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| Author | : Mariarosaria Padula |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 249 |
| Release | : 2011-07-30 |
| Genre | : Mathematics |
| ISBN | : 3642211364 |
This volume introduces a systematic approach to mathematical problems involved with thermodynamic fluids. The book is written for theoretical and applied mathematicians with an interest in compressible flow, capillarity theory, and control theory.
| Author | : Adelina Georgescu |
| Publisher | : World Scientific |
| Total Pages | : 418 |
| Release | : 2010 |
| Genre | : Mathematics |
| ISBN | : 9814289574 |
1. Mathematical models governing fluid flows stability. 1.1. General mathematical models of thermodynamics. 1.2. Classical mathematical models in thermodynamics of fluids. 1.3. Classical mathematical models in thermodynamics. 1.4. Classical perturbation models. 1.5. Generalized incompressible Navier-Stokes model -- 2. Incompressible Navier-Stokes fluid. 2.1. Back to integral setting; involvement of dynamics and bifurcation. 2.2. Stability in semidynamical systems. 2.3. Perturbations; asymptotic stability; linear stability. 2.4. Linear stability. 2.5. Prodi's linearization principle. 2.6. Estimates for the spectrum of Ã. 2.7. Universal stability criteria -- 3. Elements of calculus of variations. 3.1. Generalities. 3.2. Direct and inverse problems of calculus of variations. 3.3. Symmetrization of some matricial ordinary differential operators. 3.4. Variational principles for problems (3.3.1)-(3.3.7). 3.5. Fourier series solutions for variational problems -- 4. Variants of the energy method for non-stationary equations. 4.1. Variant based on differentiation of parameters. 4.2. Variant based on simplest symmetric part of operators. 4.3. Variants based on energy splitting -- 5. Applications to linear Bénard convections. 5.1. Magnetic Bénard convection in a partially ionized fluid. 5.2. Magnetic Bénard convection for a fully ionized fluid. 5.3. Convection in a micro-polar fluid bounded by rigid walls. 5.4. Convections governed by ode's with variable coefficients -- 6. Variational methods applied to linear stability. 6.1. Magnetic Bénard problem with Hall effect. 6.2. Lyapunov method applied to the anisotropic Bénard problem. 6.3. Stability criteria for a quasi-geostrophic forced zonal flow. 6.4. Variational principle for problem (5.3.1), (5.3.2). 6.5. Taylor-Dean problem -- 7. Applications of the direct method to linear stability. 7.1. Couette flow between two cylinders subject to a magnetic field. 7.2. Soret-Dufour driven convection. 7.3. Magnetic Soret-Dufour driven convection. 7.4. Convection in a porous medium. 7.5. Convection in the presence of a dielectrophoretic force. 7.6. Convection in an anisotropic M.H.D. thermodiffusive mixture. 7.7. Inhibition of the thermal convection by a magnetic field. 7.8. Microconvection in a binary layer subject to a strong Soret effect. 7.9. Convection in the layer between the sea bed and the permafrost.
| Author | : Yoshihiro Shibata |
| Publisher | : Springer |
| Total Pages | : 616 |
| Release | : 2016-12-01 |
| Genre | : Mathematics |
| ISBN | : 4431564578 |
This volume presents original papers ranging from an experimental study on cavitation jets to an up-to-date mathematical analysis of the Navier-Stokes equations for free boundary problems, reflecting topics featured at the International Conference on Mathematical Fluid Dynamics, Present and Future, held 11–14 November 2014 at Waseda University in Tokyo. The contributions address subjects in one- and two-phase fluid flows, including cavitation, liquid crystal flows, plasma flows, and blood flows. Written by internationally respected experts, these papers highlight the connections between mathematical, experimental, and computational fluid dynamics. The book is aimed at a wide readership in mathematics and engineering, including researchers and graduate students interested in mathematical fluid dynamics.
