The Theory of Composites

Author: Graeme W. Milton

Publisher: Cambridge University Press

ISBN: 9780521781251

Category: Mathematics

Page: 719

View: 6414

This 2002 book surveys the exciting developments in composite materials which are at the frontier of mathematics and presents many new results.

Hierarchical Materials Informatics

Novel Analytics for Materials Data

Author: Surya R. Kalidindi

Publisher: Elsevier

ISBN: 012410455X

Category: Technology & Engineering

Page: 230

View: 2965

Custom design, manufacture, and deployment of new high performance materials for advanced technologies is critically dependent on the availability of invertible, high fidelity, structure-property-processing (SPP) linkages. Establishing these linkages presents a major challenge because of the need to cover unimaginably large dimensional spaces. Hierarchical Materials Informatics addresses objective, computationally efficient, mining of large ensembles of experimental and modeling datasets to extract this core materials knowledge. Furthermore, it aims to organize and present this high value knowledge in highly accessible forms to end users engaged in product design and design for manufacturing efforts. As such, this emerging field has a pivotal role in realizing the goals outlined in current strategic national initiatives such as the Materials Genome Initiative (MGI) and the Advanced Manufacturing Partnership (AMP). This book presents the foundational elements of this new discipline as it relates to the design, development, and deployment of hierarchical materials critical to advanced technologies. Addresses a critical gap in new materials research and development by presenting a rigorous statistical framework for the quantification of microstructure Contains several case studies illustrating the use of modern data analytic tools on microstructure datasets (both experimental and modeling)

Inverse Problems, Multi-scale Analysis and Effective Medium Theory

Workshop in Seoul, Inverse Problems, Multi-scale Analysis, and Homogenization, June 22-24, 2005, Seoul National University, Seoul, Korea

Author: Habib Ammari,Hyeonbae Kang

Publisher: American Mathematical Soc.

ISBN: 0821839683

Category: Mathematics

Page: 265

View: 6995

Recent developments in inverse problems, multi-scale analysis and effective medium theory reveal that these fields share several fundamental concepts. This book is the proceedings of the research conference, ``Workshop in Seoul: Inverse Problems, Multi-Scale Analysis and Homogenization,'' held at Seoul National University, June 22-24, 2005. It highlights the benefits of sharing ideas among these areas, of merging the expertise of scientists working there, and of directing interest towards challenging issues such as imaging nanoscience and biological imaging. Contributions are written by prominent experts and are of interest to researchers and graduate students interested in partial differential equations and applications.

Mathematical and Statistical Methods for Multistatic Imaging

Author: Habib Ammari,Josselin Garnier,Wenjia Jing,Hyeonbae Kang,Mikyoung Lim,Knut Sølna,Han Wang

Publisher: Springer

ISBN: 3319025856

Category: Mathematics

Page: 361

View: 3890

This book covers recent mathematical, numerical, and statistical approaches for multistatic imaging of targets with waves at single or multiple frequencies. The waves can be acoustic, elastic or electromagnetic. They are generated by point sources on a transmitter array and measured on a receiver array. An important problem in multistatic imaging is to quantify and understand the trade-offs between data size, computational complexity, signal-to-noise ratio, and resolution. Another fundamental problem is to have a shape representation well suited to solving target imaging problems from multistatic data. In this book the trade-off between resolution and stability when the data are noisy is addressed. Efficient imaging algorithms are provided and their resolution and stability with respect to noise in the measurements analyzed. It also shows that high-order polarization tensors provide an accurate representation of the target. Moreover, a dictionary-matching technique based on new invariants for the generalized polarization tensors is introduced. Matlab codes for the main algorithms described in this book are provided. Numerical illustrations using these codes in order to highlight the performance and show the limitations of numerical approaches for multistatic imaging are presented.

Mathematical and Computational Methods in Photonics and Phononics

Author: Habib Ammari,Brian Fitzpatrick,Hyeonbae Kang,Matias Ruiz,Sanghyeon Yu,Hai Zhang

Publisher: American Mathematical Soc.

