A numerical solution of the coupled heat and mass transfer problem of non-planar solidification and melting of aqueous solutions

During freezing of aqueous solutions containing solutes like sodium chloride or glycerol, pure ice is the first solid phase to form. A numerical model is presented for the case of non-planar (dendritic) freezing, where local thermodynamic equilibrium can be assumed in the whole mushy region, allowing a one-dimensional treatment of the coupled heat and mass transfer in this region. Solute diffusion along the resulting interdendritic concentration gradient in the direction of freezing is taken into account by the model. With regard to the non-linear character of the matching condition between temperature and concentration an iterative method based on the Newton-algorithm was used to solve the system of the common non-linear heat and mass transfer equations, which were derived from the partial differential equations by a finite difference scheme. Varying the geometric and thermodynamic boundary conditions, a parameter study was performed for obtaining more information on heat transfer during thawing of regular-shaped samples (plate, cylinder, sphere). In particular, the warming rate distributions in containers filled with aqueous solution were determined, which are interesting parameters in the field of cryopreservation of biological material.Beim Gefrieren von wäßrigen Lösungen, die Substanzen wie Kochsalz oder Glyzerin enthalten, bildet sich als erste feste Phase reines Eis. Im Falle nichtplanarer (dendritischer) Erstarrung kann innerhalb der gesamten mushy region lokales thermodynamisches Gleichgewicht angenommen werden, wodurch eine eindimensionale Behandlung des gekoppelten Wärme- und Stofftransports in dieser Zone möglich wird. Dabei wird die Diffusion gelöster Stoffe entlang des resultierenden Konzentrationsgefälles im interdendritischen Zwischenraum berücksichtigt. Angeischts der nichtlinearen Anpassungsbedingung zwischen Temperatur und Konzentration wurde ein auf einem Newton-Algorithmus basierendes iteratives Verfahren verwendet, um die gewöhnlichen, nichtlinearen Wärme- und Stofftransportgleichungen zu lösen, die aus den partiellen Differentialgleichungen durch ein Finite-Differenzen-Verfahren gewonnen wurden. Unter Variation der geometrischen und thermodynamischen Randbedingungen wurde eine Parameterstudie mit dem Ziel durchgeführt, genaueren Einblick in das Auftauverhalten von Proben einfacher Geometrien (Platte, Zylinder, Kugel) zu gewinnen. Insbesondere wurden die Erwärmungsraten-Verteilungen in mit wäßriger Lösung geführten Containern bestimmt, die im Zusammenhang mit der Kryokonservierung biologischen Materials von Bedeutung sind.     

Free material optimization via mathematical programming

This paper deals with a central question of structural optimization which is formulated as the problem of finding the stiffest structure which can be made when both the distribution of material as well as the material itself can be freely varied. We consider a general multi-load formulation and include the possibility of unilateral contact. The emphasis of the presentation is on numerical procedures for this type of problem, and we show that the problems after discretization can be rewritten as mathematical programming problems of special form. We propose iterative optimization algorithms based on penalty-barrier methods and interior-point methods and show a broad range of numerical examples that demonstrates the efficiency of our approach. Supported by the project 03ZO7BAY of BMBF (Germany) and the GIF-contract 10455-214.06/95.     

über die Streuung relativistischer Elektronen im Coulombfeld

An approximative method for summing the partial wave series for the scattering amplitude of the relativistic scattering of electrons by an atomic nucleus is investigated in the simplest case of a point charge nucleus for electron energies not less 10 MeV. In the course of the computationΒ=1 is assumed (Β=v/c,v andc denote the velocity of the electron and of light, respectively). The Sommerfeld-Watson-transformation is the starting point. The method consists in setting up an asymptotic expansion in 1/sin² (θ/2) (θ is the scattering angle) of the amount coming from the Regge-poles. Two further amounts, the dependence of which on the scattering angle especially for easy nuclei is little, are computed numerically without simplification, which should be possible. The method is developed from a special way of summing the partial wave series for the non-relativistic Rutherford scattering, which may be done analytically.Mott's scattering formula is verified and finally the applicability of the method is examined for summing the relativistic partial wave series with the exact S-Matrix. The results are as exact as the expension of the cross section to order (Z/137)⁵ (Z is the nuclear charge). The method should in principle be applicable for an extended nucleus, but in this case there remain still several problems.     

Through-bond 13C-13C correlation at the natural abundance level: refining dynamic regions in the crystal structure of vitamin-D3 with solid-state NMR

Recently, we presented a novel nuclear magnetic resonance experiment for establishing through-bond connectivity in disordered solids using scalar coupling-driven correlation. This method, a variant of the popular double-quantum-filtered correlation spectroscopy experiment in liquids, is robust under fast magic-angle-spinning conditions and in the presence of dynamics. Here, we show that this new experiment, the UC2QF COSY, can be extended to 13C natural abundance correlation in moderately sized molecules, allowing the assignment of the 54 peaks of the solid-state NMR spectrum of microcrystalline vitamin-D3. In this case, comparison between the assigned peaks and ab initio calculations of the chemical shifts based on the crystal coordinates permits a refinement of the average structure in dynamic regions reported as disordered in the crystal structure.