Statistical geometry

Qiliang Yan and Juan J. DePablo, Hyper-Parallel Tempering Monte Carlo and Its Applications Pablo G. Debenedetti, Frank H. Stillinger, Thomas M. Truskett, and Catherine P. Lewis, Theory of Supercooled Liquids and Glasses Energy Landscape and Statistical Geometry Perspectives... 

Statistical Geometry of Particle Packings. I. Algorithm for Exact Determination of Connectivity, Volume, and Surface Areas of Void Space in Monodisperse and Polydisperse Sphere Packings. 

The most direct source of structural information, the diffraction studies, provides strong evidence for predominantly tetrahedral ordering of a molecule and its nearest neighbors, both in amorphous solid and liquid H2O. Other, weaker but still direct, structural evidence comes from the ratio of separations of nearest neighbor and next nearest neighbor 00 pairs in liquid water, the ubiquity of tetrahedral ordering in the several crystalline ices, and the statistical geometry of simulated water. 

In this section, we describe the role of fhe specific membrane environment on proton transport. As we have already seen in previous sections, it is insufficient to consider the membrane as an inert container for water pathways. The membrane conductivity depends on the distribution of water and the coupled dynamics of wafer molecules and protons af multiple scales. In order to rationalize structural effects on proton conductivity, one needs to take into account explicit polymer-water interactions at molecular scale and phenomena at polymer-water interfaces and in wafer-filled pores at mesoscopic scale, as well as the statistical geometry and percolation effects of the phase-segregated random domains of polymer and wafer at the macroscopic scale. 

What information about the dynamical and statistical geometry of the liquid state can be gained by studying the behavior of excess electrons in liquids ... 

It is clear from the preceding picture of statistical geometry that the geometry around the Planck scale is closely related to the geometry of hazy lumps. The... 

S. Roy, Statistical Geometry and Application to Microphysics and Cosmology, Kluwer, Dordrecht, 1998. 

M. Requardt, Spectral analysis and operator theory on (infinite) graphs..JPA (in press) math-ph/0001026 M. Requardt (Quantum) space-time as a statistical geometry of lumps in random networks, Class. Quant. Grav. 17, 2029 (2000) gr-qc/9912059. 

M. Requardt and Sisir Roy, (Quantum)Space-Time as a Statistical Geometry of Fuzzy Lumps and the Connection with Random Metric Spaces - to be published in Classical Quantum Gravity (2001). 

Eigen M, Lindemann BF, Tietze M et al. How old is the genetic code Statistical geometry of tRNA provides the answer. Science 1989 244 673. 

Statistical geometry in the study of fluids and porous media. J. Phys. Chem. 96, 4736-4747 (1992). 

As already noted in Section 8, it is practically impossible to measure the shape and size of each cell individually therefore, on uses statistical geometry methods for the calculation of the morphological parameters. Originally, these methods had been developed and used in crystallography, petrography and colloid chemistry for analyzing the macrostructures of crystals, metal alloys, minerals, suspensions, etc. 

THEORY OF SUPERCOOLED LIQUIDS AND GLASSES ENERGY LANDSCAPE AND STATISTICAL GEOMETRY PERSPECTIVES... 

Bowles, R. K., and Corti, D. S.. Statistical geometry of hard sphere systems Exact relations for first-order phase transitions in multicomponent systems. Mol. Phys. 98, 429 (2000). 

Sastry, S., Corti, D. S., Debenedetti, P. G., and Stillinger, F. H., Statistical geometry of particle packings. I. Algorithm for exact determination of connectivity, volume, and surface areas of void space in monodisperse and polydisperse sphere packings. Phys. Rev. E 56, 5524 (1997a). 

Speedy, R. J., Statistical geometry of hard-sphere systems. J. Chem. Soc. Faraday Trans II (>, 693 (1980). 

Theory of Supercooled Liquids and Glasses Energy Landscape and Statistical Geometry Perspectives... 

Thermodynamics of the Weeks-Chandler-Andersen System Inherent Structure of Two-Dimensional Liquids Statistical Geometry of the Weeks-Chandler-Andersen System... 

D. Statistical Geometry of Dense Random Packings of Hard Disks... 

D. Statistical Geometry of the Weeks-Chandler-Andersen System... 

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