- Table View
- List View
Geometric Modeling of Fractal Forms for CAD
by Christian Gentil Gilles Gouaty Dmitry SokolovDesigning and controlling complex shapes like porous volumes and rough surfaces is a challenge. Fractal geometry is an interesting approach which considerably simplify the problem. Even though underlying concepts reduce the set possible shapes, they generate a surprising variety of shapes. In this book we present a formalism to design such complex objects for geometric aided geometry design applications. The goal of this formalism is to provide to the end user the possibility to manipulate fractal objects as a standard euclidean object with standard tools of CAD system. This formalism encompass curves, surfaces, volumes, as well as NURBS and subdivision surfaces. All theoretical and practical aspects are developed, from the design up to 3D printing.
Geometric Nonlinearity in Structural Behavior: Evaluating Analytical Processes (Synthesis Lectures on Engineering, Science, and Technology)
by Anthony James DeLuzioThis book provides a fundamental understanding of the analytic process involved in solving complex problems, such as the influence of geometric nonlinearity on buckling, vibration, and second-order displacements. Because the book assumes linear behavior the solution can be evaluated using matrix math. Computer software, however, must be used to account for possible nonlinear material behavior due to the local yielding of the members that would result in changes to the elements of the stiffness matrix. Hence the computer solution must be iterative. The number of iterations and the iteration interval may be set manually by the user or internally by the software which can affect the solution.
Geometric Optics
by Antonio Romano Roberto CavaliereThis book--unique in the literature--provides readers with the mathematical background needed to design many of the optical combinations that are used in astronomical telescopes and cameras. The results presented in the work were obtained by using a different approach to third-order aberration theory as well as the extensive use of the software package Mathematica®. Replete with workout examples and exercises, Geometric Optics is an excellent reference for advanced graduate students, researchers, and practitioners in applied mathematics, engineering, astronomy, and astronomical optics. The work may be used as a supplementary textbook for graduate-level courses in astronomical optics, optical design, optical engineering, programming with Mathematica, or geometric optics.
Geometric Optimal Control
by Urszula Ledzewicz Heinz SchättlerThis book gives a comprehensive treatment of the fundamental necessary and sufficient conditions for optimality for finite-dimensional, deterministic, optimal control problems. The emphasis is on the geometric aspects of the theory and on illustrating how these methods can be used to solve optimal control problems. It provides tools and techniques that go well beyond standard procedures and can be used to obtain a full understanding of the global structure of solutions for the underlying problem. The text includes a large number and variety of fully worked out examples that range from the classical problem of minimum surfaces of revolution to cancer treatment for novel therapy approaches. All these examples, in one way or the other, illustrate the power of geometric techniques and methods. The versatile text contains material on different levels ranging from the introductory and elementary to the advanced. Parts of the text can be viewed as a comprehensive textbook for both advanced undergraduate and all level graduate courses on optimal control in both mathematics and engineering departments. The text moves smoothly from the more introductory topics to those parts that are in a monograph style were advanced topics are presented. While the presentation is mathematically rigorous, it is carried out in a tutorial style that makes the text accessible to a wide audience of researchers and students from various fields, including the mathematical sciences and engineering. Heinz Schättler is an Associate Professor at Washington University in St. Louis in the Department of Electrical and Systems Engineering, Urszula Ledzewicz is a Distinguished Research Professor at Southern Illinois University Edwardsville in the Department of Mathematics and Statistics.
Geometric Procedures for Civil Engineers
by Elias C. Tonias Constantine N. ToniasThis book provides a multitude of geometric constructions usually encountered in civil engineering and surveying practice. A detailed geometric solution is provided to each construction as well as a step-by-step set of programming instructions for incorporation into a computing system. The volume is comprised of 12 chapters and appendices that may be grouped in three major parts: the first is intended for those who love geometry for its own sake and its evolution through the ages, in general, and, more specifically, with the introduction of the computer. The second section addresses geometric features used in the book and provides support procedures used by the constructions presented. The remaining chapters and the appendices contain the various constructions. The volume is ideal for engineering practitioners in civil and construction engineering and allied areas.
