الصفحة 15
الصفحة 15
Lagrangian Transport in Geophysical Jets and Waves : The Dynamical Systems Approach
This book provides an accessible introduction to a new set of methods for the analysis of Lagrangian motion in geophysical flows. These methods were originally developed in the abstract mathematical setting of dynamical systems theory, through a geometric approach to differential equations. Despite the recent developments in this field and the existence of a substantial body of work on geophysical fluid problems in the dynamical systems and geophysical literature, this is the first introductory text that presents these methods in the context of geophysical fluid flow. The book is organized into seven chapters; the first introduces the geophysical context and the mathematical models of geophysical fluid flow that are explored in subsequent chapters. The second and third cover the simplest case of steady flow, develop basic mathematical concepts and definitions, and touch on some important topics from the classical theory of Hamiltonian systems. The fundamental elements and methods of Lagrangian transport analysis in time-dependent flows that are the main subject of the book are described in the fourth, fifth, and sixth chapters. The seventh chapter gives a brief survey of some of the rapidly evolving research in geophysical fluid dynamics that makes use of this new approach. Related supplementary material, including a glossary and an introduction to numerical methods, is given in the appendices.
Lagrangian and Hamiltonian Methods for Nonlinear Control 2006 ; Proceedings from the 3rd IFAC Workshop, Nagoya, Japan, July 2006
A Differential-Geometric Approach for Bernstein’s Degrees-of-Freedom Problem.- Nonsmooth Riemannian Optimization with Applications to Sphere Packing and Grasping.- Synchronization of Networked Lagrangian Systems.- An Algorithm to Discretize One-Dimensional Distributed Port Hamiltonian Systems.- Virtual Lagrangian Construction Method for Infinitedimensional Systems with Homotopy Operators.- Direct Discrete-Time Design for Sampled-Data Hamiltonian Control Systems.- Kinematic Compensation in Port-Hamiltonian Telemanipulation.- Interconnection and Damping Assignment Passivity-Based Control of a Four-Tank System.- Towards Power-based Control Strategies for a Class of Nonlinear Mechanical Systems.- Power Shaping Control of Nonlinear Systems: A Benchmark Example.- Total Energy Shaping Control of Mechanical Systems: Simplifying the Matching Equations via Coordinate Changes.- Simultaneous Interconnection and Damping Assignment Passivity–Based Control: Two Practical Examples.
Lacroix and the Calculus
Lacroix and the Calculus is the first major study of Lacroix’s large Traité. It uses the unique and massive bibliography given by Lacroix to explore late 18th-century calculus, and the way it is reflected in Lacroix’s account. Several particular aspects are addressed in detail, including: the foundations of differential calculus, analytic and differential geometry, conceptions of the integral, and types of solutions of differential equations (singular/complete/general integrals, geometrical interpretations, and generality of arbitrary functions).
Kolmogorovs Heritage in Mathematics
A.N. Kolmogorov (b. Tambov 1903, d. Moscow 1987) was one of the most brilliant mathematicians that the world has ever known. Incredibly deep and creative, he was able to approach each subject with a completely new point of view: in a few magnificent pages, which are models of shrewdness and imagination, and which astounded his contemporaries, he changed drastically the landscape of the subject.Most mathematicians prove what they can, Kolmogorov was of those who prove what they want. For this book several world experts were asked to present one part of the mathematical heritage left to us by Kolmogorov.
Knowledge Processing with Interval and Soft Computing
In particular, these chapters cover computing techniques for interval linear systems of equations, interval matrix singular-value decomposition, interval function approximation, and decision making with statistical and graph-based data processing. To enable these applications, the book presents a standards-based object-oriented interval computing environment in C++.
Kinetics of Catalytic Reactions--Solutions Manual
This textbook contains all the information needed for graduate students or industrial researchers to design kinetic experiments involving heterogeneous catalysts, to characterize these catalysts, to acquire valid rate data, to verify the absence of mass (and heat) transfer limitations, to propose reaction models, to derive rate expressions based on these models and, finally, to assess the consistency of these rate equations.The most recent technique to calculate heats of adsorption and activation barriers on metal surfaces, the BOC-MP approach, is discussed in detail. Methods to measure metal surface areas and crystallite sizes using x-ray diffraction, transmission electron microscopy and various chemisorption techniques are discussed. Different experimental techniques to determine the influence of mass transfer limitations, especially within the pores of a catalyst, are reviewed in detail, with a particular emphasis on liquid-phase reactions.
