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Introduction to Types of Flows

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Related Experiment Video

Updated: Jun 21, 2026

Analyzing Mixing Inhomogeneity in a Microfluidic Device by Microscale Schlieren Technique

Analyzing Mixing Inhomogeneity in a Microfluidic Device by Microscale Schlieren Technique

Published on: June 12, 2015

Persistent patterns and multifractality in fluid mixing.

Bala Sundaram¹, Andrew C Poje, Arjendu K Pattanayak

¹Department of Physics, University of Massachusetts, Boston, Massachusetts 02125, USA.

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

|August 8, 2009

Summary

This study introduces a framework to understand persistent patterns in driven systems, revealing scaling laws for pattern formation and persistence. These patterns are linked to the multifractal geometry of phase space.

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Last Updated: Jun 21, 2026

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Area of Science:

Physics
Dynamical Systems
Fluid Mechanics

Background:

Persistent patterns are observed in diverse periodically driven systems, from fluid mixing to quantum-classical transitions.
Understanding the universal mechanisms behind these patterns is crucial across scientific disciplines.

Purpose of the Study:

To present a common framework for the emergence of persistent patterns in periodically driven dynamics.
To identify scaling laws governing pattern formation and persistence in phase space.
To explore the connection between persistent patterns and the underlying phase-space geometry.

Main Methods:

Utilizing a measure of structure maintenance: the average radius of the scalar distribution in transform space.
Analyzing scaling laws associated with pattern formation and persistence.
Investigating the multifractal properties of advective phase-space geometry.

Main Results:

A unified framework for understanding persistent patterns in driven systems is proposed.
Scaling laws describing the formation and persistence of patterns in phase space are derived.
Preliminary findings link scaling exponents to the multifractal nature of phase-space geometry.

Conclusions:

The proposed framework offers a generalized approach to studying persistent patterns.
Scaling laws provide quantitative insights into pattern dynamics.
The multifractal phase-space geometry plays a key role in the emergence and stability of persistent patterns.