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Persistence Exponent for the Simple Diffusion Equation: The Exact Solution for Any Integer Dimension
Department of Theoretical Physics, Institute of Physics, Bhubaneswar, India
- 1 Department of Theoretical Physics, Institute of Physics, Bhubaneswar, India
Journal of Modern Physics·Volume 12 (2021)·Pages 1401–1408·Published 3 August 2021·DOI10.4236/jmp.2021.1210083
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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.
KeywordsNon-Equilibrium Statistical MechanicsDiffusion EquationPersistence ExponentProbability Theory
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