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Tilings of space and superhomogeneous point processes
A Gabrielli1, M Joyce, S Torquato
1SMC-INFM, Dipartimento di Fisica, Università La Sapienza, P.le A. Moro 2, I-00185, Rome, Italy.
Summary
We demonstrate how to create superhomogeneous (hyperuniform) point processes using space tilings. These processes exhibit vanishing structure factors at zero wave vector, with tunable exponents.
Area of Science:
- Statistical Physics
- Materials Science
- Cosmology
Background:
- Point processes are fundamental in describing particle distributions.
- Superhomogeneity (hyperuniformity) characterizes systems with suppressed large-scale density fluctuations.
- Understanding hyperuniformity is crucial for various physical systems.
Purpose of the Study:
- To develop algorithms for constructing hyperuniform point processes from space tilings.
- To analyze the relationship between tiling properties and the resulting point process characteristics.
- To explore methods for controlling the degree of hyperuniformity.
Main Methods:
- Generating point processes by assigning points to tiles in d-dimensional Euclidean space.
- Analyzing the structure factor S(k) to quantify hyperuniformity.
- Investigating the role of tile correlations and mass moment conservation.
- Utilizing deterministic and stochastic tiling models.
Main Results:
- Simple algorithms generate hyperuniform point processes from equal-volume tilings.
- The exponent gamma in S(k) ~ k^gamma depends on tiling correlations and mass moments.
- Assigning points to tile centers yields gamma=4 for short-range correlated tilings.
- Exponents gamma > 4 can be achieved by assigning multiple points per tile.
Conclusions:
- Explicit analytical constructions for hyperuniform point processes are provided.
- The method allows for tunable hyperuniformity exponents, including gamma > 4.
- The findings have potential applications in condensed matter physics and cosmology.
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