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Science > Physics |
| User: |
"" |
| Date: |
10 May 2007 10:26:26 AM |
| Object: |
Need mental picture |
Hello Gals,
I know what a scalar is.
I know what a vector is.
I know what a linear transformation is.
But what in the name of sweet aunt petunia is a rank 3 tensor?
Love,
Plx Mny
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| User: "Sam Wormley" |
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| Title: Re: Need mental picture |
10 May 2007 10:34:10 AM |
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wrote:
But what in the name of sweet aunt petunia is a rank 3 tensor?
See: http://www.google.com/search?q=rank+3+tensor
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| User: "" |
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| Title: Re: Need mental picture |
10 May 2007 10:43:15 AM |
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On May 10, 11:34 am, Sam Wormley <sworml...@mchsi.com> wrote:
plx...@yahoo.com wrote:
But what in the name of sweet aunt petunia is a rank 3 tensor?
See:http://www.google.com/search?q=rank+3+tensor
Sorry, but that just gives me the same old schlock. Maybe I should try
searching on
"mental picture of rank 3 tensor"?
Or how about "why google is better than talking to human beings?"
or maybe "Sam Wormley is a bot"?
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| User: "Bruce Scott TOK" |
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| Title: Re: Need mental picture |
10 May 2007 11:15:12 AM |
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I know what a scalar is.
I know what a vector is.
I know what a linear transformation is.
But what in the name of sweet aunt petunia is a rank 3 tensor?
The usual model for a 2-tensor is momentum flux
You have to keep track of the direction of the flux for a momentum which
itself has 3 components (flux vector of a vector)
So now generalise it... you have a 2-rank object like momentum flux.
Suppose you want to derive a continuity equation for that object. The
flux of _that_ object is then a 3-rank tensor.
Example: the general tensor describing heat flux is rank 3, essentially
the flux of a velocity-velocity tensor (which you might usually think of
as a 3x3 matrix). Only when assuming that the pressure tensor (rank 2)
is approximately diagonal does the heat flux reduce to a vector.
--
ciao,
Bruce
drift wave turbulence: http://www.rzg.mpg.de/~bds/
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| User: "" |
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| Title: Re: Need mental picture |
10 May 2007 12:24:06 PM |
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On May 10, 12:15 pm, Bruce Scott TOK <Use-Author-Supplied-Address-
Header@[127.1]> wrote:
..
So now generalise it... you have a 2-rank object like momentum flux.
Suppose you want to derive a continuity equation for that object. The
flux of _that_ object is then a 3-rank tensor.
I thought a little about this on my lunch break. I came up with "a
linear combination of linear combinations" which I think
is approximately what you are describing here.
In short, it's not really a notion that is worth bothering with unless
it comes up in real life?
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| User: "Bruce Scott TOK" |
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| Title: Re: Need mental picture |
11 May 2007 12:36:29 PM |
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So now generalise it... you have a 2-rank object like momentum flux.
Suppose you want to derive a continuity equation for that object. The
flux of _that_ object is then a 3-rank tensor.
I thought a little about this on my lunch break. I came up with "a
linear combination of linear combinations" which I think
is approximately what you are describing here.
In fact (that's how I think about it).
In short, it's not really a notion that is worth bothering with unless
it comes up in real life?
For a physicist, yes (with the proviso that "real life" is anything
arising in a physics problem). In mathematics, however, one usually
treats arbitrary numbers of things... if for no other reason than to
understand underlying structure. We always did mn-rank tensors (T_m^n)
in the math class. In physics it was almost always 2nd rank (with the
indices up or down depending on the situation). Sometimes you get the
3rd rank (heat fluxes, various things involving rotation, etc).
--
ciao,
Bruce
drift wave turbulence: http://www.rzg.mpg.de/~bds/
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