Anisotropy of Metamaterials

Vladimir Mityushev is 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 modelling, 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. Radosław Kycia is Head of Computer Science Division at the Faculty of Computers Science and Telecommunications at the Tadeusz Kościuszko 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 Associate Professor at the Cracow University of Technology. Her academic and scientific endeavours 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.

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.