https://doi.org/10.1140/epjp/s13360-021-01542-5
Regular Article
Modeling electrical resistivity and particle fluxes with multiply broken power-law distributions
, Sechsschimmelgasse 1 / 21-22, A-1090, Vienna, Austria
Received:
15
March
2021
Accepted:
6
May
2021
Published online: 4 June 2021
Multiply broken power-law densities are introduced to model empirical data sets extending over several logarithmic decades. Two examples demonstrating the wide range of applicability of these distributions are discussed. First, the temperature dependence of the electrical resistivity of metals (Cu, Au, Cr, Al, W, Fe, Ni) is inferred by nonlinear least-squares regression covering the solid phase up to the melting point. The regressed broken power laws are compared with high- and low-temperature scaling predictions obtained from electron–phonon and electron–electron scattering. In the intermediate temperature range, inflection points arise in Log–Log plots of the electrical resistivity, unaccounted for by the Bloch–Grüneisen theory. In the second example, the energy evolution of cosmic-ray electron and positron fluxes is analyzed in terms of multiply broken and exponentially cut power-law densities, based on recently obtained number counts. Index functions quantifying the spectral variation and survival functions (complementary cumulative distributions) of the particle and energy fluxes are calculated from the regressed densities.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021
