How do Surfaces Grow?


Le Chen

le.chen@auburn.edu
Department of Mathematics and Statistics
Auburn University

Destination STEM
Auburn, AL, Oct. 2, 2024

NSF

DMS-Probability: No. 2246850
(2023-2026)

Simons

No. 959981
(2022-2027)

Sand pile at the beach vs Snow pile in winter

Contrasting Sand and Snow Piles

Image created by OpenAI's DALL-E

Model for sand pile

Simulation by Tetris-Ballistic package

Model for snow pile

Simulation by Tetris-Ballistic package

Nonsticky

Sticky

Growing interfaces in a thin film

[4] K. A. Takeuchi, M. Sano, T. Sasamoto, and H. Spohn. Growing interfaces uncover universal fluctuations behind scale invariance. Sci. Rep., 1(1):1--5, 2011. [ bib ]

Other examples

Paper inking

[1] A.-L. Barabási and H. E. Stanley. Fractal concepts in surface growth. Cambridge University Press, Cambridge, 1995. [ bib | DOI | http ]

Paper burning

[5] J. Zhang, Y.-C. Zhang, P. Alstrøm, and M. Levinsen. Modeling forest fire by a paper-burning experiment, a realization of the interface growth mechanism. Phys. A: Stat. Mech. Appl., 189(3):383--389, 1992. [ bib | DOI | http ]

Snow pile in one dimension

[1] A.-L. Barabási and H. E. Stanley. Fractal concepts in surface growth. Cambridge University Press, Cambridge, 1995. [ bib | DOI | http ]

Diffusion-limited aggregation (DLA)

[5] T. A. Witten and L. M. Sander. Diffusion-limited aggregation, a kinetic critical phenomenon. Phys. Rev. Lett., 47:1400--1403, 1981-11. [ bib | DOI | http ]

Thank you!