Annual report of the Argonne National Laboratory Radiological and Environmental Research Division regarding activities related to ecology and funding issues during the year.

Aging of simulated nuclear waste glass by contact with a controlled-temperature, humid atmosphere results in the formation of a double hydration layer penetrating the glass, as well as the formation of minerals on the glass surface. The hydration process can be described by Arrhenius behavior between 120 and 240 C. Results suggest that simulated aging reactions are necessary for demonstrating that nuclear waste forms can meet projected Nuclear Regulatory Commission regulations.

In many nonlinear problems it is necessary to estimate the Jacobian matrix of a nonlinear mapping F. In large scale problems the Jacobian of F is usually sparse, and then estimation by differences is attractive because the number of differences can be small compared to the dimension of the problem. For example, if the Jacobian matrix is banded then the number of differences needed to estimate the Jacobian matrix is, at most, the width of the band. In this paper we describe a set of subroutines whose purpose is to estimate the Jacobian matrix of a mapping F with the least possible number of function evaluations.

A programming methodology based on schema transformations is presented. Such an approach is a logical outcome of recent developments in program manipulating systems. Concurrent development of algorithms and their proofs of correctness is a significant feature of the proposed methodology. As the development process begins with an abstract schema, it is often possible to derive several related end algorithms in a single development process. This has implications in both the economics of software development and the understanding and teaching of algorithms. The initial schematic specification (a skeleton algorithm schema), the intermediate and final algorithm schemata are all expressed in Darlington's first-order recursion equation language exploiting set-theoretic constructs. A set of transformation rules together with a set of reduction rules for set expressions is then used to successively transform the schematic specification into different algorithm schemata. Most of the transformations are applications of a small number of common rewriting rules.