Application of the monte carlo method to the problem of flow in the boundary layer of a two-dimensional turbulent jet

1972 ◽  
Vol 22 (4) ◽  
pp. 504-506
Author(s):  
F. N. Yasinskii
Keyword(s):  
Boundary Layer ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Turbulent Jet ◽  
Two Dimensional ◽  
The Monte Carlo Method

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.

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.

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.

Deposition Process and Equivalent Markov Motion of High-inertia Particles in a Long Straight Pipeline

2021 ◽  
Author(s):  
Ri Zhang ◽  
Kai Xu ◽  
Yong Liu ◽  
Yumiao Wang
Keyword(s):  
Boundary Layer ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Pipe Flow ◽  
Particle Deposition ◽  
Deposition Velocity ◽  
Deposition Process ◽  
Turbulent Pipe Flow ◽  
Probability Density Distribution ◽  
The Monte Carlo Method

Abstract Two methods are used to study the process of particle deposition in a turbulent pipe flow. The Monte Carlo method tracks 10,000 particles in the turbulent pipe flow to reproduce the deposition process of the particles. The deposition velocity of the particles is determined by calculating the proportion of particles passing through the test section. The simplified deposition model uses an equivalent Markov motion instead of the radial movement of the particle in the turbulent core. The probability that a particle leaves the turbulent core depends on the radial particle position and the probability density distribution of the random vortex. The probability that a particle penetrates the boundary layer can be solved by integrating the probability density distribution of radial particle velocity. The deposition velocity of particles can be obtained by calculating the probability of an individual particle leaving the turbulent core and penetrating the boundary layer. Five experimental data series from the literature are applied to examine the predictive abilities of the two methods. The results demonstrate that the Monte Carlo method can be properly used to track the particle deposition process in the diffusion-impaction and inertia-moderated regimes. The simplified model is suitable for high-inertia particles.

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.

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