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Nuclear Reaction Networks

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Contact: F.X.Timmes
my one page vitae,
full vitae,
research statement, and
teaching statement.
Integration of Nuclear Reaction Networks for Stellar Hydrodynamics
In this paper, methods for solving the stiff system of ordinary differential equations that constitute nuclear reaction networks are surveyed. Three semi-implicit time integration algorithms are examined; a traditional first-order-accurate Euler method, a fourth-order-accurate Kaps-Rentrop method, and a variable-order Bader-Deuflhard method. These three integration methods are coupled to eight different linear algebra packages. Four of the linear algebra packages operate on dense matrices (LAPACK, LUDCMP, LEQS, GIFT), three of them are designed for the direct solution of sparse matrices (MA28, UMFPACK, Y12M), and one uses an iterative method for sparse matrices (BiCG). The scaling properties and behavior of the 24 combinations (3 time integration methods times 8 linear algebra packages) are analyzed by running each combination on seven different nuclear reaction networks.

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13 isotope jacobian
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Kaps-Rentrop CPU time
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Bader-Deuflard CPU time


An Inexpensive Nuclear Energy Generation Network for Stellar Hydrodynamics
In this paper, we compare the nuclear energy generation rate and abundance levels given by an α-chain nuclear reaction network that contains only7 isotopes with a standard 13 isotope α-chain reaction network. The energy generation rate of these two small networks are also compared to the energy generation rate given by a 489 isotope reaction network with weak reactions turned on and off. The comparison between the seven isotope and α-chain reaction networks indicate the extent to which one can be replaced by the other, and the comparison with the 489 isotope reaction network roughly indicates under what physical conditions it is safe to use the seven isotope and α-chain reaction networks.

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Energy generation rate comparision
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Ratio of energy generation rates
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Isotope evolution

Nuclear Reaction Network Codes

Open source codes are avaliable from this link.