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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 775 records · Page 43
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

A cubic map chaos criterion theorem with applications in generalized synchronization based pseudorandom number generator and image encryption

This paper sets up a chaos criterion theorem on a kind of cubic polynomial discrete maps. Using this theorem, Zhou-Song's chaos criterion theorem on quadratic polynomial discrete maps and generalized synchronization (GS) theorem construct an eight-dimensional chaotic GS system. Numerical simulations have been carried out to verify the effectiveness of theoretical results. The chaotic GS system is used to design a chaos-based pseudorandom number generator (CPRNG). Using FIPS 140-2 test suit/Generalized FIPS 140-2, test suit tests the randomness of two 1000 key streams consisting of 20 000 bits generated by the CPRNG, respectively. The results show that there are 99.9%/98.5% key streams to have passed the FIPS 140-2 test suit/Generalized FIPS 140-2 test. Numerical simulations show that the different keystreams have an average 50.001% same codes. The key space of the CPRNG is larger than 2{sup 1345}. As an application of the CPRNG, this study gives an image encryption example. Experimental results show that the linear coefficients between the plaintext and the ciphertext and the decrypted ciphertexts via the 100 key streams with perturbed keys are less than 0.00428. The result suggests that the decrypted texts via the keystreams generated via perturbed keys of the CPRNG are almost completely independent on the original image text, and brute attacks are needed to break the cryptographic system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Quantum mechanics without potential function

In the standard formulation of quantum mechanics, one starts by proposing a potential function that models the physical system. The potential is then inserted into the Schrödinger equation, which is solved for the wavefunction, bound states energy spectrum, and/or scattering phase shift. In this work, however, we propose an alternative formulation in which the potential function does not appear. The aim is to obtain a set of analytically realizable systems, which is larger than in the standard formulation and may or may not be associated with any given or previously known potential functions. We start with the wavefunction, which is written as a bounded infinite sum of elements of a complete basis with polynomial coefficients that are orthogonal on an appropriate domain in the energy space. Using the asymptotic properties of these polynomials, we obtain the scattering phase shift, bound states, and resonances. This formulation enables one to handle not only the well-known quantum systems but also previously untreated ones. Illustrative examples are given for two- and three-parameter systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Comparison of different moment-closure approximations for stochastic chemical kinetics

In recent years, moment-closure approximations (MAs) of the chemical master equation have become a popular method for the study of stochastic effects in chemical reaction systems. Several different MA methods have been proposed and applied in the literature, but it remains unclear how they perform with respect to each other. In this paper, we study the normal, Poisson, log-normal, and central-moment-neglect MAs by applying them to understand the stochastic properties of chemical systems whose deterministic rate equations show the properties of bistability, ultrasensitivity, and oscillatory behaviour. Our results suggest that the normal MA is favourable over the other studied MAs. In particular, we found that (i) the size of the region of parameter space where a closure gives physically meaningful results, e.g., positive mean and variance, is considerably larger for the normal closure than for the other three closures, (ii) the accuracy of the predictions of the four closures (relative to simulations using the stochastic simulation algorithm) is comparable in those regions of parameter space where all closures give physically meaningful results, and (iii) the Poisson and log-normal MAs are not uniquely defined for systems involving conservation laws in molecule numbers. We also describe the new software package MOCA which enables the automated numerical analysis of various MA methods in a graphical user interface and which was used to perform the comparative analysis presented in this paper. MOCA allows the user to develop novel closure methods and can treat polynomial, non-polynomial, as well as time-dependent propensity functions, thus being applicable to virtually any chemical reaction system.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

