Recent Developments in Simulating Grain Growth with Monte Carlo Algorithms

2002 ◽  
Vol 731 ◽  
Author(s):  
Qiang Yu ◽  
Sven K. Esche
Keyword(s):  
Monte Carlo ◽  
Grain Growth ◽  
Single Phase ◽  
Rate Of Change ◽  
Monte Carlo Algorithms ◽  
Recent Developments ◽  
Grain Size Distributions ◽  
The Mean ◽  
Time Invariant ◽  
Anisotropy Degree

AbstractBoth isotropic and anisotropic single-phase grain growth processes modeled using a modified Monte Carlo method exhibit parabolic growth kinetics, and the anisotropy degree affects only the rate of change of the mean grain area. In some cases, with significantly anisotropic grain boundary energies, the normalized grain size distributions are not time-invariant during the lattice evolution.

Simulation of Fabrication for Single-Phase Al2O3 Ceramic Tool Materials at Different Fabrication Temperature

2010 ◽  
Vol 150-151 ◽  
pp. 1358-1363
Author(s):  
Bin Fang ◽  
Chuan Zhen Huang ◽  
Chong Hai Xu ◽  
Sheng Sun
Keyword(s):  
Mechanical Properties ◽  
Computer Simulation ◽  
Grain Size ◽  
Monte Carlo ◽  
Single Phase ◽  
Two Dimensional ◽  
Ceramic Tool ◽  
Tool Materials ◽  
Mean Grain Size ◽  
The Mean

The fabrication is a key process for the preparation of ceramic tool materials, which governs the mechanical properties of ceramic tool materials under the condition of the same compositions. A computer simulation coupled with fabrication temperature for the hot-pressing process of single-phase ceramic tool materials has been developed using a two-dimensional hexagon lattice model mapped from the realistic microstructure without considering the presence of pores. The fabrication of single-phase Al2O3 is simulated. The mean grain size of simulated microstructure by Monte Carlo Potts model integrated with fabrication temperature increases with an increase in fabrication temperature, which is consistent with the experiment results.

Simulation of Fabrication for Single-Phase Al2O3 Ceramic Tool Materials at Different Fabrication Pressure

2012 ◽  
Vol 499 ◽  
pp. 150-155 ◽  
Author(s):  
Bin Fang ◽  
Chuan Zhen Huang ◽  
Chong Hai Xu ◽  
Sheng Sun
Keyword(s):  
Monte Carlo ◽  
Microstructure Evolution ◽  
Potts Model ◽  
Single Phase ◽  
Two Dimensional ◽  
Ceramic Tool ◽  
Tool Materials ◽  
Mean Grain Size ◽  
The Mean ◽  
The Relationship

The relationship between fabrication pressure and microstructure evolution is proposed. A computer simulation coupled with fabrication pressure for the hot-pressing process of single-phase ceramic tool materials has been developed, which uses a two-dimensional hexagon lattice model mapped from the realistic microstructure without considering the presence of pores. The fabrication of single-phase Al2O3 is simulated. The mean grain size of simulated microstructure by Monte Carlo Potts model integrated with fabrication pressure increases with an increase in fabrication pressure, which is consistent with the experiment results. It is shown that Monte Carlo Potts model coupled with fabrication pressure may simulate the microstructure evolution of single-phase ceramic tool materials.

Monte Carlo Potts Model Simulation and Statistical Theory of 3D Grain Growth

2007 ◽  
Vol 558-559 ◽  
pp. 1219-1224 ◽  
Author(s):  
Dana Zöllner ◽  
Peter Streitenberger
Keyword(s):  
Grain Size ◽  
Monte Carlo ◽  
Grain Growth ◽  
Potts Model ◽  
Model Simulation ◽  
Mean Field Theory ◽  
Mean Field ◽  
Three Dimensional ◽  
Rate Of Change ◽  
Volumetric Rate

An improved Monte Carlo (MC) Potts model algorithm has been implemented allowing an extensive simulation of three-dimensional (3D) normal grain growth. It is shown that the simulated microstructure reaches a quasi-stationary state, where the growth of grains can be described by an average self-similar volumetric rate of change, which depends only on the relative grain size. Based on a quadratic approximation of the volumetric rate of change a generalized analytic mean-field theory yields a scaled grain size distribution function that is in excellent agreement with the simulation results.

