Showing papers on "Bessel function published in 1994"
TL;DR: A paraxial wave equation for an azimuthally polarized field propagating in free space is developed and the propagation characteristics of the azIMuthal Bessel-Gauss beam solution are compared with a solution of the more familiar scalar paraxIAL wave equation, the linearly polarized Bessel - Gauss beam.
Abstract: We develop a paraxial wave equation for an azimuthally polarized field propagating in free space. The equation's beamlike solution is composed of a plane-wave propagation factor multiplied by a Bessel function of the first kind, of order one, and a Gaussian factor, which describe the transverse characteristics of the beam. We compare the propagation characteristics of the azimuthal Bessel-Gauss beam solution with a solution of the more familiar scalar paraxial wave equation, the linearly polarized Bessel-Gauss beam.
155 citations
01 Mar 1994
129 citations
TL;DR: In this paper, expressions for the elements of the dielectric tensor for linear waves propagating at an arbitrary angle to a uniform magnetic field in a fully hot plasma whose constituent particle species σ are modeled by generalized Lorentzian distribution functions are derived.
Abstract: Expressions are derived for the elements of the dielectric tensor for linear waves propagating at an arbitrary angle to a uniform magnetic field in a fully hot plasma whose constituent particle species σ are modeled by generalized Lorentzian distribution functions. The expressions involve readily computable single integrals whose integrands involve only elementary functions, Bessel functions, and modified plasma dispersion functions, the latter being available in the form of finite algebraic series. Analytical forms for the integrals are derived in the limits λ→0 and λ→∞, where λ=(k⊥ρLσ)2/2, with k⊥ the component of wave vector perpendicular to the ambient magnetic field, and ρLσ the Larmor radius for the particle species σ. Consideration is given to the important limits of wave propagation parallel and perpendicular to the ambient magnetic field, and also to the cold plasma limit. Since most space plasmas are well modeled by generalized Lorentzian particle distribution functions, the results obtained in this paper provide a powerful tool for analyzing kinetic (micro‐) instabilities in space plasmas in a very general context, limited only by the assumptions of linear plasma theory.
122 citations
TL;DR: In this article, integral representations of formal inverses of the differential operator and the Askey-Wilson divided difference operators in different polynomial bases are studied, and the eigenvalues are related to zeros of Bessel functions, q -Bessel functions and confluent hypergeometric functions.
112 citations
110 citations
01 May 1994
100 citations
TL;DR: It is shown that the Bessel distribution (the time- frequencies distribution using Bessel kernel) meets most of the desirable properties with high time-frequency resolution and a numerical alias-free implementation of the distribution is presented.
Abstract: A kernel based on the first kind Bessel function of order one is proposed to compute the time-frequency distributions of nonstationary signals. This kernel can suppress the cross terms of the distribution effectively. It is shown that the Bessel distribution (the time-frequency distribution using Bessel kernel) meets most of the desirable properties with high time-frequency resolution. A numerical alias-free implementation of the distribution is presented. Examples of applications in time-frequency analysis of the heart's sound and Doppler blood flow signals are given to show that the Bessel distribution can be easily adapted to two very different signals for cardiovascular signal processing. By controlling a kernel parameter, this distribution can be used to compute the time-frequency representations of transient deterministic and random signals. The study confirms the potentials of the proposed distribution in nonstationary signal analysis. >
87 citations
TL;DR: In this article, a direct solution of the mode shape equation is presented and the first three dimensionless natural frequencies computed for 16 combinations of the boundary conditions are tabulated for values of truncation factors from 0·05 to 0·7.
84 citations
TL;DR: In this article, the authors present particular solutions of the discrete Painleve III (d-P III ) equation of rational and special unction (Bessel) type, which allow them to establish a close parallel between this discrete equation and its continuous counterpart.
74 citations
60 citations
TL;DR: In this article, a solution of the scalar-wave equation that is based on modified Bessel functions is introduced, which is radially nonoscillating, unbound, and non-iffractive.
Abstract: Solutions of the scalar-wave equation that are based on modified Bessel functions are introduced. These functions are radially nonoscillating, unbound, and nondiffractive. Their propagation constant is larger than that of vacuum, meaning that there is an inverse Guoy effect or a phase velocity smaller than c. The beams are physically realized by apodization of the modified Bessel profiles by means of suitable window functions. When Gaussian apodization functions are used, axial decay is slower than in the Gaussian case and the case of ordinary Bessel counterparts. Super-Gaussian and circular apodization are also examined. In the latter case a persistent narrow axial lobe that also has a nondecaying character is encountered.
TL;DR: In this paper, the exact solutions for the stability analysis of a one-step bar of varying cross-section subjected to concentrated and distributed axial loads are found first, and then the exact solution of that bar is used to derive the eigenvalue equation of a multi-stage bar of different cross-sections subjected to more complicated loads by using transition matrices.
