Wave Propagation Observation And Control In 1 D Flexible Multi Structures

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Wave Propagation, Observation and Control in 1-d Flexible Multi-Structures

Author : René Dáger
Publisher : Springer Science & Business Media
ISBN 13 : 3540377263
Total Pages : 227 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Wave Propagation, Observation and Control in 1-d Flexible Multi-Structures by : René Dáger

Download or read book Wave Propagation, Observation and Control in 1-d Flexible Multi-Structures written by René Dáger and published by Springer Science & Business Media. This book was released on 2006-08-23 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to analyze the vibrations of simpli?ed 1? d models of multi-body structures consisting of a ?nite number of ?exible strings d- tributed along planar graphs. We?rstdiscussissueson existence and uniquenessof solutions that can be solved by standard methods (energy arguments, semigroup theory, separation ofvariables,transposition,...).Thenweanalyzehowsolutionspropagatealong the graph as the time evolves, addressing the problem of the observation of waves. Roughly, the question of observability can be formulated as follows: Can we obtain complete information on the vibrations by making measu- ments in one single extreme of the network? This formulation is relevant both in the context of control and inverse problems. UsingtheFourierdevelopmentofsolutionsandtechniquesofNonharmonic Fourier Analysis, we give spectral conditions that guarantee the observability property to hold in any time larger than twice the total length of the network in a suitable Hilbert space that can be characterized in terms of Fourier series by means of properly chosen weights. When the network graph is a tree, we characterize these weights in terms of the eigenvalues of the corresponding elliptic problem. The resulting weighted observability inequality allows id- tifying the observable energy in Sobolev terms in some particular cases. That is the case, for instance, when the network is star-shaped and the ratios of the lengths of its strings are algebraic irrational numbers.

Wave Propagation, Observation and Control in 1-d Flexible Multi-Structures

Author : René Dáger
Publisher : Springer
ISBN 13 : 9783540812845
Total Pages : 230 pages
Book Rating : 4.8/5 (128 download)

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Book Synopsis Wave Propagation, Observation and Control in 1-d Flexible Multi-Structures by : René Dáger

Download or read book Wave Propagation, Observation and Control in 1-d Flexible Multi-Structures written by René Dáger and published by Springer. This book was released on 2009-09-02 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to analyze the vibrations of simpli?ed 1? d models of multi-body structures consisting of a ?nite number of ?exible strings d- tributed along planar graphs. We?rstdiscussissueson existence and uniquenessof solutions that can be solved by standard methods (energy arguments, semigroup theory, separation ofvariables,transposition,...).Thenweanalyzehowsolutionspropagatealong the graph as the time evolves, addressing the problem of the observation of waves. Roughly, the question of observability can be formulated as follows: Can we obtain complete information on the vibrations by making measu- ments in one single extreme of the network? This formulation is relevant both in the context of control and inverse problems. UsingtheFourierdevelopmentofsolutionsandtechniquesofNonharmonic Fourier Analysis, we give spectral conditions that guarantee the observability property to hold in any time larger than twice the total length of the network in a suitable Hilbert space that can be characterized in terms of Fourier series by means of properly chosen weights. When the network graph is a tree, we characterize these weights in terms of the eigenvalues of the corresponding elliptic problem. The resulting weighted observability inequality allows id- tifying the observable energy in Sobolev terms in some particular cases. That is the case, for instance, when the network is star-shaped and the ratios of the lengths of its strings are algebraic irrational numbers.

An Introduction to Mathematics of Emerging Biomedical Imaging

Author : Habib Ammari
Publisher : Springer Science & Business Media
ISBN 13 : 3540795537
Total Pages : 198 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis An Introduction to Mathematics of Emerging Biomedical Imaging by : Habib Ammari

Download or read book An Introduction to Mathematics of Emerging Biomedical Imaging written by Habib Ammari and published by Springer Science & Business Media. This book was released on 2008-05-21 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: Biomedical imaging is a fascinating research area to applied mathematicians. Challenging imaging problems arise and they often trigger the investigation of fundamental problems in various branches of mathematics. This is the first book to highlight the most recent mathematical developments in emerging biomedical imaging techniques. The main focus is on emerging multi-physics and multi-scales imaging approaches. For such promising techniques, it provides the basic mathematical concepts and tools for image reconstruction. Further improvements in these exciting imaging techniques require continued research in the mathematical sciences, a field that has contributed greatly to biomedical imaging and will continue to do so. The volume is suitable for a graduate-level course in applied mathematics and helps prepare the reader for a deeper understanding of research areas in biomedical imaging.

