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Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

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g-fractional diffusion models in bounded domains.

L Angelani^1,2, R Garra³

¹ISC-CNR, Institute for Complex Systems, Piazzale A. Moro 2, 00185 Rome, Italy.

Physical Review. E

|February 17, 2023

Summary

This summary is machine-generated.

This study introduces g-fractional diffusion, showing a finite mean first-passage time (MFPT) is achievable. This contrasts with standard fractional diffusion models, offering new insights into anomalous diffusion dynamics.

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Area of Science:

Mathematical Physics
Fractional Calculus
Anomalous Diffusion Modeling

Background:

Anomalous diffusion phenomena exhibit continuous transitions between subdiffusive regimes.
Existing literature explores g-subdiffusion equations with Caputo fractional derivatives.
The behavior of g-fractional diffusion in bounded domains with absorbing boundaries requires investigation.

Purpose of the Study:

To investigate g-fractional diffusion in a bounded domain with absorbing boundaries.
To derive the explicit solution for the initial boundary value problem.
To analyze the first-passage time distribution and mean first-passage time (MFPT).

Main Methods:

Utilized Caputo fractional derivatives with respect to another function (g-derivatives).
Developed analytical solutions for the initial boundary value problem in g-fractional diffusion.
Analyzed first-passage time statistics, including the mean first-passage time (MFPT).

Main Results:

Derived the explicit solution for the g-fractional diffusion initial boundary value problem.
Characterized the first-passage time distribution and calculated the MFPT.
Demonstrated that a specific choice of the function g yields a finite MFPT.

Conclusions:

The g-fractional diffusion model allows for a finite MFPT, unlike classical fractional heat equations.
This finding offers a novel approach to modeling anomalous diffusion with controlled escape times.
The study provides a theoretical framework for understanding and controlling anomalous diffusion processes.