A new approach to the method of source-sink potentials for molecular conduction

We re-derive the tight-binding source-sink potential (SSP) equations for ballistic conduction through conjugated molecular structures in a form that avoids singularities. This enables derivation of new results for families of molecular devices in terms of eigenvectors and eigenvalues of the adjacency matrix of the molecular graph. In particular, we define the transmission of electrons through individual molecular orbitals (MO) and through MO shells. We make explicit the behaviour of the total current and individual MO and shell currents at molecular eigenvalues. A rich variety of behaviour is found. A SSP device has specific insulation or conduction at an eigenvalue of the molecular graph (a root of the characteristic polynomial) according to the multiplicities of that value in the spectra of four defined device polynomials. Conduction near eigenvalues is dominated by the transmission curves of nearby shells. A shell may be inert or active. An inert shell does not conduct at any energy, not even at its own eigenvalue. Conduction may occur at the eigenvalue of an inert shell, but is then carried entirely by other shells. If a shell is active, it carries all conduction at its own eigenvalue. For bipartite molecular graphs (alternant molecules), orbital conduction properties are governed by a pairing theorem. Inertness of shells for families such as chains and rings is predicted by selection rules based on node counting and degeneracy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

A Laguerre expansion method for the field particle portion in the linearized Coulomb collision operator

The spherical coordinates expressions of the Rosenbluth potentials are applied to the field particle portion in the linearized Coulomb collision operator. The Sonine (generalized Laguerre) polynomial expansion formulas for this operator allowing general field particles' velocity distributions are derived. An important application area of these formulas is the study of flows of thermalized particles in NBI-heated or burning plasmas since the energy space structure of the fast ions' slowing down velocity distribution cannot be expressed by usual orthogonal polynomial expansions, and since the Galilean invariant property and the momentum conservation of the collision must be distinguished there.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Hydrodynamic description of an unmagnetized plasma with multiple ion species. I. General formulation

A generalization of the Braginskii ion fluid description [S. I. Braginskii, Sov. Phys. JETP 6, 358 (1958)] to the case of an unmagnetized collisional plasma with multiple ion species is presented. An asymptotic expansion in the ion Knudsen number is used to derive the individual ion species continuity, as well as the total ion mass density, momentum, and energy evolution equations accurate through the second order. Expressions for the individual ion species drift velocities with respect to the center of mass reference frame, as well as for the total ion heat flux and viscosity, which are required to close the fluid equations, are evaluated in terms of the first-order corrections to the lowest order Maxwellian ion velocity distribution functions. A variational formulation for evaluating such corrections and its relation to the plasma entropy are presented. Employing trial functions for the corrections, written in terms of expansions in generalized Laguerre polynomials, and maximizing the resulting functionals produces two systems of linear equations (for “vector” and “tensor” portions of the corrections) for the expansion coefficients. A general matrix formulation of the linear systems as well as expressions for the resulting transport fluxes are presented in forms convenient for numerical implementation. The general formulation is employed in the companion paper [A. N. Simakov and K. Molvig, Hydrodynamic description of an unmagnetized plasma with multiple ion species. II. Two and three ion species plasmas, submitted to Phys. Plasmas (2015)] to evaluate the individual ion drift velocities and the total ion heat flux and viscosity for specific cases of two and three ion species plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Reproducibility and calibration of MMC-based high-resolution gamma detectors

Here, we describe a prototype γ-ray detector based on a metallic magnetic calorimeter with an energy resolution of 46 eV at 60 keV and a reproducible response function that follows a simple second-order polynomial. The simple detector calibration allows adding high-resolution spectra from different pixels and different cool-downs without loss in energy resolution to determine γ-ray centroids with high accuracy. As an example of an application in nuclear safeguards enabled by such a γ-ray detector, we discuss the non-destructive assay of 242 Pu in a mixed-isotope Pu sample.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Responsivity calibration of the LoWEUS spectrometer

We performed an in situ calibration of the relative responsivity function of the Long-Wavelength Extreme Ultraviolet Spectrometer (LoWEUS), while operating on the Lithium Tokamak Experiment (LTX) at Princeton Plasma Physics Laboratory. The calibration was accomplished by measuring oxygen lines, which are typically present in LTX plasmas. The measured spectral line intensities of each oxygen charge state were then compared to the calculated emission strengths given in the CHIANTI atomic database. Normalizing the strongest line in each charge state to the CHIANTI predictions, we obtained the differences between the measured and predicted values for the relative strengths of the other lines of a given charge state. We find that a 3rd degree polynomial function provides a good fit to the data points. Our measurements show that the responsivity between about 120 and 300 Å varies by factor of ∼30.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2015

