The Navier Stokes Problem in the 21st Century

Author: Pierre Gilles Lemarie-Rieusset
Publisher: CRC Press
ISBN: 9781466566231
Release Date: 2016-04-06
Genre: Mathematics

Up-to-Date Coverage of the Navier–Stokes Equation from an Expert in Harmonic Analysis The complete resolution of the Navier–Stokes equation—one of the Clay Millennium Prize Problems—remains an important open challenge in partial differential equations (PDEs) research despite substantial studies on turbulence and three-dimensional fluids. The Navier–Stokes Problem in the 21st Century provides a self-contained guide to the role of harmonic analysis in the PDEs of fluid mechanics. The book focuses on incompressible deterministic Navier–Stokes equations in the case of a fluid filling the whole space. It explores the meaning of the equations, open problems, and recent progress. It includes classical results on local existence and studies criterion for regularity or uniqueness of solutions. The book also incorporates historical references to the (pre)history of the equations as well as recent references that highlight active mathematical research in the field.

Partial Differential Equations in Fluid Mechanics

Author: Charles L. Fefferman
Publisher: Cambridge University Press
ISBN: 9781108573597
Release Date: 2018-09-30
Genre: Mathematics

The Euler and Navier–Stokes equations are the fundamental mathematical models of fluid mechanics, and their study remains central in the modern theory of partial differential equations. This volume of articles, derived from the workshop 'PDEs in Fluid Mechanics' held at the University of Warwick in 2016, serves to consolidate, survey and further advance research in this area. It contains reviews of recent progress and classical results, as well as cutting-edge research articles. Topics include Onsager's conjecture for energy conservation in the Euler equations, weak-strong uniqueness in fluid models and several chapters address the Navier–Stokes equations directly; in particular, a retelling of Leray's formative 1934 paper in modern mathematical language. The book also covers more general PDE methods with applications in fluid mechanics and beyond. This collection will serve as a helpful overview of current research for graduate students new to the area and for more established researchers.

Lectures on Navier Stokes Equations

Author: Tai-Peng Tsai
Publisher: American Mathematical Soc.
ISBN: 9781470430962
Release Date: 2018-08-09
Genre: Fluid dynamics

This book is a graduate text on the incompressible Navier-Stokes system, which is of fundamental importance in mathematical fluid mechanics as well as in engineering applications. The goal is to give a rapid exposition on the existence, uniqueness, and regularity of its solutions, with a focus on the regularity problem. To fit into a one-year course for students who have already mastered the basics of PDE theory, many auxiliary results have been described with references but without proofs, and several topics were omitted. Most chapters end with a selection of problems for the reader. After an introduction and a careful study of weak, strong, and mild solutions, the reader is introduced to partial regularity. The coverage of boundary value problems, self-similar solutions, the uniform L3 class including the celebrated Escauriaza-Seregin-Šverák Theorem, and axisymmetric flows in later chapters are unique features of this book that are less explored in other texts. The book can serve as a textbook for a course, as a self-study source for people who already know some PDE theory and wish to learn more about Navier-Stokes equations, or as a reference for some of the important recent developments in the area.

Mathematical Analysis in Fluid Mechanics Selected Recent Results

Author: Raphaël Danchin
Publisher: American Mathematical Soc.
ISBN: 9781470436469
Release Date: 2018-06-26
Genre: Fluid mechanics

This volume contains the proceedings of the International Conference on Vorticity, Rotation and Symmetry (IV)—Complex Fluids and the Issue of Regularity, held from May 8–12, 2017, in Luminy, Marseille, France. The papers cover topics in mathematical fluid mechanics ranging from the classical regularity issue for solutions of the 3D Navier-Stokes system to compressible and non-Newtonian fluids, MHD flows and mixtures of fluids. Topics of different kinds of solutions, boundary conditions, and interfaces are also discussed.

Computational Fluid Dynamics for the 21st Century

Author: Mohamed Hafez
Publisher: Springer Science & Business Media
ISBN: 9783540449591
Release Date: 2013-03-09
Genre: Technology & Engineering

This volume contains new trends of computational fluid dynamics for the 21st century and consists of papers especially useful to the younger generation of scientists and engineers in this field. Topics include cartesian, gridless and higher-order schemes, and flow-visualization techniques.

Pascal Fermat und die Berechnung des Gl cks

Author: Keith J. Devlin
Publisher: C.H.Beck
ISBN: 3406590993
Release Date: 2009
Genre: Wahrscheinlichkeitstheorie - Geschichte

Der Autor stellt die Entstehung der Wahrscheinlichkeitsrechnung und den damit verbundenen Wandel des menschlichen Alltagslebens dar.

Computational Science for the 21st Century

Author: Marie Odile Bristeau
Publisher: John Wiley & Sons Inc
ISBN: 0471972983
Release Date: 1997-04-30
Genre: Computers

Computational science can loosely be defined as the endeavor to develop and analyse models for the simulation and control of complex processes. This is achieved by making optimal use of computer resources and by drawing upon a variety of disciplines, techniques and theories. With the emergence of advanced computational and information technologies, computational science now has a significant impact on engineering, physical, biological, management and social sciences. The contributions in this state-of-the-art volume range from theoretical and numerical topics to practical implementations. The subject matter includes modelling, mathematical and numerical analysis, differential equations, linear algebra, optimization, domain decomposition, computational fluid dynamics, computational mechanics, elasticity, structure, computational physics and chemistry, electromagnetic, control theory and other applications. This volume is dedicated to Roland Glowinski on the occasion of his 60th birthday. It is aimed at the next generation of scientists, applied mathematicians, computer scientists, practitioners and engineers who will define computational science within the context of the challenging scientific, industrial, economic and societal problems of the 21st century.

