Continued fraction calculation of spherical Bessel functions

Lentz, William J.

doi:10.1063/1.168382

Cited by 7 publications

(4 citation statements)

References 1 publication

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“…We implement an efficient scheme to evaluate the spherical Bessel function of the j-type [73] in a Fortran-90 function. The code is based on the mathematical work by Lentz [74]. In the following we just call it the Bessel function.…”

Section: Efficient Evaluation Of Spherical Bessel Functionsmentioning

confidence: 99%

Compton spectra of atoms at high x-ray intensity

Son

Geffert

Santra

2017

J. Phys. B: At. Mol. Opt. Phys.

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Abstract. Compton scattering is the nonresonant inelastic scattering of an xray photon by an electron and has been used to probe the electron momentum distribution in gas-phase and condensed-matter samples. In the low x-ray intensity regime, Compton scattering from atoms dominantly comes from bound electrons in neutral atoms, neglecting contributions from bound electrons in ions and free (ionized) electrons. In contrast, in the high x-ray intensity regime, the sample experiences severe ionization via x-ray multiphoton multiple ionization dynamics. Thus, it becomes necessary to take into account all the contributions to the Compton scattering signal when atoms are exposed to high-intensity x-ray pulses provided by x-ray free-electron lasers (XFELs). In this paper, we investigate the Compton spectra of atoms at high xray intensity, using an extension of the integrated x-ray atomic physics toolkit, xatom.As the x-ray fluence increases, there is a significant contribution from ionized electrons to the Compton spectra, which gives rise to strong deviations from the Compton spectra of neutral atoms. The present study provides not only understanding of the fundamental XFEL-matter interaction but also crucial information for single-particle imaging experiments, where Compton scattering is no longer negligible.

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Section: Efficient Evaluation Of Spherical Bessel Functionsmentioning

confidence: 99%

Compton spectra of atoms at high x-ray intensity

Son

Geffert

Santra

2017

J. Phys. B: At. Mol. Opt. Phys.

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“…This infinite continued fraction representation Equation 22needs a large number of terms for convergence to a given accuracy. In [49], the authors propose the modified Lentz's method. It reverses the order of coefficients in CFE.…”

Section: Continued Fraction Equation Methodsmentioning

confidence: 99%

Fractional Order Graph Filters: Design and Implementation

Qiu

Feng

2021

Electronics

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Existing graph filters, polynomial or rational, are mainly of integer order forms. However, there are some frequency responses which are not easily achieved by integer order approximation. It will substantially increase the flexibility of the filters if we relax the integer order to fractional ones. Motivated by fractional order models, we introduce the fractional order graph filters (FOGF), and propose to design the filter coefficients by genetic algorithm. In order to implement distributed computation on a graph, an FOGF can be approximated by the continued fraction expansion and transformed to an infinite impulse response graph filter.

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“…where in both cases x is the size parameter of the particle, a 2 vac p l , with a the particle radius and λ vac the wavelength of incoming light in a vacuum, and Here, j n (x) and y n (x) are spherical Bessel functions. The factor D n in Equations (A14) and (A15) is the logarithmic derivative computed using the continued fraction method developed by Lentz (1990). As the description of this method is lengthy and is fully documented in Prahl (2023) and Lentz (1990), we refer the reader to these publications for a full derivation.…”

Section: A3 Mie Efficiency Calculationsmentioning

confidence: 99%

“…The factor D n in Equations (A14) and (A15) is the logarithmic derivative computed using the continued fraction method developed by Lentz (1990). As the description of this method is lengthy and is fully documented in Prahl (2023) and Lentz (1990), we refer the reader to these publications for a full derivation.…”

Section: A3 Mie Efficiency Calculationsmentioning

confidence: 99%

Haze Optical Depth in Exoplanet Atmospheres Varies with Rotation Rate: Implications for Observations

Cohen,

Palmer,

Paradise

et al. 2024

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Transmission spectroscopy supports the presence of uncharacterized, light-scattering and -absorbing hazes in the atmospheres of many exoplanets. The complexity of factors influencing the formation, 3D transport, radiative impact, and removal of hazes makes it challenging to match theoretical models to the existing data. Our study simplifies these factors to focus on the interaction between planetary general circulation and haze distribution at the planetary limb. We use an intermediate-complexity general circulation model, ExoPlaSim, to simulate idealized organic haze particles as radiatively active tracers in the atmospheres of tidally locked terrestrial planets for 32 rotation rates. We find three distinct 3D spatial haze distributions, corresponding to three circulation regimes, each with a different haze profile at the limb. All regimes display significant terminator asymmetry. In our parameter space, super-Earth-sized planets with rotation periods greater than 13 days have the lowest haze optical depths at the terminator, supporting the choice of slower rotators as observing targets.

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Continued fraction calculation of spherical Bessel functions

Cited by 7 publications

References 1 publication

Compton spectra of atoms at high x-ray intensity

Compton spectra of atoms at high x-ray intensity

Fractional Order Graph Filters: Design and Implementation

Haze Optical Depth in Exoplanet Atmospheres Varies with Rotation Rate: Implications for Observations

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