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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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2013

Distorting general relativity: gravity's rainbow and f(R) theories at work

We compute the Zero Point Energy in a spherically symmetric background combining the high energy distortion of Gravity's Rainbow with the modification induced by a f(R) theory. Here f(R) is a generic analytic function of the Ricci curvature scalar R in 4D and in 3D. The explicit calculation is performed for a Schwarzschild metric. Due to the spherically symmetric property of the Schwarzschild metric we can compare the effects of the modification induced by a f(R) theory in 4D and in 3D. We find that the final effect of the combined theory is to have finite quantities that shift the Zero Point Energy. In this context we setup a Sturm-Liouville problem with the cosmological constant considered as the associated eigenvalue. The eigenvalue equation is a reformulation of the Wheeler-DeWitt equation which is analyzed by means of a variational approach based on gaussian trial functionals. With the help of a canonical decomposition, we find that the relevant contribution to one loop is given by the graviton quantum fluctuations around the given background. A final discussion on the connection of our result with the observed cosmological constant is also reported.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Haydock’s recursive solution of self-adjoint problems. Discrete spectrum

Haydock’s recursive solution is shown to underline a number of different concepts such as (i) quasi-exactly solvable models, (ii) exactly solvable models, (iii) three-term recurrence solutions based on Schweber’s quantization criterion in Hilbert spaces of entire analytic functions, and (iv) a discrete quantum mechanics of Odake and Sasaki. A recurrent theme of Haydock’s recursive solution is that the spectral properties of any self-adjoint problem can be mapped onto a corresponding sequence of polynomials (p{sub n}(E)) in energy variable E. The polynomials (p{sub n}(E)) are orthonormal with respect to the density of states n{sub 0}(E) and energy eigenstate |E〉 is the generating function of (p{sub n}(E)). The generality of Haydock’s recursive solution enables one to see the different concepts from a unified perspective and mutually benefiting from each other. Some results obtained within the particular framework of any of (i) to (iv) may have much broader significance.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

Spin ice in a field: Quasi-phases and pseudo-transitions

Thermodynamics of a short-range model of spin ice magnets in a field is considered in the Bethe-Peierls approximation. The results obtained for [111], [100], and [011] fields agree reasonably well with the existing Monte Carlo simulations and some experiments. In this approximation, all extremely sharp field-induced anomalies are described by analytic functions of temperature and the applied field. In spite of the absence of true phase transitions, the analysis of the entropy and specific heat reliefs over the H-T plane allows discerning 'pseudo-phases' with a specific character of spin fluctuations and defining the lines of relatively sharp 'pseudo-transitions' between them.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2013

On solvability and integrability of the Rabi model

The quasi-exactly solvable Rabi model is investigated within the framework of the Bargmann Hilbert space of analytic functions B. On applying the theory of orthogonal polynomials, the eigenvalue equation and eigenfunctions are shown to be determined in terms of three systems of monic orthogonal polynomials. The formal Schweber quantization criterion for an energy variable x, originally expressed in terms of infinite continued fractions, can be recast in terms of a meromorphic function F(z)=a{sub 0}+∑{sub k=1}{sup ∞}M{sub k}/(z−ξ{sub k}) in the complex plane C with real simple poles ξ{sub k} and positive residues M{sub k}. The zeros of F(x) on the real axis determine the spectrum of the Rabi model. One obtains at once that, on the real axis, (i) F(x) monotonically decreases from +∞ to −∞ between any two of its subsequent poles ξ{sub k} and ξ{sub k+1}, (ii) there is exactly one zero of F(x) for x∈(ξ{sub k},ξ{sub k+1}), and (iii) the spectrum corresponding to the zeros of F(x) does not have any accumulation point. Additionally, one can provide a much simpler proof that the spectrum in each parity eigenspace B{sub ±} is necessarily nondegenerate. Thereby the calculation of spectra is greatly facilitated. Our results allow us to critically examine recent claims regarding solvability and integrability of the Rabi model. -- Highlights: •Schweber’s criterion shown equivalent to a meromorphic function F with real simple poles and positive residues. •Calculation of spectra determined as zeros of F greatly facilitated: one has exactly one zero between subsequent poles of F. •Spectrum in a given parity eigenspace is necessarily nondegenerate. •Recent claims regarding solvability and integrability of the Rabi model found to be largely unsubstantiated.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

The internal structure of a vortex in a two-dimensional superfluid with long healing length and its implications