Kinetics of Catalytic Reactions
This textbook contains all the information needed for graduate students or industrial researchers to design kinetic experiments involving heterogeneous catalysts, to characterize these catalysts, to acquire valid rate data, to verify the absence of mass (and heat) transfer limitations, to propose reaction models, to derive rate expressions based on these models and, finally, to assess the consistency of these rate equations.Many illustrations of these and other topics are provided along with numerous problems and a Solutions Manual for instructors. This book will be applicable to any graduate course in chemical engineering, chemistry or materials science that involves kinetics of catalytic reactions, including those catalyzed by enzymes.
Jets From Young Stars III : Numerical MHD and Instabilities
This volume contains the lecture notes of the Third JETSET School on Jets from Young Stars focussing on Numerical MHD and Instabilities. The introductory lectures presented here cover the basic concepts of the numerical methods for the integration of hydrodynamic and magnetohydrodynamic equations and of the applications of these methods to the treatment of the instabilities relevant for the physics of stellar jets. The first part of the book contains an introduction to the finite difference and finite volume methods for computing the solutions of hyperbolic partial differential equations and a discussion of approximate Riemann solvers for both hydrodynamic and magnetohydrodynamic problems. The second part is devoted to the discussion of some of the main instability processes that may take place in stellar jets, namely: the Kelvin-Helmholtz, the radiative shock, the pressure driven and the thermal instabilities.
IUTAM symposium on relations of shell plate beam and 3D models ; Proceedings of the IUTAM Symposium on the relations of shell, plate, beam, and 3D models, Dedicated to the Centenary of Ilia Vekua’s Birth, held in Tbilisi, Georgia, April 23-27, 2007
Contains papers on the main topics reflecting the scientific programme of the symposium: hierarchical, refined mathematical and technical models of shells, plates, and beams; relation of 2D and 1D models to 3D linear, non-linear and physical models; junction problems. In particular, peculiarities of cusped shells, plates, and beams are emphasized and special attention is paid to junction, multibody and fluid-elastic shell (plate, beam) interaction problems and their applications.
IUTAM Symposium on Laminar-Turbulent Transition and Finite Amplitude Solutions
This volume contains refereed papers presented symposium on "Non-Uniqueness of Solutions to the Navier-Stokes equations and their Connection with Laminar-Turbulent Transition" The central objective of the symposium was to discuss the increasing amount of experimental and numerical evidence for finite amplitude solutions to the Navier-Stokes equations and to set the work into a modern theoretical context.
Iterative Approximation of Fixed Points
The aim of this monograph is to give a unified introductory treatment of the most important iterative methods for constructing fixed points of nonlinear contractive type mappings. It summarizes the most significant contributions in the area by presenting, for each iterative method considered (Picard iteration, Krasnoselskij iteration, Mann iteration, Ishikawa iteration etc.), some of the most relevant, interesting, representative and actual convergence theorems. Applications to the solution of nonlinear operator equations as well as the appropriate error analysis of the main iterative methods, are also presented.
Iterated Function Systems for Real-Time Image Synthesis
Natural phenomena can be visually described with fractal-geometry methods, where iterative procedures rather than equations are used to model objects. With the development of better modelling algorithms, the efficiency of rendering, the realism of computer-generated scenes and the interactivity of visual stimuli are reaching astonishing levels. Iterated Function Systems for Real-Time Image Synthesis gives an explanation of iterated function systems and how to use them in generation of complex objects.
Israel Gohberg and Friends : On the Occasion of his 80th Birthday
It is an expression of esteem and friendship for a great mathematician, a remarkable person and an inspiring colleague. The book contains reflections by Gohberg himself on his own mathematical activities and those of others. It also includes contributions of colleagues and co-workers, both from his time in the Soviet Union and from when he lived and worked in the West. The contributions in question are not mathematical research papers but focus on the man Israel Gohberg and are intended for a wide audience.
Comprehensive mathematics for computer scientists 2 : Calculus and ODEs, splines, probability, fourier and wavelet theory, fractals and neural networks, categories and lambda calculus
This second volume of a comprehensive tour through mathematical core subjects for computer scientists completes the first volume in two - gards: Part III first adds topology, di?erential, and integral calculus to the t- ics of sets, graphs, algebra, formal logic, machines, and linear geometry, of volume 1. With this spectrum of fundamentals in mathematical e- cation, young professionals should be able to successfully attack more involved subjects, which may be relevant to the computational sciences. In a second regard, the end of part III and part IV add a selection of more advanced topics. In view of the overwhelming variety of mathematical approaches in the computational sciences, any selection, even the most empirical, requires a methodological justi?cation. Our primary criterion has been the search for harmonization and optimization of thematic - versity and logical coherence. This is why we have, for instance, bundled such seemingly distant subjects as recursive constructions, ordinary d- ferential equations, and fractals under the unifying perspective of c- traction theory.
