- #1

Q_Goest

Science Advisor

Homework Helper

Gold Member

- 3,001

- 42

The Wikipedia article on Nonlinearity states:

Interestingly, the page regarding http://en.wikipedia.org/wiki/Nonlinearity_%28disambiguation%29" [Broken] states:

Although the Nonlinearity article specifically says that it is describing the use of the term in mathematics, the article clearly implies the use of the term to physical systems, as does the disambiguation article. Examples given at the end of the page include the Navier-Stokes equations for fluid flow.

What's your take on this? Is a physical system, such as the flow of a fluid as described by the Navier-Stokes equations, a system "whose behavior is not expressible as a sum of the behaviors of its descriptors"? By making this statement, is the intent only that one can not describe the flow of fluid mathematically, or is there something else about the flow of fluid which is inherently (strongly) emergent in the sense that it is irreducible to what happens within each volume, element or portion of the fluid field?

Also, how exactly do you define "descriptors" in this example? I would assume what is meant would be the fluid's properties such as velocity or momentum for example. What would be a complete list of "descriptors" for a fluid system as described by the NS equations?

(emphasis theirs) Ref: http://en.wikipedia.org/wiki/NonlinearityThis article describes the use of the term nonlinearity in mathematics. For other meanings, see nonlinearity (disambiguation).

In mathematics,nonlinearsystems represent systems whose behavior is not expressible as a sum of the behaviors of its descriptors. In particular, the behavior of nonlinear systems is not subject to the principle of superposition, as linear systems are. Crudely, a nonlinear system is one whose behavior is not simply the sum of its parts or their multiples.

Interestingly, the page regarding http://en.wikipedia.org/wiki/Nonlinearity_%28disambiguation%29" [Broken] states:

(Not sure what "disproportionate" truly means here either.)Nonlineargenerally refers to a situation that has a disproportionate cause and effect.

Although the Nonlinearity article specifically says that it is describing the use of the term in mathematics, the article clearly implies the use of the term to physical systems, as does the disambiguation article. Examples given at the end of the page include the Navier-Stokes equations for fluid flow.

What's your take on this? Is a physical system, such as the flow of a fluid as described by the Navier-Stokes equations, a system "whose behavior is not expressible as a sum of the behaviors of its descriptors"? By making this statement, is the intent only that one can not describe the flow of fluid mathematically, or is there something else about the flow of fluid which is inherently (strongly) emergent in the sense that it is irreducible to what happens within each volume, element or portion of the fluid field?

Also, how exactly do you define "descriptors" in this example? I would assume what is meant would be the fluid's properties such as velocity or momentum for example. What would be a complete list of "descriptors" for a fluid system as described by the NS equations?

Last edited by a moderator: