Observation of Conservations Laws in Diffusion Limited Aggregation

Details Observation of Conservations Laws in Diffusion Limited Aggregation Observation of Conservations Laws in Diffusion Limited Aggregation

1994-12-06

arxiv.org/abs/patt-sol/9412001v1

Nonlinear Sciences

Pattern Formation and Solitons

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Scientific paper

10.1103/PhysRevLett.72.880

We repeat the numerical experiments for diffusion limited aggregation (DLA) and show that there is a potentially infinite set of conserved quantities for the long time asymptotics. We connect these observations with the exact integrability of the continuum limit of the DLA (quasi-static Stefan problem). The conserved quantities of the Stefan problem (harmonic moments) when discretized are our conserved quantities. These numerical experiments show that the exact integrability of the Stefan problem may be continued beyond the formation of cusps in the moving boundary.

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