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At least 37 records · Page 2

The energy spectra of solar energetic particles

A survey of recent results on the shapes and relative slopes of the spectra of various solar energetic particle populations is presented, with emphasis on the more extensive results currently available for protons, alphas and electrons. From previous work, it is found that proton spectra 0.8 to more than 400 MeV and alpha spectra 1.4 to 80 MeV/nucleon are best characterized, on average, by a functional form involving a Bessel function in momentum/nucleon. However, proton and alpha spectral slopes using this form are not equal, and there is significant variation from event to event. From other studies, electrons 0.02 to 20 MeV are also found to have curved spectra, but seem to be better fit with a double power law in energy. The spectral properties in both cases correlate with other measures of solar particle acceleration; e.g. gamma-ray line production, hard X-ray burst spectra and microwave fluxes.

Mcguire, R. E.

A new linearized theory of laminar film condensation of two phase annular flow in a capillary pumped loop

Future large space based facilities, such as Space Station, will require energy management systems capable of transporting tens of kilowatts of heat over a hundred meters or more. This represents better than an order of magnitude improvement over current technology. Two-phase thermal systems are currently being developed to meet this challenge. Condensation heat transfer plays a very important role in this system. The present study attempts an analytic solution to the set of linearized partial differential equations. The axial velocity and temperature functions were found to be Bessel functions which have oscillatory behavior. This result agrees qualitatively with the experimental evidence from tests at both NASA Goddard Space Flight Center and elsewhere.

Hsu, Y. K.

Computer program for Bessel and Hankel functions

A set of FORTRAN subroutines for calculating Bessel and Hankel functions is presented. The routines calculate Bessel and Hankel functions of the first and second kinds, as well as their derivatives, for wide ranges of integer order and real or complex argument in single or double precision. Depending on the order and argument, one of three evaluation methods is used: the power series definition, an Airy function expansion, or an asymptotic expansion. Routines to calculate Airy functions and their derivatives are also included.

Kreider, Kevin L.

On propagation of long waves in curved ducts.

A two-dimensional detailed study of the behavior of long waves in curved ducts and in junctions between straight and curved ducts will be given. The mathematical treatment of the problem utilizes the method of separation variables. Solutions and expressions for principal mode of the wave are obtained by using the linearized equation of motion solved for its characteristic values. The unavoidable approximations in the numerical solutions of the cylindrical functions are due to use of series expansion of Bessel functions and from restrictions necessary to solve infinite matrices.

Rostafinski, W.

Further Development of a Function Generator Technique

Further features and properties of functions generated by generalization of the process originally uncovered to describe the evolution of pressure in a rigid volume due to outgassing or desorption are explored. Properties presented include development of a general Maclaurin series associated with these functions, a limitation in using integration by parts to produce asymptotic expansions, and a general description of an implicit Adams-Moulton method for numerical quadrature of transformed functions. These developments are then applied to develop and explore functions that solve the Sievert integral and the modified Bessel function of the first kind, order zero. Features of the error function and the incomplete lower gamma function are also considered.

Michael S. Woronowicz

Modifications to the three-component classification algorithm for SAR data

Previously, a scattering model was used to classify SAR data as due to three mechanisms: surface or odd-bounce scattering; double-bounce scattering; and volume scattering. A Bragg rough-surface model was used for odd-bounce scattering, and two reflecting surfaces, as in a dihedral corner reflector, represented the double-bounce scattering mechanism. A random collection of infinitely thin cylinders was used to model the volume scattering contribution. It was assumed that the cylinders are uniformly oriented in all directions. In this work, modifications are made to the above model, which include specifying a preferred orientation for the cylinders representing branches and using thin cylinders of finite thickness as opposed to infinitely thin ones. In the first case, the preferred orientation is represented by a probability density function in the form of a dirac delta function. For the second case, small argument asymptotic expansions of Bessel functions are used to express the volume scattering contributions in terms of quantities containing the average radius of the cylinders. Since in each case the number of unknowns exceeds that of equations, simplifying assumptions are made. The solutions are applied to multifrequency polarimetric SAR data to obtain the new unknowns in addition to the relative contributions of each scattering mechanism. Several results are presented. It is found that the calculated percentage of each mechanism does not change significantly compared to the original model; however, additional information is gained about the scatterers.

Moghaddam, M.

