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German scholars, against odds now not only forgotten but also hard to imagine, were striving to revivify the life of the mind which the mental and physical barbarity preached and practised by the -isms and -acies of 1933-1946 had all but eradicated. Thinking that among the disciples of these elders, restorers rather than progressives, I might find a student or two who would wish to master new mathematics but grasp it and use it with the wholeness of earlier times, in 1952 I wrote to Mr. HAMEL, one of the few then remaining mathematicians from the classical mould, to ask him to name some young men fit to study for the doc torate in The Graduate Institute for Applied Mathematics at Indiana University, flourishing at that time though soon to be destroyed by the jealous ambition of the local, stereotyped pure. Having just retired from the Technische Universitat in Charlottenburg, he passed my inquiry on to Mr. SZABO, in whose institute there NOLL was then an assistant. Although Mr.
Research and scientific progress are based upqn intuition coordinated with a wide theoretical knowledge, experimental skill, and a realistic sense of the limitations of technology. Only a deep insight into physical phenomena will supply the necessary skills to handle the problems that arise in acoustics. The acoustician today needs to be well acquainted with mathematics, dynamics, hydrodynamics, and physics; he also needs a good knowledge of statistics, signal processing, electrical theory, and of many other specialized subjects. Acquiring this background is a laborious task and would require the study of many different books. It is the goal of this volume to present this background in as thorough and readable a manner as possible so that the reader may turn to specialized publications or chapters of other books for further information without having to start at the preliminaries. In trying to accomplish this goal, mathematics serves only as a tool; the better our understanding of a physical phenomenon, the less mathematics is needed and the shorter and more concise are our computa tions. A word about the choice of subjects for this volume will be helpful to the reader. Even scientists of high standing are frequently not acquainted with the fundamentals needed in the field of acoustics. Chapters I to IX are devoted to these fundamentals. After studying Chapter I, which dis cusses the units and their relationships, the reader should have no difficulty converting from one system of units to any other.
Physical Foundations of Technical Acoustics discusses theoretical foundations of acoustical engineering. It is not so much a technical compendium as a systematic statement of physical laws so conceived that technologists might find in it all the information they need to become acquainted with the physical meaning and mathematical expression of phenomena they encounter in their work. To facilitate the acquirement of notions, which lie beyond a layman's grasp, the plan of narration adopted consists in beginning with the simplest idealized cases and then gradually moving on to the truest possible picture of real phenomena. Thus, the first part of the book, dealing with the acoustic field, begins with lossless fluid media, and passes then through perfectly elastic solid media to the real ones, showing losses and relaxations. In the second part, discussing the acoustical systems, the reader is led up from the simplest vibrating system with one degree of freedom to inhomogeneous spatial systems. Classical problems of theoretical acoustics are linked to the questions which appeared still to be the subjects of research. A special chapter has been written to deal with nonlinear acoustics, in consideration of continually growing applications of the acoustic fields of high intensity.
Foundations of Mathematical Biology, Volume III, is devoted to the treatment of behavior of whole organisms and groups of organisms. The viewpoint taken throughout the book is a holistic, phenomenological one. That is, the integrated behavior of these organisms and groups of organisms is not, in general, referred back to specific structural properties of interacting subunits (as in a reductionist scheme), but is rather treated on its own terms without invoking the properties of lower levels of organization. The book begins with an overview of organization and control in physiological systems, with emphasis on the mathematical techniques involved in more detailed investigations of specific physiological mechanisms. Separate chapters cover the cardiovascular system, with particular reference to blood flow; gross problems of organic form; a relational overview of physics, biology, and sociology; the automata theory in the context of the central nervous system; and populations of interacting organisms. The final chapter discusses the material presented in the entire work, some of its philosophical presuppositions and implications, and the possibility of constructing a unified theory of mathematical biology.
The interaction of sound waves with the medium through which they pass can be used to investigate the thermophysical properties of that medium. With the advent of modern instrumentation, it is now possible to determine the speed and absorption of sound with extremely high precision and, through the dependence of those quantities on variables like temperature, pressure, and frequency to gain a sensitive measure of one or more properties of fluid. This has led to renewed interest in such measurements and in the extraction of thermophysical properties of gases and liquids there from. Physical Acoustics and Metrology of Fluids describes both how to design experiments to achieve the highest possible accuracy and how to relate the quantities measured in those experiments to the thermophysical properties of the medium. A thorough theoretical examination of the alternative experimental methods available is designed to guide the experimentalist toward better and more accurate methods. This theoretical analysis is enhanced and complemented by an in-depth discussion of practical experimental techniques and the problems inherent within them. Bringing together the fields of thermodynamics, kinetic theory, fluid mechanics, and theoretical acoustics, plus a wealth of information about practical instruments, this book represents an essential reference on the design and execution of valuable experiments in fluid metrology and physical acoustics.
