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Ordered packing of elastic wires in a sphere
Javad Najafi1, Norbert Stoop, Falk Wittel
1Department of Physics, Institute for Advanced Studies in Basic Sciences (IASBS), P.O. Box 45195-1159, Zanjan 45137-6673, Iran.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 26, 2012
Summary
This study models ordered wire packing in spheres. The relative system size (a/R) dictates maximum packing fraction, with coil number following a power law and fractal dimension remaining constant.
Area of Science:
- Physics
- Materials Science
- Applied Mathematics
Background:
- Understanding the complex arrangements of long, flexible objects within confined spaces is crucial in various scientific and engineering fields.
- The ordered packing of wires in a spherical container presents a unique challenge due to geometric constraints and self-organization phenomena.
Purpose of the Study:
- To develop and validate an analytical model for predicting the behavior of ordered wire packing within a sphere.
- To investigate the key parameters influencing maximum packing fraction, coil formation, fractal dimension, and bending energy.
Main Methods:
- Analytical modeling to describe the packing geometry and energy.
- Experimental investigations using physical wire samples within spherical containers.
- Numerical simulations to complement theoretical predictions and experimental data.
Main Results:
- The maximum packing fraction is primarily controlled by the relative system size (ratio of wire radius to sphere radius, a/R).
- The number of coils (N) exhibits a power-law relationship with system size: N∼(R/a){1.5}.
- The fractal dimension of the packed structures is consistently 2.5, irrespective of the system size.
Conclusions:
- The proposed analytical model accurately predicts experimental and simulation results for ordered wire packing in spheres.
- Relative system size is the dominant factor governing packing efficiency.
- The observed power-law scaling and constant fractal dimension offer fundamental insights into self-organized structures.
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