# Local Number Fluctuations in Hyperuniform and Nonhyperuniform Systems: Higher-Order Moments and Distribution Functions

@article{Torquato2021LocalNF, title={Local Number Fluctuations in Hyperuniform and Nonhyperuniform Systems: Higher-Order Moments and Distribution Functions}, author={Salvatore Torquato and Jaeuk Kim and Michael Andreas Klatt}, journal={Physical Review X}, year={2021}, volume={11} }

The local number variance associated with a spherical sampling window of radius $R$ enables a classification of many-particle systems in $d$-dimensional Euclidean space according to the degree to which large-scale density fluctuations are suppressed, resulting in a demarcation between hyperuniform and nonhyperuniform phyla. To better characterize density fluctuations, we carry out an extensive study of higher-order moments, including the skewness $\gamma_1(R)$, excess kurtosis $\gamma_2(R)$ and…

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## References

SHOWING 1-10 OF 145 REFERENCES

Spatio-temporal Heterogeneity and Hyperuniformity in 2D Conserved Lattice Gas

- Physics
- 2020

Hyperuniformity is a description of hidden correlations in point distributions revealed by an anomalous scaling in fluctuations of local density at various coarse-graining length scales. We…

Characterization of maximally random jammed sphere packings. II. Correlation functions and density fluctuations.

- Mathematics, MedicinePhysical review. E
- 2016

A variety of different correlation functions that arise in rigorous expressions for the effective physical properties of MRJ sphere packings are determined and compared to the corresponding statistical descriptors for overlapping spheres and equilibrium hard-sphere systems.

Packing hyperspheres in high-dimensional Euclidean spaces.

- Mathematics, PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2006

Although the stable phase at high density is a crystalline solid, nucleation appears to be strongly suppressed with increasing dimension, consistent with a recently proposed "decorrelation principle".

Density fluctuations in many-body systems

- Physics
- 1998

The characterization of density fluctuations in systems of interacting particles is of fundamental importance in the physical sciences. We present a formalism for studying local density fluctuations…

Collective coordinate control of density distributions.

- Physics, MedicinePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2006

Numerical results reported here extend earlier one- and two-dimensional studies to include three dimensions and provide specific examples of interaction potentials whose classical ground states are configurationally degenerate and disordered.

Cloaking the underlying long-range order of randomly perturbed lattices.

- Mathematics, PhysicsPhysical review. E
- 2020

It is noteworthy that cloaked perturbed lattices allow one to easily simulate very large samples of disordered hyperuniform point patterns without Bragg peaks, and the τ order metric is a superior choice.

Hyperuniformity and its generalizations.

- Physics, MedicinePhysical review. E
- 2016

It is shown that there exist many-particle ground-state configurations in which directional hyperuniformity imparts exotic anisotropic physical properties to these states of matter, which could have technological relevance for manipulating light and sound waves in ways heretofore not thought possible.

Precise algorithm to generate random sequential addition of hard hyperspheres at saturation.

- Mathematics, PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2013

The improved algorithm is easily generalizable to generate saturated RSA packings of nonspherical particles that are guaranteed to contain no available space in a large simulation box using finite computational time with heretofore unattained precision and across the widest range of dimensions.

Point processes in arbitrary dimension from fermionic gases, random matrix theory, and number theory

- Mathematics, Physics
- 2008

It is well known that one can map certain properties of random matrices, fermionic gases, and zeros of the Riemann zeta function to a unique point process on the real line. Here we analytically…

Gaussian core model phase diagram and pair correlations in high Euclidean dimensions.

- Physics, MedicineThe Journal of chemical physics
- 2008

The goals of this paper are to characterize the behavior of the pair correlation function g(2) in various density regimes and to understand the phase properties of the Gaussian core model (GCM) as parametrized by dimension d.