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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 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

Bound state solution of Dirac equation for Hulthen plus trigonometric Rosen Morse non-central potential using Romanovski polynomial

The bound state solutions of Dirac equation for Hulthen and trigonometric Rosen Morse non-central potential are obtained using finite Romanovski polynomials. The approximate relativistic energy spectrum and the radial wave functions which are given in terms of Romanovski polynomials are obtained from solution of radial Dirac equation. The angular wave functions and the orbital quantum number are found from angular Dirac equation solution. In non-relativistic limit, the relativistic energy spectrum reduces into non-relativistic energy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Control design and robustness analysis of a ball and plate system by using polynomial chaos

In this paper, we present a mathematical model of a ball and plate system, a control law and analyze its robustness properties by using the polynomial chaos method. The ball rolls without slipping. There is an auxiliary robot vision system that determines the bodies' positions and velocities, and is used for control purposes. The actuators are to orthogonal DC motors, that changes the plate's angles with the ground. The model is a extension of the ball and beam system and is highly nonlinear. The system is decoupled in two independent equations for coordinates x and y. Finally, the resulting nonlinear closed loop systems are analyzed by the polynomial chaos methodology, which considers that some system parameters are random variables, and generates statistical data that can be used in the robustness analysis.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Robustness analysis of an air heating plant and control law by using polynomial chaos

This paper presents a robustness analysis of an air heating plant with a multivariable closed-loop control law by using the polynomial chaos methodology (MPC). The plant consists of a PVC tube with a fan in the air input (that forces the air through the tube) and a mass flux sensor in the output. A heating resistance warms the air as it flows inside the tube, and a thermo-couple sensor measures the air temperature. The plant has thus two inputs (the fan's rotation intensity and heat generated by the resistance, both measured in percent of the maximum value) and two outputs (air temperature and air mass flux, also in percent of the maximal value). The mathematical model is obtained by System Identification techniques. The mass flux sensor, which is nonlinear, is linearized and the delays in the transfer functions are properly approximated by non-minimum phase transfer functions. The resulting model is transformed to a state-space model, which is used for control design purposes. The multivariable robust control design techniques used is the LQG/LTR, and the controllers are validated in simulation software and in the real plant. Finally, the MPC is applied by considering some of the system's parameters as random variables (one at a time, and the system's stochastic differential equations are solved by expanding the solution (a stochastic process) in an orthogonal basis of polynomial functions of the basic random variables. This method transforms the stochastic equations in a set of deterministic differential equations, which can be solved by traditional numerical methods (That is the MPC). Statistical data for the system (like expected values and variances) are then calculated. The effects of randomness in the parameters are evaluated in the open-loop and closed-loop pole's positions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Connection between quantum systems involving the fourth Painlevé transcendent and k-step rational extensions of the harmonic oscillator related to Hermite exceptional orthogonal polynomial

The purpose of this communication is to point out the connection between a 1D quantum Hamiltonian involving the fourth Painlevé transcendent P{sub IV}, obtained in the context of second-order supersymmetric quantum mechanics and third-order ladder operators, with a hierarchy of families of quantum systems called k-step rational extensions of the harmonic oscillator and related with multi-indexed X{sub m{sub 1,m{sub 2,…,m{sub k}}}} Hermite exceptional orthogonal polynomials of type III. The connection between these exactly solvable models is established at the level of the equivalence of the Hamiltonians using rational solutions of the fourth Painlevé equation in terms of generalized Hermite and Okamoto polynomials. We also relate the different ladder operators obtained by various combinations of supersymmetric constructions involving Darboux-Crum and Krein-Adler supercharges, their zero modes and the corresponding energies. These results will demonstrate and clarify the relation observed for a particular case in previous papers.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Proper central and core polynomials of relatively free associative algebras with identity of Lie nilpotency of degrees 5 and 6

