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107
On Nonreflecting Boundary Conditions
 J. COMPUT. PHYS
, 1995
"... Improvements are made in nonreflecting boundary conditions at artificial boundaries for use with the Helmholtz equation. First, it is shown how to remove the difficulties that arise when the exact DtN (DirichlettoNeumann) condition is truncated for use in computation, by modifying the truncated ..."
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Cited by 219 (4 self)
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Improvements are made in nonreflecting boundary conditions at artificial boundaries for use with the Helmholtz equation. First, it is shown how to remove the difficulties that arise when the exact DtN (DirichlettoNeumann) condition is truncated for use in computation, by modifying the truncated condition. Second, the exact DtN boundary condition is derived for elliptic and spheroidal coordinates. Third, approximate local boundary conditions are derived for these coordinates. Fourth, the truncated DtN condition in elliptic and spheroidal coordinates is modified to remove difficulties. Fifth, a sequence of new and more accurate local boundary conditions is derived for polar coordinates in two dimensions. Numerical results are presented to demonstrate the usefulness of these improvements.
Control of Inhomogeneous Ensembles
, 2006
"... In this thesis, we study a class of control problems which involves controlling a large number of dynamical systems with different values of parameters governing the system dynamics by using the same control signal. We call such problems control of inhomogeneous ensembles. The motivation for looking ..."
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Cited by 17 (6 self)
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In this thesis, we study a class of control problems which involves controlling a large number of dynamical systems with different values of parameters governing the system dynamics by using the same control signal. We call such problems control of inhomogeneous ensembles. The motivation for looking into these problems comes from the manipulation of an ensemble of nuclear spins in Nuclear Magnetic Resonance (NMR) spectroscopy and imaging with dispersion in natural frequencies and the strengths of the applied radio frequency (rf) field. A systematic study of these systems has immediate applications to broad areas of the control of systems in quantum and nano domains, such as coherent spectroscopy and quantum information processing. From the standpoint of mathematical control theory, the challenge is to simultaneously steer a continuum of systems between points of interest with the same control signal. This raises the intriguing question about ensemble controllability. We show that controllability of an ensemble can be understood by the study of the algebra of polynomials defined by the noncommuting vector fields governing the system dynamics. In practical magnetic resonance applications, this work leads to the design of a compensating
Spectral estimates and nonselfadjoint perturbations of spheroidal wave operators,” mathph/0405010
, 2006
"... We derive a spectral representation for the oblate spheroidal wave operator which is holomorphic in the aspherical parameter Ω in a neighborhood of the real line. For real Ω, estimates are derived for all eigenvalue gaps uniformly in Ω. The proof of the gap estimates is based on detailed estimates f ..."
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Cited by 12 (10 self)
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We derive a spectral representation for the oblate spheroidal wave operator which is holomorphic in the aspherical parameter Ω in a neighborhood of the real line. For real Ω, estimates are derived for all eigenvalue gaps uniformly in Ω. The proof of the gap estimates is based on detailed estimates for complex solutions of the Riccati equation. The spectral representation for complex Ω is obtained using the theory of slightly nonselfadjoint perturbations. 1
A new friendly method of computing prolate spheroidal wave functions and wavelets
, 2005
"... Prolate spheroidal wave functions, because of their many remarkable properties leading to new applications, have recently experienced an upsurge of interest. They may be defined as eigenfunctions of either a differential operator or an integral operator (as observed by Slepian in the 1960’s). There ..."
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Cited by 11 (0 self)
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Prolate spheroidal wave functions, because of their many remarkable properties leading to new applications, have recently experienced an upsurge of interest. They may be defined as eigenfunctions of either a differential operator or an integral operator (as observed by Slepian in the 1960’s). There are various ways of calculating their values based on both approaches. The standard one uses an approximation based on Legendre polynomials, which, however, is valid only on a finite interval. An alternative, valid in a neighborhood of infinity, uses a Bessel function approximation. In this paper we present a new method based on an eigenvalue problem for a matrix operator equivalent to that of the integral operator. Its solution gives the values of these functions on the entire real line and is computationally more efficient. Key words: sampling theory, prolate spheroidal wave functions. 1
Exact solutions of electromagnetic fields in both near and far zones radiated by thin cicular loop antennas: a general representation
 Proc
, 1997
"... Abstract — This paper presents an alternative vector analysis of the electromagnetic (EM) fields radiated from thin circularloop antennas of arbitrary radius a. This method, which employs the dyadic Green’s function in the derivation of the EM radiated fields, makes the analysis more general, compac ..."
