scholarly journals Hard spheres on the gyroid surface

2012 ◽  
Vol 2 (5) ◽  
pp. 575-581 ◽  
Author(s):  
Tomonari Dotera ◽  
Masakiyo Kimoto ◽  
Junichi Matsuzawa
Keyword(s):  
Monte Carlo ◽  
Minimal Surface ◽  
Gaussian Curvature ◽  
Hard Spheres ◽  
Order Parameters ◽  
Unit Cell ◽  
Acceptance Ratio ◽  
Self Organized ◽  
Negative Gaussian Curvature ◽  
Circle Limit

We find that 48/64 hard spheres per unit cell on the gyroid minimal surface are entropically self-organized. Striking evidence is obtained in terms of the acceptance ratio of Monte Carlo moves and order parameters. The regular tessellations of the spheres can be viewed as hyperbolic tilings on the Poincaré disc with a negative Gaussian curvature, one of which is, equivalently, the arrangement of angels and devils in Escher's Circle Limit IV .

Formation of GaN Self-Organized Nanotips by Nanomasking Effect

2001 ◽  
Vol 707 ◽  
Author(s):  
Harumasa Yoshida ◽  
Tatsuhiro Urushido ◽  
Hideto Miyake ◽  
Kazumasa Hiramtsu
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Aspect Ratio ◽  
Formation Mechanism ◽  
High Aspect Ratio ◽  
Photoelectron Spectroscopy ◽  
Nanometer Scale ◽  
Xps Analysis ◽  
X Ray ◽  
Self Organized

ABSTRACTWe have successfully fabricated self-organized GaN nanotips by reactive ion etching using chlorine plasma, and have revealed the formation mechanism. Nanotips with a high density and a high aspect ratio have been formed after the etching. We deduce from X-ray photoelectron spectroscopy (XPS) analysis that the nanotip formation is attributed to nanometer-scale masks of SiO2 on GaN. The structures calculated by Monte Carlo simulation of our formation mechanism are very similar to the experimental nanotip structures.

Negative Gaussian curvature induces significant suppression of thermal conduction in carbon crystals

Nanoscale ◽  
2017 ◽  
Vol 9 (37) ◽  
pp. 14208-14214 ◽  
Author(s):  
Zhongwei Zhang ◽  
Jie Chen ◽  
Baowen Li
Keyword(s):  
Gaussian Curvature ◽  
Thermal Conduction ◽  
Negative Curvature ◽  
Positive Curvature ◽  
Significant Suppression ◽  
Carbon Allotropes ◽  
Zero Curvature ◽  
Negative Gaussian Curvature

From the mathematic category of surface Gaussian curvature, carbon allotropes can be classified into three types: zero curvature, positive curvature, and negative curvature.

Self-organized criticality in Monte Carlo simulated ecosystems

1992 ◽  
Vol 172 (1-2) ◽  
pp. 56-61 ◽  
Author(s):  
Ricard V. Solé ◽  
Daniel López ◽  
Marta Ginovart ◽  
Joaquim Valls
Keyword(s):  
Monte Carlo ◽  
Self Organized ◽  
Self Organized Criticality

scholarly journals Chirality in curved polyaromatic systems

2017 ◽  
Vol 46 (6) ◽  
pp. 1643-1660 ◽  
Author(s):  
Michel Rickhaus ◽  
Marcel Mayor ◽  
Michal Juríček
Keyword(s):  
Gaussian Curvature ◽  
Carbon Allotrope ◽  
Carbon Allotropes ◽  
Negative Gaussian Curvature ◽  
Helical Chirality

Chiral non-planar polyaromatic systems that display zero, positive or negative Gaussian curvature are analysed and their potential to ‘encode’ chirality of larger sp2-carbon allotropes is evaluated. Shown is a hypothetical peanut-shaped carbon allotrope, where helical chirality results from the interplay of various curvature types.

The fifth virial coefficient of a fluid of hard spheres

1964 ◽  
Vol 279 (1377) ◽  
pp. 147-160 ◽  
Keyword(s):  
Monte Carlo ◽  
Numerical Integration ◽  
Virial Coefficient ◽  
Monte Carlo Calculation ◽  
Hard Spheres ◽  
Cluster Integrals ◽  
Different Types

The fifth virial coefficient of a fluid of hard spheres is a sum of 238 irreducible cluster integrals of 10 different types. The values of 5 of these types (152 integrals) are obtained analytically, the contributions of a further 4 types (85 integrals) are obtained by a com­bination of analytical and numerical integration, and 1 integral is calculated by an approximation. The result is E = (0·1093 ± 0·0007) b 4 , b = 2/3 πN A σ 3 , where σ is the diameter of a sphere. A combination of the values of 237 of the cluster integrals obtained in this paper with the value of one integral obtained independently by Katsura & Abe from a Monte Carlo calculation yields E = (0·1101 ± 0·0003) b 4 .

scholarly journals THE SELF-ORGANIZED MULTI-LATTICE MONTE CARLO SIMULATION

2004 ◽  
Vol 15 (09) ◽  
pp. 1249-1268 ◽  
Author(s):  
DENIS HORVÁTH ◽  
MARTIN GMITRA
Keyword(s):  
Monte Carlo ◽  
Finite Size ◽  
Simulation Method ◽  
Monte Carlo Step ◽  
The Self ◽  
Square Lattice ◽  
Critical Systems ◽  
Lattice Systems ◽  
Steady Regime ◽  
Self Organized

Self-organized Monte Carlo simulations of 2D Ising ferromagnet on the square lattice are performed. The essence of the suggested simulation method is an artificial dynamics consisting of the well-known single-spin-flip Metropolis algorithm supplemented by a random walk on the temperature axis. The walk is biased towards the critical region through a feedback based on instantaneous energy and magnetization cumulants, which are updated at every Monte Carlo step and filtered through a special recursion algorithm. The simulations revealed the invariance of the temperature probability distribution function, once some self-organized critical steady regime is reached, which is called here noncanonical equilibrium. The mean value of this distribution approximates the pseudocritical temperature of canonical equilibrium. In order to suppress finite-size effects, the self-organized approach is extended to multi-lattice systems, where the feedback basis on pairs of instantaneous estimates of the fourth-order magnetization cumulant on two systems of different size. These replica-based simulations resemble, in Monte Carlo lattice systems, some of the invariant statistical distributions of standard self-organized critical systems.

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