Lattice defects as Lotka-Volterra societies

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Since the early part of this century the Lotka-Volterra or predator-prey equations have been known to simulate the stability, instability, and persistent oscillations observed in many biological and ecological societies. These equations have been modified in many ways and have been used to model phenomena as varied as childhood epidemics, enzyme reactions, and conventional warfare. In the work to be described, similarities are drawn between various lattice defects and Lotka-Volterra (LV) societies. Indeed, grain boundaries are known to ``consume`` dislocations, inclusions ``infect`` grain boundaries, and dislocations ``annihilate`` dislocations. Several specific cases of lattice defect interaction kinetics models are drawn from ... continued below

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6 p.

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Yost, F.G. July 1, 1995.

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This article is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided by UNT Libraries Government Documents Department to Digital Library, a digital repository hosted by the UNT Libraries. More information about this article can be viewed below.

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  • Sandia National Laboratories
    Publisher Info: Sandia National Labs., Albuquerque, NM (United States)
    Place of Publication: Albuquerque, New Mexico

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Description

Since the early part of this century the Lotka-Volterra or predator-prey equations have been known to simulate the stability, instability, and persistent oscillations observed in many biological and ecological societies. These equations have been modified in many ways and have been used to model phenomena as varied as childhood epidemics, enzyme reactions, and conventional warfare. In the work to be described, similarities are drawn between various lattice defects and Lotka-Volterra (LV) societies. Indeed, grain boundaries are known to ``consume`` dislocations, inclusions ``infect`` grain boundaries, and dislocations ``annihilate`` dislocations. Several specific cases of lattice defect interaction kinetics models are drawn from the materials science literature to make these comparisons. Each model will be interpreted as if it were a description of a biological system. Various approaches to the modification of this class of interaction kinetics will be presented and discussed. The earliest example is the Damask-Dienes treatment of vacancy-divacancy annealing kinetics. This historical model will be modified to include the effects of an intermediate species and the results will be compared with the original model. The second example to be examined is the Clark-Alden model for deformation-enhanced grain growth. Dislocation kinetics will be added to this model and results will be discussed considering the original model. The third example to be presented is the Ananthakrishna-Sahoo model of the Portevin-Le Chatelier effect that was offered in 1985 as an extension of the classical Cottrell atmosphere explanation. Their treatment will be modified by inclusion of random interference from a pesky but peripheral species and by allowing a rate constant to be a function of time.

Physical Description

6 p.

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OSTI as DE95015250

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  • Materials Week `95, Cleveland, OH (United States), 29 Oct - 2 Nov 1995

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  • Other: DE95015250
  • Report No.: SAND--95-0991C
  • Report No.: CONF-951026--4
  • Grant Number: AC04-94AL85000
  • Office of Scientific & Technical Information Report Number: 102193
  • Archival Resource Key: ark:/67531/metadc621936

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  • July 1, 1995

Added to The UNT Digital Library

  • June 16, 2015, 7:43 a.m.

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  • April 14, 2016, 9:04 p.m.

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Yost, F.G. Lattice defects as Lotka-Volterra societies, article, July 1, 1995; Albuquerque, New Mexico. (digital.library.unt.edu/ark:/67531/metadc621936/: accessed September 19, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.