Trimming a Combinatorical Tree

ORAL

Abstract

In computational material science, one frequently needs to know the number of unique atomic configurations in a structure. For example in an A$_{3}$B phase, two different kinds of atoms may be present on the B sites. In modeling possible alloys one needs to know the number of possible arrangements on the B sites. The obvious solution to this combinatorics problem is to generate the list of all possible configurations and then eliminate those that are symmetrically equivalent. This approach, however, suffers from a combinatoric explosion, particularly for large structures with more than two atom types. This happens even when there are a large number of symmetrically-equivalent configurations and only a few unique configurations that survive the elimination process. We developed a new algorithm that avoids this problem by not generating the entire list of configurations. Instead, it generates ``partial configurations'' and applies the symmetry operations without finding each ``complete'' configuration. This algorithm allows us to tackle much larger problems due to increases in computational efficiency.

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Authors

  • Wiley Morgan

    Brigham Young University

  • John Colton

    Brigham Young University Dept. of Physics and Astronomy, Brigham Young University, None, The College of William and Mary/Jefferson Lab, Brigham Young University-Idaho, Blue Ridge Research and Consulting LLC, Air Force Research Laboratory - Wright Patterson Air Force Base, Brigham Young Univ - Provo, Blue Ridge Research and Consulting, University of Utah, SRI International, Utah State University, Utah Valley University, Los Alamos National Laboratory, Professor, Graduate, United States Air Force Academy, Arizona State Univ, SiO2 NanoTech, Entrepix Inc, AFRL, Advisor, Brigham Young University- Provo, University of New Mexico, Univ of Utah, University of Wisconsin -- Madison, New Mexico Tech Physics Dept., Retired, Department of Physics and Astronomy, University of Utah, Department of Physics \& Astronomy, University of Hawai'i, JILA and University of Colorado, Boulder, National Institute of Standards and Technology, Boulder, University of Colorado, Boulder, Lawrence Berkeley National Laboratory, National Institute of Standards and Technology, Space Dynamics Lab, New Mexico Tech, BYU Professor, Brigham Young University -- Provo, Northern Arizona University, University of Colorado Boulder, Colorado State University, University of Utah, Department of Physics, New Mexico State University

  • John Colton

    Brigham Young University Dept. of Physics and Astronomy, Brigham Young University, None, The College of William and Mary/Jefferson Lab, Brigham Young University-Idaho, Blue Ridge Research and Consulting LLC, Air Force Research Laboratory - Wright Patterson Air Force Base, Brigham Young Univ - Provo, Blue Ridge Research and Consulting, University of Utah, SRI International, Utah State University, Utah Valley University, Los Alamos National Laboratory, Professor, Graduate, United States Air Force Academy, Arizona State Univ, SiO2 NanoTech, Entrepix Inc, AFRL, Advisor, Brigham Young University- Provo, University of New Mexico, Univ of Utah, University of Wisconsin -- Madison, New Mexico Tech Physics Dept., Retired, Department of Physics and Astronomy, University of Utah, Department of Physics \& Astronomy, University of Hawai'i, JILA and University of Colorado, Boulder, National Institute of Standards and Technology, Boulder, University of Colorado, Boulder, Lawrence Berkeley National Laboratory, National Institute of Standards and Technology, Space Dynamics Lab, New Mexico Tech, BYU Professor, Brigham Young University -- Provo, Northern Arizona University, University of Colorado Boulder, Colorado State University, University of Utah, Department of Physics, New Mexico State University