Green's Kernels and Meso-Scale Approximations in Perforated Domains

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Publisher : Springer
ISBN 13 : 3319003577
Total Pages : 258 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Green's Kernels and Meso-Scale Approximations in Perforated Domains by : Vladimir Maz'ya

Download or read book Green's Kernels and Meso-Scale Approximations in Perforated Domains written by Vladimir Maz'ya and published by Springer. This book was released on 2013-06-07 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are a wide range of applications in physics and structural mechanics involving domains with singular perturbations of the boundary. Examples include perforated domains and bodies with defects of different types. The accurate direct numerical treatment of such problems remains a challenge. Asymptotic approximations offer an alternative, efficient solution. Green’s function is considered here as the main object of study rather than a tool for generating solutions of specific boundary value problems. The uniformity of the asymptotic approximations is the principal point of attention. We also show substantial links between Green’s functions and solutions of boundary value problems for meso-scale structures. Such systems involve a large number of small inclusions, so that a small parameter, the relative size of an inclusion, may compete with a large parameter, represented as an overall number of inclusions. The main focus of the present text is on two topics: (a) asymptotics of Green’s kernels in domains with singularly perturbed boundaries and (b) meso-scale asymptotic approximations of physical fields in non-periodic domains with many inclusions. The novel feature of these asymptotic approximations is their uniformity with respect to the independent variables. This book addresses the needs of mathematicians, physicists and engineers, as well as research students interested in asymptotic analysis and numerical computations for solutions to partial differential equations.

Singularly Perturbed Boundary Value Problems

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Publisher : Springer Nature
ISBN 13 : 3030762599
Total Pages : 672 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Singularly Perturbed Boundary Value Problems by : Matteo Dalla Riva

Download or read book Singularly Perturbed Boundary Value Problems written by Matteo Dalla Riva and published by Springer Nature. This book was released on 2021-10-01 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the analysis of the basic boundary value problems for the Laplace equation in singularly perturbed domains. The main purpose is to illustrate a method called Functional Analytic Approach, to describe the dependence of the solutions upon a singular perturbation parameter in terms of analytic functions. Here the focus is on domains with small holes and the perturbation parameter is the size of the holes. The book is the first introduction to the topic and covers the theoretical material and its applications to a series of problems that range from simple illustrative examples to more involved research results. The Functional Analytic Approach makes constant use of the integral representation method for the solutions of boundary value problems, of Potential Theory, of the Theory of Analytic Functions both in finite and infinite dimension, and of Nonlinear Functional Analysis. Designed to serve various purposes and readerships, the extensive introductory part spanning Chapters 1–7 can be used as a reference textbook for graduate courses on classical Potential Theory and its applications to boundary value problems. The early chapters also contain results that are rarely presented in the literature and may also, therefore, attract the interest of more expert readers. The exposition moves on to introduce the Functional Analytic Approach. A reader looking for a quick introduction to the method can find simple illustrative examples specifically designed for this purpose. More expert readers will find a comprehensive presentation of the Functional Analytic Approach, which allows a comparison between the approach of the book and the more classical expansion methods of Asymptotic Analysis and offers insights on the specific features of the approach and its applications to linear and nonlinear boundary value problems.

Multiscale Model Reduction

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Publisher : Springer Nature
ISBN 13 : 3031204093
Total Pages : 499 pages
Book Rating : 4.0/5 (312 download)

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Book Synopsis Multiscale Model Reduction by : Eric Chung

Download or read book Multiscale Model Reduction written by Eric Chung and published by Springer Nature. This book was released on 2023-06-07 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to the study of multiscale model reduction methods from the point of view of multiscale finite element methods. Multiscale numerical methods have become popular tools for modeling processes with multiple scales. These methods allow reducing the degrees of freedom based on local offline computations. Moreover, these methods allow deriving rigorous macroscopic equations for multiscale problems without scale separation and high contrast. Multiscale methods are also used to design efficient solvers. This book offers a combination of analytical and numerical methods designed for solving multiscale problems. The book mostly focuses on methods that are based on multiscale finite element methods. Both applications and theoretical developments in this field are presented. The book is suitable for graduate students and researchers, who are interested in this topic.