Geometric Structures of Information (Signals and Communication Technology)
by Frank NielsenThis book focuses on information geometry manifolds of structured data/information and their advanced applications featuring new and fruitful interactions between several branches of science: information science, mathematics and physics. It addresses interrelations between different mathematical domains like shape spaces, probability/optimization & algorithms on manifolds, relational and discrete metric spaces, computational and Hessian information geometry, algebraic/infinite dimensional/Banach information manifolds, divergence geometry, tensor-valued morphology, optimal transport theory, manifold & topology learning, and applications like geometries of audio-processing, inverse problems and signal processing. The book collects the most important contributions to the conference GSI’2017 – Geometric Science of Information.
Geometric Tolerancing of Products: Integration Of Functionality:selected Conference Papers Of The 7th Cirp International Seminar On Computer-aided Tolerancing, Held At The École Normale Supérieure De Cachan, France, 24-25 April 2001 (Wiley-iste Ser.)
by François Villeneuve Luc MathieuThis title describes the various research results in the field of geometric tolerancing of products, an activity that highlights the difficult scientific locks. The collection is of great importance for further innovation in the development of industrial products.
Geometric Tolerancing Standard to Machine Design: A Design-for-Fit Approach
by Faryar EtesamiThis book is for students enrolled in undergraduate mechanical engineering, or similar, programs. The material presented is based on nearly thirty years of class-tested lecture notes for courses on the applications of geometric tolerancing for designers. The book’s emphasis is on fit requirements for machine components, as fit assurance makes up the majority of challenging applications in tolerancing. For design engineers, knowing how to apply geometric tolerances has been a challenge even for engineers who have practiced geometric tolerancing for a long time. The syntax and meaning of geometric tolerancing statements can be learned easily and quickly, but knowing how to use them correctly is much more difficult. In the Design-for-Fit approach, the presentation starts with the geometric requirements for various kinds of fit and then presents the geometric tolerance statements necessary to achieve those fits.
Geometrical Charged-Particle Optics
by Harald RoseThis second edition is an extended version of the first edition of Geometrical Charged-Particle Optics. The updated reference monograph is intended as a guide for researchers and graduate students who are seeking a comprehensive treatment of the design of instruments and beam-guiding systems of charged particles and their propagation in electromagnetic fields. Wave aspects are included in this edition for explaining electron holography, the Aharanov-Bohm effect and the resolution of electron microscopes limited by diffraction. Several methods for calculating the electromagnetic field are presented and procedures are outlined for calculating the properties of systems with arbitrarily curved axis. Detailed methods are presented for designing and optimizing special components such as aberration correctors, spectrometers, energy filters monochromators, ion traps, electron mirrors and cathode lenses. In particular, the optics of rotationally symmetric lenses, quadrupoles, and systems composed of these elements are discussed extensively. Beam properties such as emittance, brightness, transmissivity and the formation of caustics are outlined. Relativistic motion and spin precession of the electron are treated in a covariant way by introducing the Lorentz-invariant universal time and by extending Hamilton's principle from three to four spatial dimensions where the laboratory time is considered as the fourth pseudo-spatial coordinate. Using this procedure and introducing the self action of the electron, its accompanying electromagnetic field and its radiation field are calculated for arbitrary motion. In addition, the Stern-Gerlach effect is revisited for atomic and free electrons.
Geometrical Methods for Power Network Analysis
by Neeraj Gupta Bhupendra Nath Tiwari Stefano BellucciThis book is a short introduction to power system planning and operation using advanced geometrical methods. The approach is based on well-known insights and techniques developed in theoretical physics in the context of Riemannian manifolds. The proof of principle and robustness of this approach is examined in the context of the IEEE 5 bus system. This work addresses applied mathematicians, theoretical physicists and power engineers interested in novel mathematical approaches to power network theory.
