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 (01)
----- Original Message -----
From: "David Leal" <david.leal@xxxxxxxxxxxxxxxxxxx>
To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>; "[ontolog-forum] "
<ontolog-forum@xxxxxxxxxxxxxxxx>
Sent: Sunday, July 10, 2011 11:47 PM
Subject: Re: [ontolog-forum] Theory of properties - stress tensor (02)
> 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
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> ============================================================
>
>
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