A Test of Randomness for Finite Spatial Distributions

1994 ◽  
Vol 78 (3) ◽  
pp. 707-714 ◽  
Author(s):  
Frank O'brien
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Null Hypothesis ◽  
Nearest Neighbor ◽  
Dimensional Space ◽  
Spatial Distributions ◽  
Two Dimensional ◽  
Model Extension ◽  
Spatially Distributed ◽  
Test Of Randomness

A statistical method is presented for determining randomness of points spatially distributed in two-dimensional space. The procedure is based on a distance-to-particle (nearest neighbor) model derived from an elementary Poisson process. In a previous derivation of the method, an extension to the model was proposed and used without adequate empirical justification. Herein the test is derived in detail and its performance evaluated with Monte Carlo simulations. Results indicate that the model extension provides adequate representations when the null hypothesis is true.

Percolation in two-dimensional quasicrystals by Monte Carlo simulations

1989 ◽  
Vol 22 (14) ◽  
pp. L705-L709 ◽  
Author(s):  
S Sakamoto ◽  
F Yonezawa ◽  
K Aoki ◽  
S Nose ◽  
M Hori
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Two Dimensional

Equilibrium and nonequilibrium models on solomon networks with two square lattices

2017 ◽  
Vol 28 (08) ◽  
pp. 1750099
Author(s):  
F. W. S. Lima
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Critical Exponent ◽  
Critical Points ◽  
Majority Vote ◽  
Universality Class ◽  
2D Systems ◽  
Two Dimensional ◽  
Critical Properties ◽  
Regular Lattices

We investigate the critical properties of the equilibrium and nonequilibrium two-dimensional (2D) systems on Solomon networks with both nearest and random neighbors. The equilibrium and nonequilibrium 2D systems studied here by Monte Carlo simulations are the Ising and Majority-vote 2D models, respectively. We calculate the critical points as well as the critical exponent ratios [Formula: see text], [Formula: see text], and [Formula: see text]. We find that numerically both systems present the same exponents on Solomon networks (2D) and are of different universality class than the regular 2D ferromagnetic model. Our results are in agreement with the Grinstein criterion for models with up and down symmetry on regular lattices.

Monte Carlo simulations of long-range order kinetics in B2 phases

1995 ◽  
Vol 10 (3) ◽  
pp. 591-595 ◽  
Author(s):  
K. Yaldram ◽  
V. Pierron-Bohnes ◽  
M.C. Cadeville ◽  
M.A. Khan
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Nearest Neighbor ◽  
Vacancy Concentration ◽  
Relaxation Times ◽  
Nearest Neighbors ◽  
Migration Energy ◽  
Ordering Kinetics ◽  
Migration Barriers ◽  
Temperature Dependences

The thermodynamic parameters that drive the atomic migration in B2 alloys are studied using Monte-Carlo simulations. The model is based on a vacancy jump mechanism between nearest neighbor sites, with a constant vacancy concentration. The ordering energy is described through an Ising Hamiltonian with interaction potentials between first and second nearest neighbors. Different migration barriers are introduced fur A and B atoms. The results of the simulations compare very well with those of experiments. The ordering kinetics are well described by exponential-like behaviors with two relaxation times whose temperature dependences are Arrhenius laws yielding effective migration energies. The ordering energy contributes significantly to the total migration energy.

Parallel kNN Queries for Big Data Based on Voronoi Diagram Using MapReduce

2015 ◽  
pp. 392-414
Author(s):  
Wei Yan
Keyword(s):  
Big Data ◽  
Voronoi Diagram ◽  
Spatial Databases ◽  
Nearest Neighbor ◽  
Programming Model ◽  
Dimensional Space ◽  
Data Sets ◽  
Two Dimensional ◽  
K Nearest Neighbor ◽  
K Nearest Neighbors

In cloud computing environments parallel kNN queries for big data is an important issue. The k nearest neighbor queries (kNN queries), designed to find k nearest neighbors from a dataset S for every object in another dataset R, is a primitive operator widely adopted by many applications including knowledge discovery, data mining, and spatial databases. This chapter proposes a parallel method of kNN queries for big data using MapReduce programming model. Firstly, this chapter proposes an approximate algorithm that is based on mapping multi-dimensional data sets into two-dimensional data sets, and transforming kNN queries into a sequence of two-dimensional point searches. Then, in two-dimensional space this chapter proposes a partitioning method using Voronoi diagram, which incorporates the Voronoi diagram into R-tree. Furthermore, this chapter proposes an efficient algorithm for processing kNN queries based on R-tree using MapReduce programming model. Finally, this chapter presents the results of extensive experimental evaluations which indicate efficiency of the proposed approach.

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