Geometrical Objects
by Anthony GerbinoThis volume explores the mathematical character of architectural practice in diverse pre- and early modern contexts It takes an explicitly interdisciplinary approach, which unites scholarship in early modern architecture with recent work in the history of science, in particular, on the role of practice in the "scientific revolution" As a contribution to architectural history, the volume contextualizes design and construction in terms of contemporary mathematical knowledge, attendant forms of mathematical practice, and relevant social distinctions between the mathematical professions As a contribution to the history of science, the volume presents a series of micro-historical studies that highlight issues of process, materiality, and knowledge production in specific, situated, practical contexts Our approach sees the designer's studio, the stone-yard, the drawing floor, and construction site not merely as places where the architectural object takes shape, but where mathematical knowledge itself is deployed, exchanged, and amplified among various participants in the building process.
Geometrical Optics of Weakly Anisotropic Media
by AA FukiUntil recently, there was no effective method for describing waves in weakly anisotropic inhomogeneous media. The method of quasi-isotropic approximation (QIA) of geometrical optics was developed to overcome this problem. The QIA approach bridges the gap between geometrical optics of isotropic media (Rytov method) and that of anisotropic media (Courant-Lax approach). thus providing a complete picture of the geometrical optics of inhomogeneous media. The book explores recent developments in QIA and describes the application of the theory to different branches of wave physics, from plasma physics. quantum physics and ionospheric radio wave propagation to acoustics, optics and astrophysics. The authors present some modifications and generalisations of QIA equations, and look at electromagnetic waves and optical and acoustic effects in weakly anisotropic media, as well as geometrical optics of 3D inhomogeneous media. The book closes with some quantum mechanical analogies. This is an up-to-the minute exposition of the latest developments in an important new area, written by authors of outstanding international reputation. A rich source of both theoretical methods and practical applications, this book covers a wide range of problems of general physical significance and will be of interest to those working in optics, acoustics, electrical engineering, radio engineering and wave propagation through plasma.
Geometrical Theory of Satellite Orbits and Gravity Field (Springer Theses)
by Drazen SvehlaThis book on space geodesy presents pioneering geometrical approaches in the modelling of satellite orbits and gravity field of the Earth, based on the gravity field missions CHAMP, GRACE and GOCE in the LEO orbit. Geometrical approach is also extended to precise positioning in space using multi-GNSS constellations and space geodesy techniques in the realization of the terrestrial and celestial reference frame of the Earth. This book addresses major new developments that were taking place in space geodesy in the last decade, namely the availability of GPS receivers onboard LEO satellites, the multitude of the new GNSS satellite navigation systems, the huge improvement in the accuracy of satellite clocks and the revolution in the determination of the Earth's gravity field with dedicated satellite missions.
Geometry and Vision: First International Symposium, ISGV 2021, Auckland, New Zealand, January 28-29, 2021, Revised Selected Papers (Communications in Computer and Information Science #1386)
by Minh Nguyen Wei Qi Yan Harvey HoThis book constitutes selected papers from the First International Symposium on Geometry and Vision, ISGV 2021, held in Auckland, New Zealand, in January 2021. Due to the COVID-19 pandemic the conference was held in partially virtual format. The 29 papers were thoroughly reviewed and selected from 50 submissions. They cover topics in areas of digital geometry, graphics, image and video technologies, computer vision, and multimedia technologies.
