Visualization of Fields and Applications in Engineering 1st Edition by Stephen Tou ISBN 978-0470973974 0470973974

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Product details: 

ISBN 10:  0470973974

ISBN 13: 978-0470973974

Author: Stephen Tou

Driven by advances in computer technology, engineering analysis has developed rapidly and extensively in recent times; Visualization of Fields and Applications in Engineering presents the basic techniques for tensor field visualization and mapping of engineering data. Focusing on the fundamental aspects of post processing databases and applications outputs, the author explores existing theories and their integration in tensor field visualization and analysis. The subject covers fundamental theories through to integrated, multi-disciplinary technologies with practical applications in engineering, computer /general sciences.

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.

Offers a unique engineering approach to basic techniques for tensor field visualization and mapping
Collates together material currently disseminated throughout the literature into one accessible point of reference
Presents examples with applications beyond and across many disciplines.

Table of contents: 

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: 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: 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: 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
     7.3.2 Antisymmetric Tensor
     7.3.3 Asymmetric Tensor
    7.4 Example: Critical Point Topology
    7.5 Singular Point Visualization and Mapping
    7.6 Example: Mapping of a Point Source

8. Engineering Application Examples
    8.1 Example: Torsion of a Square Beam
    8.2 Example: Bending of a Cantilever Beam Subject to a Point Load
    8.3 Example: Squeezing Flow and Vorticity Transport
    8.4 Example: Groundwater Flows in an Anisotropic Porous Medium

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Tags: Stephen Tou, Visualization of Fields, Applications in Engineering