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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 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2013

Analytic structure of the multichannel Jost matrix for potentials with Coulombic tails

A quantum system is considered that can move in N two-body channels with the potentials that may include the Coulomb interaction. For this system, the Jost matrix is constructed in such a way that all its dependencies on the channel momenta and Sommerfeld parameters are factorized in the form of explicit analytic expressions. It is shown that the two remaining unknown matrices are single-valued analytic functions of the energy and therefore can be expanded in the Taylor series near an arbitrary point within the domain of their analyticity. It is derived a system of first-order differential equations whose solutions determine the expansion coefficients of these series. Alternatively, the unknown expansion coefficients can be used as fitting parameters for parametrizing experimental data similarly to the effective-range expansion. Such a parametrization has the advantage of preserving proper analytic structure of the Jost matrix and can be done not only near the threshold energies, but around any collision or even complex energy. As soon as the parameters are obtained, the Jost matrix (and therefore the S-matrix) is known analytically on all sheets of the Riemann surface, and thus enables one to locate possible resonances.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

A differential equation for Lerch's transcendent and associated symmetric operators in Hilbert space

The function Ψ(x,y,s)=e{sup iy}Φ(−e{sup iy},s,x), where Φ(z,s,v) is Lerch's transcendent, satisfies the following two-dimensional formally self-adjoint second-order hyperbolic differential equation, where s=1/2+iλ. The corresponding differential expression determines a densely defined symmetric operator (the minimal operator) on the Hilbert space L{sub 2}(Π), where Π=(0,1)×(0,2π). We obtain a description of the domains of definition of some symmetric extensions of the minimal operator. We show that formal solutions of the eigenvalue problem for these symmetric extensions are represented by functional series whose structure resembles that of the Fourier series of Ψ(x,y,s). We discuss sufficient conditions for these formal solutions to be eigenfunctions of the resulting symmetric differential operators. We also demonstrate a close relationship between the spectral properties of these symmetric differential operators and the distribution of the zeros of some special analytic functions analogous to the Riemann zeta function. Bibliography: 15 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Collision-induced Raman scattering and the peculiar case of neon: Anisotropic spectrum, anisotropy, and the inverse scattering problem

Owing in part to the p orbitals of its filled L shell, neon has repeatedly come on stage for its peculiar properties. In the context of collision-induced Raman spectroscopy, in particular, we have shown, in a brief report published a few years ago [M. Chrysos et al., Phys. Rev. A 80, 054701 (2009)], that the room-temperature anisotropic Raman lineshape of Ne–Ne exhibits, in the far wing of the spectrum, a peculiar structure with an aspect other than a smooth wing (on a logarithmic plot) which contrasts with any of the existing studies, and whose explanation lies in the distinct way in which overlap and exchange interactions interfere with the classical electrostatic ones in making the polarizability anisotropy, α{sub ∥} − α{sub ⊥}. Here, we delve deeper into that study by reporting data for that spectrum up to 450 cm{sup −1} and for even- and odd-order spectral moments up to M{sub 6}, as well as quantum lineshapes, generated from SCF, CCSD, and CCSD(T) models for α{sub ∥} − α{sub ⊥}, which are critically compared with the experiment. On account of the knowledge of the spectrum over the augmented frequency domain, we show how the inverse scattering problem can be tackled both effectively and economically, and we report an analytic function for the anisotropy whose quantum lineshape faithfully reproduces our observations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Exponential Synthesis in the Kernel of a Symmetric Convolution

The paper describes a certain class of homogeneous equations of convolution type in spaces of analytic functions on convex domains. We obtain sufficient conditions under which every solution of an equation from this class is approximated by its elementary solutions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Fluids confined in wedges and by edges: From cluster integrals to thermodynamic properties referred to different regions

Recently, new insights into the relation between the geometry of the vessel that confines a fluid and its thermodynamic properties were traced through the study of cluster integrals for inhomogeneous fluids. In this work, I analyze the thermodynamic properties of fluids confined in wedges or by edges, emphasizing on the question of the region to which these properties refer. In this context, the relations between the line-thermodynamic properties referred to different regions are derived as analytic functions of the dihedral angle α, for 0 < α < 2π, which enables a unified approach to both edges and wedges. As a simple application of these results, I analyze the properties of the confined gas in the low-density regime. Finally, using recent analytic results for the second cluster integral of the confined hard sphere fluid, the low density behavior of the line thermodynamic properties is analytically studied up to order two in the density for 0 < α < 2π and by adopting different reference regions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

SU-E-J-63: Estimating the Effects of Respiratory Motion On Dose Heterogeneity for ITV-Based Treatments

