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Growth Rates in the Quaquaversal Tiling [article]

Brimstone Draco, Lorenzo Sadun, Douglas Van Wieren
2018 arXiv   pre-print
A finite patch, however, cannot be perfectly isotropic, and we compute the rates at which the anisotropy scales with size. In a sample of volume N, tiles appear in O(N^1/6) distinct orientations.  ...  Conway and Radin's "quaquaversal" tiling of R^3 is known to exhibit statistical rotational symmetry in the infinite volume limit.  ...  We now have the machinery to understand the orientations of tiles in the n-fold subdivision of a single quaquaversal tile.  ... 
arXiv:math-ph/9812018v2 fatcat:hqiy4dwj55ey7imxm4vne666ea

Growth Rates in the Quaquaversal Tiling

B. Draco, L. Sadun, D. Van Wieren
2000 Discrete & Computational Geometry  
A finite patch, however, cannot be perfectly isotropic, and we compute the rates at which the anisotropy scales with size. In a sample of volume N , tiles appear in O(N 1/6 ) distinct orientations.  ...  Conway and Radin's "quaquaversal" tiling of R 3 is known to exhibit statistical rotational symmetry in the infinite volume limit.  ...  For an optimal distribution of N Growth Rates in the Quaquaversal Tiling 421 points, with N −1 prime, this supremum was shown to be 2 √ N − 1/N , and in particular to decay as N −1/2 .  ... 
doi:10.1007/pl00009510 fatcat:eek22dptarc7fnarh5dnjn5gwq

The Spectrum of the Quaquaversal Operator is Real [article]

Josiah Sugarman
2022 arXiv   pre-print
The Hecke operator associated with the Quaquaversal tiling, a highly anisotropic tiling introduced by Conway and Radin, is shown to have a real spectrum.  ...  The Quaquaversal tiling is particularly interesting because this distribution approaches uniformity at a much faster rate than what is possible for two dimensional hierarchical tilings.  ...  In 1998, Charles Radin and John Conway introduced a three dimensional hierarchical tiling, the Quaquaversal tiling [3] .  ... 
arXiv:2202.09505v2 fatcat:lscj6olvvbgd7g2dbifgner37y

Page 1833 of Mathematical Reviews Vol. , Issue 2001C [page]

2001 Mathematical Reviews  
Shashkin (Ekaterinburg) 2001¢:53001 2001¢:52029 52C23 52C22 Draco, B. (1-TX; Austin, TX); Sadun, L. (1-TX; Austin, TX); Van Wieren, D. (1-PAS-CE; University Park, PA) Growth rates in the quaquaversal tiling  ...  The so-called quaquaversal tiling is a 3-dimensional aperiodic tiling. It belongs to the family of substitution type tilings. The con- struction is described in detail in C.  ... 

Discreteness effects in simulations of hot/warm dark matter

Jie Wang, Simon D. M. White
2007 Monthly notices of the Royal Astronomical Society  
We study how discreteness noise influences the growth of nonlinear structures smaller than this coherence scale in N-body simulations of cosmic structure formation.  ...  In particular, the filaments which form in such simulations break up into regularly spaced clumps which reflect the initial grid pattern.  ...  We thank both of them and also Liang Gao for a number of very useful discussions of the material presented in this paper.  ... 
doi:10.1111/j.1365-2966.2007.12053.x fatcat:6wlxrwsxvzhltoq7undlanoi6e

Page 1279 of The Athenaeum Vol. , Issue 998 [page]

1846 The Athenaeum  
The Rates of Premium are those adopted by the principal Lie Offices; the rate without bonus is lower than that of most ver oii "eS. 2.  ...  Foe above tiles have lately been considerably reduced in pric An assortment of plain and ornamental door furniture and “tiles for fire places, &e. &e. C (YHEMICAL BALANCES.—L.  ... 

Page 1199 of The Athenaeum Vol. , Issue 995 [page]

1846 The Athenaeum  
The above tiles have ma! been considerably reduced in price. N n assortment of plain and ornamental door furniture tiles for fire-places, &c.  ...  no tendency to curl, the new growth is curly and strong.  ... 

