Dynamic scaling phenomena in growth processes

Abstract

Inhomogeneities in a deposition process may lead to formation of rough surfaces. Fluctuations in the height h(x, t), of the surface (at location x and time t) can be probed directly by scanning microscopy, or indirectly by scattering. Analytical or numerical treatments of simple growth models suggest that, quite generally, the height fluctuations have a self-similar character; their average correlations exhibiting a dynamic scaling form,. The roughness and dynamic exponents, α and z, are expected to be universal; depending only on the underlying mechanism that generates self-similar scaling. Despite its ubiquitous occurrence in theory and simulations, experimental confirmation of dynamic scaling has been scarce. In some cases where such scaling has been observed, the exponents are different from those expected on the basis of analysis or numerics. I shall briefly review the theoretical foundations of dynamic scaling, and suggest possible reasons for discrepancies with experimental results.

Roughening of the interfaces in(1+1)-dimensional two-component surface growth with an admixture of random deposition

“…The super-rough dynamics of tumor growth [15] is the first experimental observation of anomalous scaling in (1+1) dimension. Another issue is the clear experimental observation of the KPZ universality and the role of quenched noise in the asymptotic KPZ scaling [5,8,16]. For one dimensional KPZ growth, by applying a weak noise canonical phase-space method, it has been shown recently that the KPZ dynamic exponent is associated with the soliton dispersion law [17].…”

“…The theory behind kinetic roughening and the origins of scale invariance are well understood [3,5,6,7,8,9], but there are numerous instances of growth processes that neither follow one power law nor exhibit a clear-cut universality as it is expressed by the FV scaling. One group of examples is the anomalous roughening in epitaxial growth models [5,10,11], fractures [12,13] and in models with subdiffusive behavior or quenched disorder [14].…”

Thermal quench effects on ferroelectric domain walls

“…Understanding this behavior is key to the physics of many diverse disordered elastic systems (DES) [2][3][4][5][6][7][8][9] and of significant technological interest for memory and electromechanical ferroelectric applications [10][11][12] , and devices using the domain walls as nanoscale functional components 13,14 , in which control over the stability and growth of domain structures is of paramount importance.…”

Dynamics of Disordered Elastic Systems

“…We will not enter in more details about the statics here and refer the reader to the literature on that point [44,9].…”