Compact Dielectric-Rod White-Light Delay Lines

Optical delay lines of a proposed type would be made from rods of such dielectric materials as calcium fluoride, fused silica, or sapphire. These would offer advantages over prior optical delay lines, as summarized below. Optical delay lines are key components of opto-electronic microwave oscillators, narrow-band opto-electronic microwave filters, evanescent-field optical biochemical detectors, and some Fourier-Transform spectrum analyzers. Heretofore, optical delay lines used in such applications have been of two types: resonators and coiled long optical fibers, both of which have disadvantages: Resonators are compact, but excitation must be provided by narrow-band lasers. Wide-band (including noisy) laser light cannot be coupled efficiently to narrow-band resonators. When light is coupled into a narrowband resonator from a source of reasonably high power, a significant amount of optical energy circulates within the resonator, causing nonlinear loss and significant noise. Typically, a coil-type optical delay line is made of fused-silica fiber, which exhibits fundamental loss. To overcome the limit imposed by the optical loss in fused silica, it would be necessary to use fibers having crystalline cores. Although space is saved by winding fibers into coils, fiber-coil delay lines are still inconveniently bulky. The proposed compact dielectric-rod delay lines would exploit the special class of non-diffracting light beams that are denoted Bessel beams because their amplitudes are proportional to Bessel functions of the radii from their central axes. High-order Bessel beams can have large values of angular momentum. They can be generated with the help of whispering-gallery-mode optical resonators, as described, for example, in "Simplified Generation of High-Angular-Momentum Light Beams" (NPO-42965) NASA Tech Briefs, Vol. 31, No. 3 (March 2007), page 8a. In a delay line according to the proposal, the dielectric rod would be dimensioned to function as a multimode waveguide. Suitably chosen high-angular-momentum modes in such a waveguide exhibit low group velocity (hence, long delay) and no resonance. Such a delay line could perform well at any wavelength or range of wavelengths within the transparency wavelength band of the dielectric material, and the maximum possible group delay achievable through suitable design would be limited only by the optical loss in the rod material.

Maleki, Lute

Aircraft control by propeller cyclic blades

A theory is developed for aircraft control obtained from the propeller forces and moments generated by blade angle variation during a blade revolution. The propeller blade is pitched harmonically one cycle per propeller revolution which results in vehicle control forces and moments, termed cyclic-control. Using a power series respresentation of an arbitrary function of cyclic-blade angle, cyclic-control theory is developed which leads to exact solutions in terms of derivatives of steady-state thrust and power with respect to blade angle. An alternative solution, when the cyclic-blade angle function is limited to a sinusoidal cycle, is in terms of Bessel functions. An estimate of non-steady azimuth angle change or lag is presented. Cyclic-control analysis applied to the counter-rotating propeller shows that control forces or moments can be uniquely isolated from each other. Thus the dual rotor, in hovering mode, has propulsion without rotor tilt or moments, or, when in propeller mode at the tail of an air ship or submarine, vehicle control with no vehicle movement. Control isolation is also attainable from three or more propellers in-line.

Deyoung, J.

Simplified Generation of High-Angular-Momentum Light Beams

A simplified method of generating a beam of light having a relatively high value of angular momentum (see figure) involves the use of a compact apparatus consisting mainly of a laser, a whispering- gallery-mode (WGM) resonator, and optical fibers. The method also can be used to generate a Bessel beam. ( Bessel beam denotes a member of a class of non-diffracting beams, so named because their amplitudes are proportional to Bessel functions of the radii from their central axes. High-order Bessel beams can have high values of angular momentum.) High-angular-momentum light beams are used in some applications in biology and nanotechnology, wherein they are known for their ability to apply torque to make microscopic objects rotate. High-angular-momentum light beams could also be used to increase bandwidths of fiber-optic communication systems. The present simplified method of generating a high-angular-momentum light beam was conceived as an alternative to prior such methods, which are complicated and require optical setups that include, variously, holograms, modulating Fabry-Perot cavities, or special microstructures. The present simplified method exploits a combination of the complex structure of the electromagnetic field inside a WGM resonator, total internal reflection in the WGM resonator, and the electromagnetic modes supported by an optical fiber. The optical fiber used to extract light from the WGM resonator is made of fused quartz. The output end of this fiber is polished flat and perpendicular to the fiber axis. The input end of this fiber is cut on a slant and placed very close to the WGM resonator at an appropriate position and orientation. To excite the resonant whispering- gallery modes, light is introduced into the WGM resonator via another optical fiber that is part of a pigtailed fiber-optic coupler. Light extracted from the WGM resonator is transformed into a high-angular- momentum beam inside the extraction optical fiber and this beam is emitted from the polished flat output end. By adjusting the geometry of this apparatus, it is possible to generate a variety of optical beams characterized by a wide range of parameters. These beams generally have high angular momenta and can be of either Bessel or Bessel-related types.

