Showing papers on "Bessel function published in 1987"
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TL;DR: In this paper, a new type of solution of the paraxial wave equation is presented, which encompasses as limiting cases both the diffraction-free beam and the gaussian beam.
817 citations
TL;DR: In this article, a new formulation of electromagnetic wave scattering by convex, two-dimensional conducting bodies is reported, called the on-surface radiation condition (OSRC) approach, which is based upon an expansion of the radiation condition applied directly on the surface of a scatterer.
Abstract: A new formulation of electromagnetic wave scattering by convex, two-dimensional conducting bodies is reported. This formulation, called the on-surface radiation condition (OSRC) approach, is based upon an expansion of the radiation condition applied directly on the surface of a scatterer. Past approaches involved applying a radiation condition at some distance from the scatterer in order to achieve a nearly reflection-free truncation of a finite-difference time-domain lattice. However, it is now shown that application of a suitable radiation condition directly on the surface of a convex conducting scatterer can lead to substantial simplification of the frequency-domain integral equation for the scattered field, which is reduced to just a line integral. For the transverse magnetic (TM) case, the integrand is known explicitly. For the transverse electric (TE) case, the integrand can be easily constructed by solving an ordinary differential equation around the scatterer surface contour. Examples are provided which show that OSRC yields computed near and far fields which approach the exact results for canonical shapes such as the circular cylinder, square cylinder, and strip. Electrical sizes for the examples are ka = 5 and ka = 10 . The new OSRC formulation of scattering may present a useful alternative to present integral equation and uniform high-frequency approaches for convex cylinders larger than ka = 1 . Structures with edges or corners can also be analyzed, although more work is needed to incorporate the physics of singular currents at these discontinuities. Convex dielectric structures can also be treated using OSRC. These will be the subject of a forthcoming paper.
194 citations
TL;DR: In this paper, the authors evaluate the modes for a Schell-model planar source whose degree of spectral coherence is a Bessel function of zero order and whose optical intensity distribution is an arbitrary circularly symmetric function.
147 citations
TL;DR: In this article, a new method was developed for numerical integration of the one dimensional radial Schrodinger equation, which involves using different integration formulae in different parts of the range of integration rather than using the same integration formula throughout.
122 citations
TL;DR: In this paper, a method for reconstruction of the emissivity profile from projections is discussed, which is expanded into Fourier-Bessel expansions, of which coefficients are determined by the use of least square fitting method with the help of the Akaike information criterion.
Abstract: A method is discussed for reconstruction of the emissivity profile from projections. The emissivity profile is expanded into Fourier–Bessel expansions, of which coefficients are determined by the use of least‐square‐fitting method with the help of the Akaike information criterion. Tomographic reconstruction of the m=1 mode structure is obtained in JIPP T‐II tokamak during the precursor oscillation of the sawtooth crash. The m=1 mode structure fits Wesson model rather than the Kadomtsev model.
97 citations
TL;DR: In this article, a simplified derivation of the results obtained earlier by Cruzan [O. R. Cruzan, Q. Appl. Math. 20, 33 (1962)] is presented.
Abstract: Addition theorems for spherical wave solutions of the vector Helmholtz equation are discussed. The theorems allow one to expand a vector spherical wave about a given origin into spherical waves about a shifted origin. A simplified derivation of the results obtained earlier by Cruzan [O. R. Cruzan, Q. Appl. Math. 20, 33 (1962)] is presented.
67 citations
TL;DR: In this article, the Helmholtz equation is solved in an exterior domain in the plane and a perfect absorption condition on a circle which contains the obstacle is given explicitly by Bessel functions.
Abstract: We solve the Helmholtz equation in an exterior domain in the plane. A perfect absorption condition is introduced on a circle which contains the obstacle. This boundary condition is given explicitly by Bessel functions. We use a finite element method in the bounded domain. An explicit formula is used to compute the solution out of the circle. We give an error estimate and we present relevant numerical results.
55 citations
38 citations
TL;DR: In this paper, a model of a three-dimensional axisymmetric probe coil with a ferrite core in the presence of a conducting half-space (the workpiece) is developed.
Abstract: A model of a three-dimensional axisymmetric probe coil with a ferrite core in the presence of a conducting half-space (the workpiece) is developed. The half-space is accounted for by computing the appropriate Green's function by using Bessel transforms. Upon introducing equivalent Amperian currents within the core, we derive a volume integral equation, whose unknown is either the magnetic induction field, or induced magnetization, and whose kernel is the Green's function that was previously derived. The integral equation is transformed via the method of moments into a vector-matrix equation, which is then solved using a linear equation solver. This allows the computation of the magnetic induction field within the core, the driving-point impedance of the coil-core combination, and the induced eddy currents within the workpiece.
34 citations
TL;DR: In this paper, new solutions of the homogeneous spinor wave equation are obtained, which are similar to the focus wave mode solutions of Maxwell's equations leading to a Gaussian pulse energy.