Geometric properties of commutative subalgebras of partial differential operators

We investigate further algebro-geometric properties of commutative rings of partial differential operators, continuing our research started in previous articles. In particular, we start to explore the simplest and also certain known examples of quantum algebraically completely integrable systems from the point of view of a recent generalization of Sato's theory, developed by the first author. We give a complete characterization of the spectral data for a class of 'trivial' commutative algebras and strengthen geometric properties known earlier for a class of known examples. We also define a kind of restriction map from the moduli space of coherent sheaves with fixed Hilbert polynomial on a surface to an analogous moduli space on a divisor (both the surface and the divisor are part of the spectral data). We give several explicit examples of spectral data and corresponding algebras of commuting (completed) operators, producing as a by-product interesting examples of surfaces that are not isomorphic to spectral surfaces of any (maximal) commutative ring of partial differential operators of rank one. Finally, we prove that any commutative ring of partial differential operators whose normalization is isomorphic to the ring of polynomials k[u,t] is a Darboux transformation of a ring of operators with constant coefficients. Bibliography: 39 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

On centres of relatively free associative algebras with a Lie nilpotency identity

We study central polynomials of a relatively free Lie nilpotent algebra F{sup (n)} of degree n. We prove a product theorem, which generalizes the well-known results of Latyshev and Volichenko. We construct generalized Hall polynomials, by using which we prove that the core centre of the algebra F{sup (n)} is nontrivial for any n⩾5. We obtain a number of special results when n=5 and 6. Bibliography: 27 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Convergence of ray sequences of Frobenius-Padé approximants

Let σ-hat be a Cauchy transform of a possibly complex-valued Borel measure σ and {p_n} a system of orthonormal polynomials with respect to a measure μ, where supp(μ)∩supp(σ)=∅. An (m,n)th Frobenius-Padé approximant to σ-hat is a rational function P/Q, deg (P)≤m, deg (Q)≤n, such that the first m+n+1 Fourier coefficients of the remainder function Q σ-hat −P vanish when the form is developed into a series with respect to the polynomials p{sub n}. We investigate the convergence of the Frobenius-Padé approximants to σ-hat along ray sequences n/(n+m+1)→c>0, n−1≤m, when μ and σ are supported on intervals of the real line and their Radon-Nikodym derivatives with respect to the arcsine distribution of the corresponding interval are holomorphic functions. Bibliography: 30 titles. (paper)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

EXPLORING THE COSMIC REIONIZATION EPOCH IN FREQUENCY SPACE: AN IMPROVED APPROACH TO REMOVE THE FOREGROUND IN 21 cm TOMOGRAPHY

With the intent of correctly restoring the redshifted 21 cm signals emitted by neutral hydrogen during the cosmic reionization processes, we re-examine the separation approaches based on the quadratic polynomial fitting technique in frequency space in order to investigate whether they work satisfactorily with complex foreground by quantitatively evaluating the quality of restored 21 cm signals in terms of sample statistics. We construct the foreground model to characterize both spatial and spectral substructures of the real sky, and use it to simulate the observed radio spectra. By comparing between different separation approaches through statistical analysis of restored 21 cm spectra and corresponding power spectra, as well as their constraints on the mean halo bias b and average ionization fraction x{sub e} of the reionization processes, at z = 8 and the noise level of 60 mK we find that although the complex foreground can be well approximated with quadratic polynomial expansion, a significant part of the Mpc-scale components of the 21 cm signals (75% for {approx}> 6 h {sup -1} Mpc scales and 34% for {approx}> 1 h {sup -1} Mpc scales) is lost because it tends to be misidentified as part of the foreground when the single-narrow-segment separation approach is applied. The best restoration of the 21 cm signals and the tightest determination of b and x{sub e} can be obtained with the three-narrow-segment fitting technique as proposed in this paper. Similar results can be obtained at other redshifts.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

