Anomalous roughness with system-size-dependent local roughness exponent

Abstract

We note that in a system far from equilibrium the interface roughening may depend on the system size which plays the role of control parameter. To detect the size effect on the interface roughness, we study the scaling properties of rough interfaces formed in paper

Nonuniversal effects in mixing correlated-growth processes with randomness: Interplay between bulk morphology and surface roughening

“…The dynamics of correlation buildup in these physical systems, and their other properties, can then be explored with the use of surfacegrowth methodologies. Numerous examples of such studies, experimental as well as theoretical and computational, come from a variety of fields such as tumor-growth processes [1] in cancer research, growth of cell colonies [2] in biophysics, roughening of lipid bilayers [3] in softmatter biomaterials, dynamics of combustion fronts [5], imbibition processes [4], film-growth processes [6], timeseries and market price analyses in econo-physics [7], and scalability and synchronization of parallel-computing system [8,9] in computer science, to give representative examples.…”

Characterization of rough interfaces obtained by boriding

“…These exponents determine the universality class of kinetic roughening process under consideration. 3 While the self-affine and self-similar roughness of growing interfaces was observed in many physical systems (see [11][12][13][14][15]), more generally, the scaling behavior of local surface width, sðDxÞ / ðDxÞ z 2 , is characterized by the local roughness exponent z 2 , which is less or equal to the global roughness exponent, i.e., z 2 a [47][48][49][50][51][52][53][54]. The case of z 2 = a = H corresponds to self-affine (or self-similar, if z 2 = a = H = 1 [45]) surfaces, whereas surface roughness characterized by z 2 < a is termed as an ''anomalous'' roughness [47] and it is characterized by three or more independent scaling exponents, e.g., z 2 , a, and z, etc.…”

“…The Family-Vicsek and generic scaling dynamics are observed in a grain variety of physical systems [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. However, in many cases the local geometry of the interface is not pure self-similar or self-affine, rather than multi-fractal [20,22,23,[55][56][57][58] or multiaffine [59][60][61][62][63][64][65]. The multiscaling properties of such interfaces can be investigated by calculating the q-order height-height correlation function defined as…”

Depinning and dynamics of imbibition fronts in paper under increasing ambient humidity

“…x=0 |z(x) − z(x + x)| q ) 1/q (see, for details, Ref. [33]). Furthermore, in contrast to the increase of global front width W ∝ t α expected in the case of kinetic roughening and always observed in paper imbibition experiments at a constant humidity [4][5][6][7][8][9][10], we found that the global width of the wetting front moving in regime (3) tends to decrease in time (see Fig.…”