Mechanics of High-Contrast Elastic Solids

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Publisher : Springer Nature
ISBN 13 : 303124141X
Total Pages : 271 pages
Book Rating : 4.0/5 (312 download)

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Book Synopsis Mechanics of High-Contrast Elastic Solids by : Holm Altenbach

Download or read book Mechanics of High-Contrast Elastic Solids written by Holm Altenbach and published by Springer Nature. This book was released on 2023-04-11 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the most recent results in the area of strongly inhomogeneous composite structures, including layered materials as well as continua with microstructure. This collection of papers mainly arises from the Euromech Colloquium No. 626 on “Mechanics of High-Contrast Elastic Composites”. Focus is set on the peculiar mechanical behaviour caused by adjoining widely different structural elements (high contrast) in terms of material and/or geometrical properties.

Getting Acquainted with Homogenization and Multiscale

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Publisher : Springer
ISBN 13 : 303001777X
Total Pages : 178 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Getting Acquainted with Homogenization and Multiscale by : Leonid Berlyand

Download or read book Getting Acquainted with Homogenization and Multiscale written by Leonid Berlyand and published by Springer. This book was released on 2018-11-22 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: The objective of this book is to navigate beginning graduate students in mathematics and engineering through a mature field of multiscale problems in homogenization theory and to provide an idea of its broad scope. An overview of a wide spectrum of homogenization techniques ranging from classical two-scale asymptotic expansions to Gamma convergence and the rapidly developing field of stochastic homogenization is presented. The mathematical proofs and definitions are supplemented with intuitive explanations and figures to make them easier to follow. A blend of mathematics and examples from materials science and engineering is designed to teach a mixed audience of mathematical and non-mathematical students.

Harmonic Analysis and Partial Differential Equations

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Publisher : Springer Nature
ISBN 13 : 3031254244
Total Pages : 319 pages
Book Rating : 4.0/5 (312 download)

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Book Synopsis Harmonic Analysis and Partial Differential Equations by : Anatoly Golberg

Download or read book Harmonic Analysis and Partial Differential Equations written by Anatoly Golberg and published by Springer Nature. This book was released on 2023-04-26 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the course of his distinguished career, Vladimir Maz'ya has made a number of groundbreaking contributions to numerous areas of mathematics, including partial differential equations, function theory, and harmonic analysis. The chapters in this volume - compiled on the occasion of his 80th birthday - are written by distinguished mathematicians and pay tribute to his many significant and lasting achievements.

Recent Trends in Operator Theory and Partial Differential Equations

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Publisher : Birkhäuser
ISBN 13 : 3319470795
Total Pages : 313 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Recent Trends in Operator Theory and Partial Differential Equations by : Vladimir Maz'ya

Download or read book Recent Trends in Operator Theory and Partial Differential Equations written by Vladimir Maz'ya and published by Birkhäuser. This book was released on 2017-02-23 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to the eminent Georgian mathematician Roland Duduchava on the occasion of his 70th birthday. It presents recent results on Toeplitz, Wiener-Hopf, and pseudodifferential operators, boundary value problems, operator theory, approximation theory, and reflects the broad spectrum of Roland Duduchava's research. The book is addressed to a wide audience of pure and applied mathematicians.

