Search NASA⌕ Search

SEARCH · Search NASA

Results for “Analytic functions”

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
DOE OSTI2020

IRDFF-II: A New Neutron Metrology Library

High quality nuclear data is the most fundamental underpinning for all neutron metrology applications. This paper describes the release of version II of the International Reactor Dosimetry and Fusion File (IRDFF-II) that contains a consistent set of nuclear data for fission and fusion neutron metrology applications up to 60 MeV neutron energy. The library is intended to support: a) applications in research reactors; b) safety and regulatory applications in the nuclear power generation in commercial fission reactors; and c) material damage studies in support of the research and development of advanced fusion concepts. The paper describes the contents of the library, documents the thorough verification process used in its preparation, and provides an extensive set of validation data gathered from a wide range of neutron benchmark fields. The new IRDFF-II library includes 119 metrology reactions, four cover material reactions to support self-shielding corrections, five metrology metrics used by the dosimetry community, and cumulative fission products yields for seven fission products in three different neutron energy regions. In support of characterizing the measurement of the residual nuclei from the dosimetry reactions and the fission product decay modes, the present document lists the recommended decay data, particle emission energies and probabilities for 68 activation products. It also includes neutron spectral characterization data for 29 neutron benchmark fields for the validation of the library contents. Additional six reference fields were assessed (four from plutonium critical assemblies, two measured fields for thermal-neutron induced fission on 233U and 239Pu targets) but not used for validation due to systematic discrepancies in C/E reaction rate values or lack of reaction-rate experimental data. Another ten analytical functions are included that can be useful for calculating average cross sections, average energy, thermal spectrum average cross sections and resonance integrals. The IRDFF-II library and comprehensive documentation is available online at www-nds.iaea.org/IRDFF/. Evaluated cross sections can be compared with experimental data and other evaluations at www-nds.iaea.org/exfor/endf.htm. The new library is expected to become the international reference in neutron metrology for multiple applications.

IAEA IRDFF↗
DOE OSTI2016

Derivatives at the boundary for analytic Lipschitz functions

We consider the behaviour of holomorphic functions on a bounded open subset of the plane, satisfying a Lipschitz condition with exponent α, with 0<α<1, in the vicinity of an exceptional boundary point where all such functions exhibit some kind of smoothness. Specifically, we consider the relation between the abstract idea of a bounded point derivation on the algebra of such functions and the classical complex derivative evaluated as a limit of difference quotients. We show that whenever such a bounded point derivation exists at a boundary point b, it may be evaluated by taking a limit of classical difference quotients, approaching from a set having full area density at b. Bibliography: 13 titles. (paper)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Holistic Portfolio Optimization using Directed Mutations

Genetic algorithms provide attractive options for performing nonlinear multi-objective combinatorial design optimization, and they have proven very useful for optimizing individual systems. However, conventional genetic algorithms fall short when performing holistic portfolio optimizations in which the decision variables also include the integer counts of multiple system types over multiple time periods. When objective functions are formulated as analytic functions, we can formally differentiate with respect to system counts and use the resulting gradient information to generate favorable mutations in the count variables. We apply several variations on this basic idea to an idealized hanging chain example to obtain >> 1000x speedups over conventional genetic algorithms in both single - and multi-objective cases. We develop a more complex example of a notional military portfolio that includes combinatorial design variables and dependency constraints between the design choices. In this case, our initial results are mixed, but many variations are still open to further research.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1978

Extinction-sedimentation inversion technique for measuring size distribution of artificial fogs

In measuring the size distribution of artificial fog particles, it is important that the natural state of the particles not be disturbed by the measuring device, such as occurs when samples are drawn through tubes. This paper describes a method for carrying out such a measurement by allowing the fog particles to settle in quiet air inside an enclosure through which traverses a parallel beam of light for measuring the optical depth as a function of time. An analytic function fit to the optical depth time decay curve can be directly inverted to yield the size distribution. Results of one such experiment performed on artificial fogs are shown as an example. The forwardscattering corrections to the measured extinction coefficient are also discussed with the aim of optimizing the experimental design so that the error due to forwardscattering is minimized.

Deepak, A.↗
NASA NTRS1990

Neural computation of arithmetic functions

An area of application of neural networks is considered. A neuron is modeled as a linear threshold gate, and the network architecture considered is the layered feedforward network. It is shown how common arithmetic functions such as multiplication and sorting can be efficiently computed in a shallow neural network. Some known results are improved by showing that the product of two n-bit numbers and sorting of n n-bit numbers can be computed by a polynomial-size neural network using only four and five unit delays, respectively. Moreover, the weights of each threshold element in the neural networks require O(log n)-bit (instead of n-bit) accuracy. These results can be extended to more complicated functions such as multiple products, division, rational functions, and approximation of analytic functions.

