Search NASA⌕ Search

SEARCH · Search NASA

Results for “LAGUERRE FUNCTION”

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.

17 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

A New Proposal Generalized Predictive Control Algorithm With Polynomial Reference Tracking Applied for Sodium Fast Reactors

This paper proposes a generalized predictive control (GPC) with constraints and orthonormal Laguerre functions using the simplified model of the primary system (reactor core and intermediate heat exchanger (IHX)) of a prototypical sodium fast reactor (SFR). This paper develops a multiple-input multiple-output (MIMO) GPC with input constraints able to track polynomial references of any degree applied in coolant temperature difference across the core and fractional power. The manipulated variables of the GPC-SFR are the reactivity and the sodium flow rate of the primary and secondary pipes. Moreover, orthonormal Laguerre functions and step down condition number techniques were also applied to avoid the numerical ill-conditioning issue in quadratic programming of large systems. Thus, a GPC type-2 was designed to control fractional power, coolant temperature difference across the core and sodium tank temperature of the SFR primary system when temperature references change according to a linear ramp after reaching their steady-state operation, sustaining 100% power operation on the reactor. In order to analyze the load tracking capability of the GPC-SFR type-2, the load following from 100% fractional power (FP) to 60% FP at 0.8% FP/min rate is simulated. Constraints on the rate of coolant temperature difference across the core and reactivity were applied for the design safety. For comparison criteria, this paper compares the GPC-SFR type-2 with the GPC-SFR type-1, i.e., standard model predictive control (MPC), to verify the viability and superior performance of the proposal regarding: (a) ramp-tracking capability of temperature and load; (b) the rejections of a reactivity disturbance of -1 cent and a secondary sodium inlet temperature disturbance of +10°F; and (c) a simulation with uncertainty in reactor design. The simulations show that the GPC-SFR type-2 overcome the GPC-SFR type-1 robustness and performance.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
NASA NTRS1973

Algorithm for identification of a single class

The class of nonlinear dynamic systems, which is described by the integral Hammerstein operator is discussed. The input and output signals of the system, the nonlinear amplification coefficient, and weighting function are broken down by linear-independent functions in Hermite and Laguerre polynomials. The algorithm for calculating parameter estimates, and the reduction of the estimates are discussed along with generalization in the case of a multidimensional system, and the physical interpretation of the examined class of systems.

Kaminskas, V. A.↗
NASA NTRS1976

Diatomic molecule variations

The rotational energy is separated from vibrational energy in the two-particle, steady-state wave equation and to first order the solutions are harmonic oscillator functions. The classical phase integral gives a partition function valid only at high temperature, but the quantum summation is easily performed to give analytic expressions for all the thermodynamic properties of the harmonic oscillator at all temperatures. Anharmonic effects are treated by small perturbation solutions to the wave equation and the relation between energy levels and a series expansion of the perturbation potential is derived. Next, the quantum solutions for an oscillator with a Morse-function potential are derived in terms of Laguerre polynomials.

Source record↗
NASA NTRS1982

Solution to the backward-Kolmogorov equation for a nonstationary oscillation problem

The transition probability density function of a Markovian approximation of the response amplitude of an oscillator under nonstationary excitation is determined in an analytical form. A solution is presented for the associated backward-Kolmogorov equation by transforming the equation into a form amenable to solution by the method of the separation of variables. This procedure results in a boundary value problem which is then solved by using an infinite series of Laguerre polynomials. It is found that the infinite series solution is equivalent to a closed-form solution involving a Bessel function.

Solomos, G. P.↗
NASA NTRS1981

Sound diffraction around screens and wedges for arbitrary point source locations

A development is presented for the Green's function for a point source in the vicinity of a rigid wedge. The diffraction contributions to the Green's function for arbitrary source and listener location is expressed in a form which can be readily evaluated using the Laguerre technique for numerical integration. The present approach offers the advantages of efficient numerical evaluation and of relatively straightforward reduction to well-known analytical approximations in limiting cases. Comparisons with previously obtained experimental and numerical results obtained by Ambaud and Bergassoli (1972) are presented. The comparison with the experimental results is excellent; the advantages of the present numerical technique, vis a vis that of Ambaud and Bergassoli, are pointed out.

