Critical dimensions of the diffusion equation.
We study the evolution of a random initial field under pure diffusion in various space dimensions. From numerical calculations we find that the persistence properties of the system show sharp transitions at critical dimensions d(1) approximately 26 and d(2) approximately 46. We also give refined measurements of the persistence exponents for low dimensions.
Newman
T J
TJ
Department of Physics, University of Virginia, Charlottesville, VA 22904, USA. tjnewman@virginia.edu
Loinaz
W
W