Siu, Kai-Yeung↗
DOE OSTI2018

Riemann–Hilbert Problems on a Cut Plane

We consider the Riemann–Hilbert-type boundary-value problems in the case of several unknown functions and obtain solvability conditions and index formulas for the linear conjugation problem, the Riemann–Hilbert problem, and the Riemann–Hilbert–Poincaré problem on a plane cut along several regular arcs in various weighted functional classes. We also examine the general differential boundary-value problem for analytic functions and boundary-value problems with shifts and complex conjugation on a cut plane.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Correlation function induced by a generalized diffusion equation with the presence of a harmonic potential

An integro-differential diffusion equation with linear force, based on the continuous time random walk model, is considered. The equation generalizes the ordinary and fractional diffusion equations, which includes short, intermediate and long-time memory effects described by the waiting time probability density function. Analytical expression for the correlation function is obtained and analyzed, which can be used to describe, for instance, internal motions of proteins. The result shows that the generalized diffusion equation has a broad application and it may be used to describe different kinds of systems. - Highlights: • Calculation of the correlation function. • The correlation function is connected to the survival probability. • The model can be applied to the internal dynamics of proteins.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1990

Three-dimensional potential flows from functions of a 3D complex variable

Potential, or ideal, flow velocities can be found from the gradient of an harmonic function. An ordinary complex valued analytic function can be written as the sum of two real valued functions, both of which are harmonic. Thus, 2D complex valued functions serve as a source of functions that describe two-dimensional potential flows. However, this use of complex variables has been limited to two-dimensions. Recently, a new system of three-dimensional complex variables has been developed at the NASA Ames Research Center. As a step toward application of this theory to the analysis of 3D potential flow, several functions of a three-dimensional complex variable have been investigated. The results for two such functions, the 3D exponential and 3D logarithm, are presented in this paper. Potential flows found from these functions are investigated. Important characteristics of these flows fields are noted.

Kelly, Patrick↗
NASA NTRS2001

Distribution functions of probabilistic automata

Each probabilistic automaton M over an alphabet A defines a probability measure Prob sub(M) on the set of all finite and infinite words over A. We can identify a k letter alphabet A with the set {0, 1,..., k-1}, and, hence, we can consider every finite or infinite word w over A as a radix k expansion of a real number X(w) in the interval [0, 1]. This makes X(w) a random variable and the distribution function of M is defined as usual: F(x) := Prob sub(M) { w: X(w) < x }. Utilizing the fixed-point semantics (denotational semantics), extended to probabilistic computations, we investigate the distribution functions of probabilistic automata in detail. Automata with continuous distribution functions are characterized. By a new, and much more easier method, it is shown that the distribution function F(x) is an analytic function if it is a polynomial. Finally, answering a question posed by D. Knuth and A. Yao, we show that a polynomial distribution function F(x) on [0, 1] can be generated by a prob abilistic automaton iff all the roots of F'(x) = 0 in this interval, if any, are rational numbers. For this, we define two dynamical systems on the set of polynomial distributions and study attracting fixed points of random composition of these two systems.

Denotational semantics↗
NASA NTRS2010

Particle Swarm Optimization Toolbox

The Particle Swarm Optimization Toolbox is a library of evolutionary optimization tools developed in the MATLAB environment. The algorithms contained in the library include a genetic algorithm (GA), a single-objective particle swarm optimizer (SOPSO), and a multi-objective particle swarm optimizer (MOPSO). Development focused on both the SOPSO and MOPSO. A GA was included mainly for comparison purposes, and the particle swarm optimizers appeared to perform better for a wide variety of optimization problems. All algorithms are capable of performing unconstrained and constrained optimization. The particle swarm optimizers are capable of performing single and multi-objective optimization. The SOPSO and MOPSO algorithms are based on swarming theory and bird-flocking patterns to search the trade space for the optimal solution or optimal trade in competing objectives. The MOPSO generates Pareto fronts for objectives that are in competition. A GA, based on Darwin evolutionary theory, is also included in the library. The GA consists of individuals that form a population in the design space. The population mates to form offspring at new locations in the design space. These offspring contain traits from both of the parents. The algorithm is based on this combination of traits from parents to hopefully provide an improved solution than either of the original parents. As the algorithm progresses, individuals that hold these optimal traits will emerge as the optimal solutions. Due to the generic design of all optimization algorithms, each algorithm interfaces with a user-supplied objective function. This function serves as a "black-box" to the optimizers in which the only purpose of this function is to evaluate solutions provided by the optimizers. Hence, the user-supplied function can be numerical simulations, analytical functions, etc., since the specific detail of this function is of no concern to the optimizer. These algorithms were originally developed to support entry trajectory and guidance design for the Mars Science Laboratory mission but may be applied to any optimization problem.

Grant, Michael J.↗
DOE OSTI2018

Rigidity of the Laughlin Liquid

We consider general N-particle wave functions that have the form of a product of the Laughlin state with filling factor 1/ℓ and an analytic function of the N variables. This is the most general form of a wave function that can arise through a perturbation of the Laughlin state by external potentials or impurities, while staying in the lowest Landau level and maintaining the strong correlations of the original state. We show that the perturbation can only shift or lower the 1-particle density but nowhere increase it above a maximum value. Consequences of this bound for the response of the Laughlin state to external fields are discussed.

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↗