Geometry, Mechanics, and Control in Action for the Falling Cat (Lecture Notes in Mathematics #2289)
by Toshihiro IwaiThe falling cat is an interesting theme to pursue, in which geometry, mechanics, and control are in action together. As is well known, cats can almost always land on their feet when tossed into the air in an upside-down attitude. If cats are not given a non-vanishing angular momentum at an initial instant, they cannot rotate during their motion, and the motion they can make in the air is vibration only. However, cats accomplish a half turn without rotation when landing on their feet. In order to solve this apparent mystery, one needs to thoroughly understand rotations and vibrations. The connection theory in differential geometry can provide rigorous definitions of rotation and vibration for many-body systems. Deformable bodies of cats are not easy to treat mechanically. A feasible way to approach the question of the falling cat is to start with many-body systems and then proceed to rigid bodies and, further, to jointed rigid bodies, which can approximate the body of a cat. In this book, the connection theory is applied first to a many-body system to show that vibrational motions of the many-body system can result in rotations without performing rotational motions and then to the cat model consisting of jointed rigid bodies. On the basis of this geometric setting, mechanics of many-body systems and of jointed rigid bodies must be set up. In order to take into account the fact that cats can deform their bodies, three torque inputs which may give a twist to the cat model are applied as control inputs under the condition of the vanishing angular momentum. Then, a control is designed according to the port-controlled Hamiltonian method for the model cat to perform a half turn and to halt the motion upon landing. The book also gives a brief review of control systems through simple examples to explain the role of control inputs.
Geometry of Crystals, Polycrystals, and Phase Transformations
by Harshad K. Bhadeshia<p>Organized into a two-part structure aimed at readers of differing experience levels, Geometry of Crystals, Polycrystals, and Phase Transformations is accessible to both newcomers and advanced researchers within the field of crystallography. The first part of the text covers what any reader in the material sciences, physics, chemistry, earth sciences and natural sciences in general should know about crystallography. It is intentionally concise and covers sufficient material to form a firm foundation. <p>The second part is aimed at researchers and discusses phase transformations, deformations, and interface crystallography in depth. The phase transformations are limited to those dominated by crystallography. The entire book contains worked examples and uniquely deals not just with crystals but aggregates of crystals and solid-state transformations between crystals.</p>
Geometry of Surfaces: A Practical Guide for Mechanical Engineers
by Stephen P. RadzevichThis updated and expanded edition presents a highly accurate specification for part surface machining. Precise specification reduces the cost of this widely used industrial operation as accurately specified and machined part surfaces do not need to undergo costly final finishing. Dr. Radzevich describes techniques in this volume based primarily on classical differential geometry of surfaces. He then transitions from differential geometry of surfaces to engineering geometry of surfaces, and examines how part surfaces are either machined themselves, or are produced by tools with surfaces that are precisely machined. The book goes on to explain specific methods, such as derivation of planar characteristic curves based on Plücker conoid constructed at a point of the part surface, and that analytical description of part surface is vital for surfaces machined using CNC technology, and especially so for multi-axes NC machines. Providing readers with a powerful tool for analytical description of part surfaces machined on conventional machine tools and numerically controlled machines, this book maximizes understanding on optimal treatment of part surfaces to meet the requirements of today’s high tech industry.
Geometry of Surfaces: A Practical Guide for Mechanical Engineers
by Stephen P. RadzevichPresents an in-depth analysis of geometry of part surfaces and provides the tools for solving complex engineering problems Geometry of Surfaces: A Practical Guide for Mechanical Engineers is a comprehensive guide to applied geometry of surfaces with focus on practical applications in various areas of mechanical engineering. The book is divided into three parts on Part Surfaces, Geometry of Contact of Part Surfaces and Mapping of the Contacting Part Surfaces. Geometry of Surfaces: A Practical Guide for Mechanical Engineers combines differential geometry and gearing theory and presents new developments in the elementary theory of enveloping surfaces. Written by a leading expert of the field, this book also provides the reader with the tools for solving complex engineering problems in the field of mechanical engineering. Presents an in-depth analysis of geometry of part surfaces Provides tools for solving complex engineering problems in the field of mechanical engineering Combines differential geometry and gearing theory Highlights new developments in the elementary theory of enveloping surfaces Essential reading for researchers and practitioners in mechanical, automotive and aerospace engineering industries; CAD developers; and graduate students in Mechanical Engineering.
