Improved Convergence for Two-Component Activity Expansions

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It is well known that an activity expansion of the grand canonical partition function works well for attractive interactions, but works poorly for repulsive interactions, such as occur between atoms and molecules. The virial expansion of the canonical partition function shows just the opposite behavior. This poses a problem for applications that involve both types of interactions, such as occur in the outer layers of low-mass stars. We show that it is possible to obtain expansions for repulsive systems that convert the poorly performing Mayer activity expansion into a series of rational polynomials that converge uniformly to the virial expansion. ... continued below

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DeWitt, H E; Rogers, F J & Sonnad, V March 6, 2007.

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It is well known that an activity expansion of the grand canonical partition function works well for attractive interactions, but works poorly for repulsive interactions, such as occur between atoms and molecules. The virial expansion of the canonical partition function shows just the opposite behavior. This poses a problem for applications that involve both types of interactions, such as occur in the outer layers of low-mass stars. We show that it is possible to obtain expansions for repulsive systems that convert the poorly performing Mayer activity expansion into a series of rational polynomials that converge uniformly to the virial expansion. In the current work we limit our discussion to the second virial approximation. In contrast to the Mayer activity expansion the activity expansion presented herein converges for both attractive and repulsive systems.

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PDF-file: 25 pages; size: 2.2 Mbytes

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  • Journal Name: Physical Review E, E77, N/A, May 30, 2008, pp. 051133; Journal Volume: E77

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  • Report No.: UCRL-JRNL-229005
  • Grant Number: W-7405-ENG-48
  • Office of Scientific & Technical Information Report Number: 940497
  • Archival Resource Key: ark:/67531/metadc894861

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  • March 6, 2007

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  • Sept. 27, 2016, 1:39 a.m.

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  • Dec. 7, 2016, 3:31 p.m.

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DeWitt, H E; Rogers, F J & Sonnad, V. Improved Convergence for Two-Component Activity Expansions, article, March 6, 2007; Livermore, California. (digital.library.unt.edu/ark:/67531/metadc894861/: accessed December 16, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.