Mathematical Models in Photographic Science

This book presents mathematical models that arise in current photographic science. The book contains seventeen chapters, each dealing with one area of photographic science, and a final chapter containing exercises. Each chapter, except the two introductory chapters, begin with general background information at a level understandable by graduate and undergraduate students. It then proceeds to develop a mathematical model, using mathematical tools such as ordinary differential equations, partial differential equations, and stochastic processes. Next, some mathematical results are mentioned, often providing a partial solution to problems raised by the model. Finally, most chapters include open problems. The last chapter of the book contains "Modeling and Applied Mathematics" exercises based on the material presented in the earlier chapters. These exercises are intended primarily for graduate students and advanced undergraduates.

Contenu

1. History of Photography.- References.- I. The Components of a Film.- 2. An Overview.- 3. Crystal Growth - Ostwald Ripening.- 3.1 The Model.- 3.2 Mathematical Analysis.- 3.3 A More General Model.- 3.4 Open Problems.- 3.5 Ostwald Ripening in a Colloidal Dispersion.- 3.6 Exercises.- References.- 4. Crystal Growth-Sidearm Precipitation.- 4.1 The Physical Model.- 4.2 Mathematical Model for CSTR Mixer.- 4.3 Mathematical Model for PFR Mixer.- 4.4 Mathematical Analysis.- 4.5 Open Problems.- 4.6 Exercises.- References.- 5. Gelatin Swelling.- 5.1 Introduction.- 5.2 A Mathematical Model.- 5.3 Mathematical Results.- 5.4 Open Problems.- References.- 6. Gelation.- 6.1 Introduction.- 6.2 The Model.- 6.3 Mathematical Analysis.- 6.4 Open Problems.- 6.5 Exercises.- References.- 7. Polymeric Base.- 7.1 Bending Recovery of Elastic Film.- 7.2 Viscoelastic Material.- 7.3 The Bending Recovery Function for t > tw.- 7.4 Exercises.- References.- II. The Role of Surfactants.- 8. Limited Coalescence.- 8.1 Introduction.- 8.2 The Model.- 8.3 Mathematical Results.- 8.4 Open Problems.- References.- 9. Measuring Coalescence.- 9.1 The Coalescence Problem.- 9.2 Introducing Chemiluminescent Species.- 9.3 Mathematical Results.- 9.4 Open Problems.- References.- III. Coating.- 10. Newtonian Coating Flows.- 10.1 The Mathematical Model.- 10.2 The Dynamic Contact Angle.- 10.3 Mathematical Results.- 10.4 Open Problems.- 10.5 Exercise.- References.- 11. Coating Configurations.- 11.1 An Extrusion Die.- 11.2 The Basic Model.- 11.3 Fluid Flow in the Slot.- 11.4 Design Problems.- 11.5 Exercise.- References.- 12. Curtain Coating.- 12.1 Reducing the Surface Tension.- 12.2 Measuring DST.- 12.3 Potential Flow Model of a Curtain.- 12.4 Time-Dependent Liquid Curtains.- 12.5 Open Problems.- 12.6 Exercises.- References.- 13. Shear Thinning.- 13.1 Motivation.- 13.2 Viscosity Divergence.- 13.3 Brownian Dynamics.- 13.4 Numerical Results.- 13.5 Future Directions.- References.- IV. Image Capture.- 14. Latent Image Formation.- 14.1 The Physical Model.- 14.2 Monte Carlo Simulation.- 14.3 An Alternative Approach.- References.- 15. Granularity.- 15.1 Transmittance and Granularity.- 15.2 Moments of the Transmission.- 15.3 Open Problems.- References.- V. Development.- 16. A Reaction-Diffusion System.- 16.1 The Development Process.- 16.2 A Mathematical Model.- 16.3 Homogenization.- 16.4 Edge Enhancement.- 16.5 Acutance.- 16.6 Open Problems.- 16.7 Exercises.- References.- 17. Parameter Identification.- 17.1 The Direct Problem.- 17.2 The Inverse Problems.- 17.3 A Solution to an Inverse Problem.- 17.4 Open Problems.- 17.5 Exercises.- References.