Ueber die Aufnahme von Wasser durch das Nervengewebe

Ohne ZusammenfassungAus dem Englischen übersetzt von J. Matula (Wien).     

Calculation of densities of aqueous electrolyte solutions at subzero temperatures

We developed a FORTRAN program based on the Pitzer equations to calculate densities of electrolyte solutions at subzero temperatures. Data from the published literature collected at -28.9, -17.8, -12.2, -6.7, 0, and 25°C were used to calculate the Pitzer-equation parameters and to evaluate model performance. Three approaches to estimating the molar volume of the solute at infinite dilution were evaluated: (1) extrapolation of apparent molar volumes to zero square-root ionic strength; (2) calculation with the Tanger and Helgeson model; and (3) global fit of the data in which the molar volume of the solute at infinite dilution was estimated along with the Pitzer-equation parameters. The last approach gave parameter estimates that reproduced the experimental data most accurately. The parameterized model predicted accurately densities of single-electrolyte and multielectrolyte solutions at -28.9, -17.8, -12.2, -6.7, 0, and 25°C. Available experimental data are generally quite poor. Accordingly, Pitzer-equation parameters estimated for subzero temperatures should be viewed as conditional until improved measurements of single-electrolyte solution densities at subzero temperatures are made.     

An Introduction to the Adjoint Approach to Design

Optimal design methods involving the solution of an adjoint system of equations are an active area of research in computational fluid dynamics, particularly for aeronautical applications. This paper presents an introduction to the subject, emphasising the simplicity of the ideas when viewed in the context of linear algebra. Detailed discussions also include the extension to p.d.e.'s, the construction of the adjoint p.d.e. and its boundary conditions, and the physical significance of the adjoint solution. The paper concludes with examples of the use of adjoint methods for optimising the design of business jets. This revised version was published online in July 2006 with corrections to the Cover Date.     

Saddle point methods,and alogorithms,for non-symmetric linear equations ∗

This paper describes methods for solving non-singular, non-symmetric linear equations whose symmetric part is positive definite. First, the solutions are characterized as saddle points of a convex-concave function. The associated primal and dual variational principles provide quadratic, strictly convex, functions whose minima are the solutions of the original equation and which generalize the energy function for symmetric problems.

Direct iterative methods for finding the saddle point are then developed and analyzed. A globally convergent algorithm for finding the saddle points is described. We show that requiring conjugacy of successive search directions with respect to the symmetric part of the equation is a poor strategy.     

Boundary Integrals and Approximations of Harmonic Functions

Steklov expansions for a harmonic function on a rectangle are derived and studied with a view to determining an analog of the mean value theorem for harmonic functions. It is found that the value of a harmonic function at the center of a rectangle is well approximated by the mean value of the function on the boundary plus a very small number (often 3 or fewer) of specific further boundary integrals. These integrals are coefficients in the Steklov representation of the function. Similar approximations are found for the central values of solutions of Robin and Neumann boundary value problems. The results follow from analyses of the explicit expressions for the Steklov eigenvalues and eigenfunctions.