The development of advanced materials has become extremely important in the last decade, being widely used in academic and industrial research. This book examines the potential of advanced materials as well as nanotechnology to improve fiber science from fibril to fabric mode, to create better materials and products for a variety of aspects. The book presents research advances in materials behavior using fractal analysis, mathematical modeling and simulation, and other methods. Examined are electrical, mechanical, optical, and magnetic properties; size; morphology; and chemical behavior of such materials as aerogels, polymer films, nanocomposite materials, natural composites, catalysis, and more with a view to their application in the medical, engineering, and textile fields.With chapters written by eminent scientists, the book offers valuable information for academics, researchers, and engineering professionals. Contributions range from new methods to novel applications of existing methods to help readers gain understanding of the material and/or structural behavior of new and advanced systems.