Abstract
We have discovered here a duality relation between infinitely divisible subordinators which can produce both retarding and accelerating anomalous diffusion in the framework of the special Bernstein function approach. As a consequence, we show that conjugate pairs of Bernstein functions taken as Laplace exponents can produce in a natural way both retarding and accelerating anomalous diffusion (either subdiffusion or superdiffusion). This provides a unified way to control the dynamics of complex biological processes leading to transient anomalous diffusion in single-particle tracking experiments. Moreover, this permits one to explain better the relaxation diagram positioning two different power laws of relaxation, including the celebrated Havriliak-Negami law.
- Received 11 January 2020
- Revised 28 March 2020
- Accepted 21 April 2020
DOI:https://doi.org/10.1103/PhysRevE.101.052119
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