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

 To: "[ontolog-forum] " David Leal Mon, 11 Jul 2011 21:36:03 +0100 <20110711203612.5A22C138CC5@xxxxxxxxxxxxxxxxx>
 ```Dear Azamat,    (01) Can you explain the statements: - "So, the second order/rank/degree tensors or higher are nothing but properties of properties"; - "Any tensor is a variable quantity".    (02) I asserted that a tensor is a linear function (with appropriate symmetries) over a space of tuples of one or more directions. Do you disagree with this?    (03) Best regards, David    (04) At 16:20 11/07/2011, AzamatAbdoullaev wrote: >David Leal wrote: >"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". >All physical tensors, stress-energy tensor, electromagnetic tensor, >or stress/strain tensor, come under a second order property of >different natural kinds. So, the second order/rank/degree tensors or >higher are nothing by properties of properties, like as second order >predicates, fourth order predicates, etc. If you wish, call them >"physical predicates" or "geometric predicates". In the Reality >book, its generally defined as "ontological predicates". >By nature, tensors represent relationships/correspondances between >properties (sets of vectors). Any tensor is a variable quantity, and >it is often conflated with a matrix (as an array of elements/entries >of rows and colums). >In computer science, tensors are represented as multidimensional >array/table data structure of values or variables, identified by two >and more element indices. >Hope it was helpful. >Kind regards, >Azamat Abdoullaev > >----- Original Message ----- From: "David Leal" > >To: "[ontolog-forum] " ; >"[ontolog-forum] " >Sent: Sunday, July 10, 2011 11:47 PM >Subject: Re: [ontolog-forum] Theory of properties - stress tensor > > >>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    (05) ============================================================ 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 ============================================================    (06) _________________________________________________________________ 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    (07) ```
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