Chunming Wang - US grants

This award supports Professors H. T. Banks, K. Ito and C. Wang of the University of Southern California to continue their collaboration in applied mathematics research with Professor F. Kappel and others of the University of Graz and K. Kunisch of the Technical University of Graz, Austria. They share interests in control theory that focus on the problems of estimating parameters in partial differential equations from known observation of a given process and also the approximation of functional and partial differential equations stressing applications to control and inverse problems. The specific topics on which they will work include modeling and parameter estimation techniques in size/age structured population models, the identifiability of parameters in models of visco-elastic systems, and the development of an approximation framework for nonlinear dynamics in a Banach space setting. These U.S. and Austrian mathematicians have been among the leaders in the development of methods and applications in a wide variety of problems in optimization, approximation and parameter estimation for functional and partial differential equations. Their productive collaboration has already resulted in numerous publications containing applications to meaningful physical and biological problems. The proposed work promises to continue this contribution by focusing on technically interesting problems with relevance to mechanics and population dynamics.

Rosen 9704935 Sulfide corrosion of concrete in wastewater collection systems occurs when microorganisms in anaerobic films below the water surface produce hydrogen sulfide. The sulfide evaporates into the atmosphere and redissolves in moisture that has condensed on the portions of the pipe above the wastewater. Microorganisms in this environment convert the sulfide to sulfuric acid. The acid reacts with calcium hydroxide and calcium carbonate in the cement, producing sulfate minerals and causing the concrete to corrode. The investigators develop a mathematical model of the corrosion process that is tuned, tested, identified and validated via field data and laboratory experiment. The effort includes the analysis of the model equations (which take the form of a system of coupled partial differential equations with moving or free boundaries) from the point of view of well-posedness (existence, uniqueness, regularity of weak, strong, local, global solutions, etc.) and the sensitivity of solutions with respect to parameters. It also includes the development, analysis and testing of efficient, convergent and robust numerical integration schemes for numerical simulation, parameter estimation and control. In addition to using available field data to verify the model, a laboratory test-bed to provide additional data for model verification and parameter estimation is designed and fabricated. Electrochemical techniques applied to instrumented concrete samples are used to (i) characterize the concrete structures using electrochemical impedance spectroscopy (EIS), and (ii) sense the diffusion profiles of corrosive species. Correlation of the results of these two studies allows investigation of relationships between concrete microstructure and diffusion processes. Computational schemes are developed to use the field and laboratory data to identify unmeasurable parameters that appear in the model, and to test corrosion slowing control schemes based upon the model. Sulfide corrosion causes millions of dollars in damage in the U.S. each year. Attempts have been made to control sulfide corrosion in sewers. Most try to prevent the release of hydrogen sulfide into the pipe atmosphere. Strong base has been used to kill the biofilm, and cleaning has been used to remove it. The addition of trace metals precipitates the sulfide, preventing its release to the atmosphere. However, the biofilms are tenacious, and grow back rapidly, requiring additional treatment. Any anti-biofilm treatment is constrained because it must not damage the similar microorganisms that are the basis of the wastewater treatment system. Chemical precipitation requires continuous treatment. Any effort involving chemical addition must contend with the very large volumes of water flowing through wastewater collection systems: no matter how cheap the chemical, the colossal amounts that must be purchased and fed into the system are expensive. Thus an effort to first understand and to then interrupt (i.e. control) the corrosion process is needed, and may provide the only possible remedy for some cases. The results of the study should yield a deeper understanding of the corrosion process, and provide a powerful tool for engineers to use in the design of concrete wastewater systems and in the formulation, testing, tuning and evaluation of corrosion abatement procedures. The model and results should guide improvements in protection techniques where sulfide corrosion is a problem, and provide insight into the corrosion processes of other concrete structures and the substantial damage caused. They could also potentially reduce maintenance costs. The modeling ideas developed as a part of this project should be transferable to other corrosion problems, and the analytical and computational techniques that result should be of use in the area of moving boundary problems, their analysis, numerical solution, identification and control.

This research project seeks to contribute to the scientific foundation of engineering design by developing a conceptual framework that can be used to study, correlate and compare existing engineering design models, which may obtain from widely different perspectives. The resulting framework will consist of a design concept interchange language with rigorous mathematical evaluations. This interchange language will be used to explain the rationales and correlate the concepts used in different models. The mathematical evaluations will be used to explicate underlying assumptions of various design models and to evaluate their validity and limitations. Six to ten engineering design models will be selected from engineering, decision theory, and artificial intelligence fields for this research. The framework will be developed based on the critical review of these selected design models. An interdisciplinary research team, including engineers, mathematicians, and decision theorists, is assembled to develop this framework for engineering design models. Design is the essence of engineering profession; and engineering design has been a topic for researchers from different disciplines. Some of them are from various engineering disciplines, others from decision theory or artificial intelligence fields. Although a number of engineering design models have been proposed to date, little cross reference exists in these models and communication among the researcher has been difficult. It is commonly recognized that the lack of communication among researchers has become a major obstacle for the progress of engineering design research. If successful, the results of this research project will provide a common language and framework for engineering design researchers to share their insights and results in order to identify gaps between the models and directions for the future research.

The purpose of this study is to capitalize on several mature technologies to obtain regional and global maps of ionospheric irregularities and some of their statistical properties (e.g., second moment) by use of diffraction tomography. In utilizing the GPS signals for 3D mapping of ionospheric irregularities, we are taking advantage of (1) the growing number of space receivers recording GPS phase and amplitude data while occulting behind the ionosphere, (2) the very dense regional networks and large global networks of GPS ground receivers providing over 30 million links per day through the ionosphere, (3) advances made in ionospheric tomography and data assimilation techniques, (4) advances made in diffraction tomography.

This award on solar energy research is co-funded by the Divisions of Chemistry, Materials Research, and Mathematical Sciences of the Directorate for Mathematical and Physical Sciences. A collaboration of chemistry, materials science, mathematics, physics, and engineering groups at the University of Michigan and the University of Southern California will develop a unique, new, thin film solar cell based on polymer-wrapped carbon nanotubes (CNTs). These films will be used in donor-acceptor heterojunctions employing a range of new organic materials and device structures, including polymers and small molecules. The use of CNTs extends the optical sensitivity from the blue into the near infrared, allowing organic-based devices to approach nearly thermodynamically-limited power conversion efficiencies. Simulated excited state (exciton) flow and charge transport through the CNT network uses new treecode algorithms and semi-classical hydrodynamical models. Efficient, multi-dimensional optimization methods are used to develop novel aperiodic dielectric stacks that couple the broad solar spectrum into very thin films used as the active device region in solar cells. A diverse range of undergraduate and graduate students and postdoctoral fellows are engaged in this interdisciplinary research in renewable energy. These students are provided with opportunities to influence policy decisions regarding energy choices through coursework in energy policy and geopolitics on their respective university campuses. The group is also involved in the University of Michigan's Saturday Morning Physics lecture series, providing the public with insights into the latest science and technologies.