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Updated: Jun 2, 2026

Fabrication and Characterization of Disordered Polymer Optical Fibers for Transverse Anderson Localization of Light
Published on: July 29, 2013
Density fluctuations of polymers in disordered media
J M Deutsch1, M Olvera de la Cruz
1Department of Physics, University of California, Santa Cruz, California 95064, USA.
Self-avoiding walks in disordered environments exhibit multifractal statistics for monomer density. This multifractality persists even away from the percolation transition, but disappears beyond the solution
Area of Science:
- Statistical physics
- Polymer physics
- Disordered systems
Background:
- Self-avoiding walks (SAWs) are fundamental models for polymer chains.
- Disordered environments introduce complex interactions and site exclusions.
- Multifractal statistics describe systems with spatially varying properties.
Purpose of the Study:
- To investigate the statistical properties of SAWs in randomly excluded site environments.
- To analyze the monomer density distribution of single polymer chains.
- To examine the behavior of polymer solutions in disordered media.
Main Methods:
- Simulations of self-avoiding walks in 2D and 3D.
- Analysis of time-averaged monomer density statistics.
- Investigation of polymer solutions beyond the screening length.
Main Results:
- Monomer density statistics for single chains are well-described by multifractal statistics.
- This multifractal behavior is observed even far from the percolation transition.
- For polymer solutions, multifractality is lost beyond the screening length.
Conclusions:
- SAWs in disordered environments display robust multifractal characteristics.
- The presence of a disordered medium significantly impacts polymer chain statistics.
- The screening length defines a critical scale for multifractality in polymer solutions.
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