Related Experiment Video
Updated: Sep 16, 2025

Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials
Published on: September 26, 2014
Ultradense sphere packings derived from disordered stealthy hyperuniform ground states.
Jaeuk Kim1, Salvatore Torquato2
1Princeton Materials Institute, Department of Physics, Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA.
Disordered stealthy hyperuniform (SHU) materials achieve high densities with soft-core repulsions, unlike those without. This research provides formulas for maximal packing fractions in SHU systems.
Area of Science:
- Materials Science
- Condensed Matter Physics
- Statistical Mechanics
Background:
- Disordered stealthy hyperuniform (SHU) packings are exotic amorphous materials with unique properties.
- These materials are typically formed from point patterns using modified optimization schemes.
Purpose of the Study:
- To investigate the maximal packing fraction (ϕmax) in SHU systems.
- To explore the impact of soft-core repulsions and the stealthiness parameter (χ) on packing density in 1-3 dimensions.
Main Methods:
- Simulations of SHU point patterns with and without soft-core repulsions.
- Analysis of pair distance distributions and nearest-neighbor distances.
- Calculation of structure factors, pair correlation functions, and spectral density.
Main Results:
- Without soft-core repulsions, ϕmax decreases with increasing particle number (N).
- With soft-core repulsions, ϕmax becomes large and independent of N, reaching up to 1.0, 0.86, 0.63 in 1, 2, 3 dimensions, respectively.
- Soft-core repulsions significantly alter correlations and increase large-scale order with increasing χ.
Conclusions:
- Soft-core repulsions enable unprecedentedly high densities in disordered SHU materials.
- Explicit formulas for ϕmax were derived as functions of χ and N.
- These findings offer a new pathway for designing novel high-density amorphous materials.
Related Concept Videos
Electric Field of a Non Uniformly Charged Sphere
Consider a non-uniformly charged sphere, for which the density of charge depends only on the distance from a point in space and not on the direction. Such a sphere has a spherically symmetrical charge distribution. Here, the electric...
First Law: Particles in Two-dimensional Equilibrium
Newton's first law tells us about...
First Law: Particles in One-dimensional Equilibrium
Crystal Field Theory - Octahedral Complexes
To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized d orbitals of the central metal atom has been developed. This electrostatic model is crystal field theory (CFT). It helps to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.
CFT focuses on...
Electrostatic Boundary Conditions
The surface integral of an electric field is given by Gauss's law in integral form and is related to...
Potential Due to a Polarized Object

