Error bounds on block Gauss Seidel solutions of coupled\ud multiphysics problems

Mathematical models in many fields often consist of coupled sub–models, each of which describe a different physical process. For many applications, the quantity of interest from these models may be written as a linear functional of the solution to the governing equations. Mature numerical solution techniques for the individual sub–models often exist. Rather than derive a numerical solution technique for the full coupled model, it is therefore natural to investigate whether these techniques may be used by coupling in a block Gauss–Seidel fashion. In this study, we derive two a posteriori bounds for such linear functionals. These bounds may be used on each Gauss–Seidel iteration to estimate the error in the linear functional computed using the single physics solvers, without actually solving the full, coupled problem. We demonstrate the use of the bound first by using a model problem from linear algebra, and then a linear ordinary differential equation example. We then investigate the effectiveness of the bound using a non–linear coupled fluid–temperature problem. One of the bounds derived is very sharp for most linear functionals considered, allowing us to predict very accurately when to terminate our block Gauss–Seidel iteration.\ud \ud Copyright c 2000 John Wiley & Sons, Ltd

BNL Citric Acid Technology: Pilot Scale Demonstration

The objective of this project is to remove toxic metals such as lead and cadmium from incinerator ash using the Citric Acid Process developed at Brookhaven National Laboratory. In this process toxic metals in bottom ash from the incineration of municipal solid waste were first extracted with citric acid followed by biodegradation of the citric acid-metal extract by the bacterium Pseudomonas fluorescens for metals recovery. The ash contained the following metals: Al, As, Ba, Ca, Cd, Cr, Cu, Fe, Mg, Mn, Ni, Pb, Se, Sr, Ti, and Zn. Optimization of the Citric Acid Process parameters which included citric acid molarity, contact time, the impact of mixing aggressiveness during extraction and pretreatment showed lead and cadmium removal from incinerator ash of >90%. Seeding the treated ash with P. fluorescens resulted in the removal of residual citric acid and biostabilization of any leachable lead, thus allowing it to pass EPA?s Toxicity Characteristic Leaching Procedure. Biodegradation of the citric acid extract removed >99% of the lead from the extract as well as other metals such as Al, Ca, Cu, Fe, Mg, Mn, Ti, and Zn. Speciation of the bioprecipitated lead by Extended X-ray Absorption Fine Structure at the National Synchrotron Light Source showed that the lead is predominantly associated with the phosphate and carboxyl functional groups in a stable form. Citric acid was completely recovered (>99%) from the extract by sulfide precipitation technique and the extraction efficiency of recovered citric acid is similar to that of the fresh citric acid. Recycling of the citric acid should result in considerable savings in the overall treatment cost. We have shown the potential application of this technology to remove and recover the metal contaminants from incinerator ash as well as from other heavy metal bearing wastes (i.e., electric arc furnace dust from steel industry) or soils. Information developed from this project is being applied to demonstrate the remediation of lead paint contaminated soils on Long Island

Biogeochemical Cycling and Environmental Stability of Plutonium Relevant to Long-Term Stewardship of Doe Sites.

Pu is generally considered to be relatively immobile in the terrestrial environment, with the exception of transport via airborne and erosion mechanisms. More recently the transport of colloidal forms of Pu is being studied as a mobilization pathway from subsurface contaminated soils and sediments. The overall objective of this research is to understand the biogeochemical cycling of Pu in environments of interest to long-term DOE stewardship issues. Microbial processes are central to the immobilization of Pu species, through the metabolism of organically complexed Pu species and Pu associated with extracellular carrier phases and the creation of environments favorable for retardation of Pu transport

Growth of fat slits and dispersionless KP hierarchy

A "fat slit" is a compact domain in the upper half plane bounded by a curve with endpoints on the real axis and a segment of the real axis between them. We consider conformal maps of the upper half plane to the exterior of a fat slit parameterized by harmonic moments of the latter and show that they obey an infinite set of Lax equations for the dispersionless KP hierarchy. Deformation of a fat slit under changing a particular harmonic moment can be treated as a growth process similar to the Laplacian growth of domains in the whole plane. This construction extends the well known link between solutions to the dispersionless KP hierarchy and conformal maps of slit domains in the upper half plane and provides a new, large family of solutions.Comment: 26 pages, 6 figures, typos correcte

Uranium Reduction by Clostridia

The FRC groundwater and sediment contain significant concentrations of U and Tc and are dominated by low pH, and high nitrate and Al concentrations where dissimilatory metal reducing bacterial activity may be limited. The presence of Clostridia in Area 3 at the FRC site has been confirmed and their ability to reduce uranium under site conditions will be determined. Although the phenomenon of uranium reduction by Clostridia has been firmly established, the molecular mechanisms underlying such a reaction are not very clear. The authors are exploring the hypothesis that U(VI) reduction occurs through hydrogenases and other enzymes (Matin and Francis). Fundamental knowledge of metal reduction using Clostridia will allow us to exploit naturally occurring processes to attenuate radionuclide and metal contaminants in situ in the subsurface. The outline for this report are as follows: (1) Growth of Clostridium sp. under normal culture conditions; (2) Fate of metals and radionuclides in the presence of Clostridia; (3) Bioreduction of uranium associated with nitrate, citrate, and lepidocrocite; and (4) Utilization of Clostridium sp. for immobilization of uranium at the FRC Area 3 site

