Dynamical scaling of the surface of finite-density ballistic aggregation

Baiod, R.; Kessler, David A.; Ramanlal, P.; Sander, Leonard M.; Savit, Robert

doi:10.1103/physreva.38.3672

Cited by 49 publications

(17 citation statements)

References 16 publications

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“…The results for BD are scattered but two of the results [11,12] are close enough to the exact KPZ values. In two dimensions the values of the KPZ systems are not known exactly.…”

Section: Introductionmentioning

confidence: 91%

What is the connection between ballistic deposition and the Kardar-Parisi-Zhang equation?

Katzav

Schwartz

2004

Phys. Rev. E

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Ballistic deposition (BD) is believed to belong to the Kardar-Parisi-Zhang (KPZ) universality class. In this paper we study the validity of this belief by rigorously deriving a continuum equation from the BD microscopic rules, which deviates from the KPZ equation. We show that in one dimension and in the presence of noise the deviation is not important. This is not the case in the absence of noise. In more than one dimension and in the presence of noise we obtain an equation that superficially seems to be a continuum equation but in which the symmetry under rotations around the growth direction is broken.

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“…The results for BD are scattered but two of the results [11,12] are close enough to the exact KPZ values. In two dimensions the values of the KPZ systems are not known exactly.…”

Section: Introductionmentioning

confidence: 91%

What is the connection between ballistic deposition and the Kardar-Parisi-Zhang equation?

Katzav

Schwartz

2004

Phys. Rev. E

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“…The roughness exponent χ is an important parameter [31] in the studies of adsorption, catalysis [32], and optical properties [33] of a thin film. The properties of a rough surface are determined by the distribution of height fluctuations and it deserves attention both in theoretical and experimental studies of growing interfaces [4].…”

Section: Introductionmentioning

confidence: 99%

Skewness in(1+1)-dimensional Kardar-Parisi-Zhang–type growth

Singha

Nandy

2014

Phys. Rev. E

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We use the (1 + 1)-dimensional Kardar-Parisi-Zhang equation driven by a Gaussian white noise and employ the dynamic renormalization-group of Yakhot and Orszag without rescaling [J. Sci. Comput. 1, 3 (1986)]. Hence we calculate the second and third order moments of height distribution using the diagrammatic method in the large scale and long time limits. The moments so calculated lead to the value S = 0.3237 for the skewness. This value is comparable with numerical and experimental estimates.

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“…al. [15] obtained β = 1/3 in 2 dimensions and α = 0.3 and β = 0.22 in 3 dimensions; off-lattice simulations have also given β = 0.343 in 2 dimensions [16], but a clear scaling behaviour was not observed in 3 dimensions [17].…”

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confidence: 95%