Download or read book Monte Carlo Potts Model Simulation and Statistical Mean Field Theory of Normal Grain Growth written by Dana Zöllner and published by . This book was released on 2006 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Potts model Grain Growth Simulations written by and published by . This book was released on 1997 with total page 47 pages. Available in PDF, EPUB and Kindle. Book excerpt: Microstructural morphology and grain boundary properties often control the service properties of engineered materials. This report uses the Potts-model to simulate the development of microstructures in realistic materials. Three areas of microstructural morphology simulations were studied. They include the development of massively parallel algorithms for Potts-model grain grow simulations, modeling of mass transport via diffusion in these simulated microstructures, and the development of a gradient-dependent Hamiltonian to simulate columnar grain growth. Potts grain growth models for massively parallel supercomputers were developed for the conventional Potts-model in both two and three dimensions. Simulations using these parallel codes showed self similar grain growth and no finite size effects for previously unapproachable large scale problems. In addition, new enhancements to the conventional Metropolis algorithm used in the Potts-model were developed to accelerate the calculations. These techniques enable both the sequential and parallel algorithms to run faster and use essentially an infinite number of grain orientation values to avoid non-physical grain coalescence events. Mass transport phenomena in polycrystalline materials were studied in two dimensions using numerical diffusion techniques on microstructures generated using the Potts-model. The results of the mass transport modeling showed excellent quantitative agreement with one dimensional diffusion problems, however the results also suggest that transient multi-dimension diffusion effects cannot be parameterized as the product of the grain boundary diffusion coefficient and the grain boundary width. Instead, both properties are required. Gradient-dependent grain growth mechanisms were included in the Potts-model by adding an extra term to the Hamiltonian. Under normal grain growth, the primary driving term is the curvature of the grain boundary, which is included in the standard Potts-model Hamiltonian.
Download or read book Potts Model Simulation of Grain Size Distributions During Final Stage Sintering written by and published by . This book was released on 1998 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Potts Monte Carlo model was used to simulate microstructural evolution and characterize grain size distribution during the final stages of sintering. Simultaneous grain growth, pore migration and pore shrinkage were simulated in a system with an initial porosity of 10% with varying ratios of grain boundary mobility to pore shrinkage rates. This investigation shows that the presence of pores changes the grain size distribution and the topological characteristics due to pinning of grains by pores. As pores shrink away, their pinning effect decreases. Once pore shrinkage is complete, normal grain growth is achieved.
Download or read book Monte Carlo Simulations of Grain Growth in Polycrystalline Materials Using Potts Model written by Miroslav Morháč and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Monte Carlo Simulations of Grain Growth in Polycrystalline Materials Using Potts Model.
Download or read book 2D and 3D Grain Growth Modeling and Simulation written by Luis Antonio Barrales-Mora and published by Cuvillier Verlag. This book was released on 2008 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Evolution of 2D Potts Model Grain Microstructures from an Initial Hillert Size Distribution written by and published by . This book was released on 1998 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Grain growth experiments and simulations exhibit self-similar grain size distributions quite different from that derived via a mean field approach by Hillert [1]. To test whether this discrepancy is due to insufficient anneal times, two different two-dimensional grain structures with realistic topologies and Hillert grain size distributions are generated and subjected to grain growth via the Monte Carlo Potts Model (MCPM). In both cases, the observed self-similar grain size distributions deviate from the initial Hillert form and conform instead to that observed in MCPM grain growth simulations that start from a random microstructure. This suggests that the Hillert grain size distribution is not an attractor.
Download or read book Micro Macro Interactions written by Albrecht Bertram and published by Springer Science & Business Media. This book was released on 2008-10-23 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many materials or media in nature and technology possess a microstructure which determines their macroscopic behaviour. The knowledge of the relevant mechanisms is often more comprehensive on the micro than on the macro scale. On the other hand, not all information on the micro level is relevant for the understanding of this macro behaviour. Therefore, averaging and homogenization methods are needed to select only the specific information from the micro scale, which influences the macro scale. These methods also open the possibility to design or to influence microstructures with the objective to optimize their macro behaviour. This book presents the development of new methods in this interdisciplinary field of macro- micro-interactions of different engineering branches like mechanical and process engineering, applied mathematics, theoretical, and computational physics. In particular, solids with microstructures and particle systems are considered.