TL;DR: Ashbaugh and Benguria as discussed by the authors showed that the Bessel and modified Bessel functions are an increasing function of the clamped plate problem for the ball and that the A;-th positive zero of the function Ju+p(x)l'Jv{x)-{-a^Iu+ p(ax)/ Iu(ax) is an increasing functions of u in √ 2 0, 0 < (3 < 1, k = 1, 2,3, k
Abstract: The principal result here is that each positive zero of the function Ju+p(x)l'Jv{x)-{-a^Iu+p(ax)/ Iu(ax) is an increasing function of u in — /?/2 0, 0 < (3 < 1, k = 1,2,3, This implies that the A;-th positive zero of Ju(x)I r u(x) — Iv{x)J , u{x) is an increasing function of v, — | < i/ < oo, fc = 1,2,..., a result relevant to work of M. S. Ashbaugh and R. D. Benguria on eigenvalues in the clamped plate problem for the ball. The functions Jv(x) and Iv(x) are the Bessel and modified Bessel functions, respectively. 1. Background and statement of main result Motivated by their appearance as eigenvalues in the clamped plate problem for the ball, M. S. Ashbaugh and R. D. Benguria (private communication) have conjectured that the positive zeros of Six) = Mx)r„(x) J'Mhix) (i.i) increase with v > — |. J^ (x) and !„ (x) are the customary Bessel and modified Bessel functions [6]. Their conjecture will be verified here (Corollary 1), and also in a somewhat extended form (Theorem 1). The proofs will employ, La., the recursion formulae [6, §3.2(4), p. 45, §3.71(4), p. 79] xJ'u(x) vJv{x) — -xJv+\\{x), (1.2) and xl^ix) vlv{x) xly+xix). (1.3) From them it follows immediately that the fc-th positive zero 7^ of /(re) is also the fc-th positive zero of JV\\X) iv\\X) The denominators in (1.4) do not distort the discussion. If x / 0, then Iv{x) > 0, v > — 1 (as is evident from the power series [6, §3.7(2), p. 77]); a positive zero of Jv(x) cannot be a zero of f(x) since Ju(x) and Jl(x) cannot vanish simultaneously, x ^ 0 [6, §15.21, p. 479]. Received April 14, 1993, revised August 7, 1993. 1991 Mathematics Subject Classification. Primary: 33C10, 33B30, 34L15.
01 Jan 1994-Nuclear Instruments & Methods in Physics Research Section A-accelerators Spectrometers Detectors and Associated Equipment
TL;DR: In this paper, a derivation for a previously published formula, which determines the geometrical efficiency of a parallel-disk source and detector system, is presented, which involves an integral over a product of two Bessel functions.
Abstract: A derivation is presented for a previously published formula, which determines the geometrical efficiency of a parallel-disk source and detector system. The formula involves an integral over a product of two Bessel functions. An algebraic approximation to the integral is also discussed.
TL;DR: In this article, asymptotic expansions are given for the q-gamma function, the q -exponential functions, and for the Hahn-Exton q -Bessel function.
TL;DR: In this paper, the applicability of the discrete Bessel transform for the case of cylindrical or spherical symmetry was extended to non-direct product representations, and a new and efficient multidimensional pseudospectral based on Laplacian eigenfunctions was proposed.
TL;DR: In this article, a new method for representing the remainder and coefficients in Airy-type expansions of integrals is given, where quantities are written in terms of Cauchy-type integrals and are natural generalizations of integral representations of Taylor coefficients and remainders of analytic functions.
Abstract: A new method for representing the remainder and coefficients in Airy-type expansions of integrals is given. The quantities are written in terms of Cauchy-type integrals and are natural generalizations of integral representations of Taylor coefficients and remainders of analytic functions. The new approach gives a general method for extending the domain of the saddle-point parameter to unbounded domains. As a side result the conditions under which the Airy-type asymptotic expansion has a double asymptotic property become clear. An example relating to Laguerre polynomials is worked out in detail. How to apply the method to other types of uniform expansions, for example, to an expansion with Bessel functions as approximants, is explained. In this case the domain of validity can be extended to unbounded domains and the double asymptotic property can be established as well.
TL;DR: In this paper, the problem of plane thermal wave in media with linearly varying thermal conductivity κ in the absence of internal heat sources is rigorously solved in terms of Bessel functions, and an exact solution in the presence of an internal heat source arising from optical absorption is also presented.
Abstract: The problem of plane thermal waves in media with linearly varying thermal conductivity κ in the absence of internal heat sources is rigorously solved in terms of Bessel functions. An exact solution in the presence of an internal heat source arising from optical absorption is also presented. Focus is on the semi‐infinite solid. In particular, an inverse calculation procedure is outlined that is able to yield, in a very fast way, a linear κ profile that reveals the most important aspects of the actual profile.
TL;DR: In this article, the pole structure of the zeta function zeta Anu (s) is investigated on the negative real axis, where most of the singularities occur. But the analysis is restricted to the case where the eigenvalues of a Bessel operator Anu are subject to Dirichlet boundary conditions.
