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Proteins show rotational as well as lateral diffusion across the membrane. The lateral diffusion of proteins was confirmed through the cell fusion experiment where mouse and human cells were fused, resulting in hybrid cells. When the human and mouse cells fused, the specific membrane proteins on human and mouse cells were marked with the red and green-fluorescent markers, respectively. Initially, the red and green fluorescence was located on the respective hemisphere of the cell. As time...

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Updated: Jun 12, 2026

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

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

Published on: September 26, 2016

Anomalous diffusion as a stochastic component in the dynamics of complex processes.

Serge F Timashev¹, Yuriy S Polyakov, Pavel I Misurkin

¹Institute of Laser and Information Technologies, Russian Academy of Sciences, Troitsk, Pionerskaya Str. 2, Moscow Region 142190, Russia.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|May 21, 2010

Summary

This study introduces a new method using a second-order difference moment to identify anomalous diffusion in complex systems. The technique successfully analyzes diverse processes, broadening the scope for detecting anomalous diffusion.

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Area of Science:

Physics
Complex Systems Analysis
Nonlinear Dynamics

Background:

Anomalous diffusion describes non-standard particle movement in complex systems.
Characterizing stochastic dynamics in systems with nonlinear interactions is challenging.
Identifying anomalous diffusion requires robust analytical methods.

Purpose of the Study:

To propose a novel interpolation expression for identifying anomalous diffusion.
To utilize the second-order difference moment (Kolmogorov transient structural function) as a key characteristic.
To apply the method to various complex natural processes.

Main Methods:

Developing an interpolation expression based on the second-order difference moment.
Analyzing the stochastic dynamics of systems in a steady state (large time intervals).
Applying the procedure to experimental data from quantum dot fluorescence, X-ray emissions, Rayleigh-Bénard convection, and seismic geoelectrical signals.

Main Results:

The proposed interpolation expression adequately describes the experimental difference moment in all tested complex processes.
Anomalous diffusion was confirmed to manifest in blinking fluorescence, accreting object emissions, convection fluid dynamics, and seismic signals.
The method provides a reliable way to identify and quantify anomalous diffusion parameters.

Conclusions:

The developed method effectively identifies anomalous diffusion in complex systems.
The findings suggest anomalous diffusion is prevalent in a wider range of natural phenomena than previously recognized.
This research expands the toolkit for analyzing complex system dynamics.