Understand wave properties, v = f lambda, echoes, and refraction through short visual physics lessons.

The quantum and relativity theories of physics are considered to underpin all of science in an absolute sense. This monograph argues against this proposition primarily on the basis of the two theories' incompatibility and of some untenable philosophical implications of the quantum model. Elementary matter is assumed in both theories to occur as zero-dimensional point particles. In relativity theory this requires the space-like region of the underlying Minkowski space-time to be rejected as unphysical, despite its precise mathematical characterization. In quantum theory it leads to an incomprehensible interpretation of the wave nature of matter in terms of a probability function and the equally obscure concept of wave-particle duality. The most worrisome aspect about quantum mechanics as a theory of chemistry is its total inability, despite unsubstantiated claims to the contrary, to account for the fundamental concepts of electron spin, molecular structure, and the periodic table of the elements. A remedy of all these defects by reformulation of both theories as nonlinear wave models in four-dimensional space-time is described.

Everything the Power of the World does is done in a circle. The sky is round and I have heard that the earth is round like a ball and so are all the stars. The wind, in its greatest power, whirls. Birds make their nests in circles, for theirs is the same religion as ours. The sun comes forth and goes down again in a circle. The moon does the same and both are round. Even the seasons form a great circle in their changing and always come back again to where they were. The life of a man is a circle from childhood to childhood. And so it is everything where power moves. Black Elk (1863–1950) Nonlinearity is a captivating manifestation of the observable Universe, whose importance has increased over the decades, and has found more and more ?elds of application ranging from elementary particles, nuclear physics, biology, wave dynamics at any scale, ?uids, plasmas to astrophysics. The central character of this 172-year-old story is the soliton. Namely, a localized pulse traveling without spreading and having particle-like properties plus an in?nite number of conservation laws associated to its dynamics. In general, solitons arise as exact solutions of approximative models. There are di?- ent explanation, at di?erent levels, for the existence of solitons. From the experimentalist point of view, solitons can be created if the propagation c- ?gurationislongenough,narrowenough(likelongandshallowchannels,?ber optics, electric lines, etc.

Recent advances in wave propagation in random media are certainly consequences of new approaches to fundamental issues, as well as of a strong interest in potential applications. A collective effort has been made to present in this book the state of the art in fundamental concepts, as well as in biomedical imaging techniques.

This book contains a selection of research papers presented at the 11th and 12th International Ship Stability Workshops (Wageningen, 2010 and Washington DC, 2011) and the 11th International Conference on Stability of Ships and Ocean Vehicles (Athens, 2012).

The purpose of the book is a mathematical and experimental study of extreme, multivalued waves based on scalar field equations. It is known that Einstein tried to build a unified (interdisciplinary) field theory that would unite all interactions in Nature into a single system. The book uses this idea, supplemented by the idea that all fundamental interactions have a wave, resonant, nonlinear nature. The theoretical foundation of the book also consists of the results of Leonard Euler.

The purpose of the book is a mathematical and experimental study of extreme, multivalued waves based on scalar field equations. It is known that Einstein tried to build a unified (interdisciplinary) field theory that would unite all interactions in Nature into a single system. The book uses this idea, supplemented by the idea that all fundamental interactions have a wave, resonant, nonlinear nature. The theoretical foundation of the book also consists of the results of Leonard Euler.

A variety of nonlinear effects occur in a plasma. First, there are the wave­ steepening effects which can occur in any fluid in which the propagation speed depends upon the wave-amplitude. In a dispersive medium this can lead to classes of nonlinear waves which may have stationary solutions like solitons and shocks. Because the plasma also acts like an inherently nonlinear dielectric resonant interactions among waves lead to exchange of energy among them. Further, an electromagnetic wave interacting with a plasma may parametrically excite other waves in the plasma. A large-amplitude Langmuir wave undergoes a modulational instability which arises through local depressions in plasma density and the corresponding increases in the energy density of the wave electric field. Whereas a field collapse occurs in two and three dimensions, in a one-dimensional case, spatially localized stationary field structures called Langmuir solitons can result. Many other plasma waves like upper-hybrid waves, lower-hybrid waves etc.

Knowledge of and skill in physics are essential foundations for studies in science and engineering. This book offers students an introduction to the basic concepts and principles of physics. It covers various topics specifically related to waves, sound, electricity, magnetism, and optics. Each chapter begins with a summary of concepts, principles, definitions, and formulae to be discussed, as well as ending with problems and solutions that illustrate the specific topic. Steps are detailed to help build reasoning and understanding. There are 250 worked problems and 100 exercises in the book, as well as 280 figures to help the reader visualize the processes being addressed. Computer calculations and solutions are carried out using wxMaxima to give insight and help build computational skills. The book is aimed at first-year undergraduate students studying introductory physics, and would also be useful for physics teachers in their instruction, particularly the exercises at the end of each chapter.

How do waves break and what makes good surf?
What are dangerous rip currents and how do you spot one?
What would you do if you got caught in one?

In recent years there has been growing interest in the study of the nonlinear spatio-temporal dynamics of problems appearing in various ?elds of science and engineering. In a wide class of such systems an important place is - cupied by active lattice dynamical systems. Active lattice systems are, e. g. , networks of identical or almost identical interacting units ordered in space. The activity of lattices is provided by the activity of units in them that possess energy or matter sources. In real (1D, 2D or 3D) space, processes develop by means of various types of connections, the simplest being di?usion. The uniqueness of lattice systems is that they represent spatially extended systems while having a ?nite-dimensional phase space. Therefore, active lattice s- tems are of interest for the study of multidimensional dynamical systems and the theory of nonlinear waves and dissipative structures of extended systems as well. The theory of nonlinear waves and dissipative structures of spatially distributed systems demands using theoretical methods and approaches of the qualitative theory of dynamical systems, bifurcation theory, and numerical methods or computer experiments. In other words, the investigation of spat- temporal dynamics in active lattice systems demands a multitool, synergetic approach, which we shall use in this book.

The author dedicates this book to readers who are concerned with finding out the status of concepts, statements and hypotheses, and with clarifying and rearranging them in a logical order.