Gradiometry is a multidisciplinary area that combines theoretical and applied physics, ultra-low noise electronics, precision engineering, and advanced signal processing. All physical fields have spatial gradients that fall with distance from their sources more rapidly than the field strength itself. This makes the gradient measurements more difficult. However, there has been a considerable investment, both in terms of time and money, into the development of various types of gradiometers driven by the extremely valuable type of information that is contained in gradients. Applications include the search for oil, gas, and mineral resources, GPS-free navigation, defence, space missions, medical research, and some other applications. The author describes gravity gradiometers, magnetic gradiometers, and electromagnetic (EM) gradiometers. The first two types do not require any active sources of the primary physical fields whose gradients are measured, such as gravity field and ambient magnetic field. EM gradiometers do require a primary EM field, pulsed, or sinusoidal, which propagates through media and creates a secondary EM field. The latter one contains information about the non uniformness of electromagnetically active media such as conductivity and magnetic permeability contrasts. These anomalies are the boundaries of mineral deposits, oil and gas traps, underground water reserves, buried artifacts, unexploded ordnance (UXO), nuclear submarines, and even cancerous human tissue. This book provides readers with a comprehensive introduction, history, potential applications, and current developments in relation to some of the most advanced technologies in the 21st Century. Most of the developments are strictly controlled by Defence Export Control rules and regulations, introduced in all developed countries that typically require permission to transfer relevant information from one country to another. The book is based on the materials that have been available in public domain such as scientific journals, conferences, extended abstracts, and online presentations. In addition, medical applications of EM gradiometers are exempt from any control, and some new results relevant to breast cancer early detection research are published in this book for the first time.

This book is about computational methods based on operator splitting. It consists of twenty-three chapters written by recognized splitting method contributors and practitioners, and covers a vast spectrum of topics and application areas, including computational mechanics, computational physics, image processing, wireless communication, nonlinear optics, and finance. Therefore, the book presents very versatile aspects of splitting methods and their applications, motivating the cross-fertilization of ideas.

Recent important discoveries and developments in nanotechnology have had a remarkable and ever-increasing impact on many industries, especially materials science, pharmaceuticals, and biotechnology. Nanocarriers have been investigated for a wide variety of different medical applications. Some examples of these nanocarriers include polymersomes, liposomes, micelles and carbon-based nanomaterials. Within this book, the authors describe different features of carbon nanotubes (CNTs), survey the properties of both the multi-walled and single-walled varieties, and cover their applications in drug and gene delivery. In addition, the book explains the structure and properties of CNTs prepared by different method, and discussed their isolation and purification. The future of CNTs in the field of biomedical science will depend on minimizing their adverse effects by careful study of their structure and properties.

Michael Faraday (1791-1867) was one of the most important men of science in nineteenth century Britain. His discoveries of electro-magnetic rotations (1821) and electro-magnetic induction (1831) laid the foundations of the modern electrical industry. His discovery of the magneto-optical effect and diamagnetism (1845) led him to formulate the field theory of electro-magnetism, which forms one of the cornerstones of modern physics. These and a whole host of other fundamental discoveries in physics and chemistry, together with his lecturing at the Royal Institution, his work for the state (including Trinity House), his religious beliefs and his lack of mathematical ability, make Faraday one of the most fascinating scientific figures ever. All these aspects of his life and work and others, such as his health, are reflected in his letters which, in this final volume, cover Faraday's life to his death in August 1867. Also published here are letters that could not be dated and letters that should have been included in volumes one to five but which had not been located when those volumes were published. In total just over 80% of the letters in this volume are previously unpublished. The dominant topic of the 1860s (covered in nearly 40% of the letters) is Faraday's involvement with the lighthouse service relating in particular to his advice to Trinity House and the Board of Trade on matters such as electric light and the controversial issue of fog signals. Also detailed is the complex process by which his various posts were transferred to John Tyndall. Similar issues existed with Faraday's gradual withdrawal from his duties at the Royal Institution, including the misguided attempt to make him President. And, of course, running through many of the letters are comments on his declining health and impending death. Major correspondents include the Astronomer Royal G.B. Airy, the Secretary of Trinity House P.H. Berthon, the Birmingham glassmaker J.T. Chance, the Assistant Secretary of the Board of Trade T.H. Farrer, the German mathematician Julius Plucker, the Cambridge trained mathematical natural philosophers James Clerk Maxwell and William Thomson, Faraday's colleagues at the Royal Institution Henry Bence Jones, John Tyndall and Benjamin Vincent, the Swiss chemist Christian Schoenbein and the astronomer James South.

