Multiscale Potential Theory

Multiscale Potential Theory
Author: Willi Freeden
Publisher: Springer Science & Business Media
Total Pages: 522
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461220483

This self-contained text/reference provides a basic foundation for practitioners, researchers, and students interested in any of the diverse areas of multiscale (geo)potential theory. New mathematical methods are developed enabling the gravitational potential of a planetary body to be modeled using a continuous flow of observations from land or satellite devices. Harmonic wavelets methods are introduced, as well as fast computational schemes and various numerical test examples. Presented are multiscale approaches for numerous geoscientific problems, including geoidal determination, magnetic field reconstruction, deformation analysis, and density variation modelling With exercises at the end of each chapter, the book may be used as a textbook for graduate-level courses in geomathematics, applied mathematics, and geophysics. The work is also an up-to-date reference text for geoscientists, applied mathematicians, and engineers.

Geomathematically Oriented Potential Theory

Geomathematically Oriented Potential Theory
Author: Willi Freeden
Publisher: CRC Press
Total Pages: 470
Release: 2012-10-30
Genre: Mathematics
ISBN: 1439895422

As the Earth`s surface deviates from its spherical shape by less than 0.4 percent of its radius and today’s satellite missions collect their gravitational and magnetic data on nearly spherical orbits, sphere-oriented mathematical methods and tools play important roles in studying the Earth’s gravitational and magnetic field. Geomathematically Oriented Potential Theory presents the principles of space and surface potential theory involving Euclidean and spherical concepts. The authors offer new insight on how to mathematically handle gravitation and geomagnetism for the relevant observables and how to solve the resulting potential problems in a systematic, mathematically rigorous framework. The book begins with notational material and the necessary mathematical background. The authors then build the foundation of potential theory in three-dimensional Euclidean space and its application to gravitation and geomagnetism. They also discuss surface potential theory on the unit sphere along with corresponding applications. Focusing on the state of the art, this book breaks new geomathematical grounds in gravitation and geomagnetism. It explores modern sphere-oriented potential theoretic methods as well as classical space potential theory.

Geomathematically Oriented Potential Theory

Geomathematically Oriented Potential Theory
Author: Willi Freeden
Publisher: CRC Press
Total Pages: 468
Release: 2012-10-30
Genre: Mathematics
ISBN: 1439895430

As the Earth`s surface deviates from its spherical shape by less than 0.4 percent of its radius and today's satellite missions collect their gravitational and magnetic data on nearly spherical orbits, sphere-oriented mathematical methods and tools play important roles in studying the Earth's gravitational and magnetic field. Geomathematically Orien

Computational Multiscale Modeling of Fluids and Solids

Computational Multiscale Modeling of Fluids and Solids
Author: Martin Oliver Steinhauser
Publisher: Springer Science & Business Media
Total Pages: 432
Release: 2007-10-28
Genre: Science
ISBN: 3540751173

Devastatingly simple, yet hugely effective, the concept of this timely text is to provide a comprehensive overview of computational physics methods and techniques used for materials modeling on different length and time scales. Each chapter first provides an overview of the physical basic principles which are the basis for the numerical and mathematical modeling on the respective length scale. The book includes the micro scale, the meso-scale and the macro scale.

Numerical Fourier Analysis

Numerical Fourier Analysis
Author: Gerlind Plonka
Publisher: Springer
Total Pages: 624
Release: 2019-02-05
Genre: Mathematics
ISBN: 3030043061

This book offers a unified presentation of Fourier theory and corresponding algorithms emerging from new developments in function approximation using Fourier methods. It starts with a detailed discussion of classical Fourier theory to enable readers to grasp the construction and analysis of advanced fast Fourier algorithms introduced in the second part, such as nonequispaced and sparse FFTs in higher dimensions. Lastly, it contains a selection of numerical applications, including recent research results on nonlinear function approximation by exponential sums. The code of most of the presented algorithms is available in the authors’ public domain software packages. Students and researchers alike benefit from this unified presentation of Fourier theory and corresponding algorithms.

