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Resonance Raman Spectroscopy of Extreme Nanowires and Other 1D Systems
Published on: April 28, 2016
Minimal resonances in annular non-euclidean strips
Bryan Gin-Ge Chen1, Christian D Santangelo
1Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6396, USA.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 15, 2011
Summary
Differential growth causes elastic strips to buckle and wrinkle. Researchers analyzed these shapes using analytical and numerical methods, revealing a resonance condition for minimal energy configurations in biological tissues.
Area of Science:
- Biophysics
- Materials Science
- Developmental Biology
Background:
- Differential growth is a key mechanism in shaping biological tissues and leaves.
- Understanding the mechanics of elastic materials under inhomogeneous swelling is crucial for developmental biology.
Purpose of the Study:
- To investigate the shapes of closed, elastic strips undergoing inhomogeneous swelling.
- To analyze the interplay between stretching, bending energies, and compatibility constraints.
- To identify factors influencing strip shape, including wrinkles and swelling patterns.
Main Methods:
- Employed analytical and numerical calculations to model elastic strip behavior.
- Utilized a variational ansatz based on 'conical' closed strips with prescribed metric tensors.
- Compared results with a numerical bead-spring model for validation.
Main Results:
- Strip shapes were classified by wrinkle number and swelling patterns.
- The 'conical' strip ansatz showed excellent agreement with numerical simulations.
- A novel resonance condition for minimal bending energy was derived and validated.
Conclusions:
- The study provides a framework for understanding how differential growth leads to complex shapes in elastic strips.
- The findings offer insights into the formation of wrinkles and the energy minimization principles in biological structures.
- The derived resonance condition is a significant theoretical contribution to the mechanics of swelling elastic materials.
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