Mathematical Models in Photographic Science

ISBN-13: 9783540442196 / Angielski / Twarda / 2002 / 184 str.

Avner Friedman; Martin H. Schuck; A. Friedman

Opis

th Although photography has its beginning in the 17 century, it was only in the 1920 s that photography emerged as a science. And as with other s- ences, mathematics began to play an increasing role in the development of photography. The mathematical models and problems encountered in p- tography span a very broad spectrum, from the molecular level such as the interaction between photons and silver halide grains in image formation, to chemical processing in ?lm development and issues in manufacturing and quality control. In this book we present mathematical models that arise in today s p- tographic science. The book contains seventeen chapters, each dealing with oneareaofphotographicscience.Eachchapter, exceptthetwointroductory chapters, begins with general background information at a level understa- able by graduate and undergraduate students. It then proceeds to develop a mathematical model, using mathematical tools such as Ordinary Di?erential Equations, Partial Di?erential Equations, and Stochastic Processes. Next, some mathematical results are mentioned, often providing a partial solution to problemsraisedby the model.Finally, mostchaptersinclude problems.By the nature of the subject, there is quite a bit ofdisparity in the mathematical level of the various chapters."

Recenzje

This book provides an interesting and well documented presentation of mathematical topics related to photographic sciences. [...] This is an attractive and easy to read book, which is characterized by a valuable (in the reviewer¿s opinion) feature: each chapter covers the whole path from the phenomenological analysis and interpretation of the real system, to modeling, statement of problems related to the application of models, an outline of qualitative analysis, and finally to perspectives and open problems.

This book is recommended to applied mathematicians interested in industrial mathematics and is intended for applications and the development of mathematical methods for problems generated from technology. It is also a good text for advanced university courses on mathematical modeling to be joined to courses on computational methods.

Applied mathematicians will find a description of open problems which are definitely challenging even for experienced mathematicians.

MathSciNet 2004. Nicola Bellomo (I-TRNP)

Spis treści

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.