Method for simulating discontinuous physical systems
Abstract
The mathematical foundations of conventional numerical simulation of physical systems provide no consistent description of the behavior of such systems when subjected to discontinuous physical influences. As a result, the numerical simulation of such problems requires ad hoc encoding of specific experimental results in order to address the behavior of such discontinuous physical systems. In the present invention, these foundations are replaced by a new combination of generalized function theory and nonstandard analysis. The result is a class of new approaches to the numerical simulation of physical systems which allows the accurate and wellbehaved simulation of discontinuous and other difficult physical systems, as well as simpler physical systems. Applications of this new class of numerical simulation techniques to process control, robotics, and apparatus design are outlined.
 Inventors:

 Albuquerque, NM
 Issue Date:
 Research Org.:
 Sandia National Laboratories (SNL), Albuquerque, NM, and Livermore, CA (United States)
 OSTI Identifier:
 873773
 Patent Number(s):
 6243663
 Assignee:
 Sandia Corporation (Albuquerque, NM)
 Patent Classifications (CPCs):

G  PHYSICS G05  CONTROLLING G05B  CONTROL OR REGULATING SYSTEMS IN GENERAL
 DOE Contract Number:
 AC0494AL85000
 Resource Type:
 Patent
 Country of Publication:
 United States
 Language:
 English
 Subject:
 method; simulating; discontinuous; physical; systems; mathematical; foundations; conventional; numerical; simulation; provide; consistent; behavior; subjected; influences; result; requires; hoc; encoding; specific; experimental; results; address; replaced; combination; generalized; function; theory; nonstandard; analysis; approaches; allows; accurate; wellbehaved; difficult; simpler; applications; techniques; process; control; robotics; apparatus; design; outlined; physical systems; process control; systems provide; experimental results; discontinuous physical; /703/708/
Citation Formats
Baty, Roy S, and Vaughn, Mark R. Method for simulating discontinuous physical systems. United States: N. p., 2001.
Web.
Baty, Roy S, & Vaughn, Mark R. Method for simulating discontinuous physical systems. United States.
Baty, Roy S, and Vaughn, Mark R. Mon .
"Method for simulating discontinuous physical systems". United States. https://www.osti.gov/servlets/purl/873773.
@article{osti_873773,
title = {Method for simulating discontinuous physical systems},
author = {Baty, Roy S and Vaughn, Mark R},
abstractNote = {The mathematical foundations of conventional numerical simulation of physical systems provide no consistent description of the behavior of such systems when subjected to discontinuous physical influences. As a result, the numerical simulation of such problems requires ad hoc encoding of specific experimental results in order to address the behavior of such discontinuous physical systems. In the present invention, these foundations are replaced by a new combination of generalized function theory and nonstandard analysis. The result is a class of new approaches to the numerical simulation of physical systems which allows the accurate and wellbehaved simulation of discontinuous and other difficult physical systems, as well as simpler physical systems. Applications of this new class of numerical simulation techniques to process control, robotics, and apparatus design are outlined.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {2001},
month = {1}
}
Works referenced in this record:
Nonstandard electrical networks and the resurrection of Kirchhoff's laws
journal, March 1997
 Zemanian, A. H.
 IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, Vol. 44, Issue 3
A Nonstandard Analysis of a Simple Discontinuous Force Equation Modelling Continuous Motion
journal, May 1997
 Baty, R. S.; Vaughn, M. R.; Farassat, F.
 Journal of Sound and Vibration, Vol. 202, Issue 2