We analyze the motion of quantum vortices in a two-dimensional spinless superfluid within Popov’s hydrodynamic description. In the long healing length limit (where a large number of particles are inside the vortex core) the superfluid dynamics is determined by saddle points of Popov’s action, which, in particular, allows for weak solutions of the Gross–Pitaevskii equation. We solve the resulting equations of motion for a vortex moving with respect to the superfluid and find the reconstruction of the vortex core to be a non-analytic function of the force applied on the vortex. This response produces an anomalously large dipole moment of the vortex and, as a result, the spectrum associated with the vortex motion exhibits narrow resonances lying within the phonon part of the spectrum, contrary to traditional view.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Operator product expansion algebra

We establish conceptually important properties of the operator product expansion (OPE) in the context of perturbative, Euclidean φ{sup 4}-quantum field theory. First, we demonstrate, generalizing earlier results and techniques of hep-th/1105.3375, that the 3-point OPE, =Σ{sub C}C{sub A{sub 1A{sub 2A{sub 3}{sup C}}}} , usually interpreted only as an asymptotic short distance expansion, actually converges at finite, and even large, distances. We further show that the factorization identity C{sub A{sub 1A{sub 2A{sub 3}{sup B}}}}=Σ{sub C}C{sub A{sub 1A{sub 2}{sup C}}}C{sub CA{sub 3}{sup B}} is satisfied for suitable configurations of the spacetime arguments. Again, the infinite sum is shown to be convergent. Our proofs rely on explicit bounds on the remainders of these expansions, obtained using refined versions, mostly due to Kopper et al., of the renormalization group flow equation method. These bounds also establish that each OPE coefficient is a real analytic function in the spacetime arguments for non-coinciding points. Our results hold for arbitrary but finite loop orders. They lend support to proposals for a general axiomatic framework of quantum field theory, based on such “consistency conditions” and akin to vertex operator algebras, wherein the OPE is promoted to the defining structure of the theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2011

Finding physics signals with shower deconstruction

We introduce shower deconstruction, a method to look for new physics in a hadronic environment. The method aims to be a full information approach using small jets. It assigns to each event a number {chi} that is an estimate of the ratio of the probability for a signal process to produce that event to the probability for a background process to produce that event. The analytic functions we derive to calculate these probabilities mimic what full event generators like Pythia or Herwig do and can be depicted in a diagrammatic way. As an example, we apply this method to a boosted Higgs boson produced in association with a Z boson and show that this method can be useful to discriminate this signal from the Z+jets background.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2013

Algebras with convergent star products and their representations in Hilbert spaces

We study star product algebras of analytic functions for which the power series defining the products converge absolutely. Such algebras arise naturally in deformation quantization theory and in noncommutative quantum field theory. We consider different star products in a unifying way and present results on the structure and basic properties of these algebras, which are useful for applications. Special attention is given to the Hilbert space representation of the algebras and to the exact description of their corresponding operator algebras.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2019

Absorbing boundary condition (ABC) and perfectly matched layer (PML) in numerical beam propagation: a comparison

The absorbing boundary condition (ABC) and the perfectly matched layer (PML) are employed to suppress the numerical reflections in wave propagation methods. The PML has earlier been shown to fail at the grazing angle propagation of beam. The ABC is preferred over the PML where refractive index is not an analytic function. We have explored the performance of the ABC in reflection-less absorption of non-paraxial propagation of beams and have compared it against the PML. We have considered an example of the propagation of Gaussian beams through a homogeneous medium terminated with ABC or PML. We have used the collocation method for propagation. We have found that both the boundary conditions are comparable in performance. The ABC performed relatively better than the PML for beams at smaller angles. However, the performance of the PML is better than that of the ABC at larger tilt angles.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Calculation of continuum damping of Alfvén eigenmodes in tokamak and stellarator equilibria

In an ideal magnetohydrodynamic (MHD) plasma, shear Alfvén eigenmodes may experience dissipationless damping due to resonant interaction with the shear Alfvén continuum. This continuum damping can make a significant contribution to the overall growth/decay rate of shear Alfvén eigenmodes, with consequent implications for fast ion transport. One method for calculating continuum damping is to solve the MHD eigenvalue problem over a suitable contour in the complex plane, thereby satisfying the causality condition. Such an approach can be implemented in three-dimensional ideal MHD codes which use the Galerkin method. Analytic functions can be fitted to numerical data for equilibrium quantities in order to determine the value of these quantities along the complex contour. This approach requires less resolution than the established technique of calculating damping as resistivity vanishes and is thus more computationally efficient. The complex contour method has been applied to the three-dimensional finite element ideal MHD Code for Kinetic Alfvén waves. In this paper, we discuss the application of the complex contour technique to calculate the continuum damping of global modes in tokamak as well as torsatron, W7-X and H-1NF stellarator cases. To the authors' knowledge, these stellarator calculations represent the first calculation of continuum damping for eigenmodes in fully three-dimensional equilibria. The continuum damping of global modes in W7-X and H-1NF stellarator configurations investigated is found to depend sensitively on coupling to numerous poloidal and toroidal harmonics.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2012