Membrane techniques provide a broad science and technology base. Although there are several books in the traditional membrane field, there is a great need for a highly comprehensive book. This refereed book covers materials from highly respected researchers. This title is highly multidisciplinary in nature and should be extremely valuable to scientists and engineers involved in a variety of activities. Students and faculty members around the world will find this title to be an excellent reference book.
- Invited contributions from leading researchers in the field.
- Coverage of topic is of value to scientists/engineers working in a variety of related fields [separations/reactions, advanced biofunctional materials, contactor designs].
- Aims to fill market gap for a highly comprehensive book containing advances in both synthetic and biofunctional/bimimetic membranes.

This book provides a comprehensive introduction to numerical modeling of size effects in metal plasticity. The main classes of strain gradient plasticity formulations are described and efficiently implemented in the context of the finite element method. A robust numerical framework is presented and employed to investigate the role of strain gradients on structural integrity assessment. The results obtained reveal the need of incorporating the influence on geometrically necessary dislocations in the modeling of various damage mechanisms. Large gradients of plastic strain increase dislocation density, promoting strain hardening and elevating crack tip stresses. This stress elevation is quantified under both infinitesimal and finite deformation theories, rationalizing the experimental observation of cleavage fracture in the presence of significant plastic flow. Gradient-enhanced modeling of crack growth resistance, hydrogen diffusion and environmentally assisted cracking highlighted the relevance of an appropriate characterization of the mechanical response at the small scales involved in crack tip deformation. Particularly promising predictions are attained in the field of hydrogen embrittlement. The research has been conducted at the Universities of Cambridge, Oviedo, Luxembourg, and the Technical University of Denmark, in a collaborative effort to understand, model and optimize the mechanical response of engineering materials.

The present volume contains the Proceedings of the International Conference on Spectral Theory and Mathematical Physics held in Santiago de Chile in November 2014. Main topics are: Ergodic Quantum Hamiltonians, Magnetic Schroedinger Operators, Quantum Field Theory, Quantum Integrable Systems, Scattering Theory, Semiclassical and Microlocal Analysis, Spectral Shift Function and Quantum Resonances. The book presents survey articles as well as original research papers on these topics. It will be of interest to researchers and graduate students in Mathematics and Mathematical Physics.

This book provides the mathematical foundations for Feynman's operator calculus and for the Feynman path integral formulation of quantum mechanics as a natural extension of analysis and functional analysis to the infinite-dimensional setting. In one application, the results are used to prove the last two remaining conjectures of Freeman Dyson for quantum electrodynamics. In another application, the results are used to unify methods and weaken domain requirements for non-autonomous evolution equations. Other applications include a general theory of Lebesgue measure on Banach spaces with a Schauder basis and a new approach to the structure theory of operators on uniformly convex Banach spaces. This book is intended for advanced graduate students and researchers.

Handbook on the Physics and Chemistry of Rare Earths: Including Actinides is a continuous series of books covering all aspects of rare earth science, including chemistry, life sciences, materials science, and physics. The book's main emphasis is on rare earth elements [Sc, Y, and the lanthanides (La through Lu], but whenever relevant, information is also included on the closely related actinide elements. Individual chapters are comprehensive, broad, up-to-date, critical reviews written by highly experienced, invited experts. The series, which was started in 1978 by Professor Karl A. Gschneidner Jr., combines, and integrates, both the fundamentals and applications of these elements with two published volumes each year.

This volume presents the proceedings of the 11th Conference on Problems and Methods in Mathematical Physics (11th TMP), held in Chemnitz, March 25-28, 1999. The conference was dedicated to the memory of Siegfried PrAssdorf, who made important contributions to the theory and numerical analysis of operator equations and their applications in mathematical physics and mechanics. The main part of the book comprises original research papers. The topics are ranging from integral and pseudodifferential equations, boundary value problems, operator theory, boundary element and wavelet methods, approximation theory and inverse problems to various concrete problems and applications in physics and engineering, and reflect PrAssdorf's broad spectrum of research activities. The volume also contains articles describing the life and mathematical achievements of Siegfried PrAssdorf and includes a list of his publications. The book is addressed to a wide audience in the mathematical and engineering sciences.

This book gathers outstanding papers on numerical modeling in Mechanical Engineering (Volume 2) as part of the proceedings of the 1st International Conference on Numerical Modeling in Engineering (NME 2018), which was held in Ghent, Belgium. The overall objective of the conference was to bring together international scientists and engineers in academia and industry from fields related to advanced numerical techniques, such as the finite element method (FEM), boundary element method (BEM), isogeometric analysis (IGA), etc., and their applications to a wide range of engineering disciplines. This book addresses various industrial engineering applications of numerical simulations to Mechanical and Materials Engineering, including: Aerospace applications, Acoustic analysis, Biomechanical applications, Contact problems and wear, Heat transfer analysis, Vibration and dynamics, Transient analysis, Nonlinear analysis, Composite materials, Polymers, Metal alloys, Fracture mechanics, Fatigue of materials, Creep behavior, Phase transformation, and Crystal plasticity.