Multiscale Biomechanical Modeling of the Brain

Multiscale Biomechanical Modeling of the Brain
Author: Mark F. Horstemeyer
Publisher: Elsevier
Total Pages: 276
Release: 2021-11-02
Genre: Technology & Engineering
ISBN: 0128181443

Multiscale Biomechanical Modeling of the Brain discusses the constitutive modeling of the brain at various length scales (nanoscale, microscale, mesoscale, macroscale and structural scale). In each scale, the book describes the state-of-the- experimental and computational tools used to quantify critical deformational information at each length scale. Then, at the structural scale, several user-based constitutive material models are presented, along with real-world boundary value problems. Lastly, design and optimization concepts are presented for use in occupant-centric design frameworks. This book is useful for both academia and industry applications that cover basic science aspects or applied research in head and brain protection. The multiscale approach to this topic is unique, and not found in other books. It includes meticulously selected materials that aim to connect the mechanistic analysis of the brain tissue at size scales ranging from subcellular to organ levels. Presents concepts in a theoretical and thermodynamic framework for each length scale Teaches readers not only how to use an existing multiscale model for each brain but also how to develop a new multiscale model Takes an integrated experimental-computational approach and gives structured multiscale coverage of the problems

Handbook of Mathematical Geodesy

Handbook of Mathematical Geodesy
Author: Willi Freeden
Publisher: Birkhäuser
Total Pages: 938
Release: 2018-06-11
Genre: Mathematics
ISBN: 3319571818

Written by leading experts, this book provides a clear and comprehensive survey of the “status quo” of the interrelating process and cross-fertilization of structures and methods in mathematical geodesy. Starting with a foundation of functional analysis, potential theory, constructive approximation, special function theory, and inverse problems, readers are subsequently introduced to today’s least squares approximation, spherical harmonics reflected spline and wavelet concepts, boundary value problems, Runge-Walsh framework, geodetic observables, geoidal modeling, ill-posed problems and regularizations, inverse gravimetry, and satellite gravity gradiometry. All chapters are self-contained and can be studied individually, making the book an ideal resource for both graduate students and active researchers who want to acquaint themselves with the mathematical aspects of modern geodesy.

Advances in Chemical Engineering

Advances in Chemical Engineering
Author:
Publisher: Academic Press
Total Pages: 495
Release: 2008-09-22
Genre: Technology & Engineering
ISBN: 0080922929

The cross-fertilization of physico-chemical and mathematical ideas has a long historical tradition. This volume of Advances in Chemical Engineering is almost completely dedicated to a conference on "Mathematics in Chemical Kinetics and Engineering (MaCKiE-2007), which was held in Houston in February 2007, bringing together about 40 mathematicians, chemists, and chemical engineers from 10 countries to discuss the application and development of mathematical tools in their respective fields. - Updates and informs the reader on the latest research findings using original reviews - Written by leading industry experts and scholars - Reviews and analyzes developments in the field

Issues in Mechanical Engineering: 2011 Edition

Issues in Mechanical Engineering: 2011 Edition
Author:
Publisher: ScholarlyEditions
Total Pages: 2526
Release: 2012-01-09
Genre: Technology & Engineering
ISBN: 1464963754

Issues in Mechanical Engineering / 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Mechanical Engineering. The editors have built Issues in Mechanical Engineering: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Mechanical Engineering in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Mechanical Engineering: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

Multivariate Algorithms and Information-Based Complexity

Multivariate Algorithms and Information-Based Complexity
Author: Fred J. Hickernell
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 200
Release: 2020-06-08
Genre: Mathematics
ISBN: 3110633159

The contributions by leading experts in this book focus on a variety of topics of current interest related to information-based complexity, ranging from function approximation, numerical integration, numerical methods for the sphere, and algorithms with random information, to Bayesian probabilistic numerical methods and numerical methods for stochastic differential equations.