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Mathematical Models in Photographic Science

  • Kartonierter Einband
  • 196 Seiten
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th Although photography has its beginning in the 17 century, it was only in the 1920's that photography emerged as a science. And ... Weiterlesen
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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.

This is the only comprehensive monograph on the topix

Has textbook potential

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.


Titel: Mathematical Models in Photographic Science
EAN: 9783642629136
ISBN: 364262913X
Format: Kartonierter Einband
Herausgeber: Springer Berlin Heidelberg
Genre: Mathematik
Anzahl Seiten: 196
Gewicht: 306g
Größe: H235mm x B155mm x T10mm
Jahr: 2012
Auflage: Softcover reprint of the original 1st ed. 2003

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