Integral Methods in Science and Engineering

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Publisher : Birkhäuser
ISBN 13 : 3319167278
Total Pages : 717 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Integral Methods in Science and Engineering by : Christian Constanda

Download or read book Integral Methods in Science and Engineering written by Christian Constanda and published by Birkhäuser. This book was released on 2015-10-13 with total page 717 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contributed volume contains a collection of articles on state-of-the-art developments on the construction of theoretical integral techniques and their application to specific problems in science and engineering. Written by internationally recognized researchers, the chapters in this book are based on talks given at the Thirteenth International Conference on Integral Methods in Science and Engineering, held July 21–25, 2014, in Karlsruhe, Germany. A broad range of topics is addressed, from problems of existence and uniqueness for singular integral equations on domain boundaries to numerical integration via finite and boundary elements, conservation laws, hybrid methods, and other quadrature-related approaches. This collection will be of interest to researchers in applied mathematics, physics, and mechanical and electrical engineering, as well as graduate students in these disciplines and other professionals for whom integration is an essential tool.

A Panorama of Mathematics: Pure and Applied

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Publisher : American Mathematical Soc.
ISBN 13 : 1470416689
Total Pages : 279 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis A Panorama of Mathematics: Pure and Applied by : Carlos M. da Fonseca

Download or read book A Panorama of Mathematics: Pure and Applied written by Carlos M. da Fonseca and published by American Mathematical Soc.. This book was released on 2016-02-26 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Conference on Mathematics and its Applications-2014, held from November 14-17, 2014, at Kuwait University, Safat, Kuwait. Papers contained in this volume cover various topics in pure and applied mathematics ranging from an introductory study of quotients and homomorphisms of C-systems, also known as contextual pre-categories, to the most important consequences of the so-called Fokas method. Also covered are multidisciplinary topics such as new structural and spectral matricial results, acousto-electromagnetic tomography method, a recent hybrid imaging technique, some numerical aspects of sonic-boom minimization, PDE eigenvalue problems, von Neumann entropy in graph theory, the relative entropy method for hyperbolic systems, conductances on grids, inverse problems in magnetohydrodynamics, location and size estimation of small rigid bodies using elastic far-fields, and the space-time fractional Schrödinger equation, just to cite a few. Papers contained in this volume cover various topics in pure and applied mathematics ranging from an introductory study of quotients and homomorphisms of C-systems, also known as contextual pre-categories, to the most important consequences of the so-called Fokas method. Also covered are multidisciplinary topics such as new structural and spectral matricial results, acousto-electromagnetic tomography method, a recent hybrid imaging technique, some numerical aspects of sonic-boom minimization, PDE eigenvalue problems, von Neumann entropy in graph theory, the relative entropy method for hyperbolic systems, conductances on grids, inverse problems in magnetohydrodynamics, location and size estimation of small rigid bodies using elastic far-fields, and the space-time fractional Schrödinger equation, just to cite a few. - See more at: http://s350148651-preview.tizrapublisher.com/conm-658/#sthash.74nRhV3y.dpufThis volume contains the proceedings of the Conference on Mathematics and its Applications–2014, held from November 14–17, 2014, at Kuwait University, Safat, Kuwait. - See more at: http://s350148651-preview.tizrapublisher.com/conm-658/#sthash.74nRhV3y.dpuf

Flowing Matter

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Publisher : Springer Nature
ISBN 13 : 3030233707
Total Pages : 309 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Flowing Matter by : Federico Toschi

Download or read book Flowing Matter written by Federico Toschi and published by Springer Nature. This book was released on 2019-09-25 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book, published in the Soft and Biological Matter series, presents an introduction to selected research topics in the broad field of flowing matter, including the dynamics of fluids with a complex internal structure -from nematic fluids to soft glasses- as well as active matter and turbulent phenomena. Flowing matter is a subject at the crossroads between physics, mathematics, chemistry, engineering, biology and earth sciences, and relies on a multidisciplinary approach to describe the emergence of the macroscopic behaviours in a system from the coordinated dynamics of its microscopic constituents. Depending on the microscopic interactions, an assembly of molecules or of mesoscopic particles can flow like a simple Newtonian fluid, deform elastically like a solid or behave in a complex manner. When the internal constituents are active, as for biological entities, one generally observes complex large-scale collective motions. Phenomenology is further complicated by the invariable tendency of fluids to display chaos at the large scales or when stirred strongly enough. This volume presents several research topics that address these phenomena encompassing the traditional micro-, meso-, and macro-scales descriptions, and contributes to our understanding of the fundamentals of flowing matter. This book is the legacy of the COST Action MP1305 “Flowing Matter”.

