الصفحة 1
الصفحة 1
Multiscale Modeling in Epitaxial Growth
Epitaxy is a very active area of theoretical research since several years. It is experimentally well-explored and technologically relevant for thin film growth. Recently powerful numerical techniques in combination with a deep understanding of the physical and chemical phenomena during the growth process offer the possibility to link atomistic effects at the surface to the macroscopic morphology of the film. The goal of this book is to summarize recent developments in this field, with emphasis on multiscale approaches and numerical methods. It covers atomistic, step-flow, and continuum models and provides a compact overview of these approaches. It also serves as an introduction into this highly active interdisciplinary field of research for applied mathematicians, theoretical physicists and computational materials scientists.
Multiscale Modeling and Simulation of Composite Materials and Structures
Multiscale Modeling and Simulation of Composite Materials and Structures presents the state of the art in multiscale modeling and simulation techniques for composite materials and structures. The text focuses on the structural and functional properties of engineering composites and the sustainable high performance of components and structures. With contributions from leading experts in the field, Multiscale Modeling and Simulation of Composite Materials and Structures proves to be an invaluable resource for researchers, graduate students and engineers in the field of Composite Materials.
Multiscale Modeling : A Bayesian Perspective
The book is aimed at statisticians, applied mathematicians, and engineers working on problems dealing with multiscale processes in time and/or space, such as in engineering, finance, and environmetrics. The book will also be of interest to those working on multiscale computation research. The main prerequisites are knowledge of Bayesian statistics and basic Markov chain Monte Carlo methods. A number of real-world examples are thoroughly analyzed in order to demonstrate the methods and to assist the readers in applying these methods to their own work. To further assist readers, the authors are making source code (for R) available for many of the basic methods discussed herein.
Multifield Problems in Solid and Fluid Mechanics
This book summarizes the main scientific results of the Collaborative Research Center on Multifield Problems in Continuum Mechanics. The book is divided into three main sections: A: Volume-Coupled Problems, devoted to fields which are coupled inside the processing domain or volume, B: Boundary-Coupled Problems, here physical fields and processes are coupled via domain boundaries, C: Fundamental Methods, search into the mathematical concepts and backgrounds of multifield and multiscale modeling.
Mechanics and Physics of Fracture : Multiscale Modeling of the Failure Behavior of Solids
Provides a comprehensive understanding of the macroscopic failure behavior of solids from the description of the microscopic failure processes and their coupling with the microstructure. Several fundamental questions were addressed: the relation between the microstructural features of materials and their fracture properties and crack trajectories; the role of damage mechanisms and non-linear deformations near the crack tip on the failure behavior of solids; and finally the role of dynamic inertial effects during fast fracture was more briefly evoked.
Computational Multiscale Modeling of Fluids and Solids : Theory and Applications
The book includes the micro-scale, the meso-scale and the macro-scale. The chapters follow this classification. The book will explain in detail many tricks of the trade of some of the most important methods and techniques that are used to simulate materials on the perspective levels of spatial and temporal resolution. Case studies are occasionally included to further illustrate some methods or theoretical considerations. Example applications for all techniques are provided, some of which are from the author’s own contributions to some of the research areas. Methods are explained, if possible, on the basis of the original publications but also references to standard text books established in the various fields are mentioned.
Analysis, Modeling and Simulation of Multiscale Problems
This book reports recent mathematical developments in the Programme "Analysis, Modeling and Simulation of Multiscale Problems", which started as a German research initiative in 2006. Multiscale problems occur in many fields of science, such as microstructures in materials, sharp-interface models, many-particle systems and motions on different spatial and temporal scales in quantum mechanics or in molecular dynamics. The book presents current mathematical foundations of modeling, and proposes efficient numerical treatment.
