On Sun, July 10, 2011 16:47, David Leal said: (01)
[Question extracted from email]: (02)
> It is not clear to me, how a stress tensor would be included in an
> ontology for properties. Is a stress tensor regarded as a "quantity",
> like a mass? (03)
The answer to the first question would depend upon how the ontology
defined "quantity". So long as the ontology accepts matricies as
Quantities, then the tensor could be regarded as a quantity. (04)
> ... Is a von Mises's equivalent stress regarded as a
> "property" of a stress tensor? (05)
Yes, it should be. (06)
-- doug f (07)
> Dear Azamat and others,
>
> A theory of properties is interesting to me, and it may help to look
> in detail at a property which mentioned by Azamat.
>
> A small region of solid matter can have a property that is its stress
> tensor. A stress tensor is a single thing, and should not be thought
> of as a "compound property" or a "property of properties". The
> following points should be noted about a stress tensor:
>
> 1) Inevitably stress varies from position to position within a solid
> object. Sometimes when we choose a small enough neighbourhood of a
> point P within a solid object, the stress within that neighbourhood
> varies by only a small amount, so that we can say "Body B in the
> neighbourhood of point P has stress S". But if the neighbourhood is
> too small, then there is no concept of stress and instead only
> molecular bonds. Hence sometimes, we cannot say that "Body B in the
> neighbourhood of point P has stress S", because by the time we have
> shrunk the neighbourhood sufficiently to get a stress value that does
> not vary too much within the neighbourhood, the concept of stress has
> disappeared. This situation can occur at a crack tip - a location of
> particular interest to engineers.
>
> Density is also a property that can only apply to "Body B in the
> neighbourhood of a point P", if the neighbourhood is of a sufficient
> size. If some neighbourhoods have one molecule in them and others
> have two, then the variation of density from point to point is
> somewhat extreme. :)
>
> 2) A stress tensor can be thought of as bilinear function from pairs
> of direction vectors to force per unit area. The function can be
> encoded as a matrix of force per unit area values. However, this
> encoding is not the thing itself. The encoding depends upon the
> coordinate system used to express the directions. If the coordinate
> system is not Cartesian, then there are alternative co-variant and
> contra-variant matrix encodings.
>
> 3) A stress tensor has "invariants". These are quantities that are
> derived from the tensor, where the quantity is not dependent upon the
> coordinate system chosen to encode the stress tensor. An example is
> von Mises's equivalent stress.
>
> It is not clear to me, how a stress tensor would be included in an
> ontology for properties. Is a stress tensor regarded as a "quantity",
> like a mass? Is a von Mises's equivalent stress regarded as a
> "property" of a stress tensor?
>
> Best regards,
> David
>
> At 19:44 07/07/2011, AzamatAbdoullaev wrote:
>>AA: Again, we need to start from classification - what kinds of
>>properties exist: formal properties (attributes and predicates) or
>>substantial properties (real properties); intrinsic, mutual,
>>permanent, transient, emergent, simple, complex properties, or
>>compound properties as property of properties, like "stress tensor".
>>By default, in any sound classification, the property to be used is
>>a simple or basic property. The more basic property the more common
>>it is. A theory of properties is better to develop as a theory of
>>state space, an aggregate of properties.
>
>
> ============================================================
> David Leal
> CAESAR Systems Limited
> registered office: 29 Somertrees Avenue, Lee, London SE12 0BS
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> ============================================================
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> (08)
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doug foxvog doug@xxxxxxxxxx http://ProgressiveAustin.org (09)
"I speak as an American to the leaders of my own nation. The great
initiative in this war is ours. The initiative to stop it must be ours."
- Dr. Martin Luther King Jr.
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