Generating Bessel functions in Mie scattering calculations using continued fractions

Lentz, William J.

doi:10.1364/ao.15.000668

Cited by 198 publications

(66 citation statements)

References 2 publications

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“…(3) as the proportion of energy absorbed by the companion, relative to the flux of incident energy of the wave through the section of the companion. We perform a numerical computation of Q abs using a version of the Damie code, based on Lentz (1976) 2 . We have tested the program with real and complex values of N 2 , and compared the results with analytical approximations given in van de Hulst (1981) for various regions of the (x, N) parameter space.…”

Section: Absorption Coefficientmentioning

confidence: 99%

Do asteroids evaporate near pulsars? Induction heating by pulsar waves revisited

Kotera

Mottez

Voisin

et al. 2016

A&A

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Aims. We investigate the evaporation of close-by pulsar companions, such as planets, asteroids, and white dwarfs, by induction heating. Methods. Assuming that the outflow energy is dominated by a Poynting flux (or pulsar wave) at the location of the companions, we calculate their evaporation timescales, by applying the Mie theory. Results. Depending on the size of the companion compared to the incident electromagnetic wavelength, the heating regime varies and can lead to a total evaporation of the companion. In particular, we find that inductive heating is mostly inefficient for small pulsar companions, although it is generally considered the dominant process. Conclusions. Small objects like asteroids can survive induction heating for 10 4 yr at distances as small as 1 R from the neutron star. For degenerate companions, induction heating cannot lead to evaporation and another source of heating (likely by kinetic energy of the pulsar wind) has to be considered. It was recently proposed that bodies orbiting pulsars are the cause of fast radio bursts; the present results explain how those bodies can survive in the pulsar's highly energetic environment.

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Section: Absorption Coefficientmentioning

confidence: 99%

Do asteroids evaporate near pulsars? Induction heating by pulsar waves revisited

Kotera

Mottez

Voisin

et al. 2016

A&A

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“…(32). We calculate the above using Lentz's algorithm [50,53,54]. It should be noted that this continued fraction does not terminate after a finite number of terms, therefore we are not able to use it to find a finite sum of poles for the kernel.…”

Section: Boundary Kernel Calculationmentioning

confidence: 99%

Extension of the continuum time-dependent Hartree-Fock method to proton states

Pardi

Stevenson

2014

Phys. Rev. E

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This paper deals with the solution of the spherically symmetric time-dependent Hartree-Fock approximation applied to nuclear giant monopole resonances in the small amplitude regime. The problem is spatially unbounded as the resonance state is in the continuum. The practical requirement to perform the calculation in a finite-sized spatial region yields an artificial boundary, which is not present physically. The question of how to ensure the boundary does not interfere with the internal solution, while keeping the overall calculation time low is studied. Here we propose an absorbing boundary condition scheme to handle the conflict. The derivation, via a Laplace transform method, and implementation is described. An inverse Laplace transform required by the absorbing boundaries is calculated using a method of nonlinear least squares. The accuracy and efficiency of the scheme is tested and results presented to support the case that they are an effective way of handling the artificial boundary.

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“…The problem of light scattering from spheres instead of cylinders has received much more attention [10][11][12][13][14], and quite sophisticated methods have been developed that allow the precise calculation of the scattered field even for large spheres with refractive indices with a large real or imaginary part. We have analyzed the methods suggested for spheres, and applied and extended them to circular cylinders.…”

Section: Introductionmentioning

confidence: 99%

Extending the size-parameter range for plane-wave light scattering from infinite homogeneous circular cylinders

Hau‐Riege

2006

Appl. Opt.

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AbtractWe have developed an algorithm that extends the possible size-parameter range for the calculation of plane-wave light scattering from infinite homogeneous circular cylinders using a Mie-type analysis. Our algorithm is based on the calculation of the ratios of Bessel functions instead of calculating the Bessel functions or their logarithmic derivatives directly. We have found that this algorithm agrees with existing methods (when those methods converge). We have also found that our algorithm converges in cases of very large size parameters, in which case other algorithms often do not.

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Generating Bessel functions in Mie scattering calculations using continued fractions

Cited by 198 publications

References 2 publications

Do asteroids evaporate near pulsars? Induction heating by pulsar waves revisited

Do asteroids evaporate near pulsars? Induction heating by pulsar waves revisited

Extension of the continuum time-dependent Hartree-Fock method to proton states

Extending the size-parameter range for plane-wave light scattering from infinite homogeneous circular cylinders

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