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  • 1
    Electronic Resource
    Electronic Resource
    On the shape of wedding cakes (1997)
    Springer
    Journal of statistical physics 87 (1997), S. 505-518 
    Details
    ISSN: 1572-9613
    Keywords: Crystal growth ; growth instability ; surface diffusion ; singular diffusion equations ; hydrodynamic limit
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The large-scale morphology of a growing surface is characterized for a simple model of crystal growth in which interlayer transport is completely suppressed due to the Ehrlich-Schwoebel effect. In the limit where the ratio of the surface diffusion coefficient to the deposition rateD/F→∞ the surface consists of wedding-cake-like structures whose shape is given by the inverse of an error function. The shape can be viewed as a separable solution of the singular diffusion equationu 1=[u −2 u x ] x . As an application, expressions for the number of exposed layers as a function of coverage and diffusion length are derived.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02181234
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Hydrodynamics and Platoon Formation for a Totally Asymmetric Exclusion Model with Particlewise Disorder (1999)
    Springer
    Journal of statistical physics 95 (1999), S. 525-567 
    Details
    ISSN: 1572-9613
    Keywords: interacting particle systems ; quenched disorder ; asymmetric exclusion ; hydrodynamic limit ; phase separation ; traffic models
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We consider a one-dimensional totally asymmetric exclusion model with quenched random jump rates associated with the particles, and an equivalent interface growth process on the square lattice. We obtain rigorous limit theorems for the shape of the interface, the motion of a tagged particle, and the macroscopic density profile on the hydrodynamic scale. The theorems are valid under almost every realization of the disordered rates. Under suitable conditions on the distribution of jump rates the model displays a disorder-dominated low-density phase where spatial inhomogeneities develop below the hydrodynamic resolution. The macroscopic signature of the phase transition is a density discontinuity at the front of the rarefaction wave moving out of an initial step-function profile. Numerical simulations of the density fluctuations ahead of the front suggest slow convergence to the predictions of a deterministic particle model on the real line, which contains only random velocities but no temporal noise.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1007535124155
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    Paper (German National Licenses)
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