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AuthorParker, David F. author
TitleFields, Flows and Waves [electronic resource] : An Introduction to Continuum Models / by David F. Parker
ImprintLondon : Springer London : Imprint: Springer, 2003
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Descript XII, 270 p. 17 illus. online resource


Many phenomena in the physical and biological sciences involve the collective behaviour of (very large) numbers of individual objects. For example, the beยญ haviour of gases ultimately concerns the interacting motions of uncountably many atoms and molecules, but to understand flow in nozzles, around aircraft and in meteorology it is best to treat velocity and density as continuous funcยญ tions of position and time and then to analyse the associated flows. Although modern electronics involves ever smaller components, even the semiconducยญ tor devices used widely in electronic communications and in digital processing involve collective phenomena, such as electric currents and fields, which are continuously varying functions of position and time. Diffusion and reaction between various chemical constituents, the growth and spread of biological orยญ ganisms and the flow of traffic on major highways are all phenomena which may be described and analysed in terms of fields and flows, while sound, light and various other electromagnetic phenomena involve both fields and waves. Treating these using a continuum model, which does not attempt to trace the motion and evolution of individual objects, often gives good predictions. The mathematical concepts and techniques which underlie such treatments are the subject of this book. This book is designed as a first introduction to the use of mathematical techniques, within continuum theories


1. The Continuum Description -- 1.1 Densities and Fluxes -- 1.2 Conservation and Balance Laws in One Dimension -- 1.3 Heat Flow -- 1.4 Steady Radial Flow in Two Dimensions -- 1.5 Steady Radial Flow in Three Dimensions -- 2. Unsteady Heat Flow -- 2.1 Thermal Energy -- 2.2 Effects of Heat Supply -- 2.3 Unsteady, Spherically Symmetric Heat Flow -- 3. Fields and Potentials -- 3.1 Gradient of a Scalar -- 3.2 Gravitational Potential -- 3.3 Continuous Distributions of Mass -- 3.4 Electrostatics -- 4. Laplaceโ{128}{153}s Equation and Poissonโ{128}{153}s Equation -- 4.1 The Ubiquitous Laplacian -- 4.2 Separable Solutions -- 4.3 Poissonโ{128}{153}s Equation -- 4.4 Dipole Solutions -- 5. Motion of an Elastic String -- 5.1 Tension and Extension; Kinematics and Dynamics -- 5.2 Planar Motions -- 5.3 Properties of the Wave Equation -- 5.4 Dโ{128}{153}Alembertโ{128}{153}s Solution, Travelling Waves and Wave Reflections -- 5.5 Other One-dimensional Waves -- 6. Fluid Flow -- 6.1 Kinematics and Streamlines -- 6.2 Volume Flux and Mass Flux -- 6.3 Two-dimensional Flows of Incompressible Fluids -- 6.4 Pressure in a Fluid -- 6.5 Bernoulliโ{128}{153}s Equation -- 6.6 Three-dimensional, Incompressible Flows -- 7. Elastic Deformations -- 7.1 The Kinematics of Deformation -- 7.2 Polar Decomposition -- 7.3 Stress -- 7.4 Isotropic Linear Elasticity -- 8. Vibrations and Waves -- 8.2 Guided Waves -- 8.3 Love Waves in Elasticity -- 8.4 Elastic Plane Waves -- 9. Electromagnetic VVaves and Light -- 9.1 Physical Background -- 9.2 Waveguides -- 10. Chemical and Biological Models -- 10.1 Diffusion of Chemical Species -- 10.2 Population Biology -- 10.3 Biological Waves -- Solutions

Mathematics Mathematical analysis Analysis (Mathematics) Partial differential equations Applied mathematics Engineering mathematics Physics Continuum physics Mechanics Mathematics Analysis Applications of Mathematics Physics general Partial Differential Equations Classical Continuum Physics Mechanics


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