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    Nucleation and propagation of phase mixtures in a bistable chain

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    VanVleck_PRB_79(14)144123.pdf (335.0Kb)
    Issue Date
    2009-04-29
    Author
    Vainchtein, Anna
    Van Vleck, Erik S.
    Publisher
    American Physical Society
    Type
    Article
    Article Version
    Scholarly/refereed, publisher version
    Metadata
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    Abstract
    We consider a prototypical discrete model of phase transitions. The model consists of a chain of particles, each interacting with its nearest and next-to-nearest neighbors. The long-range interaction between next-to-nearest neighbors is assumed to be harmonic, while the nearest-neighbor interactions are nonlinear and bistable. We consider overdamped dynamics of the chain and after suitable rescaling obtain a discrete reaction-diffusion equation with a negative diffusion coefficient. Using a biquadratic nearest-neighbor interaction potential and introducing new variables, we construct and study traveling-wave-like solutions that describe dynamics of phase mixtures in the lattice. Depending on the value of the applied force, phase mixtures either get trapped in one of the multiple equilibrium states or propagate through the chain at a constant speed. At low velocities near the depinning threshold, the motion is of stick-slip type. Numerical results for smoother potentials also suggest the existence and stability of the steady motion in a certain range of applied loads.
    Description
    This item is copyrighted by the American physical society, and can be found electronically from http://journals.aps.org/prb/abstract/10.1103/PhysRevB.79.144123.
    URI
    http://hdl.handle.net/1808/17384
    DOI
    https://doi.org/10.1103/PhysRevB.79.144123
    ISSN
    1098-0121
    Collections
    • Mathematics Scholarly Works [282]
    Citation
    Vainchtein, Anna; Van Vleck, Erik. (2009). "Nucleation and propagation of phase mixtures in a bistable chain." Physical Revew B, 79(14):144123. http://www.dx.doi.org/10.1103/PhysRevB.79.144123

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    Contact KU ScholarWorks
    785-864-8983
    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    785-864-8983

    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    Image Credits
     

     

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