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    Model for Shock Wave Chaos

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    PhysRevLett.110.104104.pdf
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    Type
    Article
    Authors
    Kasimov, Aslan R. cc
    Faria, Luiz cc
    Rosales, Rodolfo R.
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2013-03-08
    Permanent link to this record
    http://hdl.handle.net/10754/552862
    
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    Abstract
    We propose the following model equation, ut+1/2(u2−uus)x=f(x,us) that predicts chaotic shock waves, similar to those in detonations in chemically reacting mixtures. The equation is given on the half line, x<0, and the shock is located at x=0 for any t≥0. Here, us(t) is the shock state and the source term f is taken to mimic the chemical energy release in detonations. This equation retains the essential physics needed to reproduce many properties of detonations in gaseous reactive mixtures: steady traveling wave solutions, instability of such solutions, and the onset of chaos. Our model is the first (to our knowledge) to describe chaos in shock waves by a scalar first-order partial differential equation. The chaos arises in the equation thanks to an interplay between the nonlinearity of the inviscid Burgers equation and a novel forcing term that is nonlocal in nature and has deep physical roots in reactive Euler equations.
    Citation
    Model for Shock Wave Chaos 2013, 110 (10) Physical Review Letters
    Publisher
    American Physical Society (APS)
    Journal
    Physical Review Letters
    DOI
    10.1103/PhysRevLett.110.104104
    PubMed ID
    23521260
    arXiv
    1202.2989
    Additional Links
    http://link.aps.org/doi/10.1103/PhysRevLett.110.104104
    ae974a485f413a2113503eed53cd6c53
    10.1103/PhysRevLett.110.104104
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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