Vladimir Mityushev

Applied Analysis of Composite Media: Analytical and Computational Approaches presents formulas and techniques that can used to study 2D and 3D problems in composites and random porous media. The main strength of this book is its broad range of applications that illustrate how these techniques can be applied to investigate elasticity, viscous flow and bacterial motion in composite materials. In addition to paying attention to constructive computations, the authors have also included information on codes via a designated webpage. This book will be extremely useful for postgraduate students, academic researchers, mathematicians and industry professionals who are working in structured media.

Anisotropy of Metamaterials: Beyond Conventional Paradigms provides a comprehensive introduction to the mathematical modeling of metamaterials based on the macroscopic complex-valued permittivity tensor of dispersed random composites. Key topics include physical and mathematical theory, computer simulations, constructive homogenization, classification of dispersed random composites and their applications in cancer recognition. Image processing and machine learning algorithms are used. The book also discusses the precision of various effective medium approximations, including Bruggeman and Maxwell-Garnett formulas. New analytical, approximate and exact formulas and bounds for the macroscopic permittivity and piezoelectric constants of composites are derived. This book is a valuable tool for academics and professionals in photonics, presenting sustainable materials for sensing, health diagnostics and cancer detection methodologies. Key features: Offers key insights into the current trends and techniques in the study of the macroscopic properties of metamaterials, aiming at stimulating new avenues of research Presents examples of image analysis, the primary tool for non-destructive metamaterials analysis Discusses the applications of Machine Learning to image processing, illustrated using specific code in Python programming language

Anisotropy of Metamaterials: Beyond Conventional Paradigms provides a comprehensive introduction to the mathematical modeling of metamaterials based on the macroscopic complex-valued permittivity tensor of dispersed random composites. Key topics include physical and mathematical theory, computer simulations, constructive homogenization, classification of dispersed random composites and their applications in cancer recognition. Image processing and machine learning algorithms are used. The book also discusses the precision of various effective medium approximations, including Bruggeman and Maxwell-Garnett formulas. New analytical, approximate and exact formulas and bounds for the macroscopic permittivity and piezoelectric constants of composites are derived. This book is a valuable tool for academics and professionals in photonics, presenting sustainable materials for sensing, health diagnostics and cancer detection methodologies. Key features:Offers key insights into the current trends and techniques in the study of the macroscopic properties of metamaterials, aiming at stimulating new avenues of researchPresents examples of image analysis, the primary tool for non-destructive metamaterials analysisDiscusses the applications of Machine Learning to image processing, illustrated using specific code in Python programming language

Introduction to Mathematical Modeling and Computer Simulations, Second Edition continues to serve as an engaging and accessible textbook for undergraduates studying mathematical modeling and computer simulations. The book is heavily focussed on applications, and so may have a particular appeal to applied mathematicians, engineers, and others working in applied quantitative disciplines. The book may also be useful as a reference text for reference text for early-career stage practitioners. New to this Edition:A new chapter on Machine Learning and Data Analysis in order to account for recent developments in the field. Chapter 9, ‘Asymptotic Methods in Composites’, has been entirely re-written to make it more consistent with industry and scientific standards. Includes an elementary introduction to programming in Python language. The Jupyter notebooks with examples for Chapter 10 and Appendix A are available for a download from www. Routledge.com/9781032661513.

Introduction to Mathematical Modeling and Computer Simulations is written as a textbook for readers who want to understand the main principles of Modeling and Simulations in settings that are important for the applications, without using the profound mathematical tools required by most advanced texts. It can be particularly useful for applied mathematicians and engineers who are just beginning their careers. The goal of this book is to outline Mathematical Modeling using simple mathematical descriptions, making it accessible for first- and second-year students. Chapter 1 and the Preface of this book is freely available as a downloadable Open Access PDF under a Creative Commons Attribution-Non Commercial-No Derivatives 4.0 license available at http://www.taylorfrancis.com/books/e/9781315277240

Introduction to Mathematical Modeling and Computer Simulations is written as a textbook for readers who want to understand the main principles of Modeling and Simulations in settings that are important for the applications, without using the profound mathematical tools required by most advanced texts. It can be particularly useful for applied mathematicians and engineers who are just beginning their careers. The goal of this book is to outline Mathematical Modeling using simple mathematical descriptions, making it accessible for first- and second-year students. Chapter 1 and the Preface of this book is freely available as a downloadable Open Access PDF under a Creative Commons Attribution-Non Commercial-No Derivatives 4.0 license available at http://www.taylorfrancis.com/books/e/9781315277240

Computational Analysis of Structured Media presents a systematical approach to analytical formulae for the effective properties of deterministic and random composites. Schwarz’s method and functional equations yield for use in symbolic-numeric computations relevant to the effective properties. The work is primarily concerned with constructive topics of boundary value problems, complex analysis, and their applications to composites. Symbolic-numerical computations are widely used to deduce new formulae interesting for applied mathematicians and engineers. The main line of presentation is the investigation of two-phase 2D composites with non-overlapping inclusions randomly embedded in matrices.