Necessary and sufficient conditions are given so that the Sobolev-type partial differential equations generate a contraction semigroup. It is shown that any nonlinear contraction from L/sup 1/(R) to itself that preserves the integral and commutes with translations satisfies maximum and minimum principles. This lemma is applied to the solution operator S/sub t/ to give necessary and sufficient conditions that S/t/ satisfy a maximum principle, despite the dispersive nature. Sufficient conditions are given so that the solutions converge, as nu and beta tend to zero, to the entropy solution of the conservation law. A larger class of monotone finite-difference schemes for the numerical solution of the conservation law motivated by finite-difference discretizations of the Sobolev equations, is introduced, and convergence results are proved for methods in this class. The methods analyzed include some that were previously used to approximate the solution of a linear waterflood problem in petroleum engineering.

An algorithm is proposed for the problem of minimizing a quadratic function subject to an ellipsoidal constraint which is guaranteed to produce a nearly optimal solution in a finite number of iterations. A robust and efficient algorithm for this problem is required to compute the step between iterates in trust region methods for optimization problems. We also consider the use of our algorithm in a trust region Newton's method. In particular, we prove that under reasonable assumptions the sequence (X/sub k/) generated by Newton's method has a limit point X* which satisfies the first and second order necessary conditions for a minimizer of the objective function f. Numerical results for GQTPAR, which is a Fortran implementation of our algorithm, show that GQTPAR is quite successful in a trust region method. In our tests a call to GQTPAR only required 1.6 iterations on the average.

On October 5, 1979, the Lithium Processing Test Loop (LPTL) developed a lithium leak in the electromagnetic (EM) pump channel, which damaged the pump, its surrounding support structure, and the underlying floor pan. A thorough analysis of the causes and consequences of the pump failure was conducted by personnel from CEN and several other ANL divisions. Metallurgical analyses of the elliptical pump channel and adjacent piping revealed that there was a significant buildup of iron-rich crystallites and other solid material in the region of the current-carrying bus bars (region of high magnetic field), which may have resulted in a flow restriction that contributed to the deterioration of the channel walls. The location of the failure was in a region of high residual stress (due to cold work produced during channel fabrication); this failure is typical of other cold work/stress-related failures encountered in components operated in forced-circulation lithium loops. Another important result was the isolation of crystals of a compound characterized as Li/sub x/CrN/sub y/. Compounds of this type are believed to be responsible for much of the Fe, Cr, and Ni mass transfer encountered in lithium loops constructed of stainless steel. The importance of nitrogen in the mass-transfer mechanism has …