Complex, Contact and Symmetric Manifolds : In Honor of L. Vanhecke
This volume contains introductory and contextual material, describe recent developments and research trends in spectral geometry, the theory of geodesics and curvature, contact and symplectic geometry, complex geometry, algebraic topology, homogeneous and symmetric spaces, and various applications of partial differential equations and differential systems to geometry. One of the key strengths of these articles is their appeal to non-specialists, as well as researchers and differential geometers.
Complex Numbers from A to … Z
It is impossible to imagine modern mathematics without complex numbers. Complex Numbers from A to . . . Z introduces the reader to this fascinating subject that, from the time of L. Euler, has become one of the most utilized ideas in mathematics.The exposition concentrates on key concepts and then elementary results concerning these numbers. The reader learns how complex numbers can be used to solve algebraic equations and to understand the geometric interpretation of complex numbers and the operations involving them.The theoretical parts of the book are augmented with rich exercises and problems at various levels of difficulty. A special feature of the book is the last chapter, a selection of outstanding Olympiad and other important mathematical contest problems solved by employing the methods already presented.The book reflects the unique experience of the authors. It distills a vast mathematical literature, most of which is unknown to the western public, and captures the essence of an abundant problem culture.
Compendium of Theoretical Physics
Mechanics, Electrodynamics, Quantum Mechanics, and Statistical Mechanics and Thermodynamics comprise the canonical undergraduate curriculum of theoretical physics. In Compendium of Theoretical Physics, Armin Wachter and Henning Hoeber offer a concise, rigorous and structured overview that will be invaluable for students preparing for their qualifying examinations, readers needing a supplement to standard textbooks, and research or industrial physicists seeking a bridge between extensive textbooks and formula books. The authors take an axiomatic-deductive approach to each topic, starting the discussion of each theory with its fundamental equations. By subsequently deriving the various physical relationships and laws in logical rather than chronological order, and by using a consistent presentation and notation throughout, they emphasize the connections between the individual theories. The reader’s understanding is then reinforced with exercises, solutions and topic summaries.
Compatible Spatial Discretizations
Compatible spatial discretizations are those that inherit or mimic fundamental properties of the PDE such as topology, conservation, symmetries, and positivity structures and maximum principles. It offer a snapshot of the current trends and developments in compatible spatial discretizations. The reader will find valuable insights on spatial compatibility from several different perspectives and important examples of applications compatible discretizations in computational electromagnetics, geosciences, linear elasticity, eigenvalue approximations and MHD. The contributions collected in this volume will help to elucidate relations between different methods and concepts and to generally advance our understanding of compatible spatial discretizations for PDEs.
Characteristics Finite Element Methods in Computational Fluid Dynamics
This book details a systematic characteristics-based finite element procedure to investigate incompressible, free-surface and compressible flows. The fluid dynamics equations are derived from basic thermo-mechanical principles and the multi-dimensional and infinite-directional upstream procedure is developed by combining a finite element discretization of a characteristics-bias system with an implicit Runge-Kutta time integration. For the computational solution of the Euler and Navier Stokes equations, the procedure relies on the mathematics and physics of multi-dimensional characteristics. As a result, the procedure crisply captures contact discontinuities, normal as well as oblique shocks, and generates essentially non-oscillatory solutions for incompressible, subsonic, transonic, supersonic, and hypersonic inviscid and viscous flows.
Cells and Robots : Modeling and Control of Large-Size Agent Populations
Cells and Robots is an outcome of the multidisciplinary research extending over Biology, Robotics and Hybrid Systems Theory. It is inspired by modeling reactive behavior of the immune system cell population, where each cell is considered as an independent agent. In our modeling approach, there is no difference if the cells are naturally or artificially created agents, such as robots. This appears even more evident when we introduce a case study concerning a large-size robotic population scenario. Under this scenario, we also formulate the optimal control of maximizing the probability of robotic presence in a given region and discuss the application of the Minimum Principle for partial differential equations to this problem. Simultaneous consideration of cell and robotic populations is of mutual benefit for Biology and Robotics, as well as for the general understanding of multi-agent system dynamics.The text of this monograph is based on the PhD thesis of the first author. The work was a runner-up for the fifth edition of the Georges Giralt Award for the best European PhD thesis in Robotics, annually awarded by the European Robotics Research Network (EURON).
