[en] In this report, our research is described through abstracts of journal articles, technical reports, and presentations organized into sections following the five major operating units in the division: Mathematical Sciences, Intelligent Systems, Nuclear Data and Measurement Analysis, Nuclear Analysis and Shielding, and the Engineering Physics Information Centers. Each section begins with an introduction highlighting honors, awards, and significant research accomplishments in that unit during the reporting period

[en] The possibility of Josephson tunneling between superconducting small particles is examined. The Josephson coupling between the particles, which results from tunneling of Cooper pairs, is inserted into a modified Ginzburg-Landau free energy. The local electronic properties, the effective gap Δ and the order parameter relaxation rate GAMMA, are calculated in the Hartree approximation of this coupling free energy. A general expression, valid for any number N of particles coupled in a closed chain, was derived for the effective gap. A method for deriving the spectrum of the order parameter correlation function for any N was developed and analytical expressions were obtained up to N = 8. The order parameter relaxation rate was determined as the halfwidth at half maximum of this spectrum

[en] The Josephson coupling between the particles, which results from tunneling of Cooper pairs, is inserted into a modified Ginzburg-Landau free energy. The local electronic properties, the effective gap δ and the order parameter relaxation rate Gamma, are calculated in the Hartree approximation of this coupling free energy. A general expression, valid for any number N of particles coupled in a closed chain, was derived for the effective gap. A method for deriving the spectrum of the order parameter correlation function for any N was developed and analytical expressions were obtained up to N = 8. The order parameter relaxation rate was determined as the halfwidth at half maximum of this spectrum. Extensive results for δ and Gamma were calculated for N = 8 coupled particles and the results were compared to the results for isolated particles. The overall effect of coupling was to increase the effective volume of the particles. This was most apparent for the smallest size particles. After demonstrating that the expresion for the nuclear spin lattice relaxation time T¹ for superconducting small particles in an applied magnetic field should not depend explicitly on the pair breaking energy, we calculated the nuclear spin lattice relaxation time using the results for δ and Gamma obtained for eight coupled particles. The significant result is that the effect of coupling and magnetic field nearly removes the size dependence of T¹ below T_c

[en] Methods are presented for computing eigenpairs of the quadratic lambda-matrix, M lambda² + C lambda + K, where M, C, and K are large and sparse, and have special symmetry-type properties. These properties are sufficient to insure that all the eigenvalues are real and that theory analogous to the standard symmetric eigenproblem exists. The methods employ some standard techniques such as partial tri-diagonalization via the Lanczos Method and subsequent eigenpair calculation, shift-and- invert strategy and subspace iteration. The methods also employ some new techniques such as Rayleigh-Ritz quadratic roots and the inertia of symmetric, definite, quadratic lambda-matrices

[en] An algorithm is given for computing the eigenvalues and (optionally) the eigenvectors of either a skew-symmetric matrix or a symmetric tridiagonal matrix with constant diagonal. The algorithm uses only orthogonal similarity transformations, and is believed to be the most efficient algorithm available for computing all the eigenvalues or the complete eigensystem. 2 tables

[en] The RBD (Radiological Bioassay and Dosimetry) software package was developed for the U. S. Army Material Command, Arlington, Virginia, to demonstrate compliance with the radiation protection guidance 10 CFR Part 20 (ref. 1). Designed to be run interactively on an IBM-compatible personal computer, RBD consists of a data base module to manage bioassay data and a computational module that incorporates algorithms for estimating radionuclide intake from either acute or chronic exposures based on measurement of the worker's rate of excretion of the radionuclide or the retained activity in the body. In estimating the intake,RBD uses a separate file for each radionuclide containing parametric representations of the retention and excretion functions. These files also contain dose-per-unit-intake coefficients used to compute the committed dose equivalent. For a given nuclide, if measurements exist for more than one type of assay, an auxiliary module, REPORT, estimates the intake by applying weights assigned in the nuclide file for each assay. Bioassay data and computed results (estimates of intake and committed dose equivalent) are stored in separate data bases, and the bioassay measurements used to compute a given result can be identified. The REPORT module creates a file containing committed effective dose equivalent for each individual that can be combined with the individual's external exposure

[en] A time-of-flight neutron reflectometer constructed for surface and interfacial studies, and installed at the ISIS pulsed neutron source, is described. One of its important design features is its inclined incident beam, since this allows both liquid and solid surface phenomena to be investigated. Measurements are presented to show the performance of the instrument, and new representative results, which include studies of liquid surfaces, Langmuir-Blodgett films, and thin film multilayers, are included as illustrations of the scientific potential of the method. (author)

[en] A prototype two-dimensional Diffusion Synthetic Acceleration (DSA) method on a Block-based Adaptive Mesh Refinement (BAMR) transport mesh has been developed. The Block-Adaptive Mesh Refinement Diffusion Synthetic Acceleration (BAMR-DSA) method was tested in the PARallel TIme-Dependent SN (PARTISN) deterministic transport code. The BAMR-DSA equations are derived by differencing the DSA equation using a vertex-centered diffusion discretization that is diamond-like and may be characterized as 'partially' consistent. The derivation of a diffusion discretization that is fully consistent with diamond transport differencing on BAMR mesh does not appear to be possible. However, despite being partially consistent, the BAMR-DSA method is effective for many applications. The BAMR-DSA solver was implemented and tested in two dimensions for rectangular (XY) and cylindrical (RZ) geometries. Testing results confirm that a partially consistent BAMR-DSA method will introduce instabilities for extreme cases, e.g., scattering ratios approaching 1.0 with optically thick cells, but for most realistic problems the BAMR-DSA method provides effective acceleration. The initial use of a full matrix to store and LU-Decomposition to solve the BAMR-DSA equations has been extended to include Compressed Sparse Row (CSR) storage and a Conjugate Gradient (CG) solver. The CSR and CG methods provide significantly more efficient and faster storage and solution methods.

[en] An algorithm is presented for balancing the A and B matrices prior to computing the eigensystem of the generalized eigenvalue problem Ax = lambda Bx. The three-step algorithm is specifically designed to precede the QZ-type algorithms, but improved performance is expected from most eigensystem solvers. Permutations and two-sided diagonal transformations are applied to A and B to produce matrices with certain desirable properties. Test cases are presented to illustrate the improved accuracy of the computed eigenvalues

[en] A polarised neutron reflectometer for studying surface magnetism is described. Its application to problems in surface magnetism is discussed, and its potential is illustrated by some recent results on the magnetisation of thin nickel and cobalt films. (author)