Hadden, W. J., Jr.↗
DOE OSTI2023

Adaptive methods of generating complex light arrays

Structured light arrays of various shapes have been a cornerstone in optical science, driven by the complexities of precise and adaptable generation. This study introduces an approach using a spatial light modulator (SLM) as a generator for these arrays. By projecting a holographic mask onto the SLM, it functions simultaneously as an optical convolution device, focusing mechanism, and structured light beam mask. Our approach offers unmatched versatility, allowing for the experimental fabrication of traditional beam arrays like azimuthal Laguerre–Gaussian (LG), Bessel–Gaussian (BG), and Hermite–Gauss (HG) in the far-field. Notably, it has enabled a method of generating Ince–Gauss (IG) and LG radial mode beam arrays using a convolution solution. Our system provides exceptional control over array periodicity and intensity distribution, bypassing the Talbot self-imaging phenomenon seen in traditional setups. We provide an in-depth theoretical discussion, supported by empirical evidence, of our far-field results. This method has vast potential for applications in optical communication, data processing, and multi-particle manipulation. It paves the way for rapid generation of structured light with high spatial frequencies and complex shapes, promising transformative advances in these domains.

Optics↗
NASA NTRS2016

A FDTD Solution of Scattering of Laser Beam with Orbital Angular Momentum by Dielectric Particles: Far-Field Characteristics

Electromagnetic (EM) beams with orbital angular momentum (OAM) may have great potential applications in communication technology and in remote sensing of the Earth-atmosphere system and outer planets. Study of their interaction with optical lenses and dielectric or metallic objects, or scattering of them by particles in the Earth-atmosphere system, is a necessary step to explore the advantage of the OAM EM beams. In this study, the 3-dimensional (3D) scattered-field (SF) finite-difference time domain (FDTD) technique with the convolutional perfectly matched layer (CPML) absorbing boundary conditions (ABC) is applied to calculate the scattering of the purely azimuthal (the radial mode number is assumed to be zero) Laguerre–Gaussian (LG) beams with the OAM by dielectric particles. We found that for OAM beam׳s interaction with dielectric particles, the forward-scattering peak in the conventional phase function (P11) disappears, and light scattering peak occurs at a scattering angle of ~15° to 45°. The disappearance of forward-scattering peak means that, in laser communications most of the particle-scattered noise cannot enter the receiver, thus the received light is optimally the original OAM-encoded signal. This feature of the OAM beam also implies that in lidar remote sensing of the atmospheric particulates, most of the multiple-scattering energy will be off lidar sensors, and this may result in an accurate profiling of particle layers in the atmosphere or in the oceans by lidar, or even in the ground when a ground penetration radar (GPR) with the OAM is applied. This far-field characteristics of the scattered OAM light also imply that the optical theorem, which is derived from plane-parallel wave scattering case and relates the forward scattering amplitude to the total cross section of the scatterer, is invalid for the scattering of OAM beams by dielectric particles.

Electromagnetic beams↗
DOE OSTI2021

High-throughput cell-free screening of eukaryotic membrane protein expression in lipidic mimetics

Membrane proteins play essential roles in cellular function and metabolism. Nonetheless, biophysical and structural studies of membrane proteins are impeded by the difficulty of their expression in and purification from heterologous cell-based systems. As an alternative to these cell-based systems, cell-free protein synthesis has proven to be an exquisite method for screening membrane protein targets in a variety of lipidic mimetics. Here we report a high-throughput screening workflow and applied it to screen 61eukaryotic membrane protein targets. For each target, we tested its expression in lipidic mimetics: two detergents, two liposomes, and two nanodiscs. We show that 35 membrane proteins (57%) can be expressed in a soluble fraction in at least one of the mimetics with the two detergents performing significantly better than nanodiscs and liposomes, in that order. Using the established cell-free workflow, we studied the production and biophysical assays for mitochondrial pyruvate carrier (MPC) complexes. Our studies show that the complexes produced in cell-free are functional competent in complex formation and substrate binding. Our results highlight the utility of using cell-free systems for screening and production of eukaryotic membrane proteins.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS1990

