1,254 research outputs found
A fast analysis-based discrete Hankel transform using asymptotic expansions
A fast and numerically stable algorithm is described for computing the
discrete Hankel transform of order as well as evaluating Schl\"{o}milch and
Fourier--Bessel expansions in
operations. The algorithm is based on an asymptotic expansion for Bessel
functions of large arguments, the fast Fourier transform, and the Neumann
addition formula. All the algorithmic parameters are selected from error bounds
to achieve a near-optimal computational cost for any accuracy goal. Numerical
results demonstrate the efficiency of the resulting algorithm.Comment: 22 page
Dispersion modeling and analysis for multilayered open coaxial waveguides
This paper presents a detailed modeling and analysis regarding the dispersion
characteristics of multilayered open coaxial waveguides. The study is motivated
by the need of improved modeling and an increased physical understanding about
the wave propagation phenomena on very long power cables which has a potential
industrial application with fault localization and monitoring. The
electromagnetic model is based on a layer recursive computation of
axial-symmetric fields in connection with a magnetic frill generator excitation
that can be calibrated to the current measured at the input of the cable. The
layer recursive formulation enables a stable and efficient numerical
computation of the related dispersion functions as well as a detailed analysis
regarding the analytic and asymptotic properties of the associated
determinants. Modal contributions as well as the contribution from the
associated branch-cut (non-discrete radiating modes) are defined and analyzed.
Measurements and modeling of pulse propagation on an 82 km long HVDC power
cable are presented as a concrete example. In this example, it is concluded
that the contribution from the second TM mode as well as from the branch-cut is
negligible for all practical purposes. However, it is also shown that for
extremely long power cables the contribution from the branch-cut can in fact
dominate over the quasi-TEM mode for some frequency intervals. The main
contribution of this paper is to provide the necessary analysis tools for a
quantitative study of these phenomena
Singular perturbations approach to localized surface-plasmon resonance: Nearly touching metal nanospheres
Metallic nano-structures characterised by multiple geometric length scales
support low-frequency surface-plasmon modes, which enable strong light
localization and field enhancement. We suggest studying such configurations
using singular perturbation methods, and demonstrate the efficacy of this
approach by considering, in the quasi-static limit, a pair of nearly touching
metallic nano-spheres subjected to an incident electromagnetic wave polarized
with the electric field along the line of sphere centers. Rather than
attempting an exact analytical solution, we construct the pertinent
(longitudinal) eigen-modes by matching relatively simple asymptotic expansions
valid in overlapping spatial domains. We thereby arrive at an effective
boundary eigenvalue problem in a half-space representing the metal region in
the vicinity of the gap. Coupling with the gap field gives rise to a mixed-type
boundary condition with varying coefficients, whereas coupling with the
particle-scale field enters through an integral eigenvalue selection rule
involving the electrostatic capacitance of the configuration. By solving the
reduced problem we obtain accurate closed-form expressions for the resonance
values of the metal dielectric function. Furthermore, together with an
energy-like integral relation, the latter eigen-solutions yield also
closed-form approximations for the induced-dipole moment and gap-field
enhancement under resonance. We demonstrate agreement between the asymptotic
formulas and a semi-numerical computation. The analysis, underpinned by
asymptotic scaling arguments, elucidates how metal polarization together with
geometrical confinement enables a strong plasmon-frequency redshift and
amplified near-field at resonance.Comment: 13 pages, 7 figure
Kernel Density Estimation with Linked Boundary Conditions
Kernel density estimation on a finite interval poses an outstanding challenge
because of the well-recognized bias at the boundaries of the interval.
Motivated by an application in cancer research, we consider a boundary
constraint linking the values of the unknown target density function at the
boundaries. We provide a kernel density estimator (KDE) that successfully
incorporates this linked boundary condition, leading to a non-self-adjoint
diffusion process and expansions in non-separable generalized eigenfunctions.
The solution is rigorously analyzed through an integral representation given by
the unified transform (or Fokas method). The new KDE possesses many desirable
properties, such as consistency, asymptotically negligible bias at the
boundaries, and an increased rate of approximation, as measured by the AMISE.
We apply our method to the motivating example in biology and provide numerical
experiments with synthetic data, including comparisons with state-of-the-art
KDEs (which currently cannot handle linked boundary constraints). Results
suggest that the new method is fast and accurate. Furthermore, we demonstrate
how to build statistical estimators of the boundary conditions satisfied by the
target function without apriori knowledge. Our analysis can also be extended to
more general boundary conditions that may be encountered in applications
The M-Wright function in time-fractional diffusion processes: a tutorial survey
In the present review we survey the properties of a transcendental function
of the Wright type, nowadays known as M-Wright function, entering as a
probability density in a relevant class of self-similar stochastic processes
that we generally refer to as time-fractional diffusion processes.
Indeed, the master equations governing these processes generalize the
standard diffusion equation by means of time-integral operators interpreted as
derivatives of fractional order. When these generalized diffusion processes are
properly characterized with stationary increments, the M-Wright function is
shown to play the same key role as the Gaussian density in the standard and
fractional Brownian motions. Furthermore, these processes provide stochastic
models suitable for describing phenomena of anomalous diffusion of both slow
and fast type.Comment: 32 pages, 3 figure
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