Fast Generation of Spectrally-Shaped Disorder
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866913504856899584 |
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| author | Shih, Aaron Casiulis, Mathias Martiniani, Stefano |
| author_facet | Shih, Aaron Casiulis, Mathias Martiniani, Stefano |
| contents | Media with correlated disorder display unexpected transport properties, but it is still a challenge to design structures with desired spectral features at scale. In this work, we introduce an optimal formulation of this inverse problem by means of the non-uniform fast Fourier transform, thus arriving at an algorithm capable of generating systems with arbitrary spectral properties, with a computational cost that scales $O(N \log N)$ with system size. The method is extended to accommodate arbitrary real-space interactions, such as short-range repulsion, to simultaneously control short- and long-range correlations. We thus generate the largest-ever stealthy hyperuniform configurations in $2d$ ($N = 10^9$) and $3d$ ($N > 10^7$). By an Ewald sphere construction we link the spectral and optical properties at the single-scattering level, and show that these structures in $2d$ and $3d$ generically display transmission gaps, providing a concrete example of fine-tuning of a physical property at will. We also show that large $3d$ power-law hyperuniformity in particle packings leads to single-scattering properties near-identical to those of simple hard spheres. Finally, we show that enforcing large spectral power at a small number of peaks with the right symmetry leads to the non-deterministic generation of quasicrystalline structures in both $2d$ and $3d$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_15693 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fast Generation of Spectrally-Shaped Disorder Shih, Aaron Casiulis, Mathias Martiniani, Stefano Statistical Mechanics Materials Science Computational Physics Optics Media with correlated disorder display unexpected transport properties, but it is still a challenge to design structures with desired spectral features at scale. In this work, we introduce an optimal formulation of this inverse problem by means of the non-uniform fast Fourier transform, thus arriving at an algorithm capable of generating systems with arbitrary spectral properties, with a computational cost that scales $O(N \log N)$ with system size. The method is extended to accommodate arbitrary real-space interactions, such as short-range repulsion, to simultaneously control short- and long-range correlations. We thus generate the largest-ever stealthy hyperuniform configurations in $2d$ ($N = 10^9$) and $3d$ ($N > 10^7$). By an Ewald sphere construction we link the spectral and optical properties at the single-scattering level, and show that these structures in $2d$ and $3d$ generically display transmission gaps, providing a concrete example of fine-tuning of a physical property at will. We also show that large $3d$ power-law hyperuniformity in particle packings leads to single-scattering properties near-identical to those of simple hard spheres. Finally, we show that enforcing large spectral power at a small number of peaks with the right symmetry leads to the non-deterministic generation of quasicrystalline structures in both $2d$ and $3d$. |
| title | Fast Generation of Spectrally-Shaped Disorder |
| topic | Statistical Mechanics Materials Science Computational Physics Optics |
| url | https://arxiv.org/abs/2305.15693 |