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As an independent validation, we compare our IGRF-12 candidate secular variation model with a global set of geomagnetic observatory data.
We applied a site-to-site variation model with two independent gamma distributions and the MG94 model, and tested for relevant internal branches in the tree.
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In the standard DNA setup, the GTR model was used with all model parameters estimated from the data, with among site rate variation modelled with gamma distributed rates across sites with four discrete rate categories.
Phylogenetic trees were constructed in PROML (PHYLIP 3.6) [ 61] using maximum likelihood, JTT amino acid substitution matrix, five global rearrangements with randomized sequence input order and among-site rate variation modeled with an eight rate category discrete approximation to a gamma distribution.
It is instructive to first investigate how the predictive EIGRF secular variation model compares with the secular variation of POMME5-post05 between 2005 and 2009.
The obtained secular variation model is compared with models based on CHAMP satellite data.
The corresponding physics model is the random sweeping model in the wavenumber frequency domain (Kraichnan 1964; Narita 2017; Wilczek and Narita 2012) and the random spatial variation model (Gaussian statistics) with an elliptic sense of wavevector anisotropy (Carbone et al. 1995) for power-law spectrum of elliptic wavevector anisotropy.
In comparison between the adaptive behavior models with and without individual variation, the model with individual variation tends to stabilize non-equilibrium dynamics.
The likelihood of the models was improved significantly by incorporating a Γ-distribution in rate variation models compared with relevant constant rate models (χ2 = 2ΔLn L ≫ 3.84 with d.f. = 1, see Table 1).
Open image in new window Fig. 3 Variation of model with parameters.
Secondly, these thermal variation models are associated with heat-fluid-solid coupling FE (finite element) simulation technique, to model spindle linear thermal errors on radial/axial directions and angular thermal errors by the analytical simulation method.
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