Visualization of Fields and Applications in Engineering -- Contents -- Preface -- 1 Introduction -- 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 -- 2.2.1 Polar Coordinate -- 2.2.2 Streamline (Flux Line) Coordinates -- 2.2.3 Potential-Stream Function Coordinates -- 2.3 Field Kinematics and Visual Attributes -- 2.3.1 Field Line Trajectory -- 2.3.2 Field Line Integral Curves -- 2.3.3 Field Lines, Material Lines and Path Lines -- 2.3.4 Streamlines (Flux Lines) -- 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 -- 3.4.1 Classification Based on Domain Configurations -- 3.4.2 Classification Based on Information Levels -- 3.4.3 Classification Based on Topological Skeleton -- 3.5 Scalar Potential -- 3.6 Vector Potential -- 3.7 Vector Field Specification -- 3.7.1 Helmholtz's Theorem -- 3.8 Tensor Contraction and Transport Process Visualization -- 3.8.1 Mechanical Energy Function and Heatfunction -- 3.8.2 Strain Energy Trajectory and Strain Function -- 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 -- 4.5.1 Trajectory Method -- 4.5.2 Method of Curvilinear Squares -- 4.5.3 Transfer Characteristics and Field Property Evaluation -- 4.6 Example 4.1a Visualization of Heat and Fluid Transport in a Corner -- 5 Field Mapping and Applications.

5.1 Introduction -- 5.2 Mapping of Euclidean Geometry -- 5.2.1 Congruent Mapping -- 5.2.2 Similitude Mapping -- 5.2.3 Affine Mapping -- 5.3 Inversion Mapping -- 5.3.1 Circle Inversion -- 5.4 Mapping with Complex Functions -- 5.5 Conformal Mapping and Applications -- 5.6 Hodograph Method and Mapping -- 5.6.1 Conjugate Hodograph -- 5.6.2 Hodograph -- 5.7 Hodograph Representations and Applications -- 5.7.1 Straight Boundaries -- 5.7.2 Free Surface -- 5.7.3 Special Field Patterns -- 5.7.4 Projectile Trajectory in Constant Force Fields -- 5.7.5 Motion Trajectory in Central Force Fields -- 5.7.6 Trajectory of Charged Particles in Uniform Magnetic Fields -- 5.8 Example 4.1b Mapping of Field Patterns and Image Warping -- 6 Tensor Representation, Contraction and Visualization -- 6.1 Introduction -- 6.2 Development of Tensor Visualization Techniques -- 6.2.1 Mohr's Circle -- 6.2.2 Tensor Field Line Trajectories (Lines of Principal Stress) -- 6.2.3 Isochromatics -- 6.2.4 Isoclines -- 6.2.5 Stress Trajectories -- 6.2.6 Slip Lines -- 6.2.7 Isopachs -- 6.3 Tensor Description and Representation -- 6.3.1 Tensor Icons and Classification -- 6.4 Tensor Decomposition and Tensor Rank Reduction -- 6.4.1 Strain Tensor and Stress Tensor -- 6.4.2 Rotation Tensor -- 6.4.3 Rate of Strain Tensor and Viscous Stress Tensor -- 6.4.4 Vorticity Tensor -- 6.4.5 Tensor Contractions: Tensor Vector on a Reference Plane -- 6.4.6 Tensor Contractions: Tensor Vector at a Point -- 6.5 Visualization of Symmetric Tensors -- 6.5.1 Tensor Invariants -- 6.5.2 Tensor Transformation -- 6.5.3 Principal States and Eigenanalysis -- 6.5.4 Hybrid Method of Tensor Visualization -- 6.6 Visualization of Antisymmetric Tensors -- 6.6.1 Vorticity Concepts and Dynamics -- 6.6.2 Forced Vortex -- 6.6.3 Free Vortex -- 6.6.4 Vortices Transport and Vorticity Function.

6.7 Example: 4.1c Convective Momentum Flux Tensor Visualization -- 7 Critical Point Topology, Classification and Visualization -- 7.1 Introduction -- 7.2 Complex Analysis of Critical Point -- 7.3 Critical Point Theory and Classification -- 7.3.1 Symmetric Tensor: [∇V] = [∇V]T -- Im1 = Im2 = 0 -- 7.3.2 Antisymmetric Tensor: τii = 0, i = j -- τij = -τji, i ≠ j -- 7.3.3 Asymmetric Tensor -- 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 -- References -- Index.