Mathematical Sciences: Nonlinear Partial Differential       Equations in Lubrications: A Study of Cavitation in Thin    Lubricant Films
{'Code': '03040102', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'John V. Ryff', 'PO_EMAI': None, 'PO_PHON': None}
Modeling and analysis of certain engineering questions will                be taken up in this mathematical study of free boundaries arising               in the lubrication theory.  The work involves efforts to                        understand the dynamics of thin viscous fluid films confined                    between solid boundaries, such as fluid flow between two                        concentric or eccentric rotating cylinders - a journal bearing.                 An interesting and mechanically significant aspect of journal                   bearings is the occurrence of cavitation, a phenomenon in which                 the lubricant vaporizes due to its inability to sustain large                   vacuums.  On the mathematical level, a representation of this                   phenomenon is given by a variational problem involving free                     boundaries.  The primary goal of the project is to determine                    properties of the free boundary: regularity, shape and location.                     Two particular models will be analyzed.  In both cases the                 object is to describe the pressure in the lubricant film, with                  vaporization pressure taken to be zero. The first is the solid or               non-porous bearing of finite length in which the outer and inner                cylinders are not concentric.  For small eccentricity, the region               of cavitation is known to have a single component.  Whether this                condition remain under more general conditions is yet to be                     resolved.  The second model concerns the porous, concentric                     journal bearing of infinite length.  This journal is composed of                a porous matrix which permits continuous fluid flow between the                 matrix and the lubricant.  The regularity of the pressure                       function is better understood in this case and work will                        concentrate on developing numerical approximations to the                       function by finite element methods, with special emphasis on the                convergence of the discrete free boundaries.
{'FirstName': 'Sara', 'LastName': 'Cohen', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Sara Cohen', 'EmailAddress': 'SACohen111@aol.com', 'NSF_ID': '000416052', 'StartDate': '08/01/1989', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of Wisconsin-Madison', 'CityName': 'MADISON', 'ZipCode': '537151218', 'PhoneNumber': '6082623822', 'StreetAddress': '21 North Park Street', 'StreetAddress2': 'Suite 6301', 'CountryName': 'United States', 'StateName': 'Wisconsin', 'StateCode': 'WI', 'CONGRESSDISTRICT': '02', 'CONGRESS_DISTRICT_ORG': 'WI02', 'ORG_DUNS_NUM': '161202122', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF WISCONSIN SYSTEM', 'ORG_PRNT_DUNS_NUM': '041188822'}
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{'Code': '1261', 'Text': 'CLASSICAL ANALYSIS'}
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