Abstract: New solutions of the homogeneous spinor wave equation are obtained. They are similar to the focus wave mode solutions of Maxwell’s equations leading to a Gaussian pulse energy. A weighted superposition of these modes may supply finite energy pulses. The particular case of Bessel weight functions is discussed.
32 citations
TL;DR: In this article, Bessel functions on the symmetric cone associated with a real Jordan algebra were studied, and an asymptotic formula for the Bessel function was proved.
TL;DR: In this article, the Riemann ζ-function is used to regularize the coefficients occurring in the high-temperature expansions of one-loop thermodynamic potentials, which is a powerful tool for converting Dirichlet-type series Σmam(xi)/ms into powerseries in dimensionless parameters xi.
Abstract: A recent paper using the Riemann ζ-function to regularize the (divergent) coefficients occurring in the high-temperature expansions of one-loop thermodynamic potentials is extended. This method proves to be a powerful tool for converting Dirichlet-type series Σmam(xi)/ms into powerseries in the dimensionless parameters xi. The coefficients occurring in the power series are (proportional to) ζ-functions evaluated away from their poles - this is where the regularization occurs. High-temperature expansions are just one example of this highly-nontrivial rearrangement of Dirichlet series into power series form. We discuss in considerable detail series in which am(xi) is a product of trigonometrie, algebraic and Bessel function factors. The ζ-function method is carefully explained, and a large number of new formulae are provided. The means to generalize these formulae are also provided. Previous results on thermodynamic potentials are generalized to include a nonzero constant term in the gauge potential (time component) which can be used to probe the electric sector of temperature gauge theories.
TL;DR: In this article, it was shown that smoothness conditions on the diffusion and drift coefficient of a one-dimensional stochastic differential equation imply the existence and smoothness of a first-passage density.
Abstract: The purpose of this paper is to show that smoothness conditions on the diffusion and drift coefficient of a one-dimensional stochastic differential equation imply the existence and smoothness of a first-passage density. In order to be able to prove this, we shall show that Brownian motion conditioned to first hit a point at a specified time has the same distribution as a Bessel (3)-process with changed time scale.
TL;DR: In this article, a new technique for diffusion measurement by NMR using a fixed field gradient is described, which makes use of a Bessel function fit analysis to the spin-echo signal in order to determine both the applied gradient and the diffusion coefficient simultaneously.
TL;DR: In this paper, an exact integral equation for the source function in a three-dimensional rectangular medium which scatters anisotropically is derived, where the upper boundary of the finite medium is exposed to collimated radiation, while the lower boundary has no radiation incident on it.
Abstract: An exact integral equation is derived for the source function in a three-dimensional rectangular medium which scatters anisotropically. The upper boundary of the finite medium is exposed to collimated radiation, while the lower boundary has no radiation incident on it. The problem is multidimensional because the incident radiation varies spatially. The scattering phase function is represented by a series of Legendre polynomials. A double Fourier transform reduces the problem to a one-dimensional integral equation for the source function. The transformed equation is compared with the integral equation for a two-dimensional cylindrical medium which scatters anisotropically and is exposed to Bessel-varying collimated radiation. A simple relation is found between the two source functions which will greatly reduce the number of computations required for the three-dimensional case. The relation also illustrates the wide utility of the generalized one-dimensional source function. Simplification of the two-dimensional rectangular case to the generalized source function is also presented. The results are extended to problems with a strong anisotropic phase function which has a diffraction spike in the forward direction.
TL;DR: A Poisson-type integral representation for Jackson's q-Bessel function was obtained by using Askey and Wilson's q -beta integral and Nassrallah and Rahman's integral formula for an 8ϑ7 series as discussed by the authors.
TL;DR: In this article, the longitudinal propagation of sound in quasi-one-dimensional low Mach number nozzle flow is considered, and the exact solutions of the acoustic equations for the parabolic (Figure 1) and hyperbolic (Figure 2) nozzles are obtained in terms of Bessel functions.
TL;DR: In this paper, the scattering of light from diffusers with gamma-distributed surface height profiles is studied using a thin phase screen model, and it is shown that, following a steepest-descent method, the mean scattered intensity as a function of the scattering angle follows a modified Bessel K-function.
Abstract: We present a theoretical and experimental study of the scattering of light from diffusers with gamma-distributed surface height profiles. The theory is developed using a thin-phase screen model: it is shown that, following a steepest-descent method, the mean scattered intensity as a function of the scattering angle follows a modified Bessel K-function. The theory is compared with experimental data in the two extreme cases of the gamma distribution, namely the negative exponential and Gaussian cases. The surfaces used were made by exposing photoresist-coated plates with laser speckle patterns. For the case of a negative-exponential surface it is shown that it is not possible, in practice at least, to extinguish the specular component.
TL;DR: The synthetic image generation with the lens effect consists of two consecutive processors: the hidden-surface processor, and the focus processor, where an approximation method based on the light particle theory is developed.
Abstract: The synthetic image generation with the lens effect consists of two consecutive processors: the hidden-surface processor, and the focus processor. The normal ray-tracing algorithms are used in the first processor. The second processor computes Lommel's function, which is an infinite series of Bessel functions. In order to avoid the complicated calculation and the huge memory consumption, an approximation method based on the light particle theory is developed. No noticeable differences can be detected between the results from the approximation method and those from the exact calculation.
