Precise and fast computation of inverse Fermi–Dirac integral of order 1/2 by minimax rational function approximation

Fukushima, Toshio

doi:10.1016/j.amc.2015.03.015

Cited by 11 publications

(4 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We obtain the Fermi integrals and their inverses using the routines provided by Fukushima [57,58]. These proved to be fast, accurate, and thermodynamically consistent.…”

Section: A Bulk Nuclear Mattermentioning

confidence: 99%

Open-source nuclear equation of state framework based on the liquid-drop model with Skyrme interaction

2017

View full text Add to dashboard Cite

The equation of state (EOS) of dense matter is an essential ingredient for numerical simulations of core-collapse supernovae and neutron star mergers. The properties of matter near and above nuclear saturation density are uncertain, which translates into uncertainties in astrophysical simulations and their multimessenger signatures. Therefore, a wide range of EOSs spanning the allowed range of nuclear interactions are necessary for determining the sensitivity of these astrophysical phenomena and their signatures to variations in input microphysics. We present a new set of finite temperature EOSs based on experimentally allowed Skyrme forces. We employ a liquid-drop model of nuclei to capture the nonuniform phase of nuclear matter at subsaturation density, which is blended into a nuclear statistical equilibrium EOS at lower densities. We also provide a new, open-source code for calculating EOSs for arbitrary Skyrme parametrizations. We then study the effects of different Skyrme parametrizations on thermodynamical properties of dense astrophysical matter, the neutron star mass-radius relationship, and the core collapse of 15 and 40 solar mass stars.

show abstract

“…We obtain the Fermi integrals and their inverses using the routines provided by Fukushima [57,58]. These proved to be fast, accurate, and thermodynamically consistent.…”

Section: A Bulk Nuclear Mattermentioning

confidence: 99%

Open-source nuclear equation of state framework based on the liquid-drop model with Skyrme interaction

2017

View full text Add to dashboard Cite

show abstract

“…Their values for k = −1/2, +1/2, and +3/2 as well as the inverse for k = +1/2 are computed using the subroutines of Fukushima [86,87]. The derivatives of the Fermi integrals satisfy…”

Section: Fermi Integralsmentioning

confidence: 99%

“…Because we work with variables where the nucleon densities n t and temperatures T are readily available, it is straightforward to determine η t . We use the subroutines of Fukushima to compute the above Fermi integrals and their inverses [86,87]. If the nucleon density is extremely low, floating point operations may become an issue and, thus, asymptotic limits must be used to compute the degeneracy parameters.…”

Section: Degeneracy Parametersmentioning

confidence: 99%

Akmal-Pandharipande-Ravenhall equation of state for simulations of supernovae, neutron stars, and binary mergers

et al. 2019

View full text Add to dashboard Cite

Differences in the equation of state (EOS) of dense matter translate into differences in astrophysical simulations and their multimessenger signatures. Thus, extending the number of EOSs for astrophysical simulations allows us to probe the effect of different aspects of the EOS in astrophysical phenomena. In this work, we construct the EOS of hot and dense matter based on the Akmal, Pandharipande, and Ravenhall (APR) model and thereby extend the open-source SROEOS code which computes EOSs of hot dense matter for Skyrme-type parametrizations of the nuclear forces. Unlike Skrme-type models, in which parameters of the interaction are fit to reproduce the energy density of nuclear matter and/or properties of heavy nuclei, the EOS of APR is obtained from potentials resulting from fits to nucleon-nucleon scattering and properties of light nuclei. In addition, this EOS features a phase transition to a spin-isospin ordered state of nucleons, termed a neutral pion condensate, at supranuclear densities. We show that differences in the effective masses between EOSs have consequences for the properties of nuclei in the subnuclear inhomogeneous phase of matter. We also test the new EOS of APR in spherically symmetric core-collapse of massive stars with 15 M and 40 M , respectively. We find that the phase transition in the EOS of APR speeds up the collapse of the star. However, this phase transition does not generate a second shock wave or another neutrino burst as reported for the hadron-to-quark phase transition. The reason for this difference is that the width of the coexistence region and the latent heat in the EOS of APR are substantially smaller than in the quark-to-hadron transition employed earlier, which results in a significantly smaller softening of the high density EOS.

show abstract

“…For example, a recent article written by Mohankumar and Natarajan [28] gives a very accurate method for numerically computing the Generalized Fermi-Dirac integrals. Also, recent articles by Changshi [29] and Fukushima [30] give excellent methods for numerically computing Fermi-Diractype integrals. There are many other published methods that work very well for numerically computing the Fermi-Diractype and Bose-Einstein-type integrals.…”

Section: Remarks and Conclusionmentioning

confidence: 99%

The Application of Real Convolution for Analytically Evaluating Fermi-Dirac-Type and Bose-Einstein-Type Integrals

Selvaggi

Selvaggi²

2018

Journal of Complex Analysis

View full text Add to dashboard Cite

The Fermi-Dirac-type or Bose-Einstein-type integrals can be transformed into two convergent real-convolution integrals. The transformation simplifies the integration process and may ultimately produce a complete analytical solution without recourse to any mathematical approximations. The real-convolution integrals can either be directly integrated or be transformed into the Laplace Transform inversion integral in which case the full power of contour integration becomes available. Which method is employed is dependent upon the complexity of the real-convolution integral. A number of examples are introduced which will illustrate the efficacy of the analytical approach.

show abstract

Precise and fast computation of inverse Fermi–Dirac integral of order 1/2 by minimax rational function approximation

Cited by 11 publications

References 17 publications

Open-source nuclear equation of state framework based on the liquid-drop model with Skyrme interaction

Open-source nuclear equation of state framework based on the liquid-drop model with Skyrme interaction

Akmal-Pandharipande-Ravenhall equation of state for simulations of supernovae, neutron stars, and binary mergers

The Application of Real Convolution for Analytically Evaluating Fermi-Dirac-Type and Bose-Einstein-Type Integrals

Contact Info

Product

Resources

About