A Simple Statistical Theory for Grain Growth in Materials.

1990 ◽  
Vol 209 ◽  
Author(s):  
P. Mulheran ◽  
J.H. Harding
Keyword(s):  
Growth Rate ◽  
Monte Carlo ◽  
Statistical Theory ◽  
Stochastic Model ◽  
Grain Growth ◽  
Three Dimensional ◽  
Monte Carlo Procedure ◽  
Short Time ◽  
2D And 3D ◽  
Good Agreement

A Monte Carlo procedure has been used to study the ordering of both two and three dimensional (2d and 3d) Potts Hamiltonians, further to the work of Anderson et al. For the 3d lattice, the short time growth rate is found to be much slower than previously reported, though the simulated microstructure is in agreement with the earlier studies. We propose a new stochastic model that gives good agreement with the simulations.

Non-Equilibrium Critical Relaxation of Heisenberg Ferromagnets with Long-Range Correlated Defects

2012 ◽  
Vol 190 ◽  
pp. 39-42
Author(s):  
M. Medvedeva ◽  
Pavel V. Prudnikov
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Critical Behavior ◽  
Critical Exponents ◽  
Heisenberg Model ◽  
Three Dimensional ◽  
Initial State ◽  
Short Time ◽  
Theoretic Description ◽  
Good Agreement

The dynamic critical behavior of the three-dimensional Heisenberg model with longrangecorrelated disorder was studied by using short-time Monte Carlo simulations at criticality.The static and dynamic critical exponents are determined. The simulation was performed fromordered initial state. The obtained values of the exponents are in a good agreement with resultsof the field-theoretic description of the critical behavior of this model in the two-loopapproximation.

Secondary Fluorescence of 3D Heterogeneous Materials Using a Hybrid Model

2020 ◽  
Vol 26 (3) ◽  
pp. 484-496
Author(s):  
Yu Yuan ◽  
Hendrix Demers ◽  
Xianglong Wang ◽  
Raynald Gauvin
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Analytical Model ◽  
Hybrid Model ◽  
Three Dimensional ◽  
Heterogeneous Materials ◽  
X Ray ◽  
The Monte Carlo Method ◽  
Secondary Fluorescence ◽  
Good Agreement

AbstractIn electron probe microanalysis or scanning electron microscopy, the Monte Carlo method is widely used for modeling electron transport within specimens and calculating X-ray spectra. For an accurate simulation, the calculation of secondary fluorescence (SF) is necessary, especially for samples with complex geometries. In this study, we developed a program, using a hybrid model that combines the Monte Carlo simulation with an analytical model, to perform SF correction for three-dimensional (3D) heterogeneous materials. The Monte Carlo simulation is performed using MC X-ray, a Monte Carlo program, to obtain the 3D primary X-ray distribution, which becomes the input of the analytical model. The voxel-based calculation of MC X-ray enables the model to be applicable to arbitrary samples. We demonstrate the derivation of the analytical model in detail and present the 3D X-ray distributions for both primary and secondary fluorescence to illustrate the capability of our program. Examples for non-diffusion couples and spherical inclusions inside matrices are shown. The results of our program are compared with experimental data from references and with results from other Monte Carlo codes. They are found to be in good agreement.

PREDICTION OF UNSTEADY STATES IN LID-DRIVEN CAVITIES FILLED WITH AN INCOMPRESSIBLE VISCOUS FLUID

2012 ◽  
Vol 23 (04) ◽  
pp. 1250030 ◽  
Author(s):  
FAYÇAL HAMMAMI ◽  
NADER BEN-CHEIKH ◽  
ANTONIO CAMPO ◽  
BRAHIM BEN-BEYA ◽  
TAIEB LILI
Keyword(s):  
Reynolds Number ◽  
Numerical Study ◽  
Three Dimensional ◽  
Staggered Grid ◽  
Three Dimensional Flow ◽  
Driven Cavity ◽  
Flow Evolution ◽  
2D And 3D ◽  
Benchmark Solutions ◽  
Good Agreement

In this work, a numerical study devoted to the two-dimensional and three-dimensional flow of a viscous, incompressible fluid inside a lid-driven cavity is undertaking. All transport equations are solved using the finite volume formulation on a staggered grid system and multi-grid acceleration. Quantitative aspects of two and three-dimensional flows in a lid-driven cavity for Reynolds number Re = 1000 show good agreement with benchmark results. An analysis of the flow evolution demonstrates that, with increments in Re beyond a certain critical value Rec, the steady flow becomes unstable and bifurcates into unsteady flow. It is observed that the transition from steadiness to unsteadiness follows the classical Hopf bifurcation. The time-dependent velocity distribution is studied in detail and the critical Reynolds number is localized for both 2D and 3D cases. Benchmark solutions for 2D and 3D lid-driven cavity flows are performed for Re = 1500 and 6000.

