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.

Electronic downloads

• http://www.eecs.berkeley.edu/Pubs/TechRpts/2014/EECS-2014-15.html

• 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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