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Fractal Concepts in Surface Growth

Fractal Concepts in Surface Growth,10.1063/1.2808215,Physics Today,Albert László Barabasi,H. Eugene Stanley,Leonard M. Sander

Fractal Concepts in Surface Growth   (Citations: 1423)
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Journal: Physics Today - PHYS TODAY , vol. 48, no. 10, 1995
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    • ...Let us perturb the SK energy by a non-thermal δ-correlated noise function η(t, h) such that the characteristic differential equation (<0010" ref-type="disp-formula">10) takes a form comparable with the KPZ equation The renormalisation of the one-dimensional KPZ equation yields the critical exponents exactly 21 and it is known that simple rescaling does not lead to those exponents, except for the Edwards–Wilkinson behaviour near the trivial fixed point...

    R. Oppermannet al. Non-analytic quantum oscillator image of complete replica symmetry bre...

    • ...This relation is similar to the definition of the roughness exponent on the RMS diagram of Barabási and Stanley [1995], such that...
    • ...[75] The scale at which =Ds deviates from the power law relation in Figure 14a represents the approximate maximum distance where the spatial correlation of the bed forms is maintained [Barabási and Stanley, 1995]...

    Cristian Escauriazaet al. Initial stages of erosion and bed form development in a turbulent flow...

    • ...). Such a long-tail distribution is characteristic of nonlinear complex systems near critical points, and the collapse of amplitude distribution represents the scale-invariant feature of such systems ...

    Premananda Indicet al. Scaling Behavior of Human Locomotor Activity Amplitude: Association wi...

    • ...interpreted as characteristic horizontal and vertical length scales of snow crystals, whereas L and σL are associated with the typical horizontal and vertical length scales of roughness structures emerging when the snowfall mimics a ballistic deposition process, respectively (Barabási and Stanley 1995)...

    Christof Gromkeet al. Aerodynamic Roughness Length of Fresh Snow

    • ...Certain regimes of ion�stimulated cluster growth on the solid surface are also related to them [4], for example, in the processes of molecular� beam epitaxy [5]...
    • ...As follows from [4, 5], the main atomic processes on the surface are adsorption, des� orption, surface diffusion, and incorporation into the monoatomic step...
    • ...This approach is related to using scaling considerations applied to the Kardar– Parisi–Zhang equation [5]...
    • ...If this process is analyzed using the fractal con� ception [5], then it is probable that the fractal dependences are mainly characterized by the depen� dences of the limiting process (“narrow throat”)...

    Kh. B. Ashurovet al. Simulation of fractal cluster growth on a substrate under ion bombardm...

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