Frustrated packing in a granular system under geometrical confinement
Sára Lévay1, David Fischer, Ralf Stannarius
1Department of Theoretical Physics, Budapest University of Technology and Economics, Budafoki út 8, H-1111 Budapest, Hungary. slevay@phy.bme.hu.
Soft Matter
|December 5, 2017
Summary
In 2+ dimensions, sphere packing forms a triangular lattice. The system slowly reaches its ground state through local dynamics, optimizing particle configurations and interactions.
Area of Science:
- Physics
- Materials Science
- Statistical Mechanics
Background:
- Optimal sphere packing is a solved problem in 2D and 3D.
- 3D packing is complex due to local vs. global optima, unlike 2D.
- This study explores packing in 2+ε dimensions.
Purpose of the Study:
- Investigate sphere packing in 2+ε dimensions.
- Map the packing problem to a 1/2 spin system.
- Analyze the system's dynamics and ground state.
Main Methods:
- Experimental realization in a slightly wider container.
- Numerical simulations.
- Mapping to a spin system and analyzing dynamics.
Main Results:
- Particles self-organize into a triangular lattice.
- The system exhibits spin-glass-like configurations but has a defined ground state.
- Dynamics are local, driven by 7-particle volume optimization and vertical interactions.
Conclusions:
- Sphere packing in 2+ε dimensions reveals complex emergent behavior.
- The system's slow evolution towards a ground state is governed by local interactions.
- This provides insights into frustrated systems and energy minimization.
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