From Multiscale Modeling to Meso-Science

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Publisher : Springer Science & Business Media
ISBN 13 : 3642351891
Total Pages : 497 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis From Multiscale Modeling to Meso-Science by : Jinghai Li

Download or read book From Multiscale Modeling to Meso-Science written by Jinghai Li and published by Springer Science & Business Media. This book was released on 2013-03-22 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multiscale modeling is becoming essential for accurate, rapid simulation in science and engineering. This book presents the results of three decades of research on multiscale modeling in process engineering from principles to application, and its generalization for different fields. This book considers the universality of meso-scale phenomena for the first time, and provides insight into the emerging discipline that unifies them, meso-science, as well as new perspectives for virtual process engineering. Multiscale modeling is applied in areas including: multiphase flow and fluid dynamics chemical, biochemical and process engineering mineral processing and metallurgical engineering energy and resources materials science and engineering Jinghai Li is Vice-President of the Chinese Academy of Sciences (CAS), a professor at the Institute of Process Engineering, CAS, and leader of the EMMS (Energy-minimizing multiscale) Group. Wei Ge, Wei Wang, Ning Yang and Junwu Wang are professors at the EMMS Group, part of the Institute of Process Engineering, CAS. Xinhua Liu, Limin Wang, Xianfeng He and Xiaowei Wang are associate professors at the EMMS Group, part of the Institute of Process Engineering, CAS. Mooson Kwauk is an emeritus director of the Institute of Process Engineering, CAS, and is an advisor to the EMMS Group.

Continuum Micromechanics

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Publisher : Springer
ISBN 13 : 3709126622
Total Pages : 352 pages
Book Rating : 4.7/5 (91 download)

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Book Synopsis Continuum Micromechanics by : P. Suquet

Download or read book Continuum Micromechanics written by P. Suquet and published by Springer. This book was released on 2014-05-04 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the most recent progress of fundamental nature made in the new developed field of micromechanics: transformation field analysis, variational bounds for nonlinear composites, higher-order gradients in micromechanical damage models, dynamics of composites, pattern based variational bounds.

Mathematical Modelling of Waves in Multi-Scale Structured Media

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Publisher : CRC Press
ISBN 13 : 1351651420
Total Pages : 266 pages
Book Rating : 4.3/5 (516 download)

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Book Synopsis Mathematical Modelling of Waves in Multi-Scale Structured Media by : Alexander B. Movchan

Download or read book Mathematical Modelling of Waves in Multi-Scale Structured Media written by Alexander B. Movchan and published by CRC Press. This book was released on 2017-11-09 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Modelling of Waves in Multi-Scale Structured Media presents novel analytical and numerical models of waves in structured elastic media, with emphasis on the asymptotic analysis of phenomena such as dynamic anisotropy, localisation, filtering and polarisation as well as on the modelling of photonic, phononic, and platonic crystals.

Computational Fluid and Solid Mechanics 2003

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Publisher : Elsevier
ISBN 13 : 9780080529479
Total Pages : 2524 pages
Book Rating : 4.5/5 (294 download)

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Book Synopsis Computational Fluid and Solid Mechanics 2003 by : K.J Bathe

