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

 To: "[ontolog-forum]" "doug foxvog" Mon, 11 Jul 2011 00:51:06 -0400 (EDT) <60189.70.110.17.10.1310359866.squirrel@xxxxxxxxxxxxxx>
 ```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 > 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 > ============================================================ > > > _________________________________________________________________ > Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/ > Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/ > Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx > Shared Files: http://ontolog.cim3.net/file/ > Community Wiki: http://ontolog.cim3.net/wiki/ > To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J > >    (08) ============================================================= 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. =============================================================    (010) _________________________________________________________________ Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/ Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/ Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx Shared Files: http://ontolog.cim3.net/file/ Community Wiki: http://ontolog.cim3.net/wiki/ To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J    (011) ```
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