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Constructive Models of Discrete and Continuous Physical Phenomena
Edward A. Lee

Citation
Edward A. Lee. "Constructive Models of Discrete and Continuous Physical Phenomena". Technical report, EECS Department, UC Berkeley, UCB/EECS-2014-15, February, 2014; http://www.eecs.berkeley.edu/Pubs/TechRpts/2014/EECS-2014-15.html.

Abstract
This paper studies the semantics of models for discrete physical phenomena such as rigid body collisions and switching in electronic circuits. The paper combines generalized functions (specifically the Dirac delta function), superdense time, modal models, and constructive semantics to get a rich, flexible, efficient, and rigorous approach to modeling such systems. It shows that many physical scenarios that have been problematic for modeling techniques manifest as non-constructive models, and that constructive versions of some of the models properly reflect uncertainty in the behavior of the physical systems that can arise from the principles of quantum mechanics. The paper argues that these modeling difficulties are not reasonably solved by more detailed continuous models of the underlying physical phenomena. Such more detailed models simply shift the uncertainty to other parts of the model. Since such detailed models come with a high computational cost, there is little justification in using them unless the goal of modeling is specifically to understand these more detailed physical processes.

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Citation formats  
  • HTML
    Edward A. Lee. <a
    href="http://chess.eecs.berkeley.edu/pubs/1053.html"><i>Constructive
    Models of Discrete and Continuous Physical
    Phenomena</i></a>, Technical report,  EECS
    Department, UC Berkeley, UCB/EECS-2014-15, February, 2014;
    <a
    href="http://www.eecs.berkeley.edu/Pubs/TechRpts/2014/EECS-2014-15.html"
    >http://www.eecs.berkeley.edu/Pubs/TechRpts/2014/EECS-2014-15.html</a>.
  • Plain text
    Edward A. Lee. "Constructive Models of Discrete and
    Continuous Physical Phenomena". Technical report,  EECS
    Department, UC Berkeley, UCB/EECS-2014-15, February, 2014;
    <a
    href="http://www.eecs.berkeley.edu/Pubs/TechRpts/2014/EECS-2014-15.html"
    >http://www.eecs.berkeley.edu/Pubs/TechRpts/2014/EECS-2014-15.html</a>.
  • BibTeX
    @techreport{Lee14_ConstructiveModelsOfDiscreteContinuousPhysicalPhenomena,
        author = {Edward A. Lee},
        title = {Constructive Models of Discrete and Continuous
                  Physical Phenomena},
        institution = {EECS Department, UC Berkeley},
        number = {UCB/EECS-2014-15},
        month = {February},
        year = {2014},
        note = {<a
                  href="http://www.eecs.berkeley.edu/Pubs/TechRpts/2014/EECS-2014-15.html"
                  >http://www.eecs.berkeley.edu/Pubs/TechRpts/2014/EECS-2014-15.html</a>},
        abstract = {This paper studies the semantics of models for
                  discrete physical phenomena such as rigid body
                  collisions and switching in electronic circuits.
                  The paper combines generalized functions
                  (specifically the Dirac delta function),
                  superdense time, modal models, and constructive
                  semantics to get a rich, flexible, efficient, and
                  rigorous approach to modeling such systems. It
                  shows that many physical scenarios that have been
                  problematic for modeling techniques manifest as
                  non-constructive models, and that constructive
                  versions of some of the models properly reflect
                  uncertainty in the behavior of the physical
                  systems that can arise from the principles of
                  quantum mechanics. The paper argues that these
                  modeling difficulties are not reasonably solved by
                  more detailed continuous models of the underlying
                  physical phenomena. Such more detailed models
                  simply shift the uncertainty to other parts of the
                  model. Since such detailed models come with a high
                  computational cost, there is little justification
                  in using them unless the goal of modeling is
                  specifically to understand these more detailed
                  physical processes. },
        URL = {http://chess.eecs.berkeley.edu/pubs/1053.html}
    }
    

Posted by Edward A. Lee on 22 Jan 2014.
Groups: ptolemy
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