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Anomalous diffusion with transient subordinators: a link to compound relaxation laws
Aleksander Stanislavsky1, Karina Weron2, Aleksander Weron3
1Institute of Radio Astronomy, Ukrainian National Academy of Sciences, 4 Chervonopraporna St., 61002 Kharkov, Ukraine.
This study identifies transient subordinators causing anomalous diffusion in complex systems. It links these to fractional diffusion equations and generalized relaxation laws, offering a new framework for understanding diffusion dynamics.
Area of Science:
- Physics
- Physical Chemistry
- Complex Systems
Background:
- Anomalous diffusion is observed in diverse complex systems.
- Nonscaling behavior in diffusion indicates changing time-scaling exponents.
- Understanding transient anomalous diffusion requires new theoretical frameworks.
Purpose of the Study:
- To identify the underlying mechanisms of transient anomalous diffusion.
- To develop a generalized fractional diffusion equation for these phenomena.
- To connect anomalous diffusion with compound relaxation laws.
Main Methods:
- Identification of transient subordinators.
- Derivation of fractional diffusion equations.
- Analysis of compound relaxation laws.
Main Results:
- Transient subordinators are identified as key to transient anomalous diffusion.
- A fractional diffusion equation is derived for these processes.
- Links between anomalous diffusion and generalized relaxation laws are established.
Conclusions:
- The study provides a theoretical basis for transient anomalous diffusion.
- The findings generalize existing empirical relaxation laws.
- This work offers a more comprehensive understanding of diffusion in complex systems.
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