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Visualization of Fields and Applications in Engineering is suitable for academic use and to serve as a source of reference. It will appeal to those who work in the engineering and science professions or in pursuit of academic training/ research.
1.1 A General View.
1.2 Historical Development and Progress in Visual Science.
1.3 Scientific Visualization Philosophy, Techniques and Challenges.
2 Field Descriptions and Kinematics.
2.1 Lagrangian/Eulerian Description and Transformation.
2.2 Curvilinear Coordinates.
2.3 Field Kinematics and Visual Attributes.
3 Field Model, Representation and Visualization.
3.1 Field Models and Concepts.
3.2 Scalar Fields and Representation.
3.3 Vector Fields and Representation.
3.4 Vector Icons and Classifications.
3.5 Scalar Potential.
3.6 Vector Potential.
3.7 Vector Field Specification.
3.8 Tensor Contraction and Transport Process Visualization.
3.9 Multiple Fields.
4 Complex Analysis and Complex Potentials.
4.1 Complex Variables/Functions and Applications.
4.2 Complex Analysis and Cauchy–Riemann Equation.
4.3 Differentiation of Complex Function.
4.4 Integration of Complex Functions.
4.5 Visualization of Complex Potentials.
4.6 Example 4.1a Visualization of Heat and Fluid Transport in a Corner.
5 Field Mapping and Applications.
5.2 Mapping of Euclidean Geometry.
5.3 Inversion Mapping.
5.4 Mapping with Complex Functions.
5.5 Conformal Mapping and Applications.
5.6 Hodograph Method and Mapping.
5.7 Hodograph Representations and Applications.
5.8 Example 4.1b Mapping of Field Patterns and Image Warping.
6 Tensor Representation, Contraction and Visualization.
6.2 Development of Tensor Visualization Techniques.
6.3 Tensor Description and Representation.
6.4 Tensor Decomposition and Tensor Rank Reduction.
6.5 Visualization of Symmetric Tensors.
6.6 Visualization of Antisymmetric Tensors.
6.7 Example: 4.1c Convective Momentum Flux Tensor Visualization.
7 Critical Point Topology, Classification and Visualization.
7.2 Complex Analysis of Critical Point.
7.3 Critical Point Theory and Classification.
7.4 Example 4.1d Critical Point Topology.
7.5 Singular Point Visualization and Mapping.
7.6 Example 7.1 Mapping of a Point Source.
8 Engineering Application Examples.
8.1 Example 8.1: Torsion of a Square Beam.
8.2 Example 8.2: Bending of a Cantilever Beam Subject to a Point Load.
8.3 Example 8.3: Squeezing Flow and Vorticity Transport.
8.4 Example 8.4: Groundwater Flows in an Anisotropic Porous Medium.