We study the centre of a relatively free associative algebra F{sup (n)} with the identity [x{sub 1},…,x{sub n}]=0 of Lie nilpotency of degree n=5,6 over a field of characteristic 0. It is proved that the core Z{sup ∗}(F{sup (5)}) of the algebra F{sup (5)} (the sum of all ideals of F{sup (5)} contained in its centre) is generated as a T-ideal by the weak Hall polynomial [[x,y]{sup 2},y]. It is also proved that every proper central polynomial of F{sup (5)} is contained in the sum of Z{sup ∗}(F{sup (5)}) and the T-space generated by [[x,y]{sup 2},z] and the commutator [x{sub 1},…,x{sub 4}] of degree 4. This implies that the centre of F{sup (5)} is contained in the T-ideal generated by the commutator of degree 4. Similar results are obtained for F{sup (6)}; in particular, it is proved that the core Z{sup ∗}(F{sup (6)}) is generated as a T-ideal by the commutator of degree 5. Bibliography: 15 titles. (paper)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Orthogonal Polynomials Defined by Self-Similar Measures with Overlaps

Here, we study orthogonal polynomials with respect to self-similar measures, focusing on the class of infinite Bernoulli convolutions, which are defined by iterated function systems with overlaps, especially those defined by the Pisot, Garsia, and Salem numbers. By using an algorithm of Mantica, we obtain graphs of the coefficients of the 3-term recursion relation defining the orthogonal polynomials. We use these graphs to predict whether the singular infinite Bernoulli convolutions belong to the Nevai class. Based on our numerical results, we conjecture that all infinite Bernoulli convolutions with contraction ratios greater than or equal to 1/2 belong to Nevai’s class, regardless of the probability weights assigned to the self-similar measures.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Intricacies of cosmological bounce in polynomial metric f(R) gravity for flat FLRW spacetime

In this paper we present the techniques for computing cosmological bounces in polynomial f(R) theories, whose order is more than two, for spatially flat FLRW spacetime. In these cases the conformally connected Einstein frame shows up multiple scalar potentials predicting various possibilities of cosmological evolution in the Jordan frame where the f(R) theory lives. We present a reasonable way in which one can associate the various possible potentials in the Einstein frame, for cubic f(R) gravity, to the cosmological development in the Jordan frame. The issue concerning the energy conditions in f(R) theories is presented. We also point out the very important relationships between the conformal transformations connecting the Jordan frame and the Einstein frame and the various instabilities of f(R) theory. All the calculations are done for cubic f(R) gravity but we hope the results are sufficiently general for higher order polynomial gravity.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

A superintegrable discrete harmonic oscillator based on bivariate Charlier polynomials

A simple discrete model of the two-dimensional isotropic harmonic oscillator is presented. It is superintegrable with su(2) as its symmetry algebra. It is constructed with the help of the algebraic properties of the bivariate Charlier polynomials. This adds to the other discrete superintegrable models of the oscillator based on Krawtchouk and Meixner orthogonal polynomials in several variables.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

A finite quantum oscillator model related to special sets of Racah polynomials

In [R. Oste and J. Van der Jeugt, arXiv: 1507.01821 [math-ph]] we classified all pairs of recurrence relations in which two (dual) Hahn polynomials with different parameters appear. Such pairs are referred to as (dual) Hahn doubles, and the same technique was then applied to obtain all Racah doubles. We now consider a special case concerning the doubles related to Racah polynomials. This gives rise to an interesting class of two-diagonal matrices with closed form expressions for the eigenvalues. Just as it was the case for (dual) Hahn doubles, the resulting two-diagonal matrix can be used to construct a finite oscillator model. We discuss some properties of this oscillator model, give its (discrete) position wavefunctions explicitly, and illustrate their behavior by means of some plots.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

A Thick-Restart Lanczos Algorithm with Polynomial Filtering for Hermitian Eigenvalue Problems

Polynomial filtering can provide a highly effective means of computing all eigenvalues of a real symmetric (or complex Hermitian) matrix that are located in a given interval, anywhere in the spectrum. This paper describes a technique for tackling this problem by combining a thick-restart version of the Lanczos algorithm with deflation ("locking'') and a new type of polynomial filter obtained from a least-squares technique. Furthermore, the resulting algorithm can be utilized in a “spectrum-slicing” approach whereby a very large number of eigenvalues and associated eigenvectors of the matrix are computed by extracting eigenpairs located in different subintervals independently from one another.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Parametric Synthesis of Feed Drives for CNC Machine Tools by Polynomial Approximation of Ideal Low-Frequency Filters

The relations between the dynamic characteristics of a supply drive and its design parameters and the control system based on standard polynomials approximating an ideal low-frequency filter are described. The possibility of implementing those polynomials is analyzed. The operational characteristics and design parameters of drives obtained on that basis are presented and their applications are considered.

