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Eigenfunctions of the magnetospheric radial-diffusion operator

The applicability of eigenfunction methods to the theory of magnetospheric radial diffusion is investigated analytically, with a focus on the operator (Lambda) for radiation-belt and ring-current particles. It is shown that the eigenfunctions of Lambda can be expressed in terms of a linear combination of ordinary Bessel functions of the first and second kinds, and that the solution for the drift-averaged phase-space density can be expressed as the sum of a quasi-static solution and a time-dependent superposition of the eigenfunctions of Lambda. Results for illustrative and practical sample problems are presented in extensive tables and graphs and discussed in detail.

Schulz, Michael

Unified aeroacoustics analysis for high speed turboprop aerodynamics and noise. Volume 4: Computer user's manual for UAAP turboprop aeroacoustic code

The Unified AeroAcoustic Program (UAAP) code calculates the airloads on a single rotation prop-fan, or propeller, and couples these airloads with an acoustic radiation theory, to provide estimates of near-field or far-field noise levels. The steady airloads can also be used to calculate the nonuniform velocity components in the propeller wake. The airloads are calculated using a three dimensional compressible panel method which considers the effects of thin, cambered, multiple blades which may be highly swept. These airloads may be either steady or unsteady. The acoustic model uses the blade thickness distribution and the steady or unsteady aerodynamic loads to calculate the acoustic radiation. The users manual for the UAAP code is divided into five sections: general code description; input description; output description; system description; and error codes. The user must have access to IMSL10 libraries (MATH and SFUN) for numerous calls made for Bessel functions and matrix inversion. For plotted output users must modify the dummy calls to plotting routines included in the code to system-specific calls appropriate to the user's installation.

Menthe, R. W.

Feedback instability of the ionospheric resonant cavity

A model is developed that provides a theoretical basis for previous numerical results showing a feedback instability with frequencies characteristic of Alfven travel times within the region of the large increase of Alfven speed above the ionosphere. These results have been extended to arbitrary ionospheric conductivity by developing a numerical solution of the cavity dispersion relation that involves Bessel functions of complex order and argument. It is concluded that the large contrast between the magnetospheric and ionospheric Alfven speed leads to the formation of resonant cavity modes with frequencies ranging from 0.1 to 1 Hz. The presence of the cavity leads to a modification of the reflection characteristics of Alfven waves with frequencies that compare to the cavity's normal modes.

Lysak, Robert L.

Analytical solution for boundary heat fluxes from a radiating rectangular medium

Reference is made to the work of Shah (1979) which demonstrated the possibility of partially integrating the radiative equations analytically to obtain an 'exact' solution. Shah's solution was given as a double integration of the modified Bessel function of order zero. Here, it is shown that the 'exact' solution for a rectangular region radiating to cold black walls can be conveniently derived, and expressed in simple form, by using an integral function, Sn, analogous to the exponential integral function appearing in plane-layer solutions.

Siegel, R.

Hierarchical tapered bar elements undergoing axial deformation

A method is described to model the dynamics of tapered axial bars of various cross sections based on the well-known Craig/Bampton component mode synthesis technique. This element is formed in terms of the static constraint modes and interface restrained normal modes. This is in contrast with the finite elements as implemented in NASTRAN where the interface restrained normal modes are neglected. These normal modes are in terms of Bessel functions. Restoration of a few of these modes leads to higher accuracy with fewer generalized coordinates. The proposed models are hierarchical so that all lower order element matrices are embedded in higher order element matrices. The advantages of this formulation compared to standard NASTRAN truss element formulation are demonstrated through simple numerical examples.

Ganesan, N.

Gamma-rays and neutrons as a probe of the proton spectrum during the solar flare of 1988 December 16

We have previously reported on high-energy gamma-rays and neutrons from the flare of 1988 December 16 detected by the Gamma-Ray Spectrometer on the SMM satellite. In this paper, we present results on gamma-ray lines seen by the same detector during this flare. Together, these measurements constitute a powerful probe of the proton spectrum that produces the flare neutrals. Analysis of the data suggests a Bessel-function proton spectrum with a shape parameter (alpha T) of 0.054 +/- 0.004 and the number of protons above 30 MeV equal to (9.0 +/- 0.9) x 10 exp 32. The number of neutrons detected from this flare is much smaller than what is predicted from an isotropic distribution of the protons, indicating that the distribution may be nonisotropic.

Dunphy, P. P.