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Cited by 10 (4 self)
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Abstract — This paper presents an alternative vector analysis of the electromagnetic (EM) fields radiated from thin circularloop antennas of arbitrary radius a. This method, which employs the dyadic Green’s function in the derivation of the EM radiated fields, makes the analysis more general, compact, and straightforward than those two methods published recently by Werner and Overfelt. Both near and far zones are considered so that the EM radiated fields are expressed in terms of the vectorwave eigenfunctions. Not only the exact solution of the EM fields in the near and far zones outside the region (where r>a) is derived by the use of the spherical Hankel function of the first kind, but also the closedseries form of the EM fields radiated in the near zone inside the region 0 r<a is obtained in series of the spherical Bessel functions of the first kind. As an example, a Fourier cosine series is used to expand an arbitrary current distribution along the loop and the exact representations of the EM radiated fields due to the loop everywhere are obtained in closed form. The closed form reduces to those for the sinusoidal current loop and further for the uniform current loop. Validity of the approximate formulas is discussed and clarified. Error analysis based on numerical computations of the radiated fields is also given to show the accuracy of the limiting cases. Index Terms — Closedform solution, eigenfunction expansion, electromagnetic radiation, loop antennas, vectorwave functions.
ANALYSIS OF SPECTRAL APPROXIMATIONS USING PROLATE SPHEROIDAL WAVE FUNCTIONS
"... Abstract. In this paper, the approximation properties of the prolate spheroidal wave functions of order zero (PSWFs) are studied, and a set of optimal error estimates are derived for the PSWF approximation of nonperiodic functions in Sobolev spaces. These results serve as an indispensable tool for ..."
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Cited by 7 (2 self)
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Abstract. In this paper, the approximation properties of the prolate spheroidal wave functions of order zero (PSWFs) are studied, and a set of optimal error estimates are derived for the PSWF approximation of nonperiodic functions in Sobolev spaces. These results serve as an indispensable tool for the analysis of PSWF spectral methods. A PSWF spectralGalerkin method is proposed and analyzed for elliptictype equations. Illustrative numerical results consistent with the theoretical analysis are also presented. 1.
Duality, Ancestral and Diffusion Processes in Models with Selection ∗
, 804
"... The ancestral selection graph in population genetics was introduced by Krone and Neuhauser (1997) as an analogue of the coalescent genealogy of a sample of genes from a neutrally evolving population. The number of particles in this graph, followed backwards in time, is a birth and death process with ..."
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Cited by 6 (2 self)
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The ancestral selection graph in population genetics was introduced by Krone and Neuhauser (1997) as an analogue of the coalescent genealogy of a sample of genes from a neutrally evolving population. The number of particles in this graph, followed backwards in time, is a birth and death process with quadratic death and linear birth rates. In this paper an explicit form of the probability distribution of the number of particles is obtained by using the density of the allele frequency in the corresponding diffusion model obtained by Kimura (1955). It is shown that the process of fixation of the allele in the diffusion model corresponds to convergence of the ancestral process to its stationary measure. The time to fixation of the allele conditional on fixation is studied in terms of the ancestral process.
Acoustic scattering by axisymmetric finitelength bodies: An extension of a 2dimensional conformal mapping method
 SUBMITTED TO: JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA
"... A general scattering formulation is presented for predicting the farfield scattered pressure from irregular, axisymmetric, finitelength bodies for three boundary conditions—soft, rigid and fluid. The formulation is an extension of a twodimensional conformal mapping approach [D. T. DiPerna and T ..."
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Cited by 6 (1 self)
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A general scattering formulation is presented for predicting the farfield scattered pressure from irregular, axisymmetric, finitelength bodies for three boundary conditions—soft, rigid and fluid. The formulation is an extension of a twodimensional conformal mapping approach [D. T. DiPerna and T. K. Stanton, J.> rj o" °?! Acoust. Soc. Am. 96: 30643079 (1994)] to scattering by finitelength bodies. g; ä =£
Perturbation Stability Of Coherent Riesz Systems Under Convolution Operators
 APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
, 2002
"... We study the orthogonal perturbation of various coherent function systems (Gabor systems, Wilson bases, and wavelets) under convolution operators. This problem is of key relevance in the design of modulation signal sets for digital communication over timeinvariant channels. Upper and lower bounds ..."
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Cited by 6 (2 self)
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We study the orthogonal perturbation of various coherent function systems (Gabor systems, Wilson bases, and wavelets) under convolution operators. This problem is of key relevance in the design of modulation signal sets for digital communication over timeinvariant channels. Upper and lower bounds on the orthogonal perturbation are formulated in terms of spectral spread and temporal support of the prototype, and by the approximate design of worst case convolution kernels. Among the considered bases, the WeylHeisenberg structure which generates Gabor systems turns out to be optimal whenever the class of convolution operators satisfies typical practical constraints.
Inverse source problem in an oblate spheroidal geometry
 IEEE Trans. Antennas Propagat
, 2006
"... The canonical inverse source problem of reconstructing an unknown source whose region of support is describable as a spheroidal (oblate or prolate) volume from knowledge of the farfield radiation pattern it generates is formulated and solved within the framework of the inhomogeneous scalar Helmholt ..."
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Cited by 6 (3 self)
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The canonical inverse source problem of reconstructing an unknown source whose region of support is describable as a spheroidal (oblate or prolate) volume from knowledge of the farfield radiation pattern it generates is formulated and solved within the framework of the inhomogeneous scalar Helmholtz equation via a linear inversion framework in Hilbert spaces. Particular attention is paid to the analysis and computer illustration of flat, aperturelike sources whose support is approximated by an oblate spheroidal volume. Key words: Inverse source problem, minimum energy source, nonradiating source, spheroidal wave. 1 1