Diffusion in phase space

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In order to study diffusion in any region of phase space containing nested closed curves we choose action-angle variables, {gamma}, J. the action J labels each closed phase curve and is equal to its area divided by 2{pi}. We can introduce rectangular variables Q,P by the equations Q=(2J){sup 1/2}sin{gamma}, P=(2J){sup 1/2}cos{gamma}, where the angle variable {gamma} is measured clockwise from the P-axis. The phase curves are circles in the Q,P plane with radius (2J){sup 1/2}. We assume that the motion consists of a Hamiltonian motion along a curve of fixed J (in the original coordinate system and in the system ... continued below

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11 p.

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Symon, K. April 5, 1993.

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Description

In order to study diffusion in any region of phase space containing nested closed curves we choose action-angle variables, {gamma}, J. the action J labels each closed phase curve and is equal to its area divided by 2{pi}. We can introduce rectangular variables Q,P by the equations Q=(2J){sup 1/2}sin{gamma}, P=(2J){sup 1/2}cos{gamma}, where the angle variable {gamma} is measured clockwise from the P-axis. The phase curves are circles in the Q,P plane with radius (2J){sup 1/2}. We assume that the motion consists of a Hamiltonian motion along a curve of fixed J (in the original coordinate system and in the system Q,P) plus a diffusion and a damping which can change the value of J. Now consider a system of particles described by a density {rho}(J,t), so that the number of particles between the curves J and J+dJ is dN={rho}(J,t)dJ. These cN particles are distributed uniformly in the phase space between the curves J and J+dJ.

Physical Description

11 p.

Notes

INIS; OSTI as DE95015210

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  • Other Information: PBD: 5 Apr 1993

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  • Other: DE95015210
  • Report No.: LS--221
  • Grant Number: W-31-109-ENG-38
  • DOI: 10.2172/101346 | External Link
  • Office of Scientific & Technical Information Report Number: 101346
  • Archival Resource Key: ark:/67531/metadc618360

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Office of Scientific & Technical Information Technical Reports

Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

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  • April 5, 1993

Added to The UNT Digital Library

  • June 16, 2015, 7:43 a.m.

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  • Dec. 14, 2015, 11:39 a.m.

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Symon, K. Diffusion in phase space, report, April 5, 1993; Illinois. (digital.library.unt.edu/ark:/67531/metadc618360/: accessed December 11, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.