Coulomb blockade: Difference between revisions
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[[File:StressEnergyTensor contravariant.svg|thumb|250px|right|The stress–energy tensor of a perfect fluid contains only the diagonal components.]] | |||
In [[physics]], a '''perfect fluid''' is a [[fluid]] that can be completely characterized by its rest frame [[mass density]] ρ and ''isotropic'' [[pressure]] ''p''. | |||
Real fluids are "sticky" and contain (and conduct) heat. Perfect fluids are idealized models in which these possibilities are neglected. Specifically, perfect fluids have no [[shear stress]]es, [[viscosity]], or [[heat conduction]]. | |||
In tensor notation, the [[stress–energy tensor]] of a perfect fluid can be written in the form | |||
:<math>T^{\mu\nu} = \left( \rho + \frac{p}{c^2} \right) \, U^\mu U^\nu + p \, \eta^{\mu\nu}\,</math> | |||
where ''U'' is the [[velocity]] [[vector field]] of the fluid and where <math>\eta_{\mu \nu}</math> is the metric tensor of [[Minkowski spacetime]]. | |||
Perfect fluids admit a [[Lagrangian]] formulation, which allows the techniques used in field theory, in particular, [[quantization (physics)|quantization]], to be applied to fluids. This formulation can be generalized, but unfortunately, heat conduction and anisotropic stresses cannot be treated in these generalized formulations.{{why|date=December 2013}} | |||
Perfect fluids are often used in [[general relativity]] to model idealized distributions of [[matter]], such as in the interior of a star. | |||
==See also== | |||
*[[Equation of state]] | |||
*[[Ideal gas]] | |||
*[[Fluid solution|Fluid solutions in general relativity]] | |||
==References== | |||
*The Large Scale Structure of Space-Time, by S.W.Hawking and G.F.R.Ellis, Cambridge University Press, 1973. ISBN 0-521-20016-4, ISBN 0-521-09906-4 (pbk.) | |||
==External links== | |||
*Mark D. Roberts, [A Fluid Generalization of Membranes http://www.arXiv.org/abs/hep-th/0406164 hep-th/0406164]. | |||
{{fluiddynamics-stub}} | |||
[[Category:Fluid mechanics]] |
Revision as of 17:18, 28 January 2014
In physics, a perfect fluid is a fluid that can be completely characterized by its rest frame mass density ρ and isotropic pressure p.
Real fluids are "sticky" and contain (and conduct) heat. Perfect fluids are idealized models in which these possibilities are neglected. Specifically, perfect fluids have no shear stresses, viscosity, or heat conduction.
In tensor notation, the stress–energy tensor of a perfect fluid can be written in the form
where U is the velocity vector field of the fluid and where is the metric tensor of Minkowski spacetime.
Perfect fluids admit a Lagrangian formulation, which allows the techniques used in field theory, in particular, quantization, to be applied to fluids. This formulation can be generalized, but unfortunately, heat conduction and anisotropic stresses cannot be treated in these generalized formulations.Template:Why
Perfect fluids are often used in general relativity to model idealized distributions of matter, such as in the interior of a star.
See also
References
- The Large Scale Structure of Space-Time, by S.W.Hawking and G.F.R.Ellis, Cambridge University Press, 1973. ISBN 0-521-20016-4, ISBN 0-521-09906-4 (pbk.)
External links
- Mark D. Roberts, [A Fluid Generalization of Membranes http://www.arXiv.org/abs/hep-th/0406164 hep-th/0406164].