Unitary cocycle representations of the Galilean line group: Quantum mechanical principle of equivalence

We present a formalism of Galilean quantum mechanics in non-inertial reference frames and discuss its implications for the equivalence principle. This extension of quantum mechanics rests on the Galilean line group, the semidirect product of the real line and the group of analytic functions from the real line to the Euclidean group in three dimensions. This group provides transformations between all inertial and non-inertial reference frames and contains the Galilei group as a subgroup. We construct a certain class of unitary representations of the Galilean line group and show that these representations determine the structure of quantum mechanics in non-inertial reference frames. Our representations of the Galilean line group contain the usual unitary projective representations of the Galilei group, but have a more intricate cocycle structure. The transformation formula for the Hamiltonian under the Galilean line group shows that in a non-inertial reference frame it acquires a fictitious potential energy term that is proportional to the inertial mass, suggesting the equivalence of inertial mass and gravitational mass in quantum mechanics. - Highlights: Black-Right-Pointing-Pointer A formulation of Galilean quantum mechanics in non-inertial reference frames is given. Black-Right-Pointing-Pointer The key concept is the Galilean line group, an infinite dimensional group. Black-Right-Pointing-Pointer Unitary, cocycle representations of the Galilean line group are constructed. Black-Right-Pointing-Pointer A non-central extension of the group underlies these representations. Black-Right-Pointing-Pointer Quantum equivalence principle and gravity emerge from these representations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

An updated analysis of two classes of f(R) theories of gravity

The observed accelerated cosmic expansion can be a signature of fourth-order gravity theories, where the acceleration of the Universe is a consequence of departures from Einstein General Relativity, rather than the sign of the existence of a fluid with negative pressure. In the fourth-order gravity theories, the gravity Lagrangian is described by an analytic function f(R) of the scalar curvature R subject to the demanding conditions that no detectable deviations from standard GR is observed on the Solar System scale. Here we consider two classes of f(R) theories able to pass Solar System tests and investigate their viability on cosmological scales. To this end, we fit the theories to a large dataset including the combined Hubble diagram of Type Ia Supernovae and Gamma Ray Bursts, the Hubble parameter H(z) data from passively evolving red galaxies, Baryon Acoustic Oscillations extracted from the seventh data release of the Sloan Digital Sky Survey (SDSS) and the distance priors from the Wilkinson Microwave Anisotropy Probe seven years (WMAP7) data. We find that both classes of f(R) fit very well this large dataset with the present-day values of the matter density, Hubble constant and deceleration parameter in agreement with previous estimates; however, the strong degeneracy among the f(R) parameters prevents us from strongly constraining their values. We also derive the growth factor g = dln δ/dln a, with δ = δρ{sub M}/ρ{sub M} the matter density perturbation, and show that it can still be well approximated by g(z)∝Ω{sub M}(z){sup γ}. We finally constrain γ (on some representative scales) and investigate its redshift dependence to see whether future data can discriminate between these classes of f(R) theories and standard dark energy models.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1986

A system of three-dimensional complex variables

Some results of a new theory of multidimensional complex variables are reported, including analytic functions of a three-dimensional (3-D) complex variable. Three-dimensional complex numbers are defined, including vector properties and rules of multiplication. The necessary conditions for a function of a 3-D variable to be analytic are given and shown to be analogous to the 2-D Cauchy-Riemann equations. A simple example also demonstrates the analogy between the newly defined 3-D complex velocity and 3-D complex potential and the corresponding ordinary complex velocity and complex potential in two dimensions.

Martin, E. Dale↗
NASA NTRS1991

Statistics of primordial density perturbations from discrete seed masses

The statistics of density perturbations for general distributions of seed masses with arbitrary matter accretion is examined. Formal expressions for the power spectrum, the N-point correlation functions, and the density distribution function are derived. These results are applied to the case of uncorrelated seed masses, and power spectra are derived for accretion of both hot and cold dark matter plus baryons. The reduced moments (cumulants) of the density distribution are computed and used to obtain a series expansion for the density distribution function. Analytic results are obtained for the density distribution function in the case of a distribution of seed masses with a spherical top-hat accretion pattern. More generally, the formalism makes it possible to give a complete characterization of the statistical properties of any random field generated from a discrete linear superposition of kernels. In particular, the results can be applied to density fields derived by smoothing a discrete set of points with a window function.

