This report reviews the research activities of the Applied Mathematical Sciences Section for the period April 1, 1980, through March 31, 1981. The body of the report discusses various projects carried out in three major areas of research: applied analysis, computational mathematics, and software engineering. Information on section staff, visitors, workshops, and seminars is found in the appendices.

Report of various projects carried out in applied analysis, computational mathematics, software engineering, and advanced scientific computing.

Annual report of Argonne National Laboratory project ANO115A. This report discusses research to compare migration of radionuclides in scale models versus the Pu-Am disposal areas at Los Alamos Laboratory.

The abstracts are given of thirteen papers presented at a ''SQUID Symposium'' organized by the Division of Materials Sciences of the U.S. Department of Energy and held March 23-25, 1978, at the University of Virginia. Since SQUID systems have already been utilized in feasibility demonstration in geothermal reservoir exploration, it was recognized that these devices also hold great potential for many other important scientific measurements. Many of these are energy-related, and others include forefront investigations in a diverse group of scientific areas, from biomedical to earthquake monitoring. Research in SQUIDs has advanced so rapidly in recent years that it was felt that a symposium to review the current status and future prospects of the devices would be timely. The abstracts given present an overview of work in this area and hopefully provide an opportunity to increase awareness among basic and applied scientists of the inherent implications of the extreme measurement sensitivity in advanced SQUID systems.

The research program in nuclear physics in the Physics Division spans a broad range of activities and contributes to many of the major questions in the discipline. Activities may be roughly divided into three broad categories. Research with the tandem-linac in heavy-ion physics is doing well, though laboring under severe budgetary constraints, and outside use of the facility has increased substantially. Progress on the construction of the full ATLAS facility is coming along expeditiously and it is expected to be completed on schedule in 1985. In medium-energy physics, activities are continuing at LAMPF, as well as other accelerators, though considerable effort was devoted this year to the preparation of a proposal for a national electron accelerator facility.

Report of the activities of the physics division at Argonne including the successful completion of Argonne Tandem-Linac Accelerator System.

Report on various studies in the physics division of Argonne National Laboratory, including medium-energy physics research, superconducting LINAC accelerator, and theoretical nuclear physics.

Separate abstracts were prepared for the ten summaries, dealing with various energy and nuclear topics.

Report of various activities in Argonne National Laboratory Physics Division including medium-energy physics research, research at ATLAS, theoretical nuclear physics, superconducting LINAC development, and accelerator operations.

Report of activities of the Argonne Physics Division, including medium-energy physics research, ATLAS research, theoretical nuclear physics, superconducting LINAC development, and accelerator operations.

Annual report of activities of the Argonne National Laboratory Physics Division, including research at ATLAS, medium-energy nuclear physics and weak interactions, theoretical nuclear physics, and atomic and molecular physics research.

Annual report of activities of the Argonne National Laboratory Physics Division, including research at ATLAS, medium-energy nuclear physics, theoretical nuclear physics, and atomic and molecular physics.

Annual report of activities of the Argonne National Laboratory Physics Division, including ATLAS research, medium-energy nuclear physics and weak interactions, theoretical nuclear physics, and atomic and various molecular physics research.

Annual report of activities of the Argonne National Laboratory Physics Division, including research at ATLAS, medium-energy nuclear physics and weak interactions, theoretical nuclear physics, and atomic and nuclear physics research.

Annual report of the Argonne National Laboratory Radiological and Environmental Research Division regarding activities related to ecology. This report includes studies on the effects of sulfur dioxide on Midwestern grain crops and the addition of the new research vessel, the Ekos.

Report on activities of the Division of Biological and Medical Research in carcinogenesis, low level radiation, molecular biology, and toxicology.

Computer graphic representation of the antigen-binding sites of two Bence-Jones proteins (antibody light chain diners), Loc (left) and Mcg (right). The spheres represent individual amino acids. Each binding site is composed of two variable domains and each domain consists of framework segments and the hyper-variable segments which confer the specificity to the antibody molecule.

Report on research in carcinogenesis, human radiobiology, low-level radiation, molecular biology, and toxicology.

DISPL1 is a software package for solving some second order nonlinear systems of partial differential equations including parabolic, elliptic, hyperbolic, and some mixed types such as parabolic-elliptic equations. Fairly general nonlinear boundary conditions are allowed as well as interface conditions for problems in an inhomogeneous media. The spatial domain is one or two dimensional with Cartesian, cylindrical, or spherical (in one dimension only) geometry. The numerical method is based on the use of Galerkin's procedure combined with the use of B-splines in order to reduce the system of PDE's to a system of ODE's. The latter system is then solved with a sophisticated ODE software package. Software features include extensive dump/restart facilities, free format input, moderate printed output capability, dynamic storage allocation, and three graphics packages.

This sixth symposium covers process control processes and issues involved in the conversion of fossil fuels into synthetic fuels.