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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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Published on: September 26, 2016

Two-particle anomalous diffusion: probability density functions and self-similar stochastic processes.

Gianni Pagnini¹, Antonio Mura, Francesco Mainardi

¹CRS4, Polaris Building 1, 09010 Pula, Cagliari, Italy.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences

|April 3, 2013

Summary

This study unifies two models of anomalous diffusion using self-similar stochastic processes. It computes particle separation density under time subordination, revealing insights into complex particle movement dynamics.

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Area of Science:

Physics
Mathematics
Statistical Mechanics

Background:

Anomalous diffusion describes particle movement deviating from standard Brownian motion.
Time subordination models introduce complex temporal dependencies in diffusion processes.

Purpose of the Study:

To unify two distinct time subordination models within a self-similar stochastic process framework.
To investigate two-particle dispersion under anomalous diffusion conditions.

Main Methods:

Utilizing single-particle fractional Brownian motion.
Modeling two-particle correlation functions with power-law decay.
Computing particle relative separation density under different time subordination schemes (M-Wright and Lévy stable densities).

Main Results:

The study unifies two time subordination models for anomalous diffusion.
Particle relative separation density was computed for M-Wright and Lévy stable density driven subordination.
Self-similar stochastic processes were represented using fractional Brownian motion with stochastic variance.

Conclusions:

The unified framework provides a comprehensive approach to understanding two-particle dispersion in anomalous diffusion.
The choice of subordination density (M-Wright or Lévy stable) influences the statistical properties of particle separation.
This work offers a robust mathematical representation for complex diffusion phenomena.