The Navier-Stokes equations II

Sample

A.W. Blain, F. Combes, B.T. Draine

The cold universe is the part of the universe in a cold form close to the background radiation temperature. Until recently, this cold state has been neglected because it is hard to observe, although it must inevitably play a crucial role as the original state of most of the hotter observable objects such as planets, stars, and galaxies. Fortunately, the cold universe currently becomes more and more accessible with newer instruments. This book contains the printed version of the lectures given at the 32nd Saas-Fee Advanced Course "The Cold Universe" by three eminent scientists in the field: Andrew Blain, Francoise Combes and Bruce Draine. Cold objects at cosmological distances, the origin of galaxies, the role of molecules in galaxies, and the physics of the dust in cold clouds are the main topics treated. This book contains an accessible and up-to-date review of the field and should be useful for many years to astronomy students, cosmologists, physicists and researchers.

Sample

Susanne C. Brenner, L. Ridgway Scott

This book develops the basic mathematical theory of the finite element method, the most widely used technique for engineering design and analysis. It formalizes basic tools that are commonly used by researchers in the field but not previously published. The book will be useful to mathematicians as well as engineers and physical scientists. It can be used for a course that provides an introduction to basic functional analysis, approximation theory, and numerical analysis, while building upon and applying basic techniques of real variable theory. The initial chapter provides an introduction to the entire subject, developed in the one-dimensional case. Four subsequent chapters develop the basic theory in the multidimensional case, and a fifth chapter presents basic applications of this theory. Subsequent chapters provide an introduction to multigrid methods and other iterative solution techniques, mixed methods with applications to elasticity and fluid flow models, variational "crimes" including nonconforming and isoparametric methods and numerical integration, error estimates in the maximum norm with applications to nonlinear problems, and Banach-space operator-interpolation techniques. Different course paths can be chosen, allowing the book to be used for courses designed for students with different interests. For example, courses can emphasize physical applications, or algorithmic efficiency and code development issues, or the more difficult convergence theorems of the subject.

Sample

S.S. Hasan, R.T. Gangadhara, and V. Krishan

It is well established and appreciated by now that more than 99% of the baryonic matter in the universe is in the plasma state. Most astrophysical systems could be approximated as conducting fluids in a gravitational field. It is the combined effect of these two that gives rise to the mind boggling variety of configurations in the form of filaments, loops , jets and arches. The plasma structures that cannot last for more than a second or less in a laboratory remain intact for astronomical time and spatial scales in an astrophysical setting. The case in point is the well known extragalactic jets whose collimation and stability has remained an enigma inspite of the efforts of many for many long years. The high energy radiation sources such as the active galactic nuclei again summon the coherent plasma radiation processes for their exceptionally large output from regions of relatively small physical sizes. The generation of magnetic field, anomalous transport of angular momentum with decisive bearing on star formation processes, the ubiquitous MHD turbulence under conditions irreproducible in terrestrial laboratories are some of the generic issues still awaiting a concerted effort for their understanding. Quantum Plasmas, pair plasmas and pair-ion plasmas exist under extreme conditions in planetary interiors and exotic stars. In this workshop plasma physicists, astrophysicists and plasma astrophysicists are brought together to discuss these issues.

Sample

M. Abate ... [et al

The geometry of real submanifolds in complex manifolds and the analysis of their mappings belong to the most advanced streams of contemporary Mathematics. In this area converge the techniques of various and sophisticated mathematical fields such as P.D.E.'s, boundary value problems, induced equations, analytic discs in symplectic spaces, complex dynamics. For the variety of themes and the surprisingly good interplaying of different research tools, these problems attracted the attention of some among the best mathematicians of these latest two decades. They also entered as a refined content of an advanced education. In this sense the five lectures of this volume provide an excellent cultural background while giving very deep insights of current research activity.