scholarly journals Crossover from BKT-Rough to KPZ-Rough Surfaces for Crystal Growth/Recession

2021 ◽  
Vol 2090 (1) ◽  
pp. 012075
Author(s):  
Noriko Akutsu
Keyword(s):  
Monte Carlo ◽  
Rough Surface ◽  
Two Dimensional ◽  
Nucleation Process ◽  
Crystal Surfaces ◽  
Crossover Point ◽  
Kinetic Roughening ◽  
The Monte Carlo Method ◽  
Surface Fluctuations ◽  
Negative Islands

Abstract We found a crossover from a Berezinskii-Kosterlitz-Thouless (BKT, logarithmic-rough surface to a Kardar-Parisi-Zhang (KPZ, algebraic)-rough surface for growing/recessing vicinal crystal surfaces in the non-equilibrium steady state using the Monte-Carlo method. We also found that the crossover point from a BKT-rough surface to a KPZ-rough surface is different from the kinetic roughening point for the (001) surface. Multilevel islands and negative islands (island-shaped holes) on the terrace formed by the two-dimensional nucleation process are found to block surface fluctuations, which contributes to making a BKT-rough surface.

Methods to Accelerate Ray Tracing in the Monte Carlo Method for Surface-to-Surface Radiation Transport

2006 ◽  
Vol 128 (9) ◽  
pp. 945-952 ◽  
Author(s):  
Sandip Mazumder
Keyword(s):  
Monte Carlo ◽  
Ray Tracing ◽  
Radiation Transport ◽  
Three Dimensional ◽  
Intersection Point ◽  
Surface Radiation ◽  
Computational Domain ◽  
Two Dimensional ◽  
Spatial Partitioning ◽  
The Monte Carlo Method

Two different algorithms to accelerate ray tracing in surface-to-surface radiation Monte Carlo calculations are investigated. The first algorithm is the well-known binary spatial partitioning (BSP) algorithm, which recursively bisects the computational domain into a set of hierarchically linked boxes that are then made use of to narrow down the number of ray-surface intersection calculations. The second algorithm is the volume-by-volume advancement (VVA) algorithm. This algorithm is new and employs the volumetric mesh to advance the ray through the computational domain until a legitimate intersection point is found. The algorithms are tested for two classical problems, namely an open box, and a box in a box, in both two-dimensional (2D) and three-dimensional (3D) geometries with various mesh sizes. Both algorithms are found to result in orders of magnitude gains in computational efficiency over direct calculations that do not employ any acceleration strategy. For three-dimensional geometries, the VVA algorithm is found to be clearly superior to BSP, particularly for cases with obstructions within the computational domain. For two-dimensional geometries, the VVA algorithm is found to be superior to the BSP algorithm only when obstructions are present and are densely packed.

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.

scholarly journals Плотность состояний и структура основного состояния модели Изинга на решетке Кагоме с учетом взаимодействия ближайших и следующих соседей

2018 ◽  
Vol 60 (6) ◽  
pp. 1173
Author(s):  
М.А. Магомедов ◽  
А.К. Муртазаев
Keyword(s):  
Phase Transition ◽  
Monte Carlo ◽  
Nearest Neighbor ◽  
Abnormal Behavior ◽  
Two Dimensional ◽  
Analysis Method ◽  
Neighbor Interaction ◽  
The Monte Carlo Method ◽  
Antiferromagnetic Ising Model ◽  
Second Order Phase Transition

AbstractPhase transitions and thermodynamic properties have been studied in the two-dimensional antiferromagnetic Ising model on a Kagome lattice by the Monte Carlo method with consideration for both nearest- and next-nearest-neighbor interaction. Using the histogram data analysis method, it has been shown that the studied model is characterized by a second-order phase transition. The temperature dependence of thermodynamic parameters has been revealed to exhibit abnormal behavior.

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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