Boltzman equation
Non-equilibrium heat flow from (unconventially) colored hot to cold. Source: CC-sa-unported
Published: March 30, 2010, 12:00 am
Updated: July 11, 2012, 4:50 am
This article has been reviewed by the following Topic Editor:
C Michael Hogan
The Boltzmann equation, in physics, describes the statistical behavior of a fluid wich is not in thermodynamic equilibrium. That is to say, the Boltzman equation applies where there are spatial temperature gradients, making heat flow away from warmer areas of the fluid (or gas) to cooler ones. This heat flow occurs by the random transport of fluid or gaseous particles. This formalism was first developed by Ludwig Boltzmann in the year 1872
The Navier-Stokes equations can be derived from the Boltzmann equation, also termed the Boltzmann transport equation, by considering appropriate limits, i.e. Knudsen and Mach numbers tending to zero, and appropriate averaging procedures to define new coarse-grained variables (velocity and pressure) and associated transport coefficients (viscosity and density).
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This article is written at a definitional level only. Authors wishing to expand this entry are inivited to expand the present treatment, which additions will be peer reviewed prior to publication of any expansion. |
Further reading
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Physical Oceanography Index
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M. Farge, N. Kevlahan, V. Perrier, and E. Goirand. Wavelets and turbulence. Proc. IEEE, 84:639–669, 1996.
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Leif Arkeryd. 1972. On the Boltzmann equation part I: Existence. Arch. Rational Mech. Anal. 45: 1–16.
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R.J.DiPerna and P.-L.Lions. 1989. On the Cauchy problem for Boltzmann equations: global existence and weak stability. Ann. of Math. (2) 130: 321–366.
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Citation
Steve Baum (Lead Author);C Michael Hogan (Topic Editor) "Boltzman equation". In: Encyclopedia of Earth. Eds. Cutler J. Cleveland (Washington, D.C.: Environmental Information Coalition, National Council for Science and the Environment). [First published in the Encyclopedia of Earth March 30, 2010; Last revised Date July 11, 2012; Retrieved May 21, 2013 <http://www.eoearth.org/article/Boltzman_equation>
The Author
Assistant Research Scientist, Physical Section
Department of Oceanography
Texas A&M University ... (Full Bio)
The Boltzmann equation, in physics, describes the statistical behavior of a fluid wich is not in thermodynamic equilibrium. That is to say, the Boltzman equation applies where there are spatial temperature gradients, making heat flow away from warmer areas of the fluid (or gas) to cooler ones. This heat flow occurs by the random transport of fluid or gaseous particles. This formalism was first developed by Ludwig Boltzmann in the year 1872
The Navier-Stokes equations can be derived from the Boltzmann equation, also termed the Boltzmann transport equation, by considering appropriate limits, i.e. Knudsen and Mach numbers tending to zero, and appropriate averaging procedures to define new coarse-grained variables (velocity and pressure) and associated transport coefficients (viscosity and density).
|
This article is written at a definitional level only. Authors wishing to expand this entry are inivited to expand the present treatment, which additions will be peer reviewed prior to publication of any expansion. |
Further reading
-
Physical Oceanography Index
-
M. Farge, N. Kevlahan, V. Perrier, and E. Goirand. Wavelets and turbulence. Proc. IEEE, 84:639–669, 1996.
-
Leif Arkeryd. 1972. On the Boltzmann equation part I: Existence. Arch. Rational Mech. Anal. 45: 1–16.
-
R.J.DiPerna and P.-L.Lions. 1989. On the Cauchy problem for Boltzmann equations: global existence and weak stability. Ann. of Math. (2) 130: 321–366.
Are you absolutely sure you want to delete this article? This process cannot be undone and is permanent.
Yes, Delete This Article
Are you absolutely sure you want to remove this article? This process cannot be undone and is permanent.
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