| Author | : Matthias Hieber |
| Publisher | : Springer Nature |
| Total Pages | : 471 |
| Release | : 2020-04-28 |
| Genre | : Mathematics |
| ISBN | : 3030362264 |
This book collects together a unique set of articles dedicated to several fundamental aspects of the Navier–Stokes equations. As is well known, understanding the mathematical properties of these equations, along with their physical interpretation, constitutes one of the most challenging questions of applied mathematics. Indeed, the Navier-Stokes equations feature among the Clay Mathematics Institute's seven Millennium Prize Problems (existence of global in time, regular solutions corresponding to initial data of unrestricted magnitude). The text comprises three extensive contributions covering the following topics: (1) Operator-Valued H∞-calculus, R-boundedness, Fourier multipliers and maximal Lp-regularity theory for a large, abstract class of quasi-linear evolution problems with applications to Navier–Stokes equations and other fluid model equations; (2) Classical existence, uniqueness and regularity theorems of solutions to the Navier–Stokes initial-value problem, along with space-time partial regularity and investigation of the smoothness of the Lagrangean flow map; and (3) A complete mathematical theory of R-boundedness and maximal regularity with applications to free boundary problems for the Navier–Stokes equations with and without surface tension. Offering a general mathematical framework that could be used to study fluid problems and, more generally, a wide class of abstract evolution equations, this volume is aimed at graduate students and researchers who want to become acquainted with fundamental problems related to the Navier–Stokes equations.
| Author | : Jiri Neustupa |
| Publisher | : Birkhäuser |
| Total Pages | : 271 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3034882432 |
Mathematical modeling and numerical simulation in fluid mechanics are topics of great importance both in theory and technical applications. The present book attempts to describe the current status in various areas of research. The 10 chapters, mostly survey articles, are written by internationally renowned specialists and offer a range of approaches to and views of the essential questions and problems. In particular, the theories of incompressible and compressible Navier-Stokes equations are considered, as well as stability theory and numerical methods in fluid mechanics. Although the book is primarily written for researchers in the field, it will also serve as a valuable source of information to graduate students.
| Author | : Radyadour Kh. Zeytounian |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 498 |
| Release | : 2013-06-29 |
| Genre | : Science |
| ISBN | : 3662104474 |
This book closes the gap between standard undergraduate texts on fluid mechanics and monographical publications devoted to specific aspects of viscous fluid flows. Each chapter serves as an introduction to a special topic that will facilitate later application by readers in their research work.
| Author | : Riccardo Sacco |
| Publisher | : Academic Press |
| Total Pages | : 854 |
| Release | : 2019-07-18 |
| Genre | : Technology & Engineering |
| ISBN | : 0128125195 |
A Comprehensive Physically Based Approach to Modeling in Bioengineering and Life Sciences provides a systematic methodology to the formulation of problems in biomedical engineering and the life sciences through the adoption of mathematical models based on physical principles, such as the conservation of mass, electric charge, momentum, and energy. It then teaches how to translate the mathematical formulation into a numerical algorithm that is implementable on a computer. The book employs computational models as synthesized tools for the investigation, quantification, verification, and comparison of different conjectures or scenarios of the behavior of a given compartment of the human body under physiological and pathological conditions. Presents theoretical (modeling), biological (experimental), and computational (simulation) perspectives Features examples, exercises, and MATLAB codes for further reader involvement Covers basic and advanced functional and computational techniques throughout the book
| Author | : |
| Publisher | : |
| Total Pages | : 380 |
| Release | : 1995 |
| Genre | : Aeronautics |
| ISBN | : |
Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
| Author | : D.L. Dwoyer |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 361 |
| Release | : 2013-03-09 |
| Genre | : Science |
| ISBN | : 1461247241 |
This volume is the collection of papers presented at the workshop on 'The Stability of Spatially Varying and Time Dependent Flows" sponsored by the Institute for Computer Applications in Science and Engineering (lCASE) and NASA Langley Research Center (LaRC) during August 19- 23, 1985. The purpose of this workshop was to bring together some of the experts in the field for an exchange of ideas to update the current status of knowledge and to help identify trends for future research. Among the invited speakers were D.M. Bushnell, M. Goldstein, P. Hall, Th. Herbert, R.E. Kelly, L. Mack, A.H. Nayfeh, F.T. Smith, and C. von Kerczek. The contributed papers were by A. Bayliss, R. Bodonyi, S. Cowley, C. Grosch, S. Lekoudis, P. Monkewitz, A. Patera, and C. Streett. In the first article, Bushnell provides a historical background on laminar flow control (LFC) research and summarizes the crucial role played by stability theory in LFC system design. He also identifies problem areas in stability theory requiring further research from the view-point of ap plications to LFC design. It is an excellent article for theoreticians looking for some down-to-earth applications of stability theory.