The Early History of the North-American Continent

1883 Scientific American  
naturally in quaquaversal sheets, no one eruplion being very extensive.  ...  Professor Dana thinks the primitive land originated be cause of a difference in the rate of conduction of heat during the process of refrigeration.  ...  Sent by mail, postage prepaid, to subscribers in any part of the United States or Canada. Six dollars a year, sent, pre paid, to any foreign country.  ... 
doi:10.1038/scientificamerican10061883-6468bsupp fatcat:vuw7qekzzzd3vbdqtgdrhb4s3m

The beaumont oil field, with notes on other oil fields of the Texas Region

Robert T. Hill
1902 Journal of the Franklin Institute  
In one regard, at any rate, the mushroom does resemble a beefsteak-in that it contains practically the same amount of water.  ...  quaquaversal in structure. (3) Most of the chemical phenomena of the Lucas group occur in all these mounds in varying proportions. (4) In some localities, hot water has been struck below the oil. (5)  ... 
doi:10.1016/s0016-0032(02)90309-1 fatcat:fliv6yb4y5f4hek2ifbwphn32m

The Early History of the North American Continent

C. H. Hitchcock
1883 Science  
Professor Dana thinks the primitive land originated becatse of a difference in the rate of conduction of heat during the process of refrigeration.  ...  Around vents like Vesuvius or Etna the lava accuiritulates naturally in quaquaversal sheets, no one eruption being very extensive.  ... 
fatcat:bddlswd5irg7ljkqpnbhxhjfe4

Page 1386 of Mathematical Reviews Vol. , Issue Subject Index [page]

Mathematical Reviews  
Growth rates in the quaquaversal tiling (English summary) 2001¢:52029 Grimm, Uwe see Baake, Michael, (2001f:52047) Kari, Jarkko (with Papasoglu, P.) Deterministic aperiodic tile sets.  ...  Growth rules for quasicrystals.  ... 

Impacts of pre-initial conditions on anisotropic separate universe simulations: a boosted tidal response in the epoch of reionization [article]

Shogo Masaki, Takahiro Nishimichi, Masahiro Takada
2020 arXiv   pre-print
The standard method to construct the pre-IC is to place the particles on the lattice grids evenly spaced in the three-dimensional spatial coordinates.  ...  in the redshift range 5≲ z≲ 15, indicating the importance of tidal field on structure formation at such high redshifts, e.g. during the epoch of reionization.  ...  ACKNOWLEDGEMENTS We would like to thank the anonymous referee for useful comments and suggestions.  ... 
arXiv:2007.08727v2 fatcat:zlmtyfzghfhoxf7qggqqcby664

Geology of Jones County

Samuel Calvin
1896 Iowa Geological Survey Annual Report  
the growth in this locality of gigantic coralla many fe.et in diameter.  ...  The brick are dried in t4e open air and the tile in a steam heated drying shed. The drying shed has a capacity of 50,000 tile.  ...  Lower in the quarry the ledges present the same features as in corresponding parts of other exposures.  ... 
doi:10.17077/2160-5270.1006 fatcat:z3fajkuievbxta6xt77j6xnv74

More accurate simulations with separate initial conditions for baryons and dark matter [article]

Simeon Bird, Yu Feng, Christian Pedersen, Andreu Font-Ribera
2020 arXiv   pre-print
Most simulations do not reproduce the linear prediction for the difference between the cold dark matter and baryon perturbations.  ...  We revisit techniques for performing cosmological simulations with both baryons and cold dark matter when each fluid has different initial conditions, as is the case at the end of the radiation era.  ...  [17] used a quaquaversal tiling of three dimensional space, which we do not consider as it restricts the total number of particles to a power of two. Ref.  ... 
arXiv:2002.00015v2 fatcat:qt24qmkd4zc6nci4vg7sqhe43q

Page 1425 of Mathematical Reviews Vol. 31, Issue Index [page]

Mathematical Reviews  
Quaquaversal tilings and rotations. (English summary) Invent. Math. 132 (1998), no. 1, 179-188.  ...  The phenomenon of fast convergence of the Galerkin method in diffraction theory. (Russian) Dokl. Akad. Nauk 359 (1998), no. 5, 621-624; translation in Dokl.  ... 
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