Introduction To Multiscale Mathematical Modeling

This book introduces the reader to multiscale mathematical modeling that starts by describing a physical process at the microscopic level, and is followed by the macroscopic description of that process. There are two preliminary chapters introducing the main equations of mathematical physics and serves as revision of all of the necessary mathematical notions needed to navigate the domain of multiscale research. The author gives a rigorous presentation of the tools of mathematical modeling, as well as an evaluation of the errors of the method. This allows readers to analyze the limitations and accuracy of the method. The book is accessible to a wide range of readers, from specialists in engineering to applied mathematicians working in the applications of materials science, biophysics and medicine. Contents: Preface About the Author Derivation of the Main Equations of Mathematical Physics Analysis of the Main Equations of Mathematical Physics Homogenization: From Micro-scale to Macro-scale: Application to Mechanics of Composite Materials Dimension Reduction and Multiscale Modeling for Thin Structures Appendix A: Diffusion Equation with Dirac-like Potential: Model of a Periodic Set of Small Cells in a Nutrient Appendix B: Proof of Riesz–Frechet Representation Theorem Index Readership: Master and PhD students and researchers in mathematics, engineering and biomedical applications. Key Features: Introduces the technique of multiscale modeling Contains two introductory chapters allowing readers to reach the necessary level without special mathematical education

This book introduces the reader to multiscale mathematical modeling that starts by describing a physical process at the microscopic level, and is followed by the macroscopic description of that process. There are two preliminary chapters introducing the main equations of mathematical physics and serves as revision of all of the necessary mathematical notions needed to navigate the domain of multiscale research.The author gives a rigorous presentation of the tools of mathematical modeling, as well as an evaluation of the errors of the method. This allows readers to analyze the limitations and accuracy of the method.The book is accessible to a wide range of readers, from specialists in engineering to applied mathematicians working in the applications of materials science, biophysics and medicine.