ISBN: 1470448009

Category: Photonics

Page: 509

View: 3312

The fields of photonics and phononics encompass the fundamental science of light and sound propagation and interactions in complex structures, as well as its technological applications. This book reviews new and fundamental mathematical tools, computational approaches, and inversion and optimal design methods to address challenging problems in photonics and phononics. An emphasis is placed on analyzing sub-wavelength resonators, super-focusing and super-resolution of electromagnetic and acoustic waves, photonic and phononic crystals, electromagnetic cloaking, and electromagnetic and elastic metamaterials and metasurfaces. Throughout this book, the authors demonstrate the power of layer potential techniques for solving challenging problems in photonics and phononics when they are combined with asymptotic analysis. This book might be of interest to researchers and graduate students working in the fields of applied and computational mathematics, partial differential equations, electromagnetic theory, elasticity, integral equations, and inverse and optimal design problems in photonics and phononics.

Schwarz-Christoffel Mapping

Author: Tobin A. Driscoll,Lloyd N. Trefethen

Publisher: Cambridge University Press

ISBN: 9781139433921

Category: Mathematics

Page: 132

View: 9027

This book provides a comprehensive look at the Schwarz-Christoffel transformation, including its history and foundations, practical computation, common and less common variations, and many applications in fields such as electromagnetism, fluid flow, design and inverse problems, and the solution of linear systems of equations. It is an accessible resource for engineers, scientists, and applied mathematicians who seek more experience with theoretical or computational conformal mapping techniques. The most important theoretical results are stated and proved, but the emphasis throughout remains on concrete understanding and implementation, as evidenced by the 76 figures based on quantitatively correct illustrative examples. There are over 150 classical and modern reference works cited for readers needing more details. There is also a brief appendix illustrating the use of the Schwarz-Christoffel Toolbox for MATLAB, a package for computation of these maps.

Proceedings

Mathematical, physical and engineering sciences

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Engineering

Page: N.A

View: 4341


Bernhard Riemann 1826–1866

Wendepunkte in der Auffassung der Mathematik

Author: Detlef Laugwitz

Publisher: Springer-Verlag

ISBN: 3034889836

Category: Mathematics

Page: 348

View: 9449

Das Riemannsche Integral lernen schon die Schüler kennen, die Theorien der reellen und der komplexen Funktionen bauen auf wichtigen Begriffsbildungen und Sätzen Riemanns auf, die Riemannsche Geometrie ist für Einsteins Gravitationstheorie und ihre Erweiterungen unentbehrlich, und in der Zahlentheorie ist die berühmte Riemannsche Vermutung noch immer offen. Riemann und sein um fünf Jahre jüngerer Freund Richard Dedekind sahen sich als Schüler von Gauss und Dirichlet. Um die Mitte des 19. Jahrhunderts leiteten sie den Übergang zur "modernen Mathematik" ein, der eine in Analysis und Geometrie, der andere in der Algebra mit der Hinwendung zu Mengen und Strukturen. Dieses Buch ist der erste Versuch, Riemanns wissenschaftliches Werk unter einem einheitlichen Gesichtspunkt zusammenzufassend darzustellen. Riemann gilt als einer der Philosophen unter den Mathematikern. Er stellte das Denken in Begriffen neben die zuvor vorherrschende algorithmische Auffassung von der Mathematik, welche die Gegenstände der Untersuchung, in Formeln und Figuren, in Termumformungen und regelhaften Konstruktionen als die allein legitimen Methoden sah. David Hilbert hat als Riemanns Grundsatz herausgestellt, die Beweise nicht durch Rechnung, sondern lediglich durch Gedanken zu zwingen. Hermann Weyl sah als das Prinzip Riemanns in Mathematik und Physik, "die Welt als das erkenntnistheoretische Motiv..., die Welt aus ihrem Verhalten im un- endlich kleinen zu verstehen."

Knotentheorie

Author: K. Reidemeister

Publisher: Springer-Verlag

ISBN: 3642656161

Category: Mathematics

Page: 74

View: 548

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.