Download or read book Simulation of Anisotropic Grain Growth by Ostwald Ripening written by and published by . This book was released on 1996 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, a two-dimensional Potts model that can simulate anisotropic grain growth by Ostwald ripening in liquid-phase-sintered ceramics will be presented. The model defines a Wulff shape for the grains and allows each individual grain to grow in its local environment which is controlled by the solid/liquid interfacial energy, the spatial distribution of neighboring grains, area fraction of grains, wetting by and distribution of the liquid matrix, and the concentration gradients in the liquid. The results of this simulation technique will be presented with emphasis on the kinetics and grain shape evolution and will be compared to those of isotropic grain growth. Finally, the limitations of the Potts model in such microstructural evolution processes will be discussed.
Download or read book Gibbs Measures In Biology And Physics The Potts Model written by Utkir A Rozikov and published by World Scientific. This book was released on 2022-07-28 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents recently obtained mathematical results on Gibbs measures of the q-state Potts model on the integer lattice and on Cayley trees. It also illustrates many applications of the Potts model to real-world situations in biology, physics, financial engineering, medicine, and sociology, as well as in some examples of alloy behavior, cell sorting, flocking birds, flowing foams, and image segmentation.Gibbs measure is one of the important measures in various problems of probability theory and statistical mechanics. It is a measure associated with the Hamiltonian of a biological or physical system. Each Gibbs measure gives a state of the system.The main problem for a given Hamiltonian on a countable lattice is to describe all of its possible Gibbs measures. The existence of some values of parameters at which the uniqueness of Gibbs measure switches to non-uniqueness is interpreted as a phase transition.This book informs the reader about what has been (mathematically) done in the theory of Gibbs measures of the Potts model and the numerous applications of the Potts model. The main aim is to facilitate the readers (in mathematical biology, statistical physics, applied mathematics, probability and measure theory) to progress into an in-depth understanding by giving a systematic review of the theory of Gibbs measures of the Potts model and its applications.
Download or read book Computational Materials Engineering written by Koenraad George Frans Janssens and published by Academic Press. This book was released on 2010-07-26 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational Materials Engineering is an advanced introduction to the computer-aided modeling of essential material properties and behavior, including the physical, thermal and chemical parameters, as well as the mathematical tools used to perform simulations. Its emphasis will be on crystalline materials, which includes all metals. The basis of Computational Materials Engineering allows scientists and engineers to create virtual simulations of material behavior and properties, to better understand how a particular material works and performs and then use that knowledge to design improvements for particular material applications. The text displays knowledge of software designers, materials scientists and engineers, and those involved in materials applications like mechanical engineers, civil engineers, electrical engineers, and chemical engineers. Readers from students to practicing engineers to materials research scientists will find in this book a single source of the major elements that make up contemporary computer modeling of materials characteristics and behavior. The reader will gain an understanding of the underlying statistical and analytical tools that are the basis for modeling complex material interactions, including an understanding of computational thermodynamics and molecular kinetics; as well as various modeling systems. Finally, the book will offer the reader a variety of algorithms to use in solving typical modeling problems so that the theory presented herein can be put to real-world use. - Balanced coverage of fundamentals of materials modeling, as well as more advanced aspects of modeling, such as modeling at all scales from the atomic to the molecular to the macro-material - Concise, yet rigorous mathematical coverage of such analytical tools as the Potts type Monte Carlo method, cellular automata, phase field, dislocation dynamics and Finite Element Analysis in statistical and analytical modeling
Download or read book Coupled Finite Element Potts Model Simulations of Grain Growth in Copper Interconnects written by and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The paper addresses grain growth in copper interconnects in the presence of thermal expansion mismatch stresses. The evolution of grain structure and texture in copper in the simultaneous presence of two driving forces, curvature and elastic stored energy difference, is modeled by using a hybrid Potts model simulation approach. The elastic stored energy is calculated by using the commercial finite element code ABAQUS, where the effect of elastic anisotropy on the thermal mismatch stress and strain distribution within a polycrystalline grain structure is modeled through a user material (UMAT) interface. Parametric studies on the effect of trench width and the height of the overburden were carried out. The results show that the grain structure and texture evolution are significantly altered by the presence of elastic strain energy.