On the relaxation behaviors of slow and classical glitches: Observational biases and their opposite recovery trends

We study the pulsar timing properties and the data analysis methods of glitch recoveries. In some cases one first fits the times of arrival (TOAs) to obtain the 'time-averaged' frequency ν and its first derivative ν-dot , and then fits models to them. However, our simulations show that ν and ν-dot obtained in this way are systematically biased unless the time intervals between the nearby data points of TOAs are smaller than about 10{sup 4} s, which is much shorter than typical observation intervals. Alternatively, glitch parameters can be obtained by fitting the phases directly with relatively smaller biases, but the initial recovery time scale is usually chosen by eye, which may introduce a strong bias. We also construct a phenomenological model by assuming a pulsar spin-down law of ν-dot ν{sup −3}=−H{sub 0}G(t) with G(t) = 1 + κe {sup –t/τ} for a glitch recovery, where H {sub 0} is a constant and κ and τ are the glitch parameters to be found. This model can reproduce the observed data of slow glitches from B1822–09 and the giant classical glitch of B2334+61, with κ < 0 or κ > 0, respectively. We then use this model to simulate TOA data and test several fitting procedures for a glitch recovery. The best procedure is (1) to use a very high order polynomial (e.g., to 50th order) to precisely describe the phase, (2) obtain ν(t) and ν-dot (t) from the polynomial, then (3) obtain the glitch parameters from ν(t) or ν-dot (t). Finally, the uncertainty in the starting time t {sub 0} of a classical glitch causes uncertainties in some glitch parameters, but less so for a slow glitch, t {sub 0}, of which can be determined from data.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

FOREGROUND MODEL AND ANTENNA CALIBRATION ERRORS IN THE MEASUREMENT OF THE SKY-AVERAGED λ21 cm SIGNAL AT z∼ 20

The most promising near-term observable of the cosmic dark age prior to widespread reionization (z ∼ 15-200) is the sky-averaged λ21 cm background arising from hydrogen in the intergalactic medium. Though an individual antenna could in principle detect the line signature, data analysis must separate foregrounds that are orders of magnitude brighter than the λ21 cm background (but that are anticipated to vary monotonically and gradually with frequency, e.g., they are considered {sup s}pectrally smooth{sup )}. Using more physically motivated models for foregrounds than in previous studies, we show that the intrinsic spectral smoothness of the foregrounds is likely not a concern, and that data analysis for an ideal antenna should be able to detect the λ21 cm signal after subtracting a ∼fifth-order polynomial in log ν. However, we find that the foreground signal is corrupted by the angular and frequency-dependent response of a real antenna. The frequency dependence complicates modeling of foregrounds commonly based on the assumption of spectral smoothness. Our calculations focus on the Large-aperture Experiment to detect the Dark Age, which combines both radiometric and interferometric measurements. We show that statistical uncertainty remaining after fitting antenna gain patterns to interferometric measurements is not anticipated to compromise extraction of the λ21 cm signal for a range of cosmological models after fitting a seventh-order polynomial to radiometric data. Our results generalize to most efforts to measure the sky-averaged spectrum.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

SHOCK STRENGTH IN SPACE AND ASTROPHYSICAL PLASMAS

The Rankine–Hugoniot (R–H) jump conditions are the most important and frequently used equations in studies of the properties of space and astrophysical plasmas during their passage through shock discontinuities. This paper revisits the R–H conditions for shocks, develops the formulation of the compression ratio, and examines its range of values and properties. The analysis expresses the downstream thermodynamic variables and the compression ratio as functions of the upstream thermodynamic variables, either for equal or different polytropic indices upstream and downstream of the shock. In the general case of space plasmas with an oblique magnetic field, the compression ratio is given by a quartic polynomial, which is reduced to a cubic trinomial when the upstream/downstream polytropic indices are equal. The special cases of magnetic fields that are perpendicular or parallel to the shock normal are also examined. In any case, the compression ratio polynomial has one degree larger order, when the upstream/downstream polytropic indices are different. Emphasis is placed on the maximum value of the compression ratio, which is known to be ∼4 for adiabatic polytropic index ∼5/3. However, the compression ratio can be much larger if the upstream/downstream polytropic indices are not equal to each other and less than one. Several other issues are investigated: (i) the entropic condition, showing that statistical mechanics and thermodynamics lead to the same relation of entropy variation; (ii) the effect of kappa distributions on jump conditions; and (iii) the upper limit of the upstream temperature for a shock to exist.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