Monte-Carlo Simulation of Goss Abnormal Grain Growth in Fe-3%Si Steel by Sub-Boundary Enhanced Solid-State Wetting

2012 ◽  
Vol 715-716 ◽  
pp. 146-151
Author(s):  
K.J. Ko ◽  
A.D. Rollett ◽  
N.M. Hwang
Keyword(s):  
Monte Carlo ◽  
Solid State ◽  
Grain Boundary ◽  
Grain Growth ◽  
Boundary Energy ◽  
Three Dimensional ◽  
Abnormal Grain Growth ◽  
Grain Boundary Energy ◽  
Simulation Based ◽  
Mc Simulation

The selective abnormal grain growth (AGG) of Goss grains in Fe-3%Si steel was investigated using a parallel Monte-Carlo (MC) simulation based on the new concept of sub-boundary enhanced solid-state wetting. Goss grains with low angle sub-boundaries will induce solid-state wetting against matrix grains with a moderate variation in grain boundary energy. Three-dimensional MC simulations of microstructure evolution with textures and grain boundary distributions matched to experimental data is using in this study.

A Stochastic Nonlinear Constitutive Law for Concrete

1989 ◽  
Vol 111 (4) ◽  
pp. 443-449 ◽  
Author(s):  
A. Fafitis ◽  
Y. H. Won
Keyword(s):  
Stochastic Model ◽  
Elastic Moduli ◽  
Three Dimensional ◽  
Path Dependency ◽  
Experimental Results ◽  
Constitutive Law ◽  
Induced Anisotropy ◽  
Nonproportional Loading ◽  
Strain Relationship ◽  
Good Agreement

An incremental three-dimensional stress-strain relationship for concrete with induced anisotropy has been developed. The nonlinearity and path-dependency are modeled by expressing the elastic moduli at each increment as function of the octahedral and deviatoric strains, based on a uniaxial stochastic model developed earlier. Predictions of multiaxial response under proportional and nonproportional loading are in good agreement with experimental results.

scholarly journals Ion Beam Enhanced Grain Growth in Thin Films

1986 ◽  
Vol 74 ◽  
Author(s):  
Harry A. Atwater ◽  
Carl V. Tiiompson ◽  
Henry I. Smith
Keyword(s):  
Thin Films ◽  
Growth Rate ◽  
Grain Boundary ◽  
Grain Growth ◽  
Thermal Equilibrium ◽  
Ion Beam ◽  
Defect Concentration ◽  
Growth Enhancement ◽  
Frenkel Defect ◽  
Good Agreement

AbstractIon beam enhanced grain growth has been investigated in thin films of Ge. Grain boundary mobilities are greatly enhanced over their thermal equilibrium values and exhibit a very weak temperature dependence. We propose that defects which are generated by the ion beam at or near the grain boundary are responsible for the boundary mobility enhancement. Films of Ge deposited under different conditions, either unsupported or on thermally oxidized Si, exhibit similar normal grain growth enhancement when implanted with 50 keV Ge+. Beam-enhanced grain growth in Ge was also demonstrated using Xe+, Kr+, and Ar+ ions. The variation in growth enhancement with projectile ion mass is in good agreement with the enhanced Frenkel defect population calculated using a modified Kinchin-Pease formula and Monte Carlo simulation of ion transport in thin films. Calculations based on experiments suggest that there is approximately one atomic jump across the grain boundary per defect generated. Also, the grain growth rate for a given beam-generated defect concentration near the boundary is approximately equal to the expected growth rate for the same defect concentration if thermally generated.

Three-dimensional monte-carlo simulation of grain growth in Pt-Co thin film

2002 ◽  
Vol 31 (10) ◽  
pp. 965-971 ◽  
Author(s):  
Sung Il Park ◽  
Sang Soo Han ◽  
Hyoung Gyu Kim ◽  
Joong Keun Park ◽  
Hyuck Mo Lee
Keyword(s):  
Thin Film ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Grain Growth ◽  
Three Dimensional

Effect of a Finite Boundary Junction Mobility on the Growth Rate of Two and Three Dimensional Grains

2012 ◽  
Vol 715-716 ◽  
pp. 574-578 ◽  
Author(s):  
Luis A. Barrales Mora
Keyword(s):  
Growth Rate ◽  
Three Dimensional ◽  
Granular System ◽  
Present Contribution ◽  
Von Neumann ◽  
Model Simulations ◽  
Theoretical Approaches ◽  
Dimensional Network ◽  
Zero Growth ◽  
Good Agreement

t has been shown by computer simulations that the MacPherson-Srolovitz relation predicts accurately the growth rate of a grain undergoing ideal grain growth. However, since a finite mobility of the boundary junctions (triple lines and quadruple junctions) affects the evolution of a granular system, it is necessary to modify this equation in order to take into account their effect. In the present contribution, an equation which allows considering these factors is presented and used to modify the von Neumann-Mullins and MacPherson-Srolovitz equations. In order to corroborate these equations two and three dimensional network model simulations were performed. The results showed a very good agreement with the theoretical approaches for both dimensions and all topological classes except those near the classes of zero growth rate in 3D. The reason is that the proposed function is very sensitive to small changes of the finite mobility of the junctions.

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