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The Sentinel Method and Its Application to Environmental Pollution Problems (Mathematical Modelling)

De (autor) , ,
Notă GoodReads:
en Limba Engleză Hardback – 1997
Many environmental problems contain incomplete data in the initial or boundary conditions. How do we solve problems for which some of the initial and/or boundary conditions are unknown? Using a new technique, the sentinel method, this book answers these questions and others as they pertain to inverse problems in environmental pollution, such as pollution of underground and surface waters, thermal pollution, and air pollution.
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Specificații

ISBN-13: 9780849396304
ISBN-10: 0849396301
Pagini: 224
Ilustrații: 18 tables and 542 equations
Dimensiuni: 155 x 247 x 19 mm
Greutate: 0.51 kg
Ediția: 1
Editura: CRC Press
Seriile Mathematical Modelling , CRC Mathematical Modelling


Public țintă

  • Mathematicians
  • Environmental scientists
  • Civil engineers working in water pollution

Cuprins

Introduction
Physical Motivation
Historical Background
Description of the Method
Identification of Pollution in an Aquifer
Modelling of Pollution Transport in an Aquifer
A Sentinel Attached to Each Parameter
Some Examples of Similar Problems
Flow Rate
Numerical Experiments
Sentinels and Pseudo-Inverse
Identification of Pollution in a Lake
Pollution of a Lake
Sentinels
Numerical Experiment
Adjoint State
Numerical Details
HUM Method
Time and Space Discretization
Optimal Emplacement of Sