shear stability regime are examined using the initial-value, extended-MHD code M3D-C. For monotonic q-profiles, we demonstrate a clear correlation between the convergents associated with the continued fraction representation of q 0 and the spectrum of unstable modes. Nonresonant modes are observed to be destabilized preferentially to any other resonant instability with the same toroidal mode number when n > 1. Using the observed connection between the spectrum associated with q 0 and the overall equilibrium stability properties, we suggest a technique for reducing the uncertainty on both q 0 and magnetic shear in the core region, obtained either via measurement or through the analysis and reconstruction of experimental results.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Modeling the electron cyclotron emission radiation signature from suprathermal electrons in a tokamak

An Electron Cyclotron Emission (ECE) modeling code has been developed to model ECE radiation with an arbitrary electron momentum distribution, a small oblique angle, both ordinary (O-mode) and extraordinary polarizations (X-mode), and multiple cyclotron frequency harmonics. The emission and absorption coefficients are calculated using the Poynting theorem from the cold plasma dispersion and the electron–microwave interaction from the full anti-Hermitian tensor. The modeling shows several ECE radiation signatures that can be used to diagnose the population of suprathermal electrons in a tokamak. First, in an n = 2 X-mode (X2) optically thick plasma and oblique ECE view, the modeling shows that only suprathermal electrons, which reside in a finite region of the velocity and space domains, can effectively generate cyclotron emissions to the ECE receiver. The code also finds that the O1 mode is sensitive to suprathermal electrons of both a high v ⊥ and v || , while the X2 mode is dominantly sensitive to suprathermal electrons of a high v ⊥ . Finally, the modeling shows that an oblique ECE system with both X/O polarization and a broad frequency coverage can be used to effectively yield information of the suprathermal electron population in a tokamak.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Linear-scaling quadruple excitations in local pair natural orbital coupled-cluster theory

Here, we present a fast, asymptotically linear-scaling implementation of the perturbative quadruples energy correction in coupled-cluster theory using local natural orbitals. Our work follows the domain-based local pair natural orbital (DLPNO) approach previously applied to lower levels of excitations in coupled-cluster theory. Our DLPNO-CCSDT(Q) algorithm uses converged doubles and triples amplitudes from a preceding DLPNO-CCSDT computation to compute the quadruples amplitude and energy in the quadruples natural orbital (QNO) basis. We demonstrate the compactness of the QNO space, showing that more than 95% of the (Q) correction can be recovered using relatively loose natural orbital cutoffs, compared to the tighter cutoffs used in pair and triples natural orbitals at lower levels of coupled-cluster theory. We also highlight the accuracy of our algorithm in the computation of relative energies, which yields deviations of sub-kJ mol −1 in relative energy compared to the canonical CCSDT(Q). Timings are conducted on a series of growing linear alkanes (up to 10 carbons and 608 basis functions) and water clusters (up to 49 water molecules and 2842 basis functions) to establish the asymptotic linear-scaling of our DLPNO-(Q) algorithm.

Auxiliary functions↗
DOE OSTI2022

Composite excitonic states in doped semiconductors

We present a theoretical model of composite excitonic states in doped semiconductors. Many-body interactions between a photoexcited electron-hole pair and the electron gas are integrated into a computationally tractable few-body problem, solved by the variational method. We focus on electron-doped monolayer (ML)-MoSe 2 and ML-WSe 2 due to the contrasting character of their conduction bands. In both cases, the core of the composite is a tightly bound trion (two electrons and a valence-band hole) surrounded by a region depleted of electrons. The composite in ML-WSe 2 further includes a satellite electron with different quantum numbers. The theory is general and can be applied to semiconductors with various energy-band properties, allowing one to calculate their excitonic states and to quantify the interaction with the Fermi sea.

36 MATERIALS SCIENCE↗
DOE OSTI2020

A Mystery in Chamaeleon: Serendipitous Discovery of a Galactic Symbiotic Nova

We present the serendipitous discovery of a low optical-luminosity nova occurring in a D-type symbiotic binary star system in the Milky Way. We lay out the extensive archival data alongside new follow-up observations related to the stellar object CN Cha in the constellation of Chamaeleon. The object had long period (250 days), high amplitude (3 mag) optical variability in its recent past, preceding an increase in optical brightness by 8 magnitudes and a persistence at this brightness for about 3 yr, followed by a period of 1.4 mag yr{sup −1} dimming. The object’s current optical luminosity seems to be dominated by Hα emission, which also exhibits blueshifted absorption (a P-Cygni-like profile). After consideration of a number of theories to explain these myriad observations, we determine that CN Cha is most likely a symbiotic (an evolved-star–white-dwarf binary) system that has undergone a long-duration, low optical brightness, nova, placing it squarely in the class of so-called “slow novae,” of which there are only a few known examples. The duration of the optical plateau in CN Cha would make it the shortest timescale plateau of any known slow symbiotic novae.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1973

