Protection of the Environment: Pollution Spread – Mathematical Models and Optimization

1. General Modeling Methods 1.1. Pollutant Transport 1.2. Modeling Recommendations 2. Optimization 2.1. The Effect Function 2.2. The Objective Function 2.2.1. The Gradient of the Objective Function 2.3. Constraints 2.4. Algorithmic Considerations 3. Three Important Transport Modes 3.1. Advection and Convection 3.2. Diffusion 3.3. Dispersion 3.4. Combinations 3.4.1. Numerical Considerations 4. Compartment Models 4.1. The Standard Model 4.1.1. Mass Conservation and Nonnegativity 4.1.2. Numerical Considerations 4.2. Metabolism 4.3. Examples 4.3.1. Ecosystems and Food webs 4.3.2. Individual based Chemokinetic Models 4.3.3. Age-Classes 5. Toxicology 6. Conclusions Acknowledgments Glossary Bibliography Biographical Sketch