Laplacian Growth, Elliptic Growth, and Singularities of the Schwarz Potential

The Schwarz function has played an elegant role in understanding and in generating new examples of exact solutions to the Laplacian growth (or "Hele- Shaw") problem in the plane. The guiding principle in this connection is the fact that "non-physical" singularities in the "oil domain" of the Schwarz function are stationary, and the "physical" singularities obey simple dynamics. We give an elementary proof that the same holds in any number of dimensions for the Schwarz potential, introduced by D. Khavinson and H. S. Shapiro [17] (1989). A generalization is also given for the so-called "elliptic growth" problem by defining a generalized Schwarz potential. New exact solutions are constructed, and we solve inverse problems of describing the driving singularities of a given flow. We demonstrate, by example, how \mathbb{C}^n - techniques can be used to locate the singularity set of the Schwarz potential. One of our methods is to prolong available local extension theorems by constructing "globalizing families". We make three conjectures in potential theory relating to our investigation

BNL Citric Acid Technology: Pilot Scale Demonstration

The objective of this project is to remove toxic metals such as lead and cadmium from incinerator ash using the Citric Acid Process developed at Brookhaven National Laboratory. In this process toxic metals in bottom ash from the incineration of municipal solid waste were first extracted with citric acid followed by biodegradation of the citric acid-metal extract by the bacterium Pseudomonas fluorescens for metals recovery. The ash contained the following metals: Al, As, Ba, Ca, Cd, Cr, Cu, Fe, Mg, Mn, Ni, Pb, Se, Sr, Ti, and Zn. Optimization of the Citric Acid Process parameters which included citric acid molarity, contact time, the impact of mixing aggressiveness during extraction and pretreatment showed lead and cadmium removal from incinerator ash of >90%. Seeding the treated ash with P. fluorescens resulted in the removal of residual citric acid and biostabilization of any leachable lead, thus allowing it to pass EPA?s Toxicity Characteristic Leaching Procedure. Biodegradation of the citric acid extract removed >99% of the lead from the extract as well as other metals such as Al, Ca, Cu, Fe, Mg, Mn, Ti, and Zn. Speciation of the bioprecipitated lead by Extended X-ray Absorption Fine Structure at the National Synchrotron Light Source showed that the lead is predominantly associated with the phosphate and carboxyl functional groups in a stable form. Citric acid was completely recovered (>99%) from the extract by sulfide precipitation technique and the extraction efficiency of recovered citric acid is similar to that of the fresh citric acid. Recycling of the citric acid should result in considerable savings in the overall treatment cost. We have shown the potential application of this technology to remove and recover the metal contaminants from incinerator ash as well as from other heavy metal bearing wastes (i.e., electric arc furnace dust from steel industry) or soils. Information developed from this project is being applied to demonstrate the remediation of lead paint contaminated soils on Long Island

Actinide biocolloid formation in brine by halophilic bacteria

The authors examined the ability of a halophilic bacterium (WIPP 1A) isolated from the Waste Isolation Pilot Plant (WIPP) site to accumulate uranium in order to determine the potential for biocolloid facilitated actinide transport. The bacterial cell surface functional groups involved in the complexation of the actinide were determined by titration. Uranium, added as uranyl nitrate, was removed from solution at pH 5 by cells but at pH 7 and 9 very little uranium was removed due to its limited solubility. Although present as soluble species, uranyl citrate at pH 5, 7, and 9, and uranyl carbonate at pH 9 were not removed by the bacterium because they were not bioavailable due to their neutral or negative charge. Addition of uranyl EDTA to brine at pH 5, 7, and 9 resulted in the immediate precipitation of U. Transmission electron microscopy (TEM) and energy dispersive X-ray spectroscopy (EDS) analysis revealed that uranium was not only associated with the cell surface but also accumulated intracellularly as uranium-enriched granules. Extended X-ray absorption fine structure (EXAFS) analysis of the bacterial cells indicated the bulk sample contained more than one uranium phase. Nevertheless these results show the potential for the formation of actinide bearing bacterial biocolloids that are strictly regulated by the speciation and bioavailability of the actinide

Environmental Molecular Sciences Institute support for the Center for Environmental Molecular Sciences

This project is investigating the chemical processes that govern actinide sequestration in grout materials with the goal of determining the long-term behavior of grouts used to stabilize actinides in source-terms such as high level waste tank heals. Two grouts contained portland cement, blast furnace slag and fly ash, with one formulation containing zeolite and the other fluorapatite. Earlier experimental work was conducted with funds from DOE/West Valley. CEMS funding allowed further exploration of grout behavior, beyond the scope of the original work which consisted of both batch and flow-through column experiments. The primary focus was the late stage behavior of actinides in the grout system when it is expected to be open to the atmosphere and groundwater, resulting in decreases of pH and interactions of U (and other elements) with dissolved carbonate