The Frequency of Torsional Vibration of a Tapered Beam

A solution for the equation of torsional vibration of tapered beams has been found in terms of Bessel functions for beams satisfying the following conditions: (a) the cross sections along the span are similar in shape; and (b) the torsional stiffness of a section can be expressed as a power of a linear function of distance along the span. The method of applying the analysis to actual cases has been described. Charts are given from which numerical values can be immediately obtained for most cases of practical importance. The theoretical values of the frequency ratio have been experimentally checked on five beams having different amounts of taper.

Coleman, Robert

General Theory of Aerodynamic Instability and the Mechanism of Flutter

The aerodynamic forces on an oscillating airfoil or airfoil-aileron combination of three independent degrees of freedom have been determined. The problem resolves itself into the solution of certain definite integrals, which have been identified as Bessel functions of the first and second kind and of zero and first order. The theory, being based on potential flow and the Kutta condition, is fundamentally equivalent to the conventional wing-section theory relating to the steady case. The air forces being known, the mechanism of aerodynamic instability has been analyzed in detail. An exact solution, involving potential flow and the adoption of the Kutta condition, has been analyzed in detail. An exact solution, involving potential flow and the adoption of the Kutta condition, has been arrived at. The solution is of a simple form and is expressed by means of an auxiliary parameter K.

Theodorsen, Theodore

Numerical formulation of composition segregation at curved solid-liquid interface during steady state solidification process

The lateral solute segregation that results from a curved solid-liquid interface shape during steady state unidirectional solidification of a binary alloy system has been studied both analytically and numerically by Coriell, Bosivert, Rehm, and Sekerka. The system under their study is a two dimensional rectangular system. However, most real growth systems are cylindrical systems. Thus, in a previous study, we have followed Coriell etc. formalism and obtained analytical results for lateral solute segregation for an azimuthal symmetric cylindrical binary melt system during steady state solidification process. The solid-liquid interface shape is expressed as a series combination of Bessel functions. In this study a computer program has been developed to simulate the lateral solute segregation.

Wang, Jai-Ching

Electromagnetic and corpuscular emission from the solar flare of 1991 June 15: Continuous acceleration of relativistic particles

Data on X-, gamma-ray, optical and radio emission from the 1991 June 15 solar flare are considered. We have calculated the spectrum of protons that produces gamma-rays during the gradual phase of the flare. The primary proton spectrum can be described as a Bessel-function-type up to 0.8 GeV and a power law with the spectral index approximately equal to 3 from 0.8 up to 10 GeV or above. We have also analyzed data on energetic particles near the Earth. Their spectrum differed from that of primary protons producing gamma-ray line emission. In the gradual phase of the flare additional pulses of energy release occurred and the time profiles of cm-radio emission and gamma-rays in the 0.8-10 MeV energy band and above 50 MeV coincided. A continuous and simultaneous stochastic acceleration of the protons and relativistic electrons at the gradual phase of the flare is considered as a natural explanation of the data.

Kocharov, L. G.

Analysis of ripple formation in single crystal spot welds

Stationary spot welds have been made at the (001) surface of Fe-l5%Ni-15%Cr single crystals using a Gas Tungsten Arc (GTA). On the top surface of the spot welds, very regular and concentric ripples were observed after solidification by differential interference color microscopy. Their height (typically 1--5 micrometers and spacing, typically approximately 60 micrometers) decreased with the radius of the pool. These ripples were successfully accounted for in terms of capillary-wave theory using the fundamental mode frequency f(sub 0) given by the first zero of the zero-order Bessel function. The spacing d between the ripples was then equated to v(sub s)/f(sub 0), where v(sub s) is the solidification rate. From the measured ripple spacing, the velocity of the pool was deduced as a function of the radius, and this velocity was in good agreement with the results of a heat-flow simulation.

Rappaz, M.

Controlling Fringe Sensitivity of Electro-Optic Holography Systems Using Laser Diode Current Modulation

Electro-Optic Holography (EOH) is a non-intrusive, laser-based, displacement measurement technique capable of static and dynamic displacement measurements. EOH is an optical interference technique in which fringe patterns that represent displacement contour maps are generated. At excessively large displacements the fringe density may be so great that individual fringes are not resolvable using typical EOH techniques. This thesis focuses on the development and implementation of a method for controlling the sensitivity of the EOH system. This method is known as Frequency Translated Electro-Optic Holography (FTEOH). It was determined that by modulating the current source of the laser diode at integer multiples of the object vibration, the fringe pattern is governed by higher order Bessel function of the first kind and the number of fringes that represent a given displacement can be controlled. The reduction of fringes is theoretically unlimited but physically limited by the frequency bandwidth of the signal generator, providing modulation to the laser diode. Although this research technique has been verified theoretically and experimentally in this thesis, due to the current laser diode capabilities it is a tedious and time consuming process to acquire data using the FTEOH technique.

