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Thermodynamic Sandbox

Here you can find script(s) dealing with thermodynamic-related problems

Gradient-Based minimizers

  • Julia scripts used in Riel et al.,( submitted) to use nullspace optimization approach to minimize individual solution phase model.

unconstrained_CG_BFGS/nullMin.jl

  • Tests the unconstrainted solution phase formulation using the CG and BFGS methods
  • The scripts include spinel, clinopyroxene and amphibole as formulated in Holland et al., 2018.
  • Gibbs hyperplanes for each phase have been computed using MAGEMin and the igneous database at the following conditions:
1. 12 kbar and 1100 °C for spinel
2. 3.26 kbar and 906.25 °C for the spinel solvus test
3. 12 kbar and 1100 °C for clinopyroxene
4. 5 kbar and 650 °C for amphibole

inequality_constrained_CCSAQ_SLSQP/NLopt_call_using_MAGEMin.jl

  • Tests the inequality constrained formulation of the solution phase by calling NLopt through MAGEMin and using the CCSAQ and SLSQP methods
  • The scripts include spinel, clinopyroxene and amphibole as formulated in Holland et al., 2018.
  • Gibbs hyperplanes for each phase have been computed using MAGEMin and the igneous database at the following conditions:
1. 12 kbar and 1100 °C for spinel
2. 3.26 kbar and 906.25 °C for the spinel solvus test
3. 12 kbar and 1100 °C for clinopyroxene
4. 5 kbar and 650 °C for amphibole

drawing

To fully reproduce the results, clone or download this repository and launch Julia in project mode julia --project from the folder GradientBasedMinimizers and instantiate or resolve the dependencies from within the REPL in package mode julia> ].

The scripts can be launched either from the REPL:

julia> include("GradientBasedMinimizers/NLopt_call_using_MAGEMin.jl")

or executed from the shell as:

julia --project GradientBasedMinimizers/NLopt_call_using_MAGEMin.jl

By default, the phase is spinel. To change it to amphibole or clinopyroxene, modify the ph variable in the scripts.

Gibbs free energy minimization

PhaseEquilibriumMinimizer/MAGEMin_PGE_and_LP.m

  • MATLAB script used in Riel et al., (2022) [Geochemistry, Geophysics, Geosystems, 23, 7] to present a simplified application of MAGEMin minimization approach (including feldspar, quartz and sillimanite) and compare it with linear programming.
  • The minimization is conducted in the NCKAS chemical system at 0.3 GPa and 873.15 K.
  • The Plagioclase model is taken after Holland et al., 2021
  • The Linear programming approach described in de Capitani & Brown (1987)

drawing