On the Validation of the Monte Carlo Technique in Simulation of Grain Growth in Small, Two-Dimensional Systems

2007 ◽  
pp. 1087-1092
Author(s):  
Ola Hunderi ◽  
Knut Marthinsen ◽  
Nils Ryum
Keyword(s):  
Monte Carlo ◽  
Grain Growth ◽  
Monte Carlo Technique ◽  
Two Dimensional

A new Monte Carlo method for percolation problems on a lattice

1963 ◽  
Vol 59 (2) ◽  
pp. 397-410 ◽  
Author(s):  
P. Dean
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Cluster Size ◽  
Monte Carlo Technique ◽  
Two Dimensional ◽  
Regular Lattice

AbstractA new and general Monte Carlo technique is described for solving some well-known percolation and cluster-size problems on regular lattice networks. The method has been applied to ten two-dimensional structures.

TOPOLOGY COLLAPSE OF NONTRIVIAL U(1)-BUNDLE ON LATTICIZED SPHERE

1988 ◽  
Vol 03 (15) ◽  
pp. 1489-1497
Author(s):  
HIROSHI KOIBUCHI ◽  
MITSURU YAMADA
Keyword(s):  
Monte Carlo ◽  
Statistical Mechanics ◽  
Gauge Field ◽  
Low Temperatures ◽  
Field Configuration ◽  
Chern Number ◽  
Monte Carlo Technique ◽  
Metastable States ◽  
Two Dimensional ◽  
Gauge Model

Applying the Monte Carlo technique, we study the statistical mechanics of U(1) gauge model on two dimensional spherical lattice of the Mercator type. Special emphasis is put on the topology of the gauge-field configuration. At sufficiently low temperatures, we demonstrate the existence of many metastable states, each of which has a well-defined Chern number. At higher temperatures, we observe how they lose their topology and collapse.

On the Validation of the Monte Carlo Technique in Simulation of Grain Growth in Small, Two-Dimensional Systems

2007 ◽  
Vol 558-559 ◽  
pp. 1087-1092
Author(s):  
Ola Hunderi ◽  
Knut Marthinsen ◽  
Nils Ryum
Keyword(s):  
Monte Carlo ◽  
Grain Boundary ◽  
Grain Growth ◽  
Computer Simulations ◽  
Two Dimensions ◽  
Theoretical Treatment ◽  
Two Dimensional ◽  
Simulation Techniques ◽  
Boundary Curvature ◽  
Kinetics Of

The kinetics of grain growth in real systems is influenced by several unknown factors, making a theoretical treatment very difficult. Idealized grain growth, assuming all grain boundaries to have the same energy and mobility (mobility M = k/ρ, where k is a constant and ρ is grain boundary curvature) can be treated theoretically, but the results obtained can only be compared to numerical grain growth simulations, as ideal grain growth scarcely exists in nature. The validity of the simulation techniques thus becomes of great importance. In the present investigation computer simulations of grain growth in two dimensions using Monte Carlo simulations and the grain boundary tracking technique have been investigated and compared in small grain systems, making it possible to follow the evolution of each grain in the system.

Monte-Carlo Simulation for the Grain Growth of Si3N4 during Sintering Process

2008 ◽  
Vol 368-372 ◽  
pp. 1673-1676
Author(s):  
Yu Hong Zhao ◽  
Yue Zhang ◽  
Da Hai Zhang
Keyword(s):  
Complex System ◽  
Monte Carlo ◽  
Liquid Phase ◽  
Grain Growth ◽  
Grain Orientation ◽  
Interfacial Free Energy ◽  
Liquid Phase Sintering ◽  
Square Lattice ◽  
Two Dimensional ◽  
Sintering Process

Based on the Potts model, the grain growth of Si3N4 in liquid phase sintering process was simulated by Monte-Carlo method. A two-dimensional, square lattice is used to digitize the microstructure and the components and grain orientation are distributed randomly. The periodical boundary condition is applied. In the initial simulation, the grain growth and coarsening process driven by the reduction in interfacial free energy within a complex system involving a liquid phase were investigated with 32 orientations and different fraction of a liquid phase has been considered. Simulation was carried out with 200×200 lattice. The effects of the liquid amount on the grain growth mechanism and microstructures were discussed.

A VARIATIONAL STUDY OF FERMI AND LUTTINGER LIQUID WAVEFUNCTIONS IN THE TWO-DIMENSIONAL t-J MODEL

1996 ◽  
Vol 10 (18) ◽  
pp. 873-881 ◽  
Author(s):  
FRANJO FRANJIĆ ◽  
SANDRO SORELLA
Keyword(s):  
Monte Carlo ◽  
Ground State ◽  
Liquid State ◽  
Fermi Liquid ◽  
Luttinger Liquid ◽  
Monte Carlo Technique ◽  
Two Dimensional ◽  
Variational Monte Carlo ◽  
Variational Study

Using a recently developed technique, we determine the Jastrow potential of the variational wavefunction for the two-dimensional t-J model. This wavefunction describes a Fermi liquid ground state and is compared with the Luttinger liquid wavefunction used by Gros and Valentí. Estimates of the energy of these states are calculated using the variational Monte Carlo technique, showing that the Fermi liquid state has a little power energy.

Structures and crystallization of vacuum-deposited amorphous Se and Sb films

1990 ◽  
Vol 48 (4) ◽  
pp. 140-141
Author(s):  
Makoto Shiojiri ◽  
Toshiyuki Isshiki ◽  
Tetsuya Fudaba ◽  
Yoshihiro Hirota
Keyword(s):  
Monte Carlo ◽  
Electron Microscope ◽  
Monte Carlo Method ◽  
Computer Program ◽  
Radial Distribution ◽  
Film Formation ◽  
Amorphous State ◽  
Two Dimensional ◽  
Amorphous Films ◽  
Binding Condition

In hexagonal Se crystal each atom is covalently bound to two others to form an endless spiral chain, and in Sb crystal each atom to three others to form an extended puckered sheet. Such chains and sheets may be regarded as one- and two- dimensional molecules, respectively. In this paper we investigate the structures in amorphous state of these elements and the crystallization.HRTEM and ED images of vacuum-deposited amorphous Se and Sb films were taken with a JEM-200CX electron microscope (Cs=1.2 mm). The structure models of amorphous films were constructed on a computer by Monte Carlo method. Generated atoms were subsequently deposited on a space of 2 nm×2 nm as they fulfiled the binding condition, to form a film 5 nm thick (Fig. 1a-1c). An improvement on a previous computer program has been made as to realize the actual film formation. Radial distribution fuction (RDF) curves, ED intensities and HRTEM images for the constructed structure models were calculated, and compared with the observed ones.

Sign in / Sign up

Export Citation Format

Share Document