Abstract: We investigate the pole structure of the zeta function zeta Anu (s)= Sigma k lambda k-s built out of the eigenvalues lambda k of a Bessel operator Anu subject to Dirichlet boundary conditions at one end of the domain. This leads us to the study of zeta Anu on the negative real axis, where most of the singularities occur.
01 Mar 1994
TL;DR: In this paper, a q-extension of the Wronskian was introduced to determine that the two q-difference equations form a fundamental set, and a second solution of the qdifference equation of the Hahn-Exton q-Bessel function corresponding to the classical Yn (x) was found.
Abstract: A second solution of the q-difference equation of the Hahn-Exton q-Bessel function, corresponding to the classical Yn (x) , is found. We introduce a q-extension of the Wronskian to determine that the two solutions form a fundamental set.
TL;DR: In this article, incomplete Lipschitz-Hankel integrals are used to represent transient pulses in homogeneously filled waveguides, and the resulting expressions are verified by numerically integrating the pulse distribution multiplied by the known impulse response.
Abstract: It is well known that transient electromagnetic waves in waveguides exhibit dispersion. Exact, closed-form expressions, which involve Bessel functions of the first kind, have been derived for the impulse response of a waveguide, but exact, closed-form expressions for more complex pulses are absent from the literature. In this paper, it is demonstrated that incomplete Lipschitz-Hankel integrals can be used to represent transient pulses in homogeneously filled waveguides. A continuous wave pulse is investigated in this paper, however, this technique can also be applied to a number of other transient waveforms. The resulting expressions are verified by numerically integrating the pulse distribution multiplied by the known impulse response. >
TL;DR: In this paper, the level spacing distribution for the Laguerre ensemble in a single-scaled interval, (0, s), containing no levels, was determined via Dyson's Coulomb-fluid approach.
Abstract: We determine the asymptotic level spacing distribution for the Laguerre ensemble in a single-scaled interval, (0,s), containing no levels, Ebeta (0,s), via Dyson's Coulomb-fluid approach. For the alpha =0 unitary Laguerre ensemble, we recover the exact spacing distribution found by both Edelman (1988) and Forrester (1993), while for alpha not=0, the leading terms of E2(0,s), found by Tracy and Widom (1994), are reproduced without the use of the Bessel kernel and the associated Painleve transcendent. In the same approximation, the next leading term, due to a 'finite-temperature' perturbation ( beta not=2), is found.
TL;DR: In this paper, the focal shift of unapertured Bessel-Gauss beams is studied by means of the Collins diffraction integral, and the results of unaertured Gauss beams and Bessel beams follow readily as two limiting cases of the study.
TL;DR: In this paper, a necessary and sufficient condition to transform the Bessel function into a symmetric form is given in terms of an overdetermined system of linear equations, which leads to a (symmetric) fourth-, sixth-and eighth-order differential equation, respectively.
TL;DR: In this article, a nonlinear dual-porosity formulation incorporating a quadratic gradient term in the governing flow equation is presented to avoid solving the simultaneous system of equations, decoupling of fluid pressures in the matrix from the fractures is furnished by assuming a quasi-steady-state flow with the pressure difference between matrix and fractures as a primary unknown.
01 Jan 1994
TL;DR: In this article, the authors consider the case of operators W k on L P (ℝ+) with semi almost periodic presymbols K at the expense of inflating the size of K.
Abstract: The consideration of above mentioned operators on the union of intervals and/or rays is reduced to the canonical situation of operators W k on L P (ℝ+) with semi almost periodic presymbols K at the expense of inflating the size of K. The Fredholm theory (that is, conditions of n-, d-normality and the index formula) is developed. In particular, relations between (semi-)Fredholmness of W K , invertibility of \({W_{{k_ \pm }}}\) with K ± being almost periodic representatives of K at ±∞, and factorability of K ± are established.
TL;DR: Fitouhi and Hamza as discussed by the authors gave a new proof of this result leading to a large domain of uniform convergence, and then studied a transmutation operator between two classes of perturbed Bessel operators.
TL;DR: In this article, the mean convergence of Fourier series with respect to this system for functions whose Hankel transform is supported on [0, 1] was studied for functions with Bessel functions of order μ.
Abstract: LetJμ denote the Bessel function of order μ. For α>−1, the system x−α/2−1/2Jα+2n+1(x1/2, n=0, 1, 2,..., is orthogonal onL2((0, ∞),x α dx). In this paper we study the mean convergence of Fourier series with respect to this system for functions whose Hankel transform is supported on [0, 1].
TL;DR: A number of definite integrals involving Bessel functions have been derived by finding new integral representations for the product of two Bessel function of different order and argument in terms of the generalized hypergeometric function with subsequent reduction to special cases.
TL;DR: In this paper, the exact modes of circular plates as shape functions in the Rayleigh-Ritz method were investigated, and the mass and stiffness matrices were expressed in closed form using Lommel integrals.