A comparison of internal energy calculation methods for diatomic molecules

Various methods of calculating the internal energy of diatomic molecules are studied. An accurate and efficient method for computing the eigenvalues of the vibrational Schroedinger equation for an arbitrary potential is developed. The method is based on a finite-element discretization using the cubic Lobatto element. A combination of spectrum slicing and the Laguerre algorithm is used to solve for the eigenvalues. A simple method to compute the quasi-bound states is presented. For N2 molecules, all vibrational-rotational states of eleven available electronic potentials are computed, and summed to obtain the exact internal energy function with temperature. The total computation required 314 seconds of CPU-time on NASA's Cray 2 computer. Various approximate models are discussed and compared with the exact numerical simulation. It is shown that the splitting of the macroscopic internal energy into separate electronic, rotational, and vibrational energies is not justified at high temperatures.

Liu, Yen↗
NASA NTRS1975

Programs for computing abscissas and weights for classical and nonclassical Gaussian quadrature formulas

Computer programs for computing Gaussian quadrature abscissas and weights are described. For the classical case the programs use Laguerre iteration to compute abscissas as zeros of orthogonal polynomials. The polynomials are evaluated from known recursion coefficients. The nonclassical case is handled similarly except that the recursion coefficients are computed by numerical integration. A sample problem, with input and output, is presented to illustrate the use of the programs. It computes the quadrature abscissas and weights associated with the weight function over the interval (0,1) for quadrature orders from 16 to 96 in increments of 8.

Desmarais, R. N.↗
NASA NTRS1976

Polyatomic molecule vibrations

Polyatomic molecule vibrations are analyzed as harmonic vibrations along normal coordinates. The energy eigenvalues are found for linear and nonlinear symmetric triatomic molecules for valence bond models of the potential function with arbitrary coupling coefficients; such models can usually be fitted to observed energy levels with reasonably good accuracy. Approximate normal coordinates for the H2O molecule are discussed. Degenerate vibrational modes such as occur in CO2 are analyzed and expressions for Fermi resonance between close-lying states of the same symmetry are developed. The bending modes of linear triatomic molecules are expressed in terms of Laguerre polynomials in cylindrical coordinates as well as in terms of Hermite polynomials in Cartesian coordinates. The effects of large-amplitude bending such as occur in the C3 molecule are analyzed, along with anharmonic effects, which split the usually degenerate bending mode energy levels. Finally, the vibrational frequencies, degeneracies, and symmetry properties of XY3, X2Y2, and XY4 type molecules are discussed.

Source record↗
NASA NTRS2018

Does Orbital Angular Momentum Have Effect on Laser’s Scattering by Molecular Atmosphere?

Lasers with orbital angular momentum (OAM) have potential applications in communication technology, manipulation of particles, and remote sensing. Because of its unusual light-scattering properties, the OAM laser’s interaction with a molecular atmosphere must be studied to ensure that it is not lossy for communication or remote-sensing applications that involve its transmission through an atmospheric environment. In this study, the finite-difference time-domain (FDTD) method [21] is applied to calculate the light scattering of the purely azimuthal (the radial mode number is assumed to be zero) Laguerre-Gaussian (LG) beams with OAM by very small dielectric particles. Not like Lorentz-Mie solutions, the FDTD method can calculate for particles off the central axis of the LG beam. It is found that when the particles are very small, and the topological charge number of the OAM of a laser is not extremely large, the laser’s OAM has little effect on the scattering phase function. This suggests that Rayleigh theory can be applied directly to calculate the light scattering by atmospheric molecules. The transmission of a laser beam with OAM in a molecular atmosphere is not different from that of a regular Gaussian beam.

Molecular atmosphere↗