Mathematical Sciences: The Mathematics of Reacting and      Diffusing Systems
{'Code': '03040101', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Bernard McDonald', 'PO_EMAI': None, 'PO_PHON': None}
The proposed projects involve mathematical analysis and modeling in         the fields of electro-chemistry, two-phase media and flame theory.  The         common tie among these problems is that they all deal with diffusive            and/or convective transport, and interactive processes such as chemical         reactions.  There are many electrophoretic techniques commonly used to          separate charged particles in solution.  They all give rise to                  mathematical models in need of qualitative analysis.  The specific              projects proposed here have to do with the steady-state and transient           behavior of models in isotachophoresis and isoelectric focussing                (possibly also continuous flow electrophoresis).  In the study of the           statics and dynamics of two-phase continua, phase field models of               various kinds are emerging as physically suggestive and numerically             convenient approaches.  Part of the proposal is to extend the previous          analyses of these models, by the PI and Caginalp, in the directions of          (1) higher (than second) order models, which will be closer in some             sense to the underlying discrete lattice theories, (2) taking into              account the interaction of the material with boundaries, and (3)                stability considerations.  To fully understand and model combustion in          flames, the important chemical reactions should be known, as well as the        extent of their participation in the combustion process.  Along with            this , a knowledge of the concentrations of the reactants, hence of the         reaction rates and the ( at least approximate) flame speed, is                  desirable.  The PI has very recently developed a strategy for obtaining         this knowledge, using known reaction networks and rate constant data,           ans successfully  applied it to lean hydrogen-oxygen flames.  The method        needs further development and implementation with simple computer               routines.  It is proposed to investigate aspects of some nonstandard            problems.                                                                           This project falls into the general area of research on mathematical        theory of reaction - diffusion phenomena. This theory attempts to               explain in mathematical terms the phenomena of combustion,                      electrophoresis, flame propagation and diffusion of chemicals in a              solution. It is a very active area of research nowadays.
{'FirstName': 'Paul', 'LastName': 'Fife', 'PI_MID_INIT': 'C', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Paul C Fife', 'EmailAddress': 'fife@math.utah.edu', 'NSF_ID': '000369376', 'StartDate': '06/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of Arizona', 'CityName': 'TUCSON', 'ZipCode': '85721', 'PhoneNumber': '5206266000', 'StreetAddress': '845 N PARK AVE RM 538', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Arizona', 'StateCode': 'AZ', 'CONGRESSDISTRICT': '07', 'CONGRESS_DISTRICT_ORG': 'AZ07', 'ORG_UEI_NUM': 'ED44Y3W6P7B9', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF ARIZONA', 'ORG_PRNT_UEI_NUM': None}
{'Name': None, 'CityName': None, 'StateCode': None, 'ZipCode': None, 'StreetAddress': None, 'CountryCode': None, 'CountryName': None, 'StateName': None, 'CountryFlag': None, 'CONGRESSDISTRICT': None, 'CONGRESS_DISTRICT_PERF': '""'}
{'Code': '126600', 'Text': 'APPLIED MATHEMATICS'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1987&All=true', 'xml': '8703247.xml'}