{"title":"Mathematics: Fluid Dynamics \u0026 Solid Mechanics","description":"","products":[{"product_id":"think-before-you-compute","title":"Think Before You Compute","description":"\u003cp\u003eEvery fluid dynamicist will at some point need to use computation. Thinking about the physics, constraints and the requirements early on will be rewarded with benefits in time, effort, accuracy and expense. How these benefits can be realised is illustrated in this guide for would-be researchers and beginning graduate students to some of the standard methods and common pitfalls of computational fluid mechanics. Based on a lecture course that the author has developed over twenty years, the text is split into three parts. The quick introduction enables students to solve numerically a basic nonlinear problem by a simple method in just three hours. The follow-up part expands on all the key essentials, including discretisation (finite differences, finite elements and spectral methods), time-stepping and linear algebra. The final part is a selection of optional advanced topics, including hyperbolic equations, the representation of surfaces, the boundary integral method, the multigrid method, domain decomposition, the fast multipole method, particle methods and wavelets.\u003c\/p\u003e","brand":"Cambridge University Press Bookshop","offers":[{"title":"Default Title","offer_id":42633119432943,"sku":"9781108789998","price":32.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0475\/2031\/7597\/products\/9781108789998.jpg?v=1648564443"},{"product_id":"the-fluid-dynamics-of-cell-motility","title":"The Fluid Dynamics of Cell Motility","description":"\u003cp\u003eFluid dynamics plays a crucial role in many cellular processes, including the locomotion of cells such as bacteria and spermatozoa. These organisms possess flagella, slender organelles whose time periodic motion in a fluid environment gives rise to motility. Sitting at the intersection of applied mathematics, physics and biology, the fluid dynamics of cell motility is one of the most successful applications of mathematical tools to the understanding of the biological world. Based on courses taught over several years, it details the mathematical modelling necessary to understand cell motility in fluids, covering phenomena ranging from single-cell motion to instabilities in cell populations. Each chapter introduces mathematical models to rationalise experiments, uses physical intuition to interpret mathematical results, highlights the history of the field and discusses notable current research questions. All mathematical derivations are included for students new to the field, and end-of-chapter exercises help consolidate understanding and practise applying the concepts.\u003c\/p\u003e","brand":"Cambridge University Press Bookshop","offers":[{"title":"Default Title","offer_id":42633213608175,"sku":"9781316626702","price":41.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0475\/2031\/7597\/products\/9781316626702.jpg?v=1648565175"},{"product_id":"self-exciting-fluid-dynamos","title":"Self-Exciting Fluid Dynamos","description":"Exploring the origins and evolution of magnetic fields in planets, stars and galaxies, this book gives a basic introduction to magnetohydrodynamics and surveys the observational data, with particular focus on geomagnetism and solar magnetism. Pioneering laboratory experiments that seek to replicate particular aspects of fluid dynamo action are also described. The authors provide a complete treatment of laminar dynamo theory, and of the mean-field electrodynamics that incorporates the effects of random waves and turbulence. Both dynamo theory and its counterpart, the theory of magnetic relaxation, are covered. Topological constraints associated with conservation of magnetic helicity are thoroughly explored and major challenges are addressed in areas such as fast-dynamo theory, accretion-disc dynamo theory and the theory of magnetostrophic turbulence. 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It brings together continuum mechanics, statistical mechanics, polymer and colloid science, and various branches of applied mathematics, in a self-contained and integrated treatment that provides a foundation for understanding complex fluids, with a strong emphasis on fluid dynamics. Students and researchers will find that this book is extensively cross-referenced to illustrate connections between different aspects of the field. Its focus on fundamental principles and theoretical approaches provides the necessary groundwork for research in the dynamics of flowing complex fluids.\u003c\/p\u003e","brand":"Cambridge University Press Bookshop","offers":[{"title":"Default Title","offer_id":42642687492335,"sku":"9781107695931","price":31.