Application of the Hartree-Fock method in nuclear theory

A review of the Hartree-Fock (HF) self-consistent method is presented as used in nuclear theory. After deriving the fundamental HF equations the two-particle potentials for HF calculations are shown and the particular HF methods described. Furthermore the results of some papers on HF methods are reproduced and discussed.     

Berechnung des Potentials und elektrischen Feldes einer diskreten elektrischen Doppelschicht nach der Ewaldschen Methode

Ohne Zusammenfassung     

A note on quasi-equilibrium problems

The purpose of this paper is to prove the existence of solutions of quasi-equilibrium problems without any generalized monotonicity assumption. Additionally, we give some applications.     

Landau Free Energy Expansion for Chiral Ferroelectric Smectic Liquid Crystals

The biquadratic coupling between the tilt and polarization is added to the usual bilinear coupling in the Landau free energy density expansion describing the SmA - SmC* transition. The effect on the temperature dependence of the tilt, spontaneous polarization and the pitch of the helix is studied. The results agree qualitatively with measured data.     

On the dimension of the attractor for a perturbed 3d Ladyzhenskaya model

We consider the so-called Ladyzhenskaya model of incompressible fluid, with an additional artificial smoothing term ?Δ³. We establish the global existence, uniqueness, and regularity of solutions. Finally, we show that there exists an exponential attractor, whose dimension we estimate in terms of the relevant physical quantities, independently of ? > 0.     

A hybrid global optimization algorithm for non-linear least squares regression

A hybrid global optimization algorithm is proposed aimed at the class of objective functions with properties typical of the problems of non-linear least squares regression. Three components of hybridization are considered: simplicial partition of the feasible region, indicating and excluding vicinities of the main local minimizers from global search, and computing the indicated local minima by means of an efficient local descent algorithm. The performance of the algorithm is tested using a collection of non-linear least squares problems evaluated by other authors as difficult global optimization problems.     

Fe and Co selective substitution in Ni2MnGa: Effect of magnetism on relative phase stability

We studied the effect of selective substitution in Fe and Co 3d elements on the structural and magnetic phase transitions in the prototypical magnetic shape memory alloy Ni–Mn–Ga. We determined the phase diagram for each elemental doping substitution by means of calorimetry and ac susceptibility measurements. An effort was made to substitute each constituent element by the same amounts of doping and to study the role of parameters other than electronic concentration in controlling phase stability. Specifically, selective doping with atoms of similar atomic radii but different magnetic properties allowed us to investigate the role of magnetic interactions on the relative phase stability of the ternary compound. We determined the entropy change associated with the martensitic transition for each quaternary alloy to obtain further information on the effect of magnetism on the relative stability of the involved phases exhibited by these compounds.