Scherrer, Robert J.↗
DOE OSTI2016

Evaluating marginal likelihood with thermodynamic integration method and comparison with several other numerical methods

Evaluating marginal likelihood is the most critical and computationally expensive task, when conducting Bayesian model averaging to quantify parametric and model uncertainties. The evaluation is commonly done by using Laplace approximations to evaluate semianalytical expressions of the marginal likelihood or by using Monte Carlo (MC) methods to evaluate arithmetic or harmonic mean of a joint likelihood function. This study introduces a new MC method, i.e., thermodynamic integration, which has not been attempted in environmental modeling. Instead of using samples only from prior parameter space (as in arithmetic mean evaluation) or posterior parameter space (as in harmonic mean evaluation), the thermodynamic integration method uses samples generated gradually from the prior to posterior parameter space. This is done through a path sampling that conducts Markov chain Monte Carlo simulation with different power coefficient values applied to the joint likelihood function. The thermodynamic integration method is evaluated using three analytical functions by comparing the method with two variants of the Laplace approximation method and three MC methods, including the nested sampling method that is recently introduced into environmental modeling. The thermodynamic integration method outperforms the other methods in terms of their accuracy, convergence, and consistency. The thermodynamic integration method is also applied to a synthetic case of groundwater modeling with four alternative models. The application shows that model probabilities obtained using the thermodynamic integration method improves predictive performance of Bayesian model averaging. As a result, the thermodynamic integration method is mathematically rigorous, and its MC implementation is computationally general for a wide range of environmental problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Scalable and Power Efficient Data Analytics for Hybrid Exascale Systems

This project developed a generic and optimized set of core data analytics functions. These functions organically consolidate a broad constellation of high performance analytical pipelines. As the architectures of emerging HPC systems become inherently heterogeneous, there is a need to design algorithms for data analysis kernels accelerated on hybrid multi-node, multi-core HPC architectures comprised of a mix of CPUs, GPUs, and SSDs. Furthermore, the power-aware trend drives the advances in our performance-energy tradeoff analysis framework which enables our data analysis kernels algorithms and software to be parameterized so that users can choose the right power-performance optimizations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Optimal function estimation with photonic quantum sensor networks

The problem of optimally measuring an analytic function of unknown local parameters each linearly coupled to a qubit sensor is well understood, with applications ranging from field interpolation to noise characterization. Here we resolve a number of open questions that arise when extending this framework to Mach-Zehnder interferometers and quadrature displacement sensing. In particular, we derive lower bounds on the achievable mean square error in estimating a linear function of either local phase shifts or quadrature displacements. In the case of local phase shifts, these results prove, and somewhat generalize, a conjecture by Proctor []. For quadrature displacements, we extend proofs of lower bounds to the case of arbitrary linear functions. We provide optimal protocols achieving these bounds up to small (multiplicative) constants and describe an algebraic approach to deriving new optimal protocols, possibly subject to additional constraints. Using this approach, we prove necessary conditions for the amount of entanglement needed for any optimal protocol for both local phase and displacement sensing. Published by the American Physical Society 2024

Bringewatt, Jacob↗
DOE OSTI2019

Time-strain separability in medium-amplitude oscillatory shear

Here, we derive and study equations for the weakly nonlinear medium-amplitude oscillatory shear (MAOS) response of materials exhibiting time-strain separability. Results apply to constitutive models with arbitrary linear memory function $\textit{m}$(s) and for both viscoelastic liquids and viscoelastic solids. The derived equations serve as a reference to identify which models are time-strain separable (TSS) and which may appear separable but are not, in the weakly nonlinear limit. More importantly, we study how the linear viscoelastic (LVE) relaxation spectrum, H($_\tau$), affects the frequency dependence of the TSS MAOS material functions. Continuous relaxation spectra are considered that are associated with analytical functions (log-normal and asymmetric Lorentzian distributions), fractional mechanical models (Maxwell and Zener), and molecular theories (Rouse and Doi-Edwards). TSS MAOS signatures reveal much more than just the perturbation parameter A in the shear damping function small-strain expansion, $h(_γ) = 1 + \text{A}_γ$$^2 + \mathcal{O}(_γ$$^4)$. Specifically, the distribution of terminal relaxation times is significantly more apparent in the TSS MAOS functions than their LVE counterparts. We theoretically show that this occurs because TSS MAOS material functions are sensitive to higher-order moments of the relaxation spectrum, which leads to the definition of MAOS liquids. We also show the first examples of MAOS signatures that differ from the liquid-like terminal MAOS behavior predicted by the fourth-order fluid expansion. This occurs when higher moments of the relaxation spectrum are not finite. The famous corotational Maxwell model is a subset of our results here, for which A = -1/6, and any LVE relaxation spectrum could be used.

36 MATERIALS SCIENCE↗