Since the earliest days of human existence, the clash of thunder and trembling of the hills has struck fear into the hearts of seasoned warriors and tribal villagers alike. Great gods, demi-gods, and heroes were created to explain the awesome, mysterious, and incomprehensibly powerful forces of Nature in a feeble attempt to make sense of the world around them. To our advanced scientific minds today, these explanations seem childish and ridiculous; however, the power to flatten thousands of square miles of ancient forest, create massive holes in the Earth itself, and cause mountains to tremble to their very roots are more than enough reason to believe. Indeed, perhaps our scientific advancement has caused us to not fully or completely appreciate the awesome scale and power that Nature can wield against us. The study of shock wave formation and dynamics begins with a study of waves themselves. Simple harmonic motion is used to analyze the physical mechanisms of wave generation and propagation, and the principle of superposition is used to mathematically generate constructive and destructive interference. Further development leads to the shock singularity where a single wave of immense magnitude propagates and decays through various media. Correlations with the fields of thermodynamics, meteorology, crater formation, and acoustics are made, as well as a few special applications. Direct correlation is made to events in Arizona, Siberia, and others. The mathematical requirement for this text includes trigonometry, differential equations, and large series summations, which should be accessible to most beginning and advanced university students. This text should serve well as supplementary material in a course covering discrete wave dynamics, applied thermodynamics, or extreme acoustics.
Hermann von Helmholtz (1821-1894) was a polymath of dazzling intellectual range and energy. Renowned for his co-discovery of the second law of thermodynamics and his invention of the ophthalmoscope, Helmholtz also made many other contributions to physiology, physical theory, philosophy of science and mathematics, and aesthetic thought. During the late nineteenth century, Helmholtz was revered as a scientist-sageā€”much like Albert Einstein in this century. David Cahan has assembled an outstanding group of European and North American historians of science and philosophy for this intellectual biography of Helmholtz, the first ever to critically assess both his published and unpublished writings. It represents a significant contribution not only to Helmholtz scholarship but also to the history of nineteenth-century science and philosophy in general.
This book offers alternative foundations for modern physics and natural philosophy, which have been based on Einstein's relativity theory and Shroedinger Equation in the past 100+ years. While both have led to substantial progress of modern physics and sciences, they also led to many contradictions and fallacies. The whole academics ignores their fundamental errors and sees only their coincidental successes. And now the whole modern physics is at dead end, as represented by the total failures of the Big Bang theory and inability to solve the paradoxes of EPR, Missile-Well, as well as mysteries of Double Slit Experiments, Quantum Entanglement, Graviton, Strong Force, Schroedinger Wave Function, etc.. This books, for the first time, offers rigorous disproofs of the renowned Special Relativity and General Relativity theories, and therefore takes a major cornerstone of modern physics away. Fundamental concepts like space, time, entropy are newly defined on a more solid philosophic foundation. A new gravity theory is provided that solves the nature of gravity and graviton where relativity theory failed. Maxwell Equations are reexamined and reformulated into a complex number form, with the real part representing the Electric Field and imaginary part Magnetic Field. This complex form of reformulation is critical in the effort of deriving Schroedinger Equation from basic physics principles, which has been tried by many physicists including Feynman, but completely futile, so that Schroedinger Equation is still treated as an axiom to this date and Schroedinger Wave Function wrongly interpreted as probability. New theories are also provided on redshift and nuclear energies. In summary, by abandoning relativity and correcting quantum mechanics, this book offers well-round solutions to all the difficult problems that modern physics has failed, including a photon model that satisfies all the observations, and explains Double Slit Experiments, Quantum Entanglement, a particle theory that solves the nature of proton, neutron, strong force, and models of large atoms, reformulations of thermodynamics, statistical physics, astrophysics, as well as nuclear physics. As a result, the GUT and TOE problems are basically solved. The final two chapters offers views on mankind and human societies.
In The Foundations of Quantum Mechanics - Historical Analysis and Open Questions, leading Italian researchers involved in different aspects of the foundations and history of quantum mechanics are brought together in an interdisciplinary debate. The book therefore presents an invaluable overview of the state of Italian work in the field at this moment, and of the open problems that still exist in the foundations of the theory. Audience: Physicists, logicians, mathematicians and epistemologists whose research concerns the historical analysis of quantum mechanics.