01 Dec 1987
TL;DR: In this article, the authors considered the problem of propagation along a longitudinally magnetized gyromagnetic circular waveguide with a magnetic wall and showed that the waveguide exhibits both split phase constants and cutoff numbers, and that a single continuous cutoff curve belonging to one of the two factors of the characteristic equation, need not necessarily describe the same mode throughout its entire length.
Abstract: The problem of propagation along a longitudinally magnetised gyromagnetic circular waveguide with a magnetic wall has not been fully treated in the literature. This waveguide, unlike the electric wall problem, for which only the phase constants are split, exhibits both split phase constants and cutoff numbers. It is also of note that, in keeping with the solution of the electric wall problem, a single continuous cutoff curve, belonging to one of the two factors of the characteristic equation, need not necessarily describe the same mode throughout its entire length. Such discontinuities are displayed whenever the order and polarity of the Bessel functions at the intersection of any two cutoff curves coincide. Some calculations on the open anisotropic waveguide are also included for completeness.
27 May 1987
TL;DR: In this article, a model using a solution of the approximate equation governing the lateral dependance of thickness modes is established for plane resonators having nearly arbitrary electrode shape, and an extension of the model is made to consider plane Resonators having shallow grooves outside the electrodes to improve the energy trapping.
Abstract: Trapped energy resonators of plane and bevel led geometry are widely used for frequency generation and filtering. A model using a solution of the approximate equation governing the lateral dependance of thickness modes is established for plane resonators having nearly arbitrary electrode shape. This model uses solutions in the form of serie of products of Bessel and trigonometric functions and considers the expression of the approximate continuity conditions at a discrete number of points of the -1ectrode edge. This method of solution is applied to study the influence of the shape of the electrodes on the properties of the resonators and to demonstrate on a few examples that the usual circular geometry is not optimal with respect to several criterions. Resonators with electrodes respecting approximatively the lateral anisotropy of the plate (rectangular and elliptical) are considered in these examples. An extension of the model is made to consider plane resonators having shallow grooves outside the electrodes to improve the energy trapping.
TL;DR: In this article, an algorithm for computing the multiple zeros of the derivatives of the first three orders of the cylindrical Bessel functions when the index ν takes real values is proposed.
Abstract: Algorithms are proposed for calculating the multiple zeros of the derivatives of the first three orders of the cylindrical Bessel functions J v ( z ) and y v ( z ) when the index ν takes real values. Many multiple zeros — some of which are presented in this paper — are calculated using these algorithms. A number of diagrams illustrating the qualitative behaviour of multiple zeros as a function of the change in the index are also given.
TL;DR: In this article, the authors define a new family of special functions called lattice Bessel functions, which are indexed by the N -dimensional integer lattice such that they reduce to modified Bessel function when N = 1, and the exponential function when n = 0.
Abstract: We define a new family of special functions that we call lattice Bessel functions. They are indexed by the N -dimensional integer lattice such that they reduce to modified Bessel functions when N = 1, and the exponential function when N = 0. The transition probabilities for an M / M /1 queue going from one state to another before becoming idle (exiting at 0) can be solved in terms of modified Bessel functions. In this paper, we use lattice Bessel functions to solve the analogous problem involving the exit time from the interior of the positive orthant of the N -dimensional lattice for a series Jackson network with N nodes. These special functions allow us to derive asymptotic expansions for the taboo transition probabilities, as well as for the tail of the exit-time distribution.
TL;DR: The Lanczos τ-method as discussed by the authors was used to obtain polynomial approximations for Bessel functions in the complex plane with polynomials in the form of perturbations proportional to Faber or Chebyshev coefficients.
Proceedings Article•
01 Jan 1987TL;DR: Lattice Bessel functions are used to solve the analogous problem involving the exit time from the interior of the positive orthant of the N-dimensional lattice for a series Jackson network with N nodes.
Abstract: We define a new family of special functions that we call lattice Bessel functions. They are indexed by the N-dimensional integer lattice such that they reduce to modified Bessel functions when N = 1, and the exponential function when N = 0. The transition probabilities for an M/M/1 queue going from one state to another before becoming idle (exiting at 0) can be solved in terms of modified Bessel functions. In this paper, we use lattice Bessel functions to solve the analogous problem involving the exit time from the interior of the positive orthant of the N-dimensional lattice for a series Jackson network with N nodes. These special functions allow us to derive asymptotic expansions for the taboo transition probabilities, as well as for the tail of the exit-time distribution.
TL;DR: Using the local and global versions of the central limit theorem, it was shown in this article that for the modified Bessel function Iϱ(x) for fixed ρ, I ρ (x) e −x → φ(α)−2 −1 if α(x)/x → α, 0≥α as x → ∞.
TL;DR: In this article, the boundary element solutions of the two-dimensional multi-energy-group neutron diffusion equation are derived using the modified Bessel function, which can be classified as a variety of the modified Helmholtz equation.