Mine Safety and Efficient Exploitation Facing Challenges of the 21st Century

Author: Liu Zegong
Publisher: CRC Press
ISBN: 9780203093337
Release Date: 2010-10-18
Genre: Nature

The International Mining Forum is a meeting of scientists and professionals for exchanging new ideas and experiences, evaluate previously implemented solutions, and discuss fresh ideas that might change the mining industry’s image. In recent years theory and technology in mine safety and efficient exploitation has made considerable progress in China, Poland and other countries, due to the introduction of many new theories and technologies. The International Mining Forum 2010, jointly organized by Anhui University of Science and Technology (China), AGH University of Science and Technology (Poland) and Mineral and Energy Economy Research Institute of the Polish Academy of Sciences (Poland), has provided experts all over the world with an opportunity and platform to exchange information and ideas. Purpose of the forum was to promote research and development of mine safety, efficient exploitation theory and provide theoretical and technical support for mine safety improvement. This book is addressed to researchers and professionals who work in the fields of underground mining technology, rock engineering or mine management.

Fluid Mechanics

Author: Frank Mangrom White
ISBN: 9814720178
Release Date: 2016-01-22
Genre: Fluid mechanics

Applied Mathematics Entering the 21st Century

Author: James M. Hill
Publisher: SIAM
ISBN: 0898715598
Release Date: 2004-04-01
Genre: Mathematics

Included in this volume are the Invited Talks given at the 5th International Congress of Industrial and Applied Mathematics. The authors of these papers are all acknowledged masters of their fields, having been chosen through a rigorous selection process by a distinguished International Program Committee. This volume presents an overview of contemporary applications of mathematics, with the coverage ranging from the rhythms of the nervous system, to optimal transportation, elasto-plasticity, computational drug design, hydrodynamic and meteorological modeling, and valuation in financial markets. Many papers are direct products of the computer revolution: grid generation, multi-scale modeling, high-dimensional numerical integration, nonlinear optimization, accurate floating-point computations and advanced iterative methods. Other papers demonstrate the close dependence on developments in mathematics itself, and the increasing importance of statistics. Additional topics relate to the study of properties of fluids and fluid-flows, or add to our understanding of Partial Differential Equations.

Finite Elements and Fast Iterative Solvers

Author: Howard C. Elman
Publisher: Oxford University Press (UK)
ISBN: 9780199678808
Release Date: 2014
Genre: Mathematics

This book is a description of why and how to do Scientific Computing for fundamental models of fluid flow. It contains introduction, motivation, analysis, and algorithms and is closely tied to freely available MATLAB codes that implement the methods described. The focus is on finite element approximation methods and fast iterative solution methods for the consequent linear(ized) systems arising in important problems that model incompressible fluid flow. The problems addressed are the Poisson equation, Convection-Diffusion problem, Stokes problem and Navier-Stokes problem, including new material on time-dependent problems and models of multi-physics. The corresponding iterative algebra based on preconditioned Krylov subspace and multigrid techniques is for symmetric and positive definite, nonsymmetric positive definite, symmetric indefinite and nonsymmetric indefinite matrix systems respectively. For each problem and associated solvers there is a description of how to compute together with theoretical analysis that guides the choice of approaches and describes what happens in practice in the many illustrative numerical results throughout the book (computed with the freely downloadable IFISS software). All of the numerical results should be reproducible by readers who have access to MATLAB and there is considerable scope for experimentation in the "computational laboratory" provided by the software. Developments in the field since the first edition was published have been represented in three new chapters covering optimization with PDE constraints (Chapter 5); solution of unsteady Navier-Stokes equations (Chapter 10); solution of models of buoyancy-driven flow (Chapter 11). Each chapter has many theoretical problems and practical computer exercises that involve the use of the IFISS software. This book is suitable as an introduction to iterative linear solvers or more generally as a model of Scientific Computing at an advanced undergraduate or beginning graduate level.

Numerische Str mungsmechanik

Author: Joel H. Ferziger
Publisher: Springer-Verlag
ISBN: 9783540682288
Release Date: 2008-05-14
Genre: Science

Das Buch bietet einen Überblick über die numerischen Methoden zur Lösung strömungsmechanischer Probleme. Die in der Praxis meistgenutzten Methoden werden detailliert beschrieben. Behandelt werden auch fortgeschrittene Methoden, wie die Simulation von Turbulenzen und Parallel-Verarbeitung. Das Buch beschreibt die Grundlagen und Prinzipien der verschiedenen Methoden. Numerische Genauigkeit und Abschätzung sowie Fehlerreduktion werden detailliert mit vielen Beispielen behandelt. Alle Computercodes sind über den Server des Springer-Verlages erhältlich (Internet).

Geometrie der Lage

Author: Karl Georg Christian von Staudt
ISBN: BSB:BSB10082875
Release Date: 1847
Genre: Curves

Eine kleine Geschichte der Unendlichkeit

Author: Brian Clegg
Publisher: Rowohlt Verlag GmbH
ISBN: 9783644043718
Release Date: 2015-03-27
Genre: Fiction

Philosophen und Mathematiker hat das Nachsinnen über das Wesen des Unendlichen buchstäblich den Verstand geraubt – und dennoch ist es ein Konzept, das immer wieder unser Leben bestimmt. In diesem mit Anekdoten und Geschichten gespickten Buch nimmt uns Brian Clegg mit auf eine Reise durch das Grenzland zwischen dem extrem Großen und dem Ultimativen, von Archimedes, der die Zahl der Sandkörner bestimmte, die das Universum füllen würden, bis zu den neuesten Theorien über die physikalische Realität des Unendlichen.