A Variational Procedure for Time-Dependent Processes

A simple variational Lagrangian is proposed for the time development of an arbitrary density matrix, employing the "factorization" of the density. Only the "kinetic energy" appears in the Lagrangian. The formalism applies to pure and mixed state cases, the Navier-Stokes equations of hydrodynamics, transport theory, etc. It recaptures the Least Dissipation Function condition of Rayleigh-Onsager {\bf and in practical applications is flexible}. The variational proposal is tested on a two level system interacting that is subject, in one instance, to an interaction with a single oscillator and, in another, that evolves in a dissipative mode.Comment: 25 pages, 4 figure

Hanford Site Vadose Zone Studies: An Overview

Large quantities of radioactive and chemical wastes resulting from Pu production for nuclear weapons are located in the vadose zone at the USDOE’s Hanford Site, north of Richland, WA. The vadose zone here is characterized by often highly stratified glacial-fluvial sediments that give rise to complex subsurface-flow paths that contribute to uncertainty of contaminant fate and transport. Research efforts have focused on answering questions of contaminant transport from the viewpoint of geologic, biologic, geochemical, and hydrologic controls. This special section highlights key research topics concerning vadose zone problems at the Hanford Site. Research indicates that some of the contaminant species (137Cs, 60Co, 90Sr) are retained by Hanford sediments as a result of geochemical reactions, rendering them effectively immobile except under extremely saline or acidic conditions, while other species (99Tc, 129I, 3H) are typically mobile and have moved deep into the vadose zone and subsequently into groundwater. In addition, large quantities of organics, including carbon tetrachloride, have moved in complex ways as both vapor and liquid in the subsurface. Observed transport of mobile species is linked to liquid discharges and to elevated recharge rates that occur primarily at waste sites where land surfaces are void of vegetation and where winter rains have subsequently penetrated the subsurface wastes. A series of papers in this issue documents progress to date in understanding transport rates at Hanford, why anisotropy strongly affects the distribution of subsurface contaminants, why organic contaminants are difficult to find in the deep vadose zone, and what the impacts of hypersaline fluids are on waste form degradation and subsequent transport