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Related Experiment Video

Updated: Jun 8, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow

The Diffusion of Passive Tracers in Laminar Shear Flow

Published on: May 1, 2018

Universal statistics of branched flows.

Jakob J Metzger¹, Ragnar Fleischmann, Theo Geisel

¹Max-Planck-Institute for Dynamics and Self-Organization, Bunsenstraße 10, 37073 Göttingen, Germany.

Physical Review Letters

|September 28, 2010

Summary

Weakly correlated disorder potentials cause extreme fluctuations in Hamiltonian flows, leading to flow branching in 2D systems. This study provides a quantitative theory and scaling relations for branching statistics, applicable across diverse physical systems.

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Area of Science:

Physics
Statistical Mechanics
Condensed Matter Physics

Background:

Correlated disorder potentials can induce significant fluctuations in physical systems.
Hamiltonian flows in two dimensions exhibit pronounced branching phenomena due to these fluctuations.
A quantitative theoretical framework for branching statistics in such systems is currently lacking.

Purpose of the Study:

To develop a quantitative theory for the branching statistics of Hamiltonian flows in the presence of weak correlated disorder potentials.
To derive an analytical expression for the number of branches as a function of distance from a source.
To establish universal scaling relations for this branching phenomenon.

Main Methods:

Derivation of an analytical expression for the number of branches.
Development of scaling relations to ensure universality.
Theoretical analysis of Hamiltonian flows under random potentials.

Main Results:

An analytical expression for the number of branches has been derived, valid for all distances from a source.
Universal scaling relations have been established, applicable to a wide range of random potentials.
The derived theory quantifies the branching statistics of 2D Hamiltonian flows.

Conclusions:

The developed theory provides a quantitative understanding of flow branching caused by weak correlated disorder.
The findings offer a universal framework applicable to diverse physical systems.
Potential applications span fields such as semiconductor physics and geophysics.