The continued greening of the energy sector, with inroads being made through numerous sources of materials that can produce energy, is the main focus of this, Green Chemical Processing, Volume 8. It includes contributions from area experts in widely different fields, all involved in energy production, and makes connections to the 12 Principles of Green Chemistry.

This book introduces the fundamentals of computer vision (CV), with a focus on extracting useful information from digital images and videos. Including a wealth of methods used in detecting and classifying image objects and their shapes, it is the first book to apply a trio of tools (computational geometry, topology and algorithms) in solving CV problems, shape tracking in image object recognition and detecting the repetition of shapes in single images and video frames. Computational geometry provides a visualization of topological structures such as neighborhoods of points embedded in images, while image topology supplies us with structures useful in the analysis and classification of image regions. Algorithms provide a practical, step-by-step means of viewing image structures. The implementations of CV methods in Matlab and Mathematica, classification of chapter problems with the symbols (easily solved) and (challenging) and its extensive glossary of key words, examples and connections with the fabric of CV make the book an invaluable resource for advanced undergraduate and first year graduate students in Engineering, Computer Science or Applied Mathematics. It offers insights into the design of CV experiments, inclusion of image processing methods in CV projects, as well as the reconstruction and interpretation of recorded natural scenes.

In this monograph we study the problem of construction of asymptotic solutions of equations for functions whose number of arguments tends to infinity as the small parameter tends to zero. Such equations arise in statistical physics and in quantum theory of a large number of fi elds. We consider the problem of renormalization of quantum field theory in the Hamiltonian formalism, which encounters additional difficulties related to the Stuckelberg divergences and the Haag theorem. Asymptotic methods for solving pseudodifferential equations with small parameter multiplying the derivatives, as well as the asymptotic methods developed in the present monograph for solving problems in statistical physics and quantum field theory, can be considered from a unified viewpoint if one introduces the notion of abstract canonical operator. The book can be of interest for researchers - specialists in asymptotic methods, statistical physics, and quantum fi eld theory as well as for graduate and undergraduate students of these specialities.

This volume collects contributions written by different experts in honor of Prof. Jaime Munoz Masque. It covers a wide variety of research topics, from differential geometry to algebra, but particularly focuses on the geometric formulation of variational calculus; geometric mechanics and field theories; symmetries and conservation laws of differential equations, and pseudo-Riemannian geometry of homogeneous spaces. It also discusses algebraic applications to cryptography and number theory. It offers state-of-the-art contributions in the context of current research trends. The final result is a challenging panoramic view of connecting problems that initially appear distant.

The design of circuits capable of generating short electrical pulses at very high power levels has been the subject of considerable research over the last 50 years. Much of this work is dispersed throughout conference proceedings and journals. There are very few books dedicated to the subject. Transient Electronics redresses the balance with a comprehensive survey of the most significant work in the field. It will serve as a self-contained guide to the application of pulsed circuit techniques in pulsed power technology.

Features include:

• A comprehensive guide to the use of the Laplace transform method for the analysis of the transient response of electronic circuits and transmission lines.

• A survey of pulse forming line and pulse forming network techniques including detailed analysis of their performance.

• A review of the many different types of pulsed transformer including transmission line transformers.

• Coverage of a wide range of specialised pulse generating circuits used in pulsed power generation.

• A chapter on the relatively new field of non-linear pulsed circuit technology.

Computational Approaches in Physics reviews computational schemes which are used in the simulations of physical systems. These range from very accurate ab initio techniques up to coarse-grained and mesoscopic schemes. The choice of the method is based on the desired accuracy and computational efficiency. A bottom-up approach is used to present the various simulation methods used in Physics, starting from the lower level and the most accurate methods, up to particle-based ones. The book outlines the basic theory underlying each technique and its complexity, addresses the computational implications and issues in the implementation, as well as present representative examples. A link to the most common computational codes, commercial or open source is listed in each chapter. The strengths and deficiencies of the variety of techniques discussed in this book are presented in detail and visualization tools commonly used to make the simulation data more comprehensive are also discussed. In the end, specific techniques are used as bridges across different disciplines. To this end, examples of different systems tackled with the same methods are presented. The appendices include elements of physical theory which are prerequisites in understanding the simulation methods.