Number theory, spectral geometry, and fractal geometry are interlinked in this study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary. The Riemann hypothesis is given a natural geometric reformulation in context of vibrating fractal strings, and the book offers explicit formulas extended to apply to the geometric, spectral and dynamic zeta functions associated with a fractal.

This 2015 advanced textbook, now OA, provides students with a unified understanding of all matter at a fundamental level.

Solid particles are followed from their creation through their evolution in the Galaxy to their participation in the formation of solar systems like our own, these being now clearly deduced from observations by the Hubble Space Telescope as well as by IR and visual observations of protostellar disks, like that of the famous Beta Pictoris object. The most recent observational, laboratory and theoretical methods are examined in detail. In our own solar system, studies of meteorites, comets and comet dust reveal many features that follow directly from the interstellar dust from which they formed. The properties of interstellar dust provide possible keys to its origin in comets and asteroids and its ultimate origin in the early solar system. But this is a continuing story: what happens to the solid particles in space after they emerge from stellar sources has important scientific consequences since it ultimately bears on our own origins - the origins of solar systems and, especially, of our own earth and life in the universe.

You can never step in the same river twice, goes the old adage of philosophy. An observation on the transitory nature of fluids in motion, this saying also describes the endless variations researchers face when studying human movement. Understanding these biodynamics-why the wirewalker doesn't fall-requires a grasp of the constant fluctuations and fine tunings which maintain balance in the complex, fluid system of human locomotion. Taking a comprehensive approach to the phenomenon of locomotion, Biodynamics: Why the Wirewalker Doesn't Fall integrates physical laws and principles with concepts of fractals, chaos, and randomness. In so doing, it formulates a description of both the large-scale, smooth aspects of locomotion and the more minute, randomized mechanisms of this physiological process. Ideal for beginners in this subject, Biodynamics provides an elegant explanation without assuming the reader's understanding of complex physical principles or mathematical equations. Chapter topics include: * Dimensions, measurement, and scaling * Mechanics and dynamics * Biometrics * Conservation of momentum * Biomechanics * Bioelectricity * Bioenergetics * Fluid mechanics and dynamics * Data analysis * Biostatistics Packed with problem sets, examples, and original line drawings, Biodynamics is an invaluable text for advanced undergraduates, graduate students, and instructors in medicine, biology, physiology, biophysics, and bioengineering.

Throughout history, nature has served as an inspiration for architecture and designers have tried to incorporate the harmonies and patterns of nature into architectural form. Alberti, Charles Renee Macintosh, Frank Lloyd Wright, and Le Courbusier are just a few of the well- known figures who have taken this approach and written on this theme. With the development of fractal geometry--the study of intricate and interesting self- similar mathematical patterns--in the last part of the twentieth century, the quest to replicate nature’s creative code took a stunning new turn. Using computers, it is now possible to model and create the organic, self-similar forms of nature in a way never previously realized. In Fractal Architecture, architect James Harris presents a definitive, lavishly illustrated guide that explains both the “how” and “why” of incorporating fractal geometry into architectural design.

Probably the first book to describe computational methods for numerically computing steady state and Hopf bifurcations. Requiring only a basic knowledge of calculus, and using detailed examples, problems, and figures, this is an ideal textbook for graduate students.

This book gives a fresh point of view on the curing processes, structure and properties of crosslinked polymers. The general view is that the structure and properties of crosslinked polymers are defined by their density, this book demonstrates that the parameters are defined by the supermolecular (a more precisely, supersegmental structure) of the crosslinked polymers.The quantitative relationships of the structures/properties are obtained for these polymers. Using an epoxy polymer as a nanofiller for a nanocomposite is discussed and a new class of polymer is proposed. The introduction of the nanofiller gives variation in the mechanical properties, degree of crystallinity, gas permeability and so on. The use of these crosslinked polymers as natural nanocomposites is proposed. Practical methods of crosslinked polymer's supersegmental structure regulation are considered, and all the changes that this gives their properties are detailed.This book will be of significance to all material scientists and students of material science.