Analysis of Mossbauer Fe-57 absorption in an F.C.C. Fe-Co-V alloy

Mossbauer Fe-57 absorption spectra of superparamagnetic F.C.C. Fe sub .34 Co sub .52 V sub 14 (Vicalloy II) have been analyzed using a cluster model and magnetic resonance relaxation theory. The number and magnetic moment of the clusters were determined from magnetization data. A least squares fit to the spectrum at 4.2 K gives sub Hhyp = 175. kG, substantially greater than the value 55 kG inferred just from the observed broadening of the single line spectrum. From this broadening an estimate of 40 kG is obtained for the width of the distribution in Hhyp at 4.2 K arising from compositional fluctuations sub and small cluster effects.

Bambakidis, G.↗
NASA NTRS1975

Hydrogen interactions with metals

Review of the literature on the nature and extent of hydrogen interactions with metals and the role of hydrogen in metal failure. The classification of hydrogen-containing systems is discussed, including such categories as covalent hydrides, volatile hydrides, polymeric hydrides, and transition metal hydride complexes. The use of electronegativity as a correlating parameter in determining hydride type is evaluated. A detailed study is made of the thermodynamics of metal-hydrogen systems, touching upon such aspects as hydrogen solubility, the positions occupied by hydrogen atoms within the solvent metal lattice, the derivation of thermodynamic functions of solid solutions from solubility data, and the construction of statistical models for hydrogen-metal solutions. A number of theories of hydrogen-metal bonding are reviewed, including the rigid-band model, the screened-proton model, and an approach employing the augmented plane wave method to solve the one-electron energy band problem. Finally, the mechanism of hydrogen embrittlement is investigated on the basis of literature data concerning stress effects and the kinetics of hydrogen transport to critical sites.

Mclellan, R. B.↗
NASA NTRS1975

Thermal energy storage

The principles involved in thermal energy storage by sensible heat, chemical potential energy, and latent heat of fusion are examined for the purpose of evolving selection criteria for material candidates in the low ( 0 C) and high ( 100 C) temperature ranges. The examination identifies some unresolved theoretical considerations and permits a preliminary formulation of an energy storage theory. A number of candidates in the low and high temperature ranges are presented along with a rating of candidates or potential candidates. A few interesting candidates in the 0 to 100 C region are also included. It is concluded that storage by means of reactions whose reversibility can be controlled either by product removal or by catalytic means appear to offer appreciable advantages over storage with reactions whose reversability cannot be controlled. Among such advantages are listed higher heat storage capacities and more favorable options regarding temperatures of collection, storage, and delivery. Among the disadvantages are lower storage efficiencies.

Grodzka, P. G.↗
NASA NTRS1977

Spectra of turbulent static pressure fluctuations in jet mixing layers

Spectral similarity laws are derived for the power spectra of turbulent static pressure fluctuations by application of dimensional analysis in the limit of large turbulent Reynolds number. The theory predicts that pressure spectra are generated by three distinct types of interaction in the velocity fields: a fourth order interaction between fluctuating velocities, an interaction between the first order mean shear and the third order velocity fluctuations, and an interaction between the second order mean shear rate and the second order fluctuating velocity. Measurements of one-dimensional power spectra of the turbulent static pressure fluctuations in the driven mixing layer of a subsonic, circular jet are presented, and the spectra are examined for evidence of spectral similarity. Spectral similarity is found for the low wavenumber range when the large scale flow on the centerline of the mixing layer is self-preserving. The data are also consistent with the existence of universal inertial subranges for the spectra of each interaction mode.

Jones, B. G.↗
NASA NTRS1979

Electronic properties of PbMo6S8 and CuxMo6S8

Normal-state properties of sputtered, evaporated, and sintered PbMo6S8 and CuxMo6S8 (where x is between 1.6 and 2.5) samples are reported. These include the temperature dependence of resistivity, magnetoresistance, and Hall effect. When combined with superconducting properties (measured on the same samples) and theory, a number of Fermi-surface and superconducting parameters are derived. Fits to the temperature dependence of the resistivity are compared with similar fits for A-15 structure superconductors.

Woollam, J. A.↗