Semigroup Methods for Evolution Equations on Networks

Author : Delio Mugnolo
Publisher : Springer
ISBN 13 : 3319046217
Total Pages : 294 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Semigroup Methods for Evolution Equations on Networks by : Delio Mugnolo

Download or read book Semigroup Methods for Evolution Equations on Networks written by Delio Mugnolo and published by Springer. This book was released on 2014-05-21 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: This concise text is based on a series of lectures held only a few years ago and originally intended as an introduction to known results on linear hyperbolic and parabolic equations. Yet the topic of differential equations on graphs, ramified spaces, and more general network-like objects has recently gained significant momentum and, well beyond the confines of mathematics, there is a lively interdisciplinary discourse on all aspects of so-called complex networks. Such network-like structures can be found in virtually all branches of science, engineering and the humanities, and future research thus calls for solid theoretical foundations. This book is specifically devoted to the study of evolution equations – i.e., of time-dependent differential equations such as the heat equation, the wave equation, or the Schrödinger equation (quantum graphs) – bearing in mind that the majority of the literature in the last ten years on the subject of differential equations of graphs has been devoted to elliptic equations and related spectral problems. Moreover, for tackling the most general settings - e.g. encoded in the transmission conditions in the network nodes - one classical and elegant tool is that of operator semigroups. This book is simultaneously a very concise introduction to this theory and a handbook on its applications to differential equations on networks. With a more interdisciplinary readership in mind, full proofs of mathematical statements have been frequently omitted in favor of keeping the text as concise, fluid and self-contained as possible. In addition, a brief chapter devoted to the field of neurodynamics of the brain cortex provides a concrete link to ongoing applied research.

Analysis on Graphs and Its Applications

Author : Pavel Exner
Publisher : American Mathematical Soc.
ISBN 13 : 0821844717
Total Pages : 721 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Analysis on Graphs and Its Applications by : Pavel Exner

Download or read book Analysis on Graphs and Its Applications written by Pavel Exner and published by American Mathematical Soc.. This book was released on 2008 with total page 721 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses a new interdisciplinary area emerging on the border between various areas of mathematics, physics, chemistry, nanotechnology, and computer science. The focus here is on problems and techniques related to graphs, quantum graphs, and fractals that parallel those from differential equations, differential geometry, or geometric analysis. Also included are such diverse topics as number theory, geometric group theory, waveguide theory, quantum chaos, quantum wiresystems, carbon nano-structures, metal-insulator transition, computer vision, and communication networks.This volume contains a unique collection of expert reviews on the main directions in analysis on graphs (e.g., on discrete geometric analysis, zeta-functions on graphs, recently emerging connections between the geometric group theory and fractals, quantum graphs, quantum chaos on graphs, modeling waveguide systems and modeling quantum graph systems with waveguides, control theory on graphs), as well as research articles.

Computational Geometry, Topology and Physics of Digital Images with Applications

Author : James F. Peters
Publisher : Springer Nature
ISBN 13 : 303022192X
Total Pages : 455 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Computational Geometry, Topology and Physics of Digital Images with Applications by : James F. Peters

Download or read book Computational Geometry, Topology and Physics of Digital Images with Applications written by James F. Peters and published by Springer Nature. This book was released on 2019-10-03 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the computational geometry, topology and physics of digital images and video frame sequences. This trio of computational approaches encompasses the study of shape complexes, optical vortex nerves and proximities embedded in triangulated video frames and single images, while computational geometry focuses on the geometric structures that infuse triangulated visual scenes. The book first addresses the topology of cellular complexes to provide a basis for an introductory study of the computational topology of visual scenes, exploring the fabric, shapes and structures typically found in visual scenes. The book then examines the inherent geometry and topology of visual scenes, and the fine structure of light and light caustics of visual scenes, which bring into play catastrophe theory and the appearance of light caustic folds and cusps. Following on from this, the book introduces optical vortex nerves in triangulated digital images. In this context, computational physics is synonymous with the study of the fine structure of light choreographed in video frames. This choreography appears as a sequence of snapshots of light reflected and refracted from surface shapes, providing a solid foundation for detecting, analyzing and classifying visual scene shapes.

