scholarly journals Simulation of Two-Dimensional Images for Ion-Irradiation Induced Change in Lattice Structures and Magnetic States in Oxides by Using Monte Carlo Method

2021 ◽  
Vol 5 (2) ◽  
pp. 13
Author(s):  
Akihiro Iwase ◽  
Shigeru Nishio
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Ion Irradiation ◽  
Ion Beam ◽  
Distribution Functions ◽  
Lattice Structures ◽  
Two Dimensional ◽  
The Monte Carlo Method ◽  
Magnetic States ◽  
Two Dimensional Images

A Monte Carlo method was used to simulate the two-dimensional images of ion-irradiation-induced change in lattice structures and magnetic states in oxides. Under the assumption that the lattice structures and the magnetic states are modified only inside the narrow one-dimensional region along the ion beam path (the ion track), and that such modifications are affected by ion track overlapping, the exposure of oxide targets to spatially random ion impacts was simulated by the Monte Carlo method. Through the Monte Carlo method, the evolutions of the two-dimensional images for the amorphization of TiO2, the lattice structure transformation of ZrO2, and the transition of magnetic states of CeO2 were simulated as a function of ion fluence. The total fractions of the modified areas were calculated from the two-dimensional images. They agree well with the experimental results and those estimated by using the Poisson distribution functions.

scholarly journals Application of the Monte Carlo Method for the Assessment of Long-term Success in Keratoprosthesis Surgery

2002 ◽  
Vol 4 (3) ◽  
pp. 183-190 ◽  
Author(s):  
W. Hitzl ◽  
G. Grabner
Keyword(s):  
Monte Carlo ◽  
Visual Acuity ◽  
Survival Analysis ◽  
Monte Carlo Method ◽  
Surgical Techniques ◽  
Distribution Functions ◽  
Time Interval ◽  
Specific Method ◽  
The Monte Carlo Method

The comparison of different methods of keratoprosthesis (KP) regarding their long-term success, as far as visual acuity is concerned, is difficult: this is the case both as a standardized reporting method agreed upon by all research groups has not been reported and far less accepted, and as the quality of life for the patient not only depends on the level of visual acuity, but also quite significantly on the “survival time” of the implant. Therefore, an analysis of a single series of patients with Osteo–Odonto–Keratoprosthesis (OOKP) was performed. Statistical analysis methods used by others in similar groups of surgical procedures have included descriptive statistics, survival analysis and ANOVA. These methods comprised comparisons of empirical densities or distribution functions and empirical survival curves. It is the objective of this paper to provide an inductive statistical method to avoid the problems with descriptive techniques and survival analysis. This statistical model meets four important standards: (1) the efficiency of a surgical technique can be assessed within an arbitrary time interval by a new index (VAT-index), (2) possible autocorrelations of the data are taken into consideration and (3) the efficiency is not only stated by a point estimator, but also 95% point-wise confidence limits are computed based on the Monte Carlo method, and finally, (4) the efficiency of a specific method is illustrated by line and range plots for quick illustration and can also be used for the comparison of different other surgical techniques such as refractive techniques, glaucoma and retinal surgery.

Concentration Phase Transition in a Two-Dimensional Ferromagnet

2020 ◽  
Vol 312 ◽  
pp. 244-250
Author(s):  
Alexander Konstantinovich Chepak ◽  
Leonid Lazarevich Afremov ◽  
Alexander Yuryevich Mironenko
Keyword(s):  
Phase Transition ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Thermal Effect ◽  
Spin State ◽  
Critical Concentration ◽  
Two Dimensional ◽  
Percolation Transition ◽  
Magnetic Cluster ◽  
The Monte Carlo Method

The concentration phase transition (CPT) in a two-dimensional ferromagnet was simulated by the Monte Carlo method. The description of the CPT was carried out using various order parameters (OP): magnetic, cluster, and percolation. For comparison with the problem of the geometric (percolation) phase transition, the thermal effect on the spin state was excluded, and thus, CPT was reduced to percolation transition. For each OP, the values ​​of the critical concentration and critical indices of the CPT are calculated.

Modelling of nitrogen implantation processes into WC-Co indexable knives for wood-based material machining using ion implanters with or without direct ion beam

2019 ◽  
Vol 108 ◽  
pp. 68-78
Author(s):  
MAREK BARLAK ◽  
JACEK WILKOWSKI ◽  
ZBIGNIEW WERNER
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Ion Beam ◽  
Nitrogen Implantation ◽  
Depth Profiles ◽  
The Monte Carlo Method ◽  
Acceleration Voltage

Modelling of nitrogen implantation processes into WC-Co indexable knives for wood-based material machining using ion implanters with or without direct ion beam. The paper presents the results of modelling of the depth profiles of nitrogen implanted to W-C-Co material using ion implanters with or without direct ion beam. The modelling was performed using the Monte Carlo method. The results were obtained for one fluence of the implanted ions and three different values of the acceleration voltage.