Geomining: Systems and Decision-Oriented Perspective (Studies in Systems, Decision and Control #224)
by Azer Shukurov Oksana Vovk Artur Zaporozhets Natalia ZuievskaThis book represents a comprehensive exploration of the intricate intersection between geology and mining through the lens of system-oriented perspectives. Geomining stands at the forefront of modern resource extraction, blending the principles of geology, engineering, transport, and environmental science to optimize the extraction of minerals and other valuable resources from the Earth's crust. It is a dynamic field that continually evolves in response to technological advancements, environmental concerns, and economic realities. In this book, we aim to capture the essence of geomining as a holistic system, emphasizing the interconnectedness of its various components and the importance of integrated approaches to resource management. The geomining is a complex of heavy industry sectors that includes the exploration of mineral deposits, the extraction of minerals from the Earth's subsurface, and the enrichment of valuable minerals. Among the main groups of the geomining industry, the following are distinguished—fuel extraction (coal, oil, shale, peat, natural gas extraction); ore mining (iron ore, manganese ore, extraction of non-ferrous ores, precious and rare metals, etc.); mining and chemical industry (extraction of potassium salts, rock salt, apatites, nephelines, bauxites, sulfur, phosphorites, etc.); extraction of mineral raw materials for the construction industry; extraction of mineral raw materials for refractory and ceramic industries; hydromeliorative activities. The concept of a system-oriented view on geomining recognizes that mining activities do not occur in isolation but are part of larger, interconnected systems that encompass geological, environmental, social, and economic dimensions. By adopting a systems perspective, we can better understand the complexities inherent in resource extraction and develop more sustainable and efficient mining practices. This book is divided into 3 parts, each focusing on different aspects of geomining from a systems perspective.
GeomInt—Discontinuities in Geosystems From Lab to Field Scale (SpringerBriefs in Earth System Sciences)
by Olaf Kolditz Keita Yoshioka Tuanny Cajuhi Ralf-Michael Günther Holger Steeb Frank Wuttke Thomas NagelThis is an open access book. In view of growing conflicts over strategic georesources, the use of the geological subsurface in the sense of a regional resource is becoming increasingly important. In this context, georeservoirs are playing an important role for the energy transition not only as a source of energy but also as a storage facility and deep geological disposal for energy waste. The success of the energy transition also depends to a large extent on the efficient and safe use of underground resources.This book complements the previous basic book (GeomInt—Integrity of Host Rocks) with a series of application examples in different rock formations, clay, salt, and crystalline. The methodology developed in GeomInt is used, among others, in the Mont Terri underground research laboratory (Opalinus Clay), in the large borehole test in Springen (salt rock) and in the “Reiche Zeche” teaching and research mine (crystalline rock). In addition, new methodological developments are also taken up in experiments and models and embedded in workflows for geotechnical system analyses. The present book summarizes the results of the collaborative project “GeomInt2: Geomechanical integrity of host and barrier rocks - experiment, modeling and analysis of discontinuities” within the program: Geo Research for Sustainability (GEO: N) of the Federal Ministry of Education and Research (BMBF).
Geomorphological Hazards and Disaster Prevention
by Irasema Alcántara-Ayala Andrew S. GoudieHuman activities have had a huge impact on the environment and landscape, through industrialisation and land-use change, leading to climate change, deforestation, desertification, land degradation, and air and water pollution. These impacts are strongly linked to the occurrence of geomorphological hazards, such as floods, landslides, snow avalanches, soil erosion, and others. Geomorphological work includes not only the understanding but the mapping and modelling of Earth's surface processes, many of which directly affect human societies. In addition, geomorphologists are becoming increasingly involved with the dimensions of societal problem solving, through vulnerability analysis, hazard and risk assessment and management. The work of geomorphologists is therefore of prime importance for disaster prevention. An international team of geomorphologists have contributed their expertise to this volume, making this a scientifically rigorous work for a wide audience of geomorphologists and other Earth scientists, including those involved in environmental science, hazard and risk assessment, management and policy.
