dorsal/arxiv
View SchemaPhysical foundation of the mathematical concepts in the nonstandard analysis theory of turbulence
| Authors | Feng Wu |
|---|---|
| Categories | |
| ArXiv ID | physics/0601125 |
| URL | https://arxiv.org/abs/physics/0601125 |
Abstract
The physical foundation of the main mathematical concepts in the nonstandard analysis theory of turbulence are presented and discussed. The basic fact is that there does not exist the absolute zero fluid-volume. Therefore, the corresponding physical object to the absolute point is just the uniform fluid-particle. The fluid-particle, in general, corresponds to the monad. The uniform fluid-particle corresponds to the uniform monad, the nonuniform fluid-particle to the nonuniform monad. There are two kinds of the differentiations, one based on the absolute point, another based on the monad. The former is adopted in the Navier-Stokes equations, the latter in the fundamental equations, the closed forms are the equations (7)-(11) in this article, in the nonstandard analysis theory of turbulence. The continuity of fluid is shown by virtue of the concepts of the fluid-particle and fluid-particle in lower level. The character of the continuity in two cases, the standard and nonstandard analysis, is presented in the paper. And the difference in the discretization between the Navier-Stokes equations and the equations (7)-(11) is pointed out too.
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"abstract": "The physical foundation of the main mathematical concepts in the nonstandard\nanalysis theory of turbulence are presented and discussed. The basic fact is\nthat there does not exist the absolute zero fluid-volume. Therefore, the\ncorresponding physical object to the absolute point is just the uniform\nfluid-particle. The fluid-particle, in general, corresponds to the monad. The\nuniform fluid-particle corresponds to the uniform monad, the nonuniform\nfluid-particle to the nonuniform monad. There are two kinds of the\ndifferentiations, one based on the absolute point, another based on the monad.\nThe former is adopted in the Navier-Stokes equations, the latter in the\nfundamental equations, the closed forms are the equations (7)-(11) in this\narticle, in the nonstandard analysis theory of turbulence. The continuity of\nfluid is shown by virtue of the concepts of the fluid-particle and\nfluid-particle in lower level. The character of the continuity in two cases,\nthe standard and nonstandard analysis, is presented in the paper. And the\ndifference in the discretization between the Navier-Stokes equations and the\nequations (7)-(11) is pointed out too.",
"arxiv_id": "physics/0601125",
"authors": [
"Feng Wu"
],
"categories": [
"physics.flu-dyn"
],
"title": "Physical foundation of the mathematical concepts in the nonstandard analysis theory of turbulence",
"url": "https://arxiv.org/abs/physics/0601125"
},
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