On the computation of Bessel functions of first kind

Balla, K.; Guk, O. S.; Vicsek, M.

doi:10.1007/bf02280041

Cited by 8 publications

(1 citation statement)

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“…The Bessel function J s (x s ) in Eq. 4is an oscillatory function and can be evaluated by its asymptotic functions J 1,s and J 2,s [48]. The use of these two functions allows us to approximate arbitrarily the VT transition probability Eq.…”

Section: Approximate Fho Modelmentioning

confidence: 99%

Simple model for vibration-translation exchange at high temperatures: Effects of multiquantum transitions on the relaxation of aN2gas flow behind a shock

2011

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In this paper a simple model is proposed for computation of rate coefficients related to vibration-translation transitions based on the forced harmonic oscillator theory. This model, which is developed by considering a quadrature method, provides rate coefficients that are in very good agreement with those found in the literature for the high temperature regime (≳10,000 K). This model is implemented to study a one-dimensional nonequilibrium inviscid N(2) flow behind a plane shock by considering a state-to-state approach. While the effects of ionization and chemical reactions are neglected in our study, our results show that multiquantum transitions have a great influence on the relaxation of the macroscopic parameters of the gas flow behind the shock, especially on vibrational distributions of high levels. All vibrational states are influenced by multiquantum processes, but the effective number of transitions decreases inversely according to the vibrational quantum number. For the initial conditions considered in this study, excited electronic states are found to be weakly populated and can be neglected in modeling. Moreover, the computing time is considerably reduced with the model described in this paper compared to others found in the literature.

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Section: Approximate Fho Modelmentioning

confidence: 99%