modelDoubleFDIntegrals

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Extends from Modelica.Icons.Example (Icon for runnable examples).

Information

Evaluation of double Fermi-Dirac integrals. e.g., ... 

∫_-∞^y F_-1/2(x) F_-1/2(x) dx 

or more generally ... 

[Γ(m)]^-1 ∫_-∞^y (y-x)^m-1 F_j(x) F_k(x) dx = G_m,jk(y)  , where m>0. 

Such integrals arise in calculations of pairwise fermion interactions in condensed matter systems, e.g., when calculating the electron EM exchange energy (see, e.g., the 'specfunc.ElectronDegPres' example and § 80 in Landau and Lifshitz, Statistical Physics Part 1 (3rd edition), 1980).

The values of y and m can be adjusted via the integrand parameters during model runtime. The values of j and k, however, must be chosen before creating (compiling) the integrand (see 'DoubleFDIntegrand').

Note that here -y_max is chosen instead of -∞ since for most such integrals, very little contribution arises from the x<<-1 region.

For values of m<1, care must be taken with the choice of integration routine as a singularity at x=y will appear in the integrand.