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- Path: sparky!uunet!think.com!ames!agate!dog.ee.lbl.gov!csa2.lbl.gov!sichase
- From: sichase@csa2.lbl.gov (SCOTT I CHASE)
- Newsgroups: sci.physics
- Subject: Re: Continuos vs. discrete models Was: The size of electrons, ...
- Date: 16 Nov 1992 10:36 PST
- Organization: Lawrence Berkeley Laboratory - Berkeley, CA, USA
- Lines: 36
- Distribution: world
- Message-ID: <16NOV199210360062@csa2.lbl.gov>
- References: <1992Nov7.214329.24552@galois.mit.edu> <1992Nov13.194334.20447@sun0.urz.uni-heidelberg.de> <350@mtnmath.UUCP> <1992Nov16.065208.28725@murdoch.acc.Virginia.EDU>
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- In article <1992Nov16.065208.28725@murdoch.acc.Virginia.EDU>, crb7q@kelvin.seas.Virginia.EDU (Cameron Randale Bass) writes...
- >>
- >>As one simple example consider the difference between a model based on
- >>finite difference equations and one based on partial differential
- >>equations.
- >
- > Name a physical system in which the FDE is considered more fundamental
- > than the PDE? For most of us, we take the 'true' PDE and muck it
- > up, introducing loads of spurious conservation laws and higher
- > order terms, by deriving a finite difference formulation of it.
- > I'd be interested in a system in which we did the reverse.
-
- How about your favorite and mine - the flexible string. Since the string
- is really atomic at the smallest scale, the "most" appropriate equation
- is the FDE. It is only in the approximation that the discrete nature of the
- string is irrelevant (a damn good approximation, I admit) that the PDE
- becomes a useful description.
-
- In older textbooks, like Morse and Feshbach, they put more of an emphasis
- on these distinctions than modern books do, which tend to be more abstract.
- M&F go to some length to emphasize that the PDE's are not the "true"
- models of many systems. They make a clear distinction between physical
- systems which are inseparable from their description in terms of fields
- (i.e., PDE's), such as electromagnetic fields, and systems for which
- the fields *are* separable from the physical system, such as the string,
- where it is really the finite number atomic positions which are fundamental,
- the field being a useful characterization but not one that is intrinsic
- to the system, which is properly a discrete system.
-
- -Scott
- --------------------
- Scott I. Chase "It is not a simple life to be a single cell,
- SICHASE@CSA2.LBL.GOV although I have no right to say so, having
- been a single cell so long ago myself that I
- have no memory at all of that stage of my
- life." - Lewis Thomas
-