Two-dimensional Janus-like particles on a triangular lattice

Soft Matter ◽  
2020 ◽  
Vol 16 (28) ◽  
pp. 6633-6642
Author(s):  
A. Patrykiejew ◽  
W. Rżysko
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Triangular Lattice ◽  
Canonical Ensemble ◽  
Grand Canonical Ensemble ◽  
Dimensional System ◽  
Two Dimensional ◽  
The Monte Carlo Method ◽  
Two Dimensional System ◽  
Grand Canonical

We have studied the phase behavior of a two-dimensional system of Janus-like particles on a triangular lattice using the Monte Carlo method in a grand canonical ensemble.

Numerical solution of the multidimensional Gelfand–Levitan equation

2015 ◽  
Vol 23 (5) ◽  
Author(s):  
Sergey I. Kabanikhin ◽  
Karl K. Sabelfeld ◽  
Nikita S. Novikov ◽  
Maxim A. Shishlenin
Keyword(s):  
Inverse Problem ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Two Dimensional ◽  
Nonlinear Inverse Problem ◽  
Coefficient Inverse Problem ◽  
Specific Point ◽  
The Monte Carlo Method ◽  
Linear Integral ◽  
Linear Integral Equations

AbstractThe coefficient inverse problem for the two-dimensional wave equation is solved. We apply the Gelfand–Levitan approach to transform the nonlinear inverse problem to a family of linear integral equations. We consider the Monte Carlo method for solving the Gelfand–Levitan equation. We obtain the estimation of the solution of the Gelfand–Levitan equation in one specific point, due to the properties of the method. That allows the Monte Carlo method to be more effective in terms of span cost, compared with regular methods of solving linear system. Results of numerical simulations are presented.

Monte Carlo Computations on Molten Caesium Bromide

1975 ◽  
Vol 30 (1) ◽  
pp. 83-86 ◽  
Author(s):  
Chiara Margheritis ◽  
Cesare Sinistri
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Thermodynamic Properties ◽  
Total Energy ◽  
Distribution Functions ◽  
Radial Distribution Functions ◽  
Pair Potentials ◽  
The Monte Carlo Method ◽  
Different Temperatures ◽  
Increasing Temperature

Abstract Molten CsBr was computer simulated tat 1 atm and four different temperatures using the Monte Carlo method. Structural and thermodynamic properties of the melt were obtained on the basis of pair potentials. In particular, radial distribution functions, volume, and energy with its coulomb, dipole-dipole, and repulsive components were determined. Separately, the polarization energy was also evaluated: this quantity increases with increasing temperature and ranges between 2 and 4% of the total energy.

Computer simulation of the Potts model with the number of spin states q = 4 on a triangular lattice

2020 ◽  
pp. 57-64
Author(s):  
Magomedsheikh Ramazanov ◽  
Akai Murtazaev
Keyword(s):  
Computer Simulation ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Thermodynamic Properties ◽  
Potts Model ◽  
Triangular Lattice ◽  
Nearest Neighbors ◽  
Spin States ◽  
Two Dimensional ◽  
The Monte Carlo Method

Based on the Wang-Landau algorithm, the Monte Carlo method is used to study the thermodynamic properties of the two-dimensional Potts model with the number of spin states $q=4$ on a triangular lattice, taking into account the interactions of the first and second nearest neighbors. It is shown that taking into account antiferromagnetic interactions of the second nearest neighbors leads to frustration.

Equilibrium and nonequilibrium models on Solomon networks

2016 ◽  
Vol 27 (11) ◽  
pp. 1650134 ◽  
Author(s):  
F. W. S. Lima
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Critical Exponents ◽  
Majority Vote ◽  
Universality Class ◽  
Nonequilibrium Systems ◽  
Two Dimensional ◽  
Critical Properties ◽  
The Monte Carlo Method ◽  
Regular Lattices

We investigate the critical properties of the equilibrium and nonequilibrium systems on Solomon networks. The equilibrium and nonequilibrium systems studied here are the Ising and Majority-vote models, respectively. These systems are simulated by applying the Monte Carlo method. We calculate the critical points, as well as the critical exponents ratio [Formula: see text], [Formula: see text] and [Formula: see text]. We find that both systems present identical exponents on Solomon networks and are of different universality class as the regular two-dimensional ferromagnetic model. Our results are in agreement with the Grinstein criterion for models with up and down symmetry on regular lattices.

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