摘要翻译:
我们考虑了在D维欧几里得空间中,用等体积的平铺块构造点过程。我们证明,我们可以用简单的算法将一个或多个点赋给每个平铺,产生“超均匀”(或“超均匀”)的点过程,即当波数k趋于零时,结构因子S(k)消失。主导小k行为的指数以一种简单的方式依赖于特定瓷砖的相关性质的性质和瓷砖的质量矩守恒。对每个瓷砖的质量中心指定一点,对于任何瓷砖的形状和方向都是短程相关的瓷砖,给出指数\γ=4。在4-d<γ<4范围内(因此对于d\leq4),在后者具有长程关联的情况下,可以得到更小的指数。通过适当地给每个平铺分配一个以上的点,我们证明了在这两种情况下都可以得到任意高的指数。我们用已知的确定性倾斜和一些简单的随机倾斜的显式构造来说明我们的结果,对于这些倾斜,我们可以精确地计算S(k)。我们的结果提供了,我们相信,第一个显式的解析构造点过程\γ>4。简要讨论了在凝聚态物理和宇宙学中的应用。
---
英文标题:
《Tilings of space and superhomogeneous point processes》
---
作者:
Andrea Gabrielli, Michael Joyce and Salvatore Torquato
---
最新提交年份:
2007
---
分类信息:
一级分类:Physics 物理学
二级分类:Statistical Mechanics 统计力学
分类描述:Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变,热力学,场论,非平衡现象,重整化群和标度,可积模型,湍流
--
一级分类:Physics 物理学
二级分类:Statistical Mechanics 统计力学
分类描述:Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变,热力学,场论,非平衡现象,重整化群和标度,可积模型,湍流
--
一级分类:Physics 物理学
二级分类:Materials Science 材料科学
分类描述:Techniques, synthesis, characterization, structure. Structural phase transitions, mechanical properties, phonons. Defects, adsorbates, interfaces
技术,合成,表征,结构。结构相变,力学性质,声子。缺陷,吸附质,界面
--
---
英文摘要:
We consider the construction of point processes from tilings, with equal volume tiles, of d-dimensional Euclidean space. We show that one can generate, with simple algorithms ascribing one or more points to each tile, point processes which are "superhomogeneous'' (or "hyperuniform''), i.e., for which the structure factor S(k) vanishes when the wavenumber k tends to zero. The exponent of the leading small-k behavior depends in a simple manner on the nature of the correlation properties of the specific tiling and on the conservation of the mass moments of the tiles. Assigning one point to the center of mass of each tile gives the exponent \gamma=4 for any tiling in which the shapes and orientations of the tiles are short-range correlated. Smaller exponents, in the range 4-d<\gamma<4 (and thus always superhomogeneous for d\leq 4), may be obtained in the case that the latter quantities have long-range correlations. Assigning more than one point to each tile in an appropriate way, we show that one can obtain arbitrarily higher exponents in both cases. We illustrate our results with explicit constructions using known deterministic tilings, as well as some simple stochastic tilings for which we can calculate S(k) exactly. Our results provide, we believe, the first explicit analytical construction of point processes with \gamma > 4. Applications to condensed matter physics, and also to cosmology, are briefly discussed.
---
PDF链接:
https://arxiv.org/pdf/711.3963