The LTE Saha–Boltzman plasma ionization balance model and the Braginskii plasma electric resistance model are compared with the results by the suit of codes based on the average atom model, which is a quantum-mechanical version of the Temperature Dependent Thomas–Fermi Theory. The analysis is focused on low-Z Al, mid-Z Cu and higher-Z Mo plasmas in a broad ranges of electron temperature Te and ...

We place the Thomas-Fermi model of the quantum theory of atoms, molecules, and solids on a firm mathematical footing. Our results include: (1) A proof of existence and uniqueness of solutions of the nonlinear Thomas-Fermi equations as well as the fact that these solutions minimize the Thomas-Fermi energy functional, (2) a proof that in a suitable large nuclear charge limit, the quantum mechanic...

We study the strong segregation limit for mixtures of Bose-Einstein condensates modelled by a Gross-Pitaievskii functional. Our first main result is that in presence of a trapping potential, for different intracomponent strengths, the Thomas-Fermi limit is sufficient to determine the shape of the minimizers. Our second main result is that for asymptotically equal intracomponent strengths, one n...

A Thomas-Fermi model of a spherical shell of positive charge is investigated, under various boundary conditions. The electron distribution and the ionization charge are given particular attention.

In the non relativistic case, some emphasis has been placed on the question of an appropriate choice of the coefficient λ of the gradient term connected to the kinetic energy. The non relativistic gradient correction λ(∇ρ)2/ρ was initially derived by Weizsäcker [14] with a value λ = 1, whereas the systematic gradient expansion by Kirznits [7, 6] leads to λ = 1/9. In the derivation of Tomishima ...

We consider almost-complex structures on P whose total Chern classes differ from that of the standard (integrable) almost-complex structure. E. Thomas established the existence of many such structures. We show that if there exists an “exotic” integrable almost-complex structures, then the resulting complex manifold would have specific Hodge numbers which do not vanish. We also give a necessary ...

Nuclei interacting with electrons in dense plasmas acquire electronic bound states, modify continuum states, generate resonances and hopping electron states, and generate short-range ionic order. The mean ionization state (MIS), i.e, the mean charge Z of an average ion in such plasmas, is a valuable concept: Pseudopotentials, pair-distribution functions, equations of state, transport properties...