Bybee, Shannon J.

Trellis Coding of Non-coherent Multiple Symbol Full Response M-ary CPFSK with Modulation Index 1/M

This paper introduces a trellis coded modulation (TCM) scheme for non-coherent multiple full response M-ary CPFSK with modulation index 1/M. A proper branch metric for the trellis decoder is obtained by employing a simple approximation of the modified Bessel function for large signal to noise ratio (SNR). Pairwise error probability of coded sequences is evaluated by applying a linear approximation to the Rician random variable.

trellis coded modulation TCM

The SMM Model as a Boundary Value Problem Using the Discrete Diffusion Equation

A generalized single step stepwise mutation model (SMM) is developed that takes into account an arbitrary initial state to a certain partial difference equation. This is solved in both the approximate continuum limit and the more exact discrete form. A time evolution model is developed for Y DNA or mtDNA that takes into account the reflective boundary modeling minimum microsatellite length and the original difference equation. A comparison is made between the more widely known continuum Gaussian model and a discrete model, which is based on modified Bessel functions of the first kind. A correction is made to the SMM model for the probability that two individuals are related that takes into account a reflecting boundary modeling minimum microsatellite length. This method is generalized to take into account the general n-step model and exact solutions are found. A new model is proposed for the step distribution.

Campbell, Joel

FPGA Coprocessor Design for an Onboard Multi-Angle Spectro-Polarimetric Imager

A multi-angle spectro-polarimetric imager (MSPI) is an advanced camera system currently under development at JPL for possible future consideration on a satellite-based Aerosol-Cloud-Environ - ment (ACE) interaction study. The light in the optical system is subjected to a complex modulation designed to make the overall system robust against many instrumental artifacts that have plagued such measurements in the past. This scheme involves two photoelastic modulators that are beating in a carefully selected pattern against each other. In order to properly sample this modulation pattern, each of the proposed nine cameras in the system needs to read out its imager array about 1,000 times per second. The onboard processing required to compress this data involves least-squares fits (LSFs) of Bessel functions to data from every pixel in realtime, thus requiring an onboard computing system with advanced data processing capabilities in excess of those commonly available for space flight. As a potential solution to meet the MSPI onboard processing requirements, an LSF algorithm was developed on the Xilinx Virtex-4FX60 field programmable gate array (FPGA). In addition to configurable hardware capability, this FPGA includes Power -PC405 microprocessors, which together enable a combination hardware/ software processing system. A laboratory demonstration was carried out based on a hardware/ software co-designed processing architecture that includes hardware-based data collection and least-squares fitting (computationally), and softwarebased transcendental function computation (algorithmically complex) on the FPGA. Initial results showed that these calculations can be handled using a combination of the Virtex- 4TM Power-PC core and the hardware fabric.

Pingree, Paula J.

Radiation Belt Electron Dynamics Driven by Large-Amplitude Whistlers

Acceleration of radiation belt electrons driven by oblique large-amplitude whistler waves is studied. We show analytically and numerically that this is a stochastic process; the intensity of which depends on the wave power modified by Bessel functions. The type of this dependence is determined by the character of the nonlinear interaction due to coupling between action and phase. The results show that physically significant quantities have a relatively weak dependence on the wave power.

whistlers

Fracture Mechanics Analysis of an Annular Crack in a Three-concentric-cylinder Composite Model

A boundary-value problem governing a three-phase concentric-cylinder model was analytically modeled to analyze annular interfacial crack problems with Love s strain functions in order to find the stress intensity factors (SIFs) and strain energy release rates (SERRs) at the tips of an interface crack in a nonhomogeneous medium. The complex form of a singular integral equation (SIE) of the second kind was formulated using Bessel s functions in the Fourier domain, and the SIF and total SERR were calculated using Jacoby polynomials. For the validity of the SIF equations to be established, the SIE of the three-concentric-cylinder model was reduced to the SIE for a two-concentric-cylinder model, and the results were compared with the previous results of Erdogan. A preliminary set of parametric studies was carried out to show the effect of interphase properties on the SERR. The method presented here provides insight about the effect of interphase properties on the crack driving force.

Kuguoglu, Latife H.