42 ENGINEERING↗
NASA NTRSDate not supplied

Combined Bernstein Polynomial, Optimal Reciprocal Collision Avoidance, Differential Dynamic Programming for Trajectory Replanning and Collision Avoidance for UAM Vehicles

This paper presents an integration of Differential Dynamic Programming (DDP) with the Optimal Reciprocal Collision Avoidance (ORCA) algorithm as the basis for a new algorithm, titled Combined Bernstein Polynomial Optimal Reciprocal Collision Avoidance DDP (COBRA-DDP), for trajectory replanning and collision avoidance for Urban Air Mobility (UAM) vehicles. State-constrained variants of DDP provide the ability to plan trajectories while avoiding obstacles, but these methods require a large increase in computational time per iteration which hinders the overall speed of the algorithm. ORCA utilizes simplified dynamics to recognize potential collisions along a trajectory and provides an optimal velocity for the avoidance of multiple vehicles. These velocity commands, however, may not result in a dynamically feasible trajectory for DDP to plan around. As such, a Bernstein polynomial curve that considers the general dynamic constraints of the vehicle is generated to approximate a trajectory based on the velocity commands. COBRA-DDP optimizes this suggested trajectory via unconstrained DDP to provide a dynamically feasible trajectory that provides collision avoidance. This new trajectory can be applied to the vehicle or used to warm start the state constrained DDP algorithms to decrease computation time. Its benefits and effectiveness of the algorithm are demonstrated on a UAM Vertical Takeoff and Landing (VTOL) vehicle simulation with highly nonlinear dynamics.

Optimal Reciprocal Collision Avoidance↗
DOE OSTI2018

Application of polynomial chaos expansion in inverse transport problems with neutron multiplication measurements and multiple unknowns - 25623

The polynomial chaos expansion technique is used to build surrogate models of the dependences of gamma-ray fluxes and neutron multiplication to unknown physical parameters in radiological source/shield systems. These surrogate models are used with the Differential Evolution Adaptive Metropolis (DREAM), a method to solve and quantify uncertainty in inverse transport problems. Measured data in the inverse problems includes both passive gamma rays and neutron multiplication. The polynomial chaos expansion approach is shown to increase the speed of DREAM by factors of greater than 60 while not degrading the accuracy of the solution. (authors)

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2015

Image Reconstruction from Under sampled Fourier Data Using the Polynomial Annihilation Transform

Fourier samples are collected in a variety of applications including magnetic resonance imaging and synthetic aperture radar. The data are typically under-sampled and noisy. In recent years, l 1 regularization has received considerable attention in designing image reconstruction algorithms from under-sampled and noisy Fourier data. The underlying image is assumed to have some sparsity features, that is, some measurable features of the image have sparse representation. The reconstruction algorithm is typically designed to solve a convex optimization problem, which consists of a fidelity term penalized by one or more l 1 regularization terms. The Split Bregman Algorithm provides a fast explicit solution for the case when TV is used for the l1l1 regularization terms. Due to its numerical efficiency, it has been widely adopted for a variety of applications. A well known drawback in using TV as an l 1 regularization term is that the reconstructed image will tend to default to a piecewise constant image. This issue has been addressed in several ways. Recently, the polynomial annihilation edge detection method was used to generate a higher order sparsifying transform, and was coined the “polynomial annihilation (PA) transform.” This paper adapts the Split Bregman Algorithm for the case when the PA transform is used as the l 1 regularization term. In so doing, we achieve a more accurate image reconstruction method from under-sampled and noisy Fourier data. Our new method compares favorably to the TV Split Bregman Algorithm, as well as to the popular TGV combined with shearlet approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Uncertainty propagation through an aeroelastic wind turbine model using polynomial surrogates