Purpose: To quantify the relationship between the amount of dose heterogeneity in a treatment plan that uses an internal target volume (ITV) to account for respiratory motion and the true amount of heterogeneity in the dose delivered to the tumor contained within that ITV. Methods: We develop a convolution-based framework for calculating dose delivered to a tumor moving inside an ITV according to a common sinusoid-based breathing model including asymmetry. We model the planned ITV dose distribution as a centrally peaked analytic function approximating the profile of clinical stereotactic body radiotherapy treatments. Expressions for the minimum and maximum dose received by the tumor are derived and evaluated for a range of clinically relevant parameters. Results of the model are validated with phantom measurements using an ion chamber array. Results: An analytic expression is presented for the maximum and minimum doses received by the tumor relative to the planned ITV dose. The tumor dose heterogeneity depends solely on the ratio of tumor size to ITV size, the peak dose in the planned ITV dose distribution, and the respiratory asymmetry parameter. Under the assumptions of this model, using a typical breathing asymmetry parameter and a dose distribution with a fixed size ITV covered by the 100% line and with a 130% hotspot, the maximum dose to the tumor varies between 113%–130%, and the minimum dose varies between 100%–116% depending on the amount of tumor motion. Conclusion: This modeling exercise demonstrates the interplay between motion and dose heterogeneity. Tumors that exhibit large amounts of respiratory motion relative to their size will receive a more homogeneous dose and a larger minimum dose than would be inferred from the ITV dose distribution. This effect is not captured in current clinical treatment planning methods unless 4D dose calculation techniques are used. This work was partially supported by a Varian Medical Systems research grant.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2022

Accurate parameterization of the kinetic energy functional

The absence of a reliable formulation of kinetic energy density functional has hindered the development of orbital free density functional theory. Using the data-aided learning paradigm, we propose a simple prescription to accurately model the kinetic energy density of any system. Our method relies on a dictionary of functional forms for local and nonlocal contributions which have been proposed in the literature and the appropriate coefficients are calculated via a linear regression framework. To model the nonlocal contributions, we explore two new nonlocal functionals - a functional that captures fluctuations in electronic density and a functional that incorporates gradient information. Since, the analytical functional forms of the kernels present in these nonlocal terms are not known from theory, we propose a basis function expansion to model these seemingly difficult nonlocal quantities. This allows us to easily reconstruct kernels for any system using only a few structures. The proposed method is able to learn kinetic energy densities and total kinetic energies of molecular and periodic systems, such as H 2 , LiH, LiF and a one-dimensional chain of 8 hydrogens using data from Kohn-Sham density functional theory calculations for only a few structures. For the ease of reproduction, codes used to generate the models are provided in the supporting materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS2002

Cosmic-Ray Background Flux Model Baed on a Gamma-Ray Large Area Space Telescope Baloon Flight Engineering

Cosmic-ray background fluxes were modeled based on existing measurements and theories and are presented here. The model, originally developed for the Gamma-ray Large Area Space Telescope (GLAST) Balloon Experiment, covers the entire solid angle (4(pi) sr), the sensitive energy range of the instrument ((approx) 10 MeV to 100 GeV) and abundant components (proton, alpha, e(sup -), e(sup +), (mu)(sup -), (mu)(sup +) and gamma). It is expressed in analytic functions in which modulations due to the solar activity and the Earth geomagnetism are parameterized. Although the model is intended to be used primarily for the GLAST Balloon Experiment, model functions in low-Earth orbit are also presented and can be used for other high energy astrophysical missions. The model has been validated via comparison with the data of the GLAST Balloon Experiment.

COSMIC RADIATION↗
DOE OSTI2013

Leading singularities and off-shell conformal integrals

The three-loop four-point function of stress-tensor multiplets in N=4 super Yang-Mills theory contains two so far unknown, off-shell, conformal integrals, in addition to the known, ladder-type integrals. In our paper we evaluate the unknown integrals, thus obtaining the three-loop correlation function analytically. The integrals have the generic structure of rational functions multiplied by (multiple) polylogarithms. We use the idea of leading singularities to obtain the rational coefficients, the symbol — with an appropriate ansatz for its structure — as a means of characterising multiple polylogarithms, and the technique of asymptotic expansion of Feynman integrals to obtain the integrals in certain limits. The limiting behaviour uniquely fixes the symbols of the integrals, which we then lift to find the corresponding polylogarithmic functions. The final formulae are numerically confirmed. Furthermore, we develop techniques that can be applied more generally, and we illustrate this by analytically evaluating one of the integrals contributing to the same four-point function at four loops. This example shows a connection between the leading singularities and the entries of the symbol.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Domains of analyticity for response solutions in strongly dissipative forced systems

We study the ordinary differential equation εx{sup ¨}+x{sup .}+εg(x)=εf(ωt), where g and f are real-analytic functions, with f quasi-periodic in t with frequency vector ω. If c{sub 0}∈R is such that g(c{sub 0}) equals the average of f and g′(c{sub 0}) ≠ 0, under very mild assumptions on ω there exists a quasi-periodic solution close to c{sub 0} with frequency vector ω. We show that such a solution depends analytically on ε in a domain of the complex plane tangent more than quadratically to the imaginary axis at the origin.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Discrete Approximations of Determinantal Point Processes on Continuous Spaces: Tree Representations and Tail Triviality

We prove tail triviality of determinantal point processes μ on continuous spaces. Tail triviality has been proved for such processes only on discrete spaces, and hence we have generalized the result to continuous spaces. To do this, we construct tree representations, that is, discrete approximations of determinantal point processes enjoying a determinantal structure. There are many interesting examples of determinantal point processes on continuous spaces such as zero points of the hyperbolic Gaussian analytic function with Bergman kernel, and the thermodynamic limit of eigenvalues of Gaussian random matrices for Sine{sub 2},Airy{sub 2},Bessel{sub 2}, and Ginibre point processes. Our main theorem proves all these point processes are tail trivial.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
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 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 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↗