An Introduction to Continuum Physics

This volume is dedicated to direct numerical simulations (DNS). The numerical solution of the Navier-Stokes equation is able to describe the flow variable as a function of space and time. It is called direct numerical simulations (DNS), which is the subject matter of this book

This book provides an introduction to geometrically non-linear single crystal plasticity with continuously distributed dislocations. A symbolic tensor notation is used to focus on the physics. The book also shows the implementation of the theory into the finite element method. Moreover, a simple simulation example demonstrates the capability of the theory to describe the emergence of planar lattice defects (subgrain boundaries) and introduces characteristics of pattern forming systems. Numerical challenges involved in the localization phenomena are discussed in detail.

This upper-level undergraduate and beginning graduate textbook primarily covers the theory and application of Newtonian and Lagrangian, but also of Hamiltonian mechanics. In addition, included are elements of continuum mechanics and the accompanying classical field theory, wherein four-vector notation is introduced without explicit reference to special relativity.

This augmented and updated fourth edition introduces a new complement of computational tools and examples for each chapter and continues to provide a grounding in the tensor-based theory of elasticity for students in mechanical, civil, aeronautical and biomedical engineering and materials and earth science.

These notes are based on a one-quarter (i. e. very short) course in fluid mechanics taught in the Department of Mathematics of the University of California, Berkeley during the Spring of 1978. The goal of the course was not to provide an exhaustive account of fluid mechanics, nor to assess the engineering value of various approxima­ tion procedures. The goals were: (i) to present some of the basic ideas of fluid mechanics in a mathematically attractive manner (which does not mean "fully rigorous"); (ii) to present the physical back­ ground and motivation for some constructions which have been used in recent mathematical and numerical work on the Navier-Stokes equations and on hyperbolic systems; (iil. ) 'to interest some of the students in this beautiful and difficult subject.