Polynomial surrogates are used to characterize the energy production and lifetime equivalent fatigue loads for different components of the DTU 10 MW reference wind turbine under realistic atmospheric conditions. The variability caused by different turbulent inflow fields are captured by creating independent surrogates for the mean and standard deviation of each output with respect to the inflow realizations. A global sensitivity analysis shows that the turbulent inflow realization has a bigger impact on the total distribution of equivalent fatigue loads than the shear coefficient or yaw miss-alignment. The methodology presented extends the deterministic power and thrust coefficient curves to uncertainty models and adds new variables like damage equivalent fatigue loads in different components of the turbine. These surrogate models can then be implemented inside other work-flows such as: estimation of the uncertainty in annual energy production due to wind resource variability and/or robust wind power plant layout optimization. It can be concluded that it is possible to capture the global behavior of a modern wind turbine and its uncertainty under realistic inflow conditions using polynomial response surfaces. In conclusion, the surrogates are a way to obtain power and load estimation under site specific characteristics without sharing the proprietary aeroelastic design.

17 WIND ENERGY↗
DOE OSTI2016

Efficient Temperature-Dependent Green’s Functions Methods for Realistic Systems: Compact Grids for Orthogonal Polynomial Transforms

The Matsubara Green’s function that is used to describe temperature-dependent behavior is expressed on a numerical grid. While such a grid usually has a couple of hundred points for low-energy model systems, for realistic systems with large basis sets the size of an accurate grid can be tens of thousands of points, constituting a severe computational and memory bottleneck. In this paper, we determine efficient imaginary time grids for the temperature-dependent Matsubara Green’s function formalism that can be used for calculations on realistic systems. Here we show that, because of the use of an orthogonal polynomial transform, we can restrict the imaginary time grid to a few hundred points and reach micro-Hartree accuracy in the electronic energy evaluation. Moreover, we show that only a limited number of orthogonal polynomial expansion coefficients are necessary to preserve accuracy when working with a dual representation of the Green’s function or self-energy and transforming between the imaginary time and frequency domain.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Polynomial Scaling Localized Active Space Unitary Selective Coupled Cluster Singles and Doubles

We present a polynomial-scaling algorithm for the localized active space unitary selective coupled cluster singles and doubles (LAS-USCCSD) method. In this approach, cluster excitations are selected based on a threshold ϵ determined by the absolute gradients of the LAS-UCCSD energy with respect to cluster amplitudes. Using the generalized Wick’s theorem for multireference wave functions, we derive the gradient expression as a polynomial function of one-, two-, and three-body reduced density matrices and 1- and 2-electron integrals, valid for any multireference wave function. The resulting gradient implementation exhibits a memory scaling of 𝒪(N 6 ), with N spin orbitals in the combined active space of all fragments. The variational quantum eigensolver is used to optimize the selected cluster excitations on a quantum simulator. Furthermore, by plotting the energy error, defined as the difference between the LAS-USCCSD and corresponding CASCI energies, against the inverse cluster amplitude selection threshold (ϵ –1 ) for polyene chains containing 2 to 5 π-bond units, we establish a relationship between the energy error and the threshold. To further validate the accuracy of LAS-USCCSD, we computed the cis–trans isomerization energy of stilbene (a 20-qubit system) and the magnetic coupling constant of the tris-hydroxo-bridged chromium dimer [Cr 2 (OH) 3 (NH 3 ) 6 ] 3+ (evaluated as both 12- and 20-qubit systems) using the Qiskit-Qulacs simulator. Assessing such examples is important to determine the practical feasibility of quantum simulations for chemically realistic systems. Toward this goal, with the LAS-USCCSD algorithm we estimated the quantum resources required for simulating an active space of (30e,22o) in [Cr 2 (OH) 3 (NH 3 ) 6 ] 3+ , a size that remains beyond the reach of current quantum simulators for accurate treatment.

Algorithms↗