The authors present a generating function formalism for growth processes in general, and introduce a new cell renormalisation scheme. As examples, they treat the 'true' self-avoiding walk and the Eden process (or growing animals) in two and three dimensions using small cells. The results in both cases indicate a substantial increase in the fractal dimension D compared with their equilibrium counterparts. The case of the Eden process may, however, suggest a peculiar convergence behaviour as the cell size b tends to infinity.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)