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Author: Claude Sabbah Publisher: Springer ISBN: 3642316956 Category : Mathematics Languages : en Pages : 254
Book Description
This research monograph provides a geometric description of holonomic differential systems in one or more variables. Stokes matrices form the extended monodromy data for a linear differential equation of one complex variable near an irregular singular point. The present volume presents the approach in terms of Stokes filtrations. For linear differential equations on a Riemann surface, it also develops the related notion of a Stokes-perverse sheaf. This point of view is generalized to holonomic systems of linear differential equations in the complex domain, and a general Riemann-Hilbert correspondence is proved for vector bundles with meromorphic connections on a complex manifold. Applications to the distributions solutions to such systems are also discussed, and various operations on Stokes-filtered local systems are analyzed.
Author: Claude Sabbah Publisher: Springer ISBN: 3642316956 Category : Mathematics Languages : en Pages : 254
Book Description
This research monograph provides a geometric description of holonomic differential systems in one or more variables. Stokes matrices form the extended monodromy data for a linear differential equation of one complex variable near an irregular singular point. The present volume presents the approach in terms of Stokes filtrations. For linear differential equations on a Riemann surface, it also develops the related notion of a Stokes-perverse sheaf. This point of view is generalized to holonomic systems of linear differential equations in the complex domain, and a general Riemann-Hilbert correspondence is proved for vector bundles with meromorphic connections on a complex manifold. Applications to the distributions solutions to such systems are also discussed, and various operations on Stokes-filtered local systems are analyzed.
Author: Hedwig Heizinger Publisher: Logos Verlag Berlin GmbH ISBN: 383254061X Category : Mathematics Languages : en Pages : 74
Book Description
In this thesis we develop a way of examining the Stokes structure of certain irregular singular D-modules, namely the direct image of exponentially twisted meromorphic connections with regular singularities, in a topological point of view. We use this topological description to compute linear Stokes data for an explicit example.
Author: Steven P. Starkovich Publisher: Springer Nature ISBN: 3030734498 Category : Electronic books Languages : en Pages :
Book Description
This textbook serves as an introduction to groups, rings, fields, vector and tensor spaces, algebras, topological spaces, differentiable manifolds and Lie groups --- mathematical structures which are foundational to modern theoretical physics. It is aimed primarily at undergraduate students in physics and mathematics with no previous background in these topics. Applications to physics --- such as the metric tensor of special relativity, the symplectic structures associated with Hamilton's equations and the Generalized Stokes's Theorem --- appear at appropriate places in the text. Worked examples, end-of-chapter problems (many with hints and some with answers) and guides to further reading make this an excellent book for self-study. Upon completing this book the reader will be well prepared to delve more deeply into advanced texts and specialized monographs in theoretical physics or mathematics.
Author: Peter K. Friz Publisher: Springer Nature ISBN: 3030415562 Category : Mathematics Languages : en Pages : 354
Book Description
With many updates and additional exercises, the second edition of this book continues to provide readers with a gentle introduction to rough path analysis and regularity structures, theories that have yielded many new insights into the analysis of stochastic differential equations, and, most recently, stochastic partial differential equations. Rough path analysis provides the means for constructing a pathwise solution theory for stochastic differential equations which, in many respects, behaves like the theory of deterministic differential equations and permits a clean break between analytical and probabilistic arguments. Together with the theory of regularity structures, it forms a robust toolbox, allowing the recovery of many classical results without having to rely on specific probabilistic properties such as adaptedness or the martingale property. Essentially self-contained, this textbook puts the emphasis on ideas and short arguments, rather than aiming for the strongest possible statements. A typical reader will have been exposed to upper undergraduate analysis and probability courses, with little more than Itô-integration against Brownian motion required for most of the text. From the reviews of the first edition: "Can easily be used as a support for a graduate course ... Presents in an accessible way the unique point of view of two experts who themselves have largely contributed to the theory" - Fabrice Baudouin in the Mathematical Reviews "It is easy to base a graduate course on rough paths on this ... A researcher who carefully works her way through all of the exercises will have a very good impression of the current state of the art" - Nicolas Perkowski in Zentralblatt MATH
Author: Fotis Spyropoulos Publisher: Royal Society of Chemistry ISBN: 1788019059 Category : Technology & Engineering Languages : en Pages : 516
Book Description
The most useful properties of food, i.e. the ones that are detected through look, touch and taste, are a manifestation of the food’s structure. Studies about how this structure develops or can be manipulated during food production and processing are a vital part of research in food science. This book provides the status of research on food structure and how it develops through the interplay between processing routes and formulation elements. It covers food structure development across a range of food settings and consider how this alters in order to design food with specific functionalities and performance. Food structure has to be considered across a range of length scales and the book includes a section focusing on analytical and theoretical approaches that can be taken to analyse/characterise food structure from the nano- to the macro-scale. The book concludes by outlining the main challenges arising within the field and the opportunities that these create in terms of establishing or growing future research activities. Edited and written by world class contributors, this book brings the literature up-to-date by detailing how the technology and applications have moved on over the past 10 years. It serves as a reference for researchers in food science and chemistry, food processing and food texture and structure.