The dark energy cosmic clock: a new way to parametrise the equation of state

We propose a new parametrisation of the dark energy equation of state, which uses the dark energy density, Ω{sub e} as a cosmic clock. We expand the equation of state in a series of orthogonal polynomials, with Ω{sub e} as the expansion parameter and determine the expansion coefficients by fitting to SNIa and H(z) data. Assuming that Ω{sub e} is a monotonic function of time, we show that our parametrisation performs better than the popular Chevallier-Polarski-Linder (CPL) and Gerke and Efstathiou (GE) parametrisations, and we demonstrate that it is robust to the choice of prior. Expanding in orthogonal polynomials allows us to relate models of dark energy directly to our parametrisation, which we illustrate by placing constraints on the expansion coefficients extracted from two popular quintessence models. Finally, we comment on how this parametrisation could be modified to accommodate high redshift data, where any non-monotonicity of Ω{sub e} would need to be accounted for.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Bounce cosmology from F(R) gravity and F(R) bigravity

We reconstruct F(R) gravity models with exponential and power-law forms of the scale factor in which bounce cosmology can be realized. We explore the stability of the reconstructed models with analyzing the perturbations from the background solutions. Furthermore, we study an F(R) gravity model with a sum of exponentials form of the scale factor, where the bounce in the early universe as well as the late-time cosmic acceleration can be realized in a unified manner. As a result, we build a second order polynomial type model in terms of R and show that it could be stable. Moreover, when the scale factor is expressed by an exponential form, we derive F(R) gravity models of a polynomial type in case of the non-zero spatial curvature and that of a generic type in that of the zero spatial curvature. In addition, for an exponential form of the scale factor, an F(R) bigravity model realizing the bouncing behavior is reconstructed. It is found that in both the physical and reference metrics the bouncing phenomenon can occur, although in general the contraction and expansion rates are different each other.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

An optimal FFT-based anisotropic power spectrum estimator

Measurements of line-of-sight dependent clustering via the galaxy power spectrum's multipole moments constitute a powerful tool for testing theoretical models in large-scale structure. Recent work shows that this measurement, including a moving line-of-sight, can be accelerated using Fast Fourier Transforms (FFTs) by decomposing the Legendre polynomials into products of Cartesian vectors. Here, we present a faster, optimal means of using FFTs for this measurement. We avoid redundancy present in the Cartesian decomposition by using a spherical harmonic decomposition of the Legendre polynomials. With this method, a given multipole of order ℓ requires only 2ℓ+1 FFTs rather than the (ℓ+1)(ℓ+2)/2 FFTs of the Cartesian approach. For the hexadecapole (ℓ = 4), this translates to 40% fewer FFTs, with increased savings for higher ℓ. The reduction in wall-clock time enables the calculation of finely-binned wedges in P ( k ,μ), obtained by computing multipoles up to a large ℓ{sub max} and combining them. This transformation has a number of advantages. We demonstrate that by using non-uniform bins in μ, we can isolate plane-of-sky (angular) systematics to a narrow bin at 0μ ≅ while eliminating the contamination from all other bins. We also show that the covariance matrix of clustering wedges binned uniformly in μ becomes ill-conditioned when combining multipoles up to large values of ℓ{sub max}, but that the problem can be avoided with non-uniform binning. As an example, we present results using ℓ{sub max}=16, for which our procedure requires a factor of 3.4 fewer FFTs than the Cartesian method, while removing the first μ bin leads only to a 7% increase in statistical error on f σ{sub 8}, as compared to a 54% increase with ℓ{sub max}=4.

79 ASTRONOMY AND ASTROPHYSICS↗