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0475\/2031\/7597\/products\/9781107695931i.jpg?v=1648731489"},{"product_id":"topographic-effects-in-stratified-flows","title":"Topographic Effects in Stratified Flows","description":"\u003cdiv id=\"m_excelWebRenderer_ewaCtl_headerDiv\" data-mce-fragment=\"1\"\u003e\n\u003cdiv id=\"m_excelWebRenderer_ewaCtl_m_formulaBar\" class=\"ewa-fb-nb\" data-mce-fragment=\"1\"\u003e\n\u003cdiv class=\"ewa-fb drop-down\" data-mce-fragment=\"1\"\u003e\n\u003cdiv class=\"ewa-fb-text-box\" wrap=\"virtual\" spellcheck=\"false\" role=\"textbox\" id=\"formulaBarTextDivId\" aria-label=\"formula bar\" tabindex=\"0\" data-mce-fragment=\"1\" data-mce-tabindex=\"0\" autocorrect=\"off\" contenteditable=\"false\"\u003eCovering both theory and experiment, this text describes the behaviour of homogeneous and density-stratified fluids over and around topography. Its presentation is suitable for advanced undergraduate and graduate students in fluid mechanics, as well as for practising scientists, engineers, and researchers. Using laboratory experiments and illustrations to further understanding, the author explores topics ranging from the classical hydraulics of single-layer flow to more complex situations involving stratified flows over two- and three-dimensional topography, including complex terrain. A particular focus is placed on applications to the atmosphere and ocean, including discussions of downslope windstorms, and of oceanic flow over continental shelves and slopes. 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Part One covers inviscid fluid mechanics, guiding readers from the very basics of how to represent fluid flows through to the incompressible Euler equations and many real-world applications. Part Two covers viscous fluid mechanics, from the stress\/rate of strain relation to deriving the incompressible Navier-Stokes equations, through to Beltrami flows, the Reynolds number, Stokes flows, lubrication theory and boundary layers. Also included is a self-contained guide on the global existence of solutions to the incompressible Navier-Stokes equations. Students can test their understanding on 100 progressively structured exercises and look beyond the scope of the text with carefully selected mini-projects. 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Ample examples, problems and computer exercises are provided to allow students to test their understanding of a variety of numerical methods for solving flow physics problems, including the point-vortex method, numerical methods for hydrodynamic stability analysis, spectral methods and traditional CFD topics.","brand":"Cambridge University Press Bookshop","offers":[{"title":"Default Title","offer_id":42673956618479,"sku":"9781316630969","price":48.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0475\/2031\/7597\/products\/9781316630969i.jpg?v=1649429682"},{"product_id":"introduction-to-hydrodynamic-stability","title":"Introduction to Hydrodynamic Stability","description":"\u003cp\u003eInstability of flows and their transition to turbulence are widespread phenomena in engineering and the natural environment, and are important in applied mathematics, astrophysics, biology, geophysics, meteorology, oceanography and physics as well as engineering. This is a textbook to introduce these phenomena at a level suitable for a graduate course, by modelling them mathematically, and describing numerical simulations and laboratory experiments. The visualization of instabilities is emphasized, with many figures, and in references to more still and moving pictures. The relation of chaos to transition is discussed at length. Many worked examples and exercises for students illustrate the ideas of the text. Readers are assumed to be fluent in linear algebra, advanced calculus, elementary theory of ordinary differential equations, complex variables and the elements of fluid mechanics. 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Part II considers many-body dynamics, covering shear flows and sedimentation, bulk flow properties and collective phenomena. An interlude between the two parts provides the basic statistical techniques needed to employ the results of the first (microscopic) in the second (macroscopic). The authors introduce theoretical, mathematical concepts through concrete examples, making the material accessible to non-mathematicians. They also include some of the many open questions in the field to encourage further study. 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They provide a mathematical and numerical treatment of the interactions between electrically conducting fluids and magnetic fields that lead to the complex structures and rich behaviour observed on the Sun and other stars, as well as in the interiors of planets like the Earth. The authors' combined analytical and computational approach provides a model for the study of a wide range of related problems. 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