Anisotropy of Metamaterials: Beyond Conventional Paradigms provides a comprehensive introduction to the mathematical modelling of metamaterials based on the macroscopic complex-valued permittivity tensor of dispersed random composites.
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
Preface. About the authors. Section 1: Physics of metamaterials.
Chapter 1: Electromagnetics of metamaterials. Section 2: Mathematical model of complex permittivity in composites.
Chapter 2: Generalized alternating method of Schwarz.
Chapter 3: Effective Medium Approximation.
Chapter 4: Circular and elliptic inclusions. Section 3: Macroscopic properties of 2D piezoelectric composites.
Chapter 5: Fibrous magneto-electro-elastic composites. Section 4: Image analysis and machine learning.
Chapter 6: Digital Image Processing and basic granulometry.
Chapter 7: Cancer cells detection using Neural Networks.
Chapter 8: Applications. Appendix A: Elliptic functions. References. Index.
Vladimir Mityushev is a professor at the Cracow University of Technology and a leader of the research group at www.materialica.plus. His expertise lies in the fields of mathematical modeling, computer simulations, porous media, permeability, diffusion, effective properties of composites with deterministic and random structures, representative volume elements, biomathematics, bioinformatics and industrial mathematics.
Professor Tatjana Gric has been engaged in the investigation of waveguide devices (waveguide modulators, filters, etc.), namely in proposing their electrodynamical analysis, since 2009. Another major goal of her studies is plasmonics as the examination of the interaction between electromagnetic field and free electrons in a metal. During the past few years, she has been working on the investigation of nanostructured composites and their fascinating properties. She has authored and co-authored over 70 articles in refereed journals and conference proceedings. She also holds a 1LT patent.
Radosaw Kycia is Head of the Computer Science Division at the Faculty of Computers Science and Telecommunications at the Tadeusz Kociuszko Cracow University of Technology. He specializes in multidisciplinary research involving computer science, physics and mathematics. Currently, he is interested in machine learning and data analysis.
Natalia Rylko is an Associate Professor at the Cracow University of Technology. Her academic and scientific endeavors revolve around interdisciplinary research encompassing physics, material science, computer simulations and machine learning. Her primary field lies in the study of the effective properties of composites and their wide-ranging applications within the field of material sciences.