scholarly journals Convergence rates for optimised adaptive importance samplers

2021 ◽  
Vol 31 (2) ◽  
Author(s):  
Ömer Deniz Akyildiz ◽  
Joaquín Míguez
Keyword(s):  
Monte Carlo ◽  
Rate Of Convergence ◽  
Exponential Family ◽  
Convergence Rates ◽  
Adaptation Strategy ◽  
Adaptive Monte Carlo ◽  
Asymptotic Bounds ◽  
Monte Carlo Algorithms ◽  
The Mean ◽  
Number Of Iterations

AbstractAdaptive importance samplers are adaptive Monte Carlo algorithms to estimate expectations with respect to some target distribution which adapt themselves to obtain better estimators over a sequence of iterations. Although it is straightforward to show that they have the same $$\mathcal {O}(1/\sqrt{N})$$ O ( 1 / N ) convergence rate as standard importance samplers, where N is the number of Monte Carlo samples, the behaviour of adaptive importance samplers over the number of iterations has been left relatively unexplored. In this work, we investigate an adaptation strategy based on convex optimisation which leads to a class of adaptive importance samplers termed optimised adaptive importance samplers (OAIS). These samplers rely on the iterative minimisation of the $$\chi ^2$$ χ 2 -divergence between an exponential family proposal and the target. The analysed algorithms are closely related to the class of adaptive importance samplers which minimise the variance of the weight function. We first prove non-asymptotic error bounds for the mean squared errors (MSEs) of these algorithms, which explicitly depend on the number of iterations and the number of samples together. The non-asymptotic bounds derived in this paper imply that when the target belongs to the exponential family, the $$L_2$$ L 2 errors of the optimised samplers converge to the optimal rate of $$\mathcal {O}(1/\sqrt{N})$$ O ( 1 / N ) and the rate of convergence in the number of iterations are explicitly provided. When the target does not belong to the exponential family, the rate of convergence is the same but the asymptotic $$L_2$$ L 2 error increases by a factor $$\sqrt{\rho ^\star } > 1$$ ρ ⋆ > 1 , where $$\rho ^\star - 1$$ ρ ⋆ - 1 is the minimum $$\chi ^2$$ χ 2 -divergence between the target and an exponential family proposal.

Simulations of anisotropic grain growth in single phase materials using Q-state Monte Carlo

2013 ◽  
Vol 71 ◽  
pp. 25-32 ◽  
Author(s):  
J.B. Allen ◽  
C.F. Cornwell ◽  
B.D. Devine ◽  
C.R. Welch
Keyword(s):  
Monte Carlo ◽  
Grain Growth ◽  
Single Phase

Simulations of Anisotropic Grain Growth Subject to Thermal Gradients Using Q-State Monte Carlo

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
J. B. Allen ◽  
C. F. Cornwell ◽  
B. D. Devine ◽  
C. R. Welch
Keyword(s):  
Monte Carlo ◽  
Grain Boundary ◽  
Grain Growth ◽  
Single Phase ◽  
Boundary Surface ◽  
Normal Growth ◽  
Thermal Gradients ◽  
Surface Energies ◽  
Generalized Heat Equation ◽  
Mobility Coefficient

The Q-state Monte Carlo, Potts model is used to investigate 2D, anisotropic, grain growth of single-phase materials subject to temperature gradients. Anisotropy is simulated via the use of nonuniform grain boundary surface energies, and thermal gradients are simulated through the use of variable grain boundary mobilities. Hexagonal grain elements are employed, and elliptical Wulff plots are used to assign surface energies to grain lattices. The mobility is set to vary in accordance with solutions to a generalized heat equation and is solved for two separate values of the mobility coefficient. Among other findings, the results reveal that like isotropic grain growth, under the influence of a thermal gradient, anisotropic grain growth also demonstrates locally normal growth kinetics.

Simulation of the Effect of Sintering Pressure on Microstructure Evolution in Nanocomposite Ceramic Tool Materials

2013 ◽  
Vol 395-396 ◽  
pp. 262-265 ◽  
Author(s):  
Hong Mei Cheng ◽  
Chuan Zhen Huang
Keyword(s):  
Grain Size ◽  
Monte Carlo ◽  
Grain Growth ◽  
Microstructure Evolution ◽  
Growth Process ◽  
Sintering Process ◽  
Ceramic Tool ◽  
Tool Materials ◽  
Mean Grain Size ◽  
The Mean

A Monte Carlo Potts model coupled with sintering pressure for the sintering process of nanocomposite ceramic tool materials is proposed, the relation between grain growth and sintering pressure is presented. The grain growth process at different sintering pressure is investigated in this model, and the effect of sintering pressure on microstructure evolution is discussed, it is found that the mean grain size increases with the increase of sintering pressure during simulation. The results from this simulation are shown to correlate well with the experimental observations.

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