Download or read book Computational Fluid and Solid Mechanics 2003 written by K.J Bathe and published by Elsevier. This book was released on 2003-06-02 with total page 2524 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bringing together the world's leading researchers and practitioners of computational mechanics, these new volumes meet and build on the eight key challenges for research and development in computational mechanics. Researchers have recently identified eight critical research tasks facing the field of computational mechanics. These tasks have come about because it appears possible to reach a new level of mathematical modelling and numerical solution that will lead to a much deeper understanding of nature and to great improvements in engineering design. The eight tasks are: The automatic solution of mathematical models Effective numerical schemes for fluid flows The development of an effective mesh-free numerical solution method The development of numerical procedures for multiphysics problems The development of numerical procedures for multiscale problems The modelling of uncertainties The analysis of complete life cycles of systems Education - teaching sound engineering and scientific judgement Readers of Computational Fluid and Solid Mechanics 2003 will be able to apply the combined experience of many of the world's leading researchers to their own research needs. Those in academic environments will gain a better insight into the needs and constraints of the industries they are involved with; those in industry will gain a competitive advantage by gaining insight into the cutting edge research being carried out by colleagues in academia. Features Bridges the gap between academic researchers and practitioners in industry Outlines the eight main challenges facing Research and Design in Computational mechanics and offers new insights into the shifting the research agenda Provides a vision of how strong, basic and exciting education at university can be harmonized with life-long learning to obtain maximum value from the new powerful tools of analysis

Wave Scattering by Small Bodies of Arbitrary Shapes

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Publisher : World Scientific
ISBN 13 : 9812561862
Total Pages : 314 pages
Book Rating : 4.8/5 (125 download)

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Book Synopsis Wave Scattering by Small Bodies of Arbitrary Shapes by : Alexander G. Ramm

Download or read book Wave Scattering by Small Bodies of Arbitrary Shapes written by Alexander G. Ramm and published by World Scientific. This book was released on 2005 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents analytical formulas which allow one to calculate the S-matrix for the acoustic and electromagnetic wave scattering by small bodies or arbitrary shapes with arbitrary accuracy. Equations for the self-consistent field in media consisting of many small bodies are derived. Applications of these results to ultrasound mammography and electrical engineering are considered.The above formulas are not available in the works of other authors. Their derivation is based on a mathematical theory for solving integral equations of electrostatics, magnetostatics, and other static fields. These equations are at a simple characteristic value. Convergent iterative processes are constructed for stable solution of these equations. The theory completes the classical work of Rayleigh on scattering by small bodies by providing analytical formulas for polarizability tensors for bodies of arbitrary shapes.

Aerosol Science

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Publisher : John Wiley & Sons
ISBN 13 : 1119977924
Total Pages : 522 pages
Book Rating : 4.1/5 (199 download)

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Book Synopsis Aerosol Science by : Ian Colbeck

Download or read book Aerosol Science written by Ian Colbeck and published by John Wiley & Sons. This book was released on 2014-02-03 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: AEROSOL SCIENCE TECHNOLOGY AND APPLICATIONS Aerosols influence many areas of our daily life. They are at the core of environmental problems such as global warming, photochemical smog and poor air quality. They can also have diverse effects on human health, where exposure occurs in both outdoor and indoor environments. However, aerosols can have beneficial effects too; the delivery of drugs to the lungs, the delivery of fuels for combustion and the production of nanomaterials all rely on aerosols. Advances in particle measurement technologies have made it possible to take advantage of rapid changes in both particle size and concentration. Likewise, aerosols can now be produced in a controlled fashion. Reviewing many technological applications together with the current scientific status of aerosol modelling and measurements, this book includes: Satellite aerosol remote sensing The effects of aerosols on climate change Air pollution and health Pharmaceutical aerosols and pulmonary drug delivery Bioaerosols and hospital infections Particle emissions from vehicles The safety of emerging nanomaterials Radioactive aerosols: tracers of atmospheric processes With the importance of this topic brought to the public's attention after the eruption of the Icelandic volcano Eyjafjallajökull, this book provides a timely, concise and accessible overview of the many facets of aerosol science.

Science and Hebrew Tradition

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Publisher :
ISBN 13 :
Total Pages : 402 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Science and Hebrew Tradition by : Thomas Henry Huxley

Download or read book Science and Hebrew Tradition written by Thomas Henry Huxley and published by . This book was released on 1898 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: