TY - JOUR
T1 - Diffusive persistence and the "sign-time" distribution
AU - Newman, T. J.
AU - Toroczkai, Z.
PY - 1998/9/1
Y1 - 1998/9/1
N2 - We present a method for extracting the persistence exponent ? for the diffusion equation, based on the distribution P of "sign times." With the aid of a numerically verified ansatz for P, we derive an analytic formula for ? (in arbitrary spatial dimension d) which we conjecture to be the exact result. Our results are in excellent agreement with previous numerical studies. Furthermore, our results indicate a qualitative change in P above d = 36, signaling the existence of a sharp change in the ergodic properties of the diffusion field.
AB - We present a method for extracting the persistence exponent ? for the diffusion equation, based on the distribution P of "sign times." With the aid of a numerically verified ansatz for P, we derive an analytic formula for ? (in arbitrary spatial dimension d) which we conjecture to be the exact result. Our results are in excellent agreement with previous numerical studies. Furthermore, our results indicate a qualitative change in P above d = 36, signaling the existence of a sharp change in the ergodic properties of the diffusion field.
UR - https://www.scopus.com/pages/publications/0000260753
U2 - 10.1103/PhysRevE.58.R2685
DO - 10.1103/PhysRevE.58.R2685
M3 - Article
AN - SCOPUS:0000260753
SN - 1550-2376
VL - 58
SP - R2685-R2688
JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
IS - 3
ER -