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Orientational Transition in a Liquid Crystal Triggered by the Thermodynamic Growth of Interfacial Wetting Sheets

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Published on: May 15, 2017

Scaling ansatz for the jamming transition.

Carl P Goodrich¹, Andrea J Liu², James P Sethna³

¹Department of Physics, University of Pennsylvania, Philadelphia, PA 19104; School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138; goodrich@g.harvard.edu.

Proceedings of the National Academy of Sciences of the United States of America

|August 12, 2016

Summary

We introduce a new scaling theory for the critical jamming transition. This theory reveals universal scaling relations between various system properties, simplifying the understanding of this complex phenomenon.

Keywords:

jamming transition nonequilibrium critical phenomena scaling ansatz

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Area of Science:

Physics
Materials Science
Statistical Mechanics

Background:

The jamming transition is a critical phenomenon observed in many disordered systems, such as granular materials and dense suspensions.
Understanding the scaling behavior near the jamming point is crucial for predicting material properties.

Purpose of the Study:

To propose a novel scaling ansatz for the critical jamming transition.
To establish universal scaling relations between key physical quantities.

Main Methods:

Development of a Widom-like scaling ansatz for elastic energy.
Extraction of scaling exponents from existing numerical and theoretical data.
Numerical verification of scaling predictions for energy and residual shear stress.

Main Results:

Identified three independent scaling exponents governing the jamming transition.
Derived a scaling relation between pressure and residual shear stress.
Demonstrated emergent scale invariance in the jamming transition.

Conclusions:

The proposed scaling theory provides a unified framework for understanding critical jamming.
The findings pave the way for developing a renormalization group theory for jamming.
The theory offers insights into the differing scaling of shear and bulk moduli.