Author: Rajeev Kumar Jaiman Publisher: Springer Nature ISBN: 9811653550 Category : Technology & Engineering Languages : en Pages : 337
Book Description
This book is intended to provide a compilation of the state-of-the-art numerical methods for nonlinear fluid-structure interaction using the moving boundary Lagrangian-Eulerian formulation. Single and two-phase viscous incompressible fluid flows are considered with the increasing complexity of structures ranging from rigid-body, linear elastic and nonlinear large deformation to fully-coupled flexible multibody system. This book is unique with regard to computational modeling of such complex fluid-structure interaction problems at high Reynolds numbers, whereby various coupling techniques are introduced and systematically discussed. The techniques are demonstrated for large-scale practical problems in aerospace and marine/offshore engineering. This book also provides a comprehensive understanding of underlying unsteady physics and coupled mechanical aspects of the fluid-structure interaction from a computational point of view. Using the body-fitted and moving mesh formulations, the physical insights associated with structure-to-fluid mass ratios (i.e., added mass effects), Reynolds number, large structural deformation, free surface, and other interacting physical fields are covered. The book includes the basic tools necessary to build the concepts required for modeling such coupled fluid-structure interaction problems, thus exposing the reader to advanced topics of multiphysics and multiscale phenomena.
Author: A.K. Noor Publisher: Elsevier ISBN: 1483287041 Category : Technology & Engineering Languages : en Pages : 467
Book Description
Computational structural mechanics (CSM) and computational fluid dynamics (CFD) have emerged in the last two decades as new disciplines combining structural mechanics and fluid dynamics with approximation theory, numerical analysis and computer science. Their use has transformed much of theoretical mechanics and abstract science into practical and essential tools for a multitude of technological developments which affect many facets of our life. This collection of over 40 papers provides an authoritative documentation of major advances in both CSM and CFD, helping to identify future directions of development in these rapidly changing fields. Key areas covered are fluid structure interaction and aeroelasticity, CFD technology and reacting flows, micromechanics, stability and eigenproblems, probabilistic methods and chaotic dynamics, perturbation and spectral methods, element technology (finite volume, finite elements and boundary elements), adaptive methods, parallel processing machines and applications, and visualization, mesh generation and artificial intelligence interfaces.
Author: Minoo H Patel Publisher: Butterworth-Heinemann ISBN: 1483163342 Category : Technology & Engineering Languages : en Pages : 409
Book Description
Dynamics of Offshore Structures provides an integrated treatment of the main subject areas that contribute to the design, construction, installation, and operation of fixed and floating offshore structures. The book begins with an overview of offshore oil and gas development and offshore structures. Separate chapters follow on the ocean environment; basic fluid mechanics; gravity wave theories; fluid loading on offshore structures; hydrostatics and dynamic response of floating bodies; and model testing of offshore structures. This book is prepared with particular emphasis on the fundamentals of oceanography, basic fluid mechanics, wave theory, hydrodynamics, naval architecture, and structural analysis to meet the needs of students reading ocean engineering or naval architecture, at both undergraduate and postgraduate levels. Basic equations and theoretical results are derived in a rigorous manner but sections on model testing, full-scale measurements, design, and certification are also induced to ensure that the book is of value to professional engineers seeking a balanced treatment of fundamental and practical issues.
Author: Ian M Davies Publisher: World Scientific ISBN: 9814487058 Category : Mathematics Languages : en Pages : 383
Book Description
This volume contains recent research papers presented at the international workshop on “Probabilistic Methods in Fluids” held in Swansea. The central problems considered were turbulence and the Navier-Stokes equations but, as is now well known, these classical problems are deeply intertwined with modern studies of stochastic partial differential equations, jump processes and random dynamical systems. The volume provides a snapshot of current studies in a field where the applications range from the design of aircraft through the mathematics of finance to the study of fluids in porous media.
Author: Claude Sabbah
Author: Claude Sabbah
Author: Hedwig Heizinger
Author: Steven P. Starkovich
Author: Peter K. Friz
Author: Fotis Spyropoulos
Author: Rajeev Kumar Jaiman
Author: A.K. Noor
Author: David MacGibbon
Author: Minoo H Patel
Author: Ian M Davies