Kinetische Herleitung verallgemeinerter NERNST-PLANCK-Gleichungen. I

The aim of this paper is the derivation of equations of motion for ions in a membrane system. The startingpoint is not the BBGKY-hierarchy, but equations for the densities and correlation-functions in the sense of Boltzmann. The advantage of this method is the fact, that the interaction splits automatically into terms describing short range and long range forces. With the help of the short range parts in the following paper friction terms can be derived, which directly lead to Onsager coefficients.     

Kinetische Herleitung verallgemeinerter NERNST-PLANCK-Gleichungen. II.

The equations of motion derived in part I contain three terms, which don't allow the immediate application of these equations: The pressure tensors, the collective force in the equation of the pair distributions, and the term containing the short range interaction. The latter can be transformed, with the help of an assumption concerning the macroscopic state of the system, into the first moments of Boltzmann collision operators. These operators and the pressure tensors are evaluated in the hydrodynamic approximation. From the assumption concerning the macroscopic state it follows that the three particle densities are functionals of the pair distributions. Thus one has a closed system of equations for the densities, the pairdensities, the mean velocities and the correlation velocities.     

Kinetische Herleitung verallgemeinerter NERNST-PLANCK-Gleichungen. III. Eindimensionales Membranmodell

In this part onedimensional models of membranesystems are treated, i.e. such membranes, which are unbounded in two dimensions y, z. The equations of motion for such systems can be derived using the results of part I or of part II. The equation of motion containing the one particle densities can be written in the form of an Onsager relation, the coefficients L_αβ of which are symmetric. The dependence of L_αβ on the densities is calculated. The approximation used up to now in the literature is seen to be the lowest order one. Global balancy equations yield the boundary conditions on surfaces of discontinuities. It is shown that the usually used formula for the Donnan equilibrium is only formally correct.     

Kinetische Herleitung korrelierter Plasmagleichungen. I

Kinetic Derivation of Correlated Plasma-Equations. I. The contribution of this paper is to point out a derivation of plasma-equations of motion and energy in an electromagnetic field by the Boltzmann method. The advantage of this method is the fact, that the interaction-terms split into parts describing long range and short range interactions. The latter lead us to friction terms. The system of equations can be closed with a superposition-ansatz for three-particle-correlations.     

Kinetische Herleitung korrelierter Plasmagleichungen II

Kinetic Derivation of Correlated Plasma-Equations. II Because of the short range of the correlations, the one-particle-functions can be estimated as constant over the range of the correlations, but not in the whole system. Thus we can calculate the correlation-functions and correlation-integrals in the one-particle-equations derived in part I in terms of one-particle-functions.     

Trilocal structures. IV. momentum-dependent tree functions

Enlarging the set of tree functions to include those which depend on the momentum vector has the effect of introducing new families and subfamilies of functions. Four auxiliary conditions are used in the generation of these functions. These auxiliary conditions introduce, as eigenvalues, four parameters in terms of which the coefficients of the momentum-dependent functions can then be expressed as linear combinations of the 16 leading coefficients. These 16 are all rest-system coefficients. Thus the momentum-dependent part of the expansion is expressible in terms of the rest-system portion, using only these four parameters.     

Short-range correlations with pseudopotentials. IV

Using a unitary model operator, the short-range correlations between nucleons in nuclei have been considered. To achieve healing in the wave functions, short-range pseudopotentials are required to be added to the nucleon-nucleon potential. With the introduction of the pseudopotentials, the matrix element for the effective interaction in nuclei is developed with correlated basis wave functions. The tensor forces and the short-range pseudopotentials are renormalized in second-order perturbation theory. Hartree-Fock calculations are carried out for the two finite closed-shell spherical nuclei¹⁶O and⁴⁰Ca. The calculations of the resulting effective Hamiltonian are carried out with an effective interaction derived from the Tabakin potential. The present calculations of the binding energies per particle for the¹⁶O and⁴⁰Ca nuclei are in agreement with the experimental measurements.