Research Initiation:  Eigenvalue Inclusion Regions to Study Model Approximations for Distributed Parameter Systems
{'Code': '07020000', 'Directorate': {'Abbreviation': 'ENG', 'LongName': 'Directorate For Engineering'}, 'Division': {'Abbreviation': 'CBET', 'LongName': 'Div Of Chem, Bioeng, Env, & Transp Sys'}}
{'SignBlockName': 'Maria Burka', 'PO_EMAI': None, 'PO_PHON': None}
Heat, mass or momentum transfer equations often contain gradients in            many spatial directions and perhaps accumulation terms to bring about           dependence on time.  Modeling such systems involves the solution of a           series of partial differential equations (PDEs) which accurately                represent reality but complicate the analysis procedures since they             seldom have analytical solutions.  This necessitates the use of                 numerical techniques to obtain an approximation to the exact solution.          The relationship between the approximate and exact solution leads to            the problem of "robustness" when such approximations constitute                 elements in feedback control loops.  Such process controllers function          with limited process information since their design is based on the             aproximate models resulting in the loss of system performance and               sometimes, stability.                                                                                                                                           This work is geared towards the development of appropriate                      mathematical tools to investigate the model approximations for                  distributed parameter systems in an effort to guide dynamics and                control studies.  The PI is proposing to exploit the eigenstructure of          the approximate and the rigorous models in order to gain some insight           towards the variation of system eigenvalues, the dominant system                modes, the degree of model aproximation and most importantly the                characterization of the neglected system modes to judge the capability          of process controllers to maintain smooth and effective operation.              The PI has been growing dislocation free single crystals of GaAs using          a modified Bridgman type furnace and is setting up a pilot scale                furnace assembly to verify the results.  The modeling and the control           of such a system is critical to ensure the development of optimal               temperature profiles in the crystal and the melt and this in turn               requires a sound assessment of the relationship between the rigorous            model and its numerical approximation.  This system represents a                typical problem facing the process control engineer and is an ideal             candidate to test the results of this project.
{'FirstName': 'Ahmet', 'LastName': 'Palazoglu', 'PI_MID_INIT': 'N', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Ahmet N Palazoglu', 'EmailAddress': 'anpalazoglu@ucdavis.edu', 'NSF_ID': '000159708', 'StartDate': '06/15/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of California-Davis', 'CityName': 'DAVIS', 'ZipCode': '956186153', 'PhoneNumber': '5307547700', 'StreetAddress': '1850 RESEARCH PARK DR STE 300', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'California', 'StateCode': 'CA', 'CONGRESSDISTRICT': '04', 'CONGRESS_DISTRICT_ORG': 'CA04', 'ORG_UEI_NUM': 'TX2DAGQPENZ5', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF CALIFORNIA, DAVIS', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '140300', 'Text': 'Proc Sys, Reac Eng & Mol Therm'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1988&All=true', 'xml': '8810318.xml'}