KPZ scaling exponentsin higher dimensions

KPZ scaling exponents in dimensions d = 2,3,4,5

Odor et al., Phys. Rev. E 81 (2010) 031112

0 0.1 0.2 0.3 0.41/L

2

1.5

1.6

1.7

1.8

1.9

2

z eff

0.00 0.02 0.04 0.06 0.08 0.101/L

0.18

0.2

0.22

0.24

0.26

0.28

0.3

0.32

0.34

0.36

0.38

0.4

0.42α ef

f

KPZ roughness exponent in dimension d = 2

Kelling and Odor, Phys. Rev. E 84 (2011) 061150

0 0.005 0.011/L

0.38

0.385

0.39

0.395

0.4α ef

f 102

103

104

L

1

10

W(in

f.)

Growth models

Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and ProbabilityVolume 4: Contributions to Biology and Problems of Medicine

Berkeley: University of California Press, 1961

Simulation of clusters up to 215= 32768 cells

M. Eden, 1961

”It is to be seen that the colony is essentially circular in outline. Needlessto say, there are a number of properties of each growing colony as wellas properties of the ensemble that may be worth examining, for example,moments, the eccentricity of the configurations, the roughness of the edge.”

Cluster shape and edge roughness

P. Meakin (1989)

Off-lattice Eden model

K.A. Takeuchi, JSTAT (2012) P05007

-1000 -500 0 500 1000

-1000

-500

0

500

1000φ

(a) (b)

Ballistic deposition on a line

P. Meakin, 1988

Cluster growth by ballistic deposition

P. Meakin, 1988

Cluster growth by ballistic deposition

P. Meakin, 1988

Cluster growth by ballistic deposition

P. Meakin, 1988

Cluster growth by off-lattice ballistic deposition

P. Meakin, 1988

Cluster growth by off-lattice ballistic deposition

P. Meakin, 1988

Cluster growth by three-dimensional ballistic deposition

P. Meakin, 1988

KPZ asymptotics for one-dimensional ballistic deposition

B. Farnudi, D.D. Vvedensky, Phys. Rev. E 83 (2011) 020103

KPZ asymptotics for one-dimensional ballistic deposition

B. Farnudi, D.D. Vvedensky, Phys. Rev. E 83 (2011) 020103