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Re: [ontolog-forum] Theory of properties - stress tensor

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>, "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: David Leal <david.leal@xxxxxxxxxxxxxxxxxxx>
Date: Sun, 10 Jul 2011 21:47:13 +0100
Message-id: <20110710205938.1AEED138CC4@xxxxxxxxxxxxxxxxx>
Dear Azamat and others,    (01)

A theory of properties is interesting to me, and it may help to look 
in detail at a property which mentioned by Azamat.    (02)

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:    (03)

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.    (04)

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. :)    (05)

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.    (06)

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.    (07)

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?    (08)

Best regards,
David    (09)

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.    (010)

David Leal
CAESAR Systems Limited
registered office: 29 Somertrees Avenue, Lee, London SE12 0BS
registered in England no. 2422371
tel:      +44 (0)20 8857 1095
mob:      +44 (0)77 0702 6926
e-mail:   david.leal@xxxxxxxxxxxxxxxxxxx
web site: http://www.caesarsystems.co.uk
============================================================     (011)

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