Download or read book Cellular Potts Models written by Marco Scianna and published by CRC Press. This book was released on 2013-03-26 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: A flexible, cell-level, and lattice-based technique, the cellular Potts model accurately describes the phenomenological mechanisms involved in many biological processes. Cellular Potts Models: Multiscale Extensions and Biological Applications gives an interdisciplinary, accessible treatment of these models, from the original methodologies to the latest developments. The book first explains the biophysical bases, main merits, and limitations of the cellular Potts model. It then proposes several innovative extensions, focusing on ways to integrate and interface the basic cellular Potts model at the mesoscopic scale with approaches that accurately model microscopic dynamics. These extensions are designed to create a nested and hybrid environment, where the evolution of a biological system is realistically driven by the constant interplay and flux of information between the different levels of description. Through several biological examples, the authors demonstrate a qualitative and quantitative agreement with the relative experimental data. The cellular Potts model is increasingly being used for the mathematical modeling of a wide range of biological phenomena, including wound healing, tumor growth, and cancer cell migration. This book shows how the cellular Potts model can be used as a framework for model building and how extended models can achieve even better biological practicality, accuracy, and predictive power.
Download or read book Microdynamics Simulation written by Paul Bons and published by Springer Science & Business Media. This book was released on 2007-10-24 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: A complete starting package for students and researchers of the earth science community interested in numerical modeling of microstructures. This excellent book deals with the numerical simulation of such microstructures in rocks. It starts with an introduction to existing methods and techniques for optical and electron microscopic analysis. The main part of the book contains examples of numerical modeling of processes and microstructures in rocks, using the software package "ELLE".
Download or read book Continuum Scale Simulation of Engineering Materials written by Dierk Raabe and published by John Wiley & Sons. This book was released on 2006-03-06 with total page 885 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book fills a gap by presenting our current knowledge and understanding of continuum-based concepts behind computational methods used for microstructure and process simulation of engineering materials above the atomic scale. The volume provides an excellent overview on the different methods, comparing the different methods in terms of their respective particular weaknesses and advantages. This trains readers to identify appropriate approaches to the new challenges that emerge every day in this exciting domain. Divided into three main parts, the first is a basic overview covering fundamental key methods in the field of continuum scale materials simulation. The second one then goes on to look at applications of these methods to the prediction of microstructures, dealing with explicit simulation examples, while the third part discusses example applications in the field of process simulation. By presenting a spectrum of different computational approaches to materials, the book aims to initiate the development of corresponding virtual laboratories in the industry in which these methods are exploited. As such, it addresses graduates and undergraduates, lecturers, materials scientists and engineers, physicists, biologists, chemists, mathematicians, and mechanical engineers.
Download or read book Microstructure evolution in strontium titanate Investigated by means of grain growth simulations and x ray diffraction contrast tomography experiments written by Syha, Melanie and published by KIT Scientific Publishing. This book was released on 2014-09-25 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding the physical processes during fabrication and annealing of ceramic materials is a long sought goal among material scientists. Using strontium titanate as a model system for perovskite ceramics, the present work combines advanced non-destructive 3D characterization techniques and computational modeling of microstructure evolution in order to link grain morphology, interface anisotropy and microstructure evolution to macroscopic physical properties .
Download or read book Simulation of Material Processing Theory Methods and Application written by Ken-ichiro Mori and published by CRC Press. This book was released on 2001-01-01 with total page 1170 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains about 180 papers including seven keynotes presented at the 7th NUMIFORM Conference. It reflects the state-of-the-art of simulation of industrial forming processes such as rolling, forging, sheet metal forming, injection moulding and casting.
Download or read book Ceramic Microstructures written by Antoni P. Tomsia and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 841 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, titled Proceedings of the International Materials Symposium on Ce ramic Microstructures: Control at the Atomic Level summarizes the progress that has been achieved during the past decade in understanding and controlling microstructures in ceram ics. A particular emphasis of the symposium, and therefore of this volume, is advances in the characterization, understanding, and control of micro structures at the atomic or near-atomic level. This symposium is the fourth in a series of meetings, held every ten years, devoted to ceramic microstructures. The inaugural meeting took place in 1966, and focussed on the analysis, significance, and production of microstructure; the symposium emphasized the need for, and importance of characterization in achieving a more complete understanding of the physical and chemical characteristics of ceramics. A consensus emerged at that meeting on the critical importance of characterization in achieving a more complete understanding of ceramic properties. That point of view became widely accepted in the ensuing decade. The second meeting took place in 1976 at a time of world-wide energy shortages and thus emphasized energy-related applications of ceramics, and more specifically, microstructure-property relationships of those materials. The third meeting, held in 1986, was devoted to the role that interfaces played both during processing, and in influencing the ultimate properties of single and polyphase ceramics, and ceramic-metal systems.