Savchenkov, Anatoliy

WGM-Resonator/Tapered-Waveguide White-Light Sensor Optics

Theoretical and experimental investigations have demonstrated the feasibility of compact white-light sensor optics consisting of unitary combinations of (1) low-profile whispering-gallery-mode (WGM) resonators and (2) tapered rod optical waveguides. These sensors are highly wavelength-dispersive and are expected to be especially useful in biochemical applications for measuring absorption spectra of liquids. These sensor optics exploit the properties of a special class of non-diffracting light beams that are denoted Bessel beams because their amplitudes are proportional to Bessel functions of the radii from their central axes. High-order Bessel beams can have large values of angular momentum. In a sensor optic of this type, a low-profile WGM resonator that supports modes having large angular momenta is used to generate high-order Bessel beams. As used here, "low-profile" signifies that the WGM resonator is an integral part of the rod optical waveguide but has a radius slightly different from that of the adjacent part(s).

Stekalov, Dmitry

Time-dependent treatment of scattering. II - Novel integral equation approach to quantum wave packets

The novel wave-packet propagation scheme presented is based on the time-dependent form of the Lippman-Schwinger integral equation and does not require extensive matrix inversions, thereby facilitating application to systems in which some degrees of freedom express the potential in a basis expansion. The matrix to be inverted is a function of the kinetic energy operator, and is accordingly diagonal in a Bessel function basis set. Transition amplitudes for various orbital angular momentum quantum numbers are obtainable via either Fourier transform of the amplitude density from the time to the energy domain, or the direct analysis of the scattered wave packet.

Sharafeddin, Omar A.

Cross-spectral functions based on von Karman's spectral equation

Cross-spectral functions for the vertical and longitudinal components of turbulence of a two-dimensional gust field are derived from the point correlation function for turbulence due to von Karman. Closed form solutions in terms of Bessel functions of order 5/6 and 11/6 are found. An asymptotic expression for large values of the frequency argument, and series results for small values of frequency, are also given. These results now form the base for studying the effect of spanwise variations in turbulence for a turbulence environment which is characterized by the von Karman isotropic spectral relations. Previous studies were based mainly on the Dryden-type spectral representation.

Houbolt, J. C.

Force Density Function Relationships in 2-D Granular Media

An integral transform relationship is developed to convert between two important probability density functions (distributions) used in the study of contact forces in granular physics. Developing this transform has now made it possible to compare and relate various theoretical approaches with one another and with the experimental data despite the fact that one may predict the Cartesian probability density and another the force magnitude probability density. Also, the transforms identify which functional forms are relevant to describe the probability density observed in nature, and so the modified Bessel function of the second kind has been identified as the relevant form for the Cartesian probability density corresponding to exponential forms in the force magnitude distribution. Furthermore, it is shown that this transform pair supplies a sufficient mathematical framework to describe the evolution of the force magnitude distribution under shearing. Apart from the choice of several coefficients, whose evolution of values must be explained in the physics, this framework successfully reproduces the features of the distribution that are taken to be an indicator of jamming and unjamming in a granular packing. Key words. Granular Physics, Probability Density Functions, Fourier Transforms

Youngquist, Robert C.

Viscous-fluid reaction to a torsionally oscillating spheroid Linearized steady-state weak-separation solution

For both the linearized prolate and oblate problems, perturbation series for all orders of eccentricity are obtained. The 'weak separation' method of solving partial-differential-equation boundary-value problems assumes that each linearly independent solution is a sum of products of single-variable functions. The method is applied to a hierarchy of partial differential equations. The weak-separation solutions are constructed by generalizing only the Bessel functions of the homogeneous solution.

Tompkins, D. R., Jr.

A note of expansions of functions of velocity in the two-body problem

Fourier expansions based on both the true anomaly and the mean anomaly are obtained for the functions of velocity in the two-body problem; the series of coefficients is written from classical formulae involving associated Legendre polynomials, Gegenbauer polynomials, or Bessel functions. The Fourier expansions are compared with the expansions in powers of eccentricity developed by Broucke (1974) through use of computerized Poisson series manipulation.

Kinoshita, H.