Singularities: Formation, Structure, and Propagation

Singularities: Formation, Structure, and Propagation
Author: J. Eggers
Publisher: Cambridge University Press
Total Pages: 471
Release: 2015-09-10
Genre: Mathematics
ISBN: 1316352390

Many key phenomena in physics and engineering are described as singularities in the solutions to the differential equations describing them. Examples covered thoroughly in this book include the formation of drops and bubbles, the propagation of a crack and the formation of a shock in a gas. Aimed at a broad audience, this book provides the mathematical tools for understanding singularities and explains the many common features in their mathematical structure. Part I introduces the main concepts and techniques, using the most elementary mathematics possible so that it can be followed by readers with only a general background in differential equations. Parts II and III require more specialised methods of partial differential equations, complex analysis and asymptotic techniques. The book may be used for advanced fluid mechanics courses and as a complement to a general course on applied partial differential equations.

Introduction to Magnetohydrodynamics

Introduction to Magnetohydrodynamics
Author: P. A. Davidson
Publisher: Cambridge University Press
Total Pages: 802
Release: 2016-12-22
Genre: Science
ISBN: 1316861953

Magnetohydrodynamics (MHD) plays a crucial role in astrophysics, planetary magnetism, engineering and controlled nuclear fusion. This comprehensive textbook emphasizes physical ideas, rather than mathematical detail, making it accessible to a broad audience. Starting from elementary chapters on fluid mechanics and electromagnetism, it takes the reader all the way through to the latest ideas in more advanced topics, including planetary dynamos, stellar magnetism, fusion plasmas and engineering applications. With the new edition, readers will benefit from additional material on MHD instabilities, planetary dynamos and applications in astrophysics, as well as a whole new chapter on fusion plasma MHD. The development of the material from first principles and its pedagogical style makes this an ideal companion for both undergraduate students and postgraduate students in physics, applied mathematics and engineering. Elementary knowledge of vector calculus is the only prerequisite.

Analysis of Singularities for Partial Differential Equations

Analysis of Singularities for Partial Differential Equations
Author: Shuxing Chen
Publisher: World Scientific
Total Pages: 207
Release: 2011
Genre: Mathematics
ISBN: 9814304832

The book provides a comprehensive overview on the theory on analysis of singularities for partial differential equations (PDEs). It contains a summarization of the formation, development and main results on this topic. Some of the author's discoveries and original contributions are also included, such as the propagation of singularities of solutions to nonlinear equations, singularity index and formation of shocks.

Introduction to Complex Variables and Applications

Introduction to Complex Variables and Applications
Author: Mark J. Ablowitz
Publisher: Cambridge University Press
Total Pages: 421
Release: 2021-03-25
Genre: Mathematics
ISBN: 110883261X

An introduction to complex variables that caters for undergraduate students in applied mathematics, science, and engineering.

Microhydrodynamics, Brownian Motion, and Complex Fluids

Microhydrodynamics, Brownian Motion, and Complex Fluids
Author: Michael D. Graham
Publisher: Cambridge University Press
Total Pages: 281
Release: 2018-09-13
Genre: Mathematics
ISBN: 1107024641

Provides a foundation for understanding complex fluids by integrating fluid dynamics, statistical physics, and polymer and colloid science.

Numerical Linear Algebra

Numerical Linear Algebra
Author: Holger Wendland
Publisher: Cambridge University Press
Total Pages: 420
Release: 2017-11-16
Genre: Computers
ISBN: 1108548636

This self-contained introduction to numerical linear algebra provides a comprehensive, yet concise, overview of the subject. It includes standard material such as direct methods for solving linear systems and least-squares problems, error, stability and conditioning, basic iterative methods and the calculation of eigenvalues. Later chapters cover more advanced material, such as Krylov subspace methods, multigrid methods, domain decomposition methods, multipole expansions, hierarchical matrices and compressed sensing. The book provides rigorous mathematical proofs throughout, and gives algorithms in general-purpose language-independent form. Requiring only a solid knowledge in linear algebra and basic analysis, this book will be useful for applied mathematicians, engineers, computer scientists, and all those interested in efficiently solving linear problems.

Discrete Systems and Integrability

Discrete Systems and Integrability
Author: J. Hietarinta
Publisher: Cambridge University Press
Total Pages: 461
Release: 2016-09
Genre: Mathematics
ISBN: 1107042720

A first introduction to the theory of discrete integrable systems at a level suitable for students and non-experts.

Stochastic Modelling of Reaction–Diffusion Processes

Stochastic Modelling of Reaction–Diffusion Processes
Author: Radek Erban
Publisher: Cambridge University Press
Total Pages: 322
Release: 2020-01-30
Genre: Mathematics
ISBN: 1108572995

This practical introduction to stochastic reaction-diffusion modelling is based on courses taught at the University of Oxford. The authors discuss the essence of mathematical methods which appear (under different names) in a number of interdisciplinary scientific fields bridging mathematics and computations with biology and chemistry. The book can be used both for self-study and as a supporting text for advanced undergraduate or beginning graduate-level courses in applied mathematics. New mathematical approaches are explained using simple examples of biological models, which range in size from simulations of small biomolecules to groups of animals. The book starts with stochastic modelling of chemical reactions, introducing stochastic simulation algorithms and mathematical methods for analysis of stochastic models. Different stochastic spatio-temporal models are then studied, including models of diffusion and stochastic reaction-diffusion modelling. The methods covered include molecular dynamics, Brownian dynamics, velocity jump processes and compartment-based (lattice-based) models.