Curved x-ray multilayer mirrors focus synchrotron beams down to tens of nano metres. A wave-optical theory describing propagation of two waves in an elliptically curved focusing multilayer mirror is developed in this thesis. Using numerical integration, the layer shapes can be optimised for reflectivity and aberrations. Within this framework, performance of both existing and currently upgraded synchrotron beamlines is simulated. Using a more theoretical model case, limits of the theory are studied. A significant part of this work is dedicated to partial spatial coherence, modelled using the method of stochastic superpositions. Coherence propagation and filtering by x-ray waveguides is shown analytically and numerically. This comprehensive model is put forward that shall help in development and testing of new algorithms for a variety of imaging techniques using coherent x-ray beams. Advanced simulations accounting for real structure effects are compared to experimental data obtained at the GINIX instrument at the coherence beamline P10 at PETRA III, DESY. This thesis presents results of a collaboration between the Georg-August-Universität Göttingen and the European Synchrotron Radiation Facility (ESRF) Grenoble.

This book is intended as an introduction to classical water wave theory for the college senior or first year graduate student. The material is self-contained; almost all mathematical and engineering concepts are presented or derived in the text, thus making the book accessible to practicing engineers as well.The book commences with a review of fluid mechanics and basic vector concepts. The formulation and solution of the governing boundary value problem for small amplitude waves are developed and the kinematic and pressure fields for short and long waves are explored. The transformation of waves due to variations in depth and their interactions with structures are derived. Wavemaker theories and the statistics of ocean waves are reviewed. The application of the water particle motions and pressure fields are applied to the calculation of wave forces on small and large objects. Extension of the linear theory results to several nonlinear wave properties is presented. Each chapter concludes with a set of homework problems exercising and sometimes extending the material presented in the chapter. An appendix provides a description of nine experiments which can be performed, with little additional equipment, in most wave tank facilities.

The study of internal gravity waves provides many challenges: they move along interfaces as well as in fully three-dimensional space, at relatively fast temporal and small spatial scales, making them difficult to observe and resolve in weather and climate models. Solving the equations describing their evolution poses various mathematical challenges associated with singular boundary value problems and large amplitude dynamics. This book provides the first comprehensive treatment of the theory for small and large amplitude internal gravity waves. Over 120 schematics, numerical simulations and laboratory images illustrate the theory and mathematical techniques, and 130 exercises enable the reader to apply their understanding of the theory. This is an invaluable single resource for academic researchers and graduate students studying the motion of waves within the atmosphere and ocean, and also mathematicians, physicists and engineers interested in the properties of propagating, growing and breaking waves.

A timely and authoritative guide to the state of the art of wave scattering Scattering of Electromagnetic Waves offers in three volumes a complete and up-to-date treatment of wave scattering by random discrete scatterers and rough surfaces. Written by leading scientists who have made important contributions to wave scattering over three decades, this new work explains the principles, methods, and applications of this rapidly expanding, interdisciplinary field. It covers both introductory and advanced material and provides students and researchers in remote sensing as well as imaging, optics, and electromagnetic theory with a one-stop reference to a wealth of current research results. Plus, Scattering of Electromagnetic Waves contains detailed discussions of both analytical and numerical methods, including cutting-edge techniques for the recovery of earth/land parametric information. The three volumes are entitled respectively Theories and Applications, Numerical Simulation, and Advanced Topics. In the first volume, Theories and Applications, Leung Tsang (University of Washington) Jin Au Kong (MIT), and Kung-Hau Ding (Air Force Research Lab) cover: * Basic theory of electromagnetic scattering * Fundamentals of random scattering * Characteristics of discrete scatterers and rough surfaces * Scattering and emission by layered media * Single scattering and applications * Radiative transfer theory and solution techniques * One-dimensional random rough surface scattering

A new set of time-dependent Boussinesq equations is derived to simulate nonlinear long wave propagation in coastal regions. Following the approaches by Nwogu and later by Chen and Liu, the velocity (or velocity potential) at a certain water depth corresponding to the optimum linear dispersion property is used as a dependent variable. Therefore, the resulting equations are valid in intermediate water depth as well as for highly nonlinear waves. Coefficients for second order bound waves and the third order Schrodinger equation are derived and compared with exact solutions. A numerical model using a combination of second and fourth order schemes to discretize equation terms is developed for obtaining solutions to the equations. A fourth order predictor-corrector scheme is employed for time stepping and the first order derivative terms are finite differenced to fourth order accuracy, making the truncation errors smaller than the dispersive terms in the equations. Linear stability analysis is performed to determine the corresponding numerical stability range for the model. To avoid the problem of wave reflection from the conventional incident boundary condition, internal wave generation by source function is employed for the present model. Numerical filtering is applied at specified time steps in the model to eliminate short waves (about 2 to 5 times of the grid size) which are generated by the nonlinear interaction of long waves. To simulate the wave breaking process, additional terms for artificial eddy viscosity are included in the model equations to dissipate wave energy. The dissipation terms are activated when the horizontal gradient of the horizontal velocity exceeds the specified breaking criteria. Some of the existing models for simulating the process of wave runup are reviewed and we attempt to incorporate the present model to simulate the process by maintaining a thin layer of water over the physically dry grids.

This book considers the formation of the signal reflected from the sea surface when sensing in the radio and optical range. Currently, remote sensing from space is the main source of information about the processes taking place in the atmosphere and ocean. The correct interpretation of remote sensing data requires detailed information about the rough surface that forms the reflected signal. The first three chapters describe the statistical and spatial-temporal characteristics of the sea surface, focusing on the effects associated with the nonlinearity of sea surface waves. The analysis makes extensive use of data obtained by the authors on a stationary oceanographic platform located on the Black sea. In the next seven chapters, the authors analyze how the nonlinearity of waves affects the formation of a signal reflected from the sea surface.This book is geared for advanced level research in the general subject area of remote sensing and modeling as they apply to the coastal marine environment. It is of value to scientists and engineers involved in the development of methods and instruments of remote sensing, analysis and interpretation of data. It is useful for students who have decided to devote themselves to the study of the oceans.

An important contribution to the literature that introduces powerful new methods for modeling and simulating radio wave propagation A thorough understanding of electromagnetic wave propagation is fundamental to the development of sophisticated communication and detection technologies. The powerful numerical methods described in this book represent a major step forward in our ability to accurately model electromagnetic wave propagation in order to establish and maintain reliable communication links, to detect targets in radar systems, and to maintain robust mobile phone and broadcasting networks. The first new book on guided wave propagation modeling and simulation to appear in nearly two decades, Radio Wave Propagation and Parabolic Equation Modeling addresses the fundamentals of electromagnetic wave propagation generally, with a specific focus on radio wave propagation through various media. The authors explore an array of new applications, and detail various virtual electromagnetic tools for solving several frequent electromagnetic propagation problems. All of the methods described are presented within the context of real-world scenarios typifying the differing effects of various environments on radio-wave propagation. This valuable text: Addresses groundwave and surface wave propagation Explains radar applications in terms of parabolic equation modeling and simulation approaches Introduces several simple and sophisticated MATLAB scripts Teaches applications that work with a wide range of electromagnetic, acoustic and optical wave propagation modeling Presents the material in a quick-reference format ideal for busy researchers and engineers Radio Wave Propagation and Parabolic Equation Modeling is a critical resource forelectrical, electronics, communication, and computer engineers working on industrial and military applications that rely on the directed propagation of radio waves. It is also a useful reference for advanced engineering students and academic researchers.