Persistence Exponent for the Simple Diffusion Equation: The Exact Solution for Any Integer Dimension ()
ABSTRACT
The persistence exponent
for the simple diffusion equation
, with random Gaussian initial condition, has been calculated exactly using a method known as selective averaging. The probability that the value of the field
at a specified spatial coordinate remains positive throughout for a certain time
t behaves as
for asymptotically large time
t. The value of
, calculated here for any integer dimension
d, is
for
and 1 otherwise. This exact theoretical result is being reported possibly for the first time and is not in agreement with the accepted values
for
respectively.
Share and Cite:
Sanyal, D. (2021) Persistence Exponent for the Simple Diffusion Equation: The Exact Solution for Any Integer Dimension.
Journal of Modern Physics,
12, 1401-1408. doi:
10.4236/jmp.2021.1210083.
Cited by
No relevant information.