ANALYTICAL FLUID DYNAMICS IN LAGRANGIAN VARIABLES

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The monograph focuses on the analytical challenges of describing incompressible fluid flows using Lagrangian variables. The Lagrangian method is presented as a complementary approach to the Eulerian method for studying fluid motion. The fundamental nature of fluid dynamics is linked to tracing the trajectories of individual fluid particles, which is precisely what the Lagrangian method facilitates. The purpose of this publication is to reflect as fully as possible the achievements of analytical fluid dynamics in Lagrangian variables. A significant part of it consists of original articles by the author. Considerable attention is paid to the subtleties of the Lagrangian description and its popularization among experts in fluid dynamics, students, postgraduates, and anyone interested in problems of fluid mechanics. The book can be considered, among other things, as a tutorial on Lagrangian fluid dynamics. The book covers issues of the general description of the movement of incompressible fluid, problems of classical hydrodynamics and geophysical hydrodynamics. Fundamental topics include free-boundary motion, vortices in fluids, and water waves. The book includes a number of problems that take into account the stratification and viscosity of fluids, as well as the rotation of the Earth. Sample Chapter(s) Preface Chapter 7: Two-Dimensional Vortex Flow Contents: Description of Basics: Ideal Fluid Equations Potential Motion Vortex Motion Waves on Water: Potential Approximation Gerstner Wave Weakly Vortex Waves Exact Solutions in Vortex Dynamics: Two-Dimensional Vortex Flow Localized Two-Dimensional Vortices in the External Flow Spatial Vortex Flows Generalized Gerstner Waves: Waves on Water at Unstable Pressure Vortex Model of Rogue Waves Breaking of the Surface Gravity Wave Non-Stationary Edge Waves Viscous Fluid Flows: Basic Equations and Examples Gravity Waves on the Surface of a Viscous Fluid The Earth's Rotation Effect: Exact Solutions for Waves Vortices in a Rotating Fluid Readership: This book can be targeted by a various levels of researchers from undergraduate and beginner to graduate and professional levels for both industry and academic sectors in green and sustainable energy.

Emerging Analytical Techniques for Chemical Speciation Studies Part 1

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【簡介】 Guest-edited by Dr Michel Meyer (CNRS, Université de Bourgogne, Dijon) and Prof. Demetrio Milea (Università degli Studi di Messina), Emerging Analytical Techniques for Chemical Speciation Studies focuses on a selection of valuable instrumental methods for investigating complex formation equilibria in solution, providing information on the speciation (stoichiometry and in some instances structure of the formed species) but also allowing the measurement of thermodynamic parameters (equilibrium constants, reaction enthalpy and entropy). The title is split into two volumes belonging to the Series on Chemistry, Energy and the Environment. Part 1 (Volume 15 of this series), discusses various electrochemical, electromigration, and thermophoresis-based methods. Authored by eminent practitioners in their field, each of the four chapters covers both the theoretical and the practical aspects with helpful experimental guidelines. The latest technical and computational advances are described in a way that unambiguously show the major contributions of the authors at the top of their field. Hence, this book is intended to be a valuable introduction to newcomers, while being at the same time a helpful companion to more experienced users of each instrumental techniques. It provides an up-to-date overview with useful tips and hints on the application of selected cutting-edge analytical methods that allow unravelling and modelling intricate complex formation equilibria. So far, there has been no such book focussing specifically on the measurement of thermodynamic parameters, while covering such a wide panel of techniques. This book will be of interest to a broad readership, including analytical, coordination, supramolecular, environmental, instrumental, and physical chemists, radiochemists, electrochemists, and biochemists among others. 【目錄】

How to Derive a Formula Volume 2: Further Analytical Skills and Methods for Physical Scientists

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Will artificial intelligence make scientific formulae redundant by eventually solving all current and future physical problems? The authors of this book would argue that there is still a vital role for humans to play in making sense of the laws of nature. To derive a formula one follows a series of steps, only the last of which is to check that the result is correct. The book is about unravelling this machinery. Mathematics is the 'queen of all sciences', but students encounter many obstacles in learning the subject: familiarization with the proofs of hundreds of theorems, mysterious symbols, and technical routines for which the usefulness is not obvious upfront. Learners could lose motivation, not seeing the wood for the trees. This two-volume book How to Derive a Formula is an attempt to engage learners by presenting mathematical methods in as simple terms as possible, with more of an emphasis on skills as opposed to technical knowledge. Based on intuition and common sense rather than mathematical rigour, it teaches students from scratch using pertinent examples, many taken from across the physical sciences to demonstrate the application of the methods taught. This book draws on humour and historical facts to provide an interesting new perspective on what a mathematics textbook could be. The two volumes are presented as an ascent to Everest. Volume 1 covered the necessary basics, taking readers from Base Camp to Camps 1 and 2. This volume moves readers from Camp 2 up to Camps 3 and 4, tackling more advanced methods for deriving formulae. Inevitably, Volume 2 requires readers to tackle more challenging terrain than was experienced in Volume 1 and so is targeted at more advanced students. Request Inspection Copy Errata(s) Errata (158 KB) Sample Chapter(s) Preface Chapter 1: Multiple Integration in More Depth Contents: Preface About the Authors From Camp 2: In the Multidimensional and Complex World: Multiple Integration in More Depth Surfaces and Vectors Vector Fields and More Vector Calculus Differential Eigenvalue Equations and Special Functions Coupled Linear Second Order Differential Equations and Higher Order Equations Approximation Techniques for Ordinary Differential Equations Homogeneous Partial Differential Equations Complex Contour Integration More Involved Methods for the Summation of Series Concluding Remarks From Camp 3: From Becoming at Ease with Inhomogeneous Partial Differential Equations to a Glimpse of Integral Equations, Functionals, Variation Calculus, Functional Integration, and a Snapshot of the 'Fractional World': Dealing with Inhomogeneous Partial Differential Equations A Brief Look into the World of Integral Equations Principles of Variational Calculus Path Integrals — A First Look In the Thin Air of the Fractional World Concluding Remarks The Final Ascent to Everest Readership: Undergraduate and graduate students (in any disciplines of exact sciences), and postdoctoral researchers in physical sciences, university lecturers for teaching the material of some of the chapters of the book.