Geons, Black Holes, and Quantum Foam: A Life in Physics
by Kenneth Ford John Archibald WheelerThe autobiography of one of the preeminent figures in twentieth-century physics. He studied with Niels Bohr, taught Richard Feynman, and boned up on relativity with his friend and colleague Albert Einstein. John Archibald Wheeler's fascinating life brings us face to face with the central characters and discoveries of modern physics. He was the first American to learn of the discovery of nuclear fission, later coined the term "black hole," led a renaissance in gravitation physics, and helped to build Princeton University into a mecca for physicists. From nuclear physics, to quantum theory, to relativity and gravitation, Wheeler's work has set the trajectory of research for half a century. His career has brought him into contact with the most brilliant minds of his field; Fermi, Bethe, Rabi, Teller, Oppenheimer, and Wigner are among those he called colleagues and friends. In this rich autobiography, Wheeler reveals in fascinating detail the excitement of each discovery, the character of each colleague, and the underlying passion for knowledge that drives him still.
Geopedology
by Joseph Alfred Zinck Graciela Metternicht Gerardo Bocco Héctor Francisco Del ValleThis book offers a proven approach for reliable mapping of soil-landscape relationships to derive information for policy, planning and management at scales ranging from local to regional. It presents the theoretical and conceptual framework of the geopedologic approach and a bulk of applied research showing its application and benefits for knowledge generation relevant to geohazard studies, land use conflict analysis, land use planning, land degradation assessment, and land suitability analysis. Soil is a vital resource for society at large and an important determinant of the economic status of nations. The intensification of natural disasters and the increased land use competition for food and energy have raised awareness of the relevant role the pedosphere plays in natural and anthropogenic environments. Recent papers and global initiatives show a renewed interest in soil research and its applications for improved planning and management of this fragile and finite resource.
Geopedology: An Integration Of Geomorphology And Pedology For Soil And Landscape Studies
by Joseph Alfred Zinck Graciela Metternicht Héctor Francisco del Valle Marcos Angelini<p>This updated and revised second edition brings geopedology issues into the current context. This new edition extends the work on popular topics such as digital soil mapping, GIS and landscape mapping, and it also gives valuable insight with up-to-date theoretical discussions and new application with relevant case studies. This textbook offers a proven approach for reliable mapping of soil-landscape relationships to derive information for policy, planning and management at scales ranging from local to regional. Filled with didactic elements such as case studies, visual aids (maps, charts and figures), questions and answers, the book is of interest to geohazard studies, land use conflict analysis, land use planning, land degradation assessment, and land suitability analysis.<p> <p>Soil is a vital resource for society at large and an important determinant of the economic status of nations. The intensification of natural disasters and the increased land use competition for food and energy have raised awareness of the relevant role the pedosphere plays in natural and anthropogenic environments. Recent papers and global initiatives show a renewed interest in soil research and its applications for improved planning and management of this fragile and finite resource.<p>
Geopedology: An Integration of Geomorphology and Pedology for Soil and Landscape Studies
by Joseph Alfred Zinck Graciela Metternicht Héctor Francisco del Valle Marcos AngeliniThis updated and revised second edition brings geopedology issues into the current context. This new edition extends the work on popular topics such as digital soil mapping, GIS and landscape mapping, and it also gives valuable insight with up-to-date theoretical discussions and new application with relevant case studies. This textbook offers a proven approach for reliable mapping of soil-landscape relationships to derive information for policy, planning and management at scales ranging from local to regional. Filled with didactic elements such as case studies, visual aids (maps, charts and figures), questions and answers, the book is of interest to geohazard studies, land use conflict analysis, land use planning, land degradation assessment, and land suitability analysis. Soil is a vital resource for society at large and an important determinant of the economic status of nations. The intensification of natural disasters and the increased land use competition for food and energy have raised awareness of the relevant role the pedosphere plays in natural and anthropogenic environments. Recent papers and global initiatives show a renewed interest in soil research and its applications for improved planning and management of this fragile and finite resource.