Numerical Models for Differential Problems

Author : Alfio Quarteroni
Publisher : Springer Science & Business Media
ISBN 13 : 8847010713
Total Pages : 611 pages
Book Rating : 4.8/5 (47 download)

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Book Synopsis Numerical Models for Differential Problems by : Alfio Quarteroni

Download or read book Numerical Models for Differential Problems written by Alfio Quarteroni and published by Springer Science & Business Media. This book was released on 2010-01-22 with total page 611 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this text, we introduce the basic concepts for the numerical modelling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as well as equations representing conservation laws, saddle-point problems and optimal control problems. Furthermore, we provide numerous physical examples which underline such equations. In particular, we discuss the algorithmic and computer implementation aspects and provide a number of easy-to-use programs. The text does not require any previous advanced mathematical knowledge of partial differential equations: the absolutely essential concepts are reported in a preliminary chapter. It is therefore suitable for students of bachelor and master courses in scientific disciplines, and recommendable to those researchers in the academic and extra-academic domain who want to approach this interesting branch of applied mathematics.

Control of Partial Differential Equations

Author : Fatiha Alabau-Boussouira
Publisher : Springer
ISBN 13 : 3642278930
Total Pages : 355 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Control of Partial Differential Equations by : Fatiha Alabau-Boussouira

Download or read book Control of Partial Differential Equations written by Fatiha Alabau-Boussouira and published by Springer. This book was released on 2012-04-23 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: The term “control theory” refers to the body of results - theoretical, numerical and algorithmic - which have been developed to influence the evolution of the state of a given system in order to meet a prescribed performance criterion. Systems of interest to control theory may be of very different natures. This monograph is concerned with models that can be described by partial differential equations of evolution. It contains five major contributions and is connected to the CIME Course on Control of Partial Differential Equations that took place in Cetraro (CS, Italy), July 19 - 23, 2010. Specifically, it covers the stabilization of evolution equations, control of the Liouville equation, control in fluid mechanics, control and numerics for the wave equation, and Carleman estimates for elliptic and parabolic equations with application to control. We are confident this work will provide an authoritative reference work for all scientists who are interested in this field, representing at the same time a friendly introduction to, and an updated account of, some of the most active trends in current research.

Problems in Mathematical Biophysics

Author : Alberto d’Onofrio
Publisher : Springer Nature
ISBN 13 : 3031607732
Total Pages : 292 pages
Book Rating : 4.0/5 (316 download)

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Book Synopsis Problems in Mathematical Biophysics by : Alberto d’Onofrio

Download or read book Problems in Mathematical Biophysics written by Alberto d’Onofrio and published by Springer Nature. This book was released on with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Introduction to Quantum Graphs

Author : Gregory Berkolaiko
Publisher : American Mathematical Soc.
ISBN 13 : 0821892118
Total Pages : 291 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Introduction to Quantum Graphs by : Gregory Berkolaiko

Download or read book Introduction to Quantum Graphs written by Gregory Berkolaiko and published by American Mathematical Soc.. This book was released on 2013 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: A ``quantum graph'' is a graph considered as a one-dimensional complex and equipped with a differential operator (``Hamiltonian''). Quantum graphs arise naturally as simplified models in mathematics, physics, chemistry, and engineering when one considers propagation of waves of various nature through a quasi-one-dimensional (e.g., ``meso-'' or ``nano-scale'') system that looks like a thin neighborhood of a graph. Works that currently would be classified as discussing quantum graphs have been appearing since at least the 1930s, and since then, quantum graphs techniques have been applied successfully in various areas of mathematical physics, mathematics in general and its applications. One can mention, for instance, dynamical systems theory, control theory, quantum chaos, Anderson localization, microelectronics, photonic crystals, physical chemistry, nano-sciences, superconductivity theory, etc. Quantum graphs present many non-trivial mathematical challenges, which makes them dear to a mathematician's heart. Work on quantum graphs has brought together tools and intuition coming from graph theory, combinatorics, mathematical physics, PDEs, and spectral theory. This book provides a comprehensive introduction to the topic, collecting the main notions and techniques. It also contains a survey of the current state of the quantum graph research and applications.

Mathematics of Complexity and Dynamical Systems

Author : Robert A. Meyers
Publisher : Springer Science & Business Media
ISBN 13 : 1461418054
Total Pages : 1885 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Mathematics of Complexity and Dynamical Systems by : Robert A. Meyers

Download or read book Mathematics of Complexity and Dynamical Systems written by Robert A. Meyers and published by Springer Science & Business Media. This book was released on 2011-10-05 with total page 1885 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.

Modelling and Optimisation of Flows on Networks

Author : Luigi Ambrosio
Publisher : Springer
ISBN 13 : 3642321607
Total Pages : 507 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Modelling and Optimisation of Flows on Networks by : Luigi Ambrosio

Download or read book Modelling and Optimisation of Flows on Networks written by Luigi Ambrosio and published by Springer. This book was released on 2012-12-14 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years flows in networks have attracted the interest of many researchers from different areas, e.g. applied mathematicians, engineers, physicists, economists. The main reason for this ubiquity is the wide and diverse range of applications, such as vehicular traffic, supply chains, blood flow, irrigation channels, data networks and others. This book presents an extensive set of notes by world leaders on the main mathematical techniques used to address such problems, together with investigations into specific applications. The main focus is on partial differential equations in networks, but ordinary differential equations and optimal transport are also included. Moreover, the modeling is completed by analysis, numerics, control and optimization of flows in networks. The book will be a valuable resource for every researcher or student interested in the subject.

Advances in Partial Differential Equations and Control

Author : Kaïs Ammari
Publisher : Springer Nature
ISBN 13 : 3031622650
Total Pages : 250 pages
Book Rating : 4.0/5 (316 download)

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Book Synopsis Advances in Partial Differential Equations and Control by : Kaïs Ammari

Download or read book Advances in Partial Differential Equations and Control written by Kaïs Ammari and published by Springer Nature. This book was released on with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Inverse Dynamics Problems

Author : Hamed Kalhori
Publisher : MDPI
ISBN 13 : 3036510664
Total Pages : 218 pages
Book Rating : 4.0/5 (365 download)

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Book Synopsis Inverse Dynamics Problems by : Hamed Kalhori

Download or read book Inverse Dynamics Problems written by Hamed Kalhori and published by MDPI. This book was released on 2021-06-15 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: The inverse dynamics problem was developed in order to provide researchers with the state of the art in inverse problems for dynamic and vibrational systems. Contrasted with a forward problem, which solves for the system output in a straightforward manner, an inverse problem searches for the system input through a procedure contaminated with errors and uncertainties. An inverse problem, with a focus on structural dynamics, determines the changes made to the system and estimates the inputs, including forces and moments, to the system, utilizing measurements of structural vibration responses only. With its complex mathematical structure and need for more reliable input estimations, the inverse problem is still a fundamental subject of research among mathematicians and engineering scientists. This book contains 11 articles that touch upon various aspects of inverse dynamic problems.

Research in PDEs and Related Fields

Author : Kaïs Ammari
Publisher : Springer Nature
ISBN 13 : 3031142683
Total Pages : 192 pages
Book Rating : 4.0/5 (311 download)

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Book Synopsis Research in PDEs and Related Fields by : Kaïs Ammari

Download or read book Research in PDEs and Related Fields written by Kaïs Ammari and published by Springer Nature. This book was released on 2022-11-07 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents an accessible overview of mathematical control theory and analysis of PDEs, providing young researchers a snapshot of these active and rapidly developing areas. The chapters are based on two mini-courses and additional talks given at the spring school "Trends in PDEs and Related Fields” held at the University of Sidi Bel Abbès, Algeria from 8-10 April 2019. In addition to providing an in-depth summary of these two areas, chapters also highlight breakthroughs on more specific topics such as: Sobolev spaces and elliptic boundary value problems Local energy solutions of the nonlinear wave equation Geometric control of eigenfunctions of Schrödinger operators Research in PDEs and Related Fields will be a valuable resource to graduate students and more junior members of the research community interested in control theory and analysis of PDEs.

SIAM Journal on Control and Optimization

Author : Society for Industrial and Applied Mathematics
Publisher :
ISBN 13 :
Total Pages : 804 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis SIAM Journal on Control and Optimization by : Society for Industrial and Applied Mathematics

Download or read book SIAM Journal on Control and Optimization written by Society for Industrial and Applied Mathematics and published by . This book was released on 2007 with total page 804 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Observation and Control for Operator Semigroups

Author : Marius Tucsnak
Publisher : Springer Science & Business Media
ISBN 13 : 376438994X
Total Pages : 488 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Observation and Control for Operator Semigroups by : Marius Tucsnak

Download or read book Observation and Control for Operator Semigroups written by Marius Tucsnak and published by Springer Science & Business Media. This book was released on 2009-06-10 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies observation and control operators for linear systems where the free evolution of the state can be described by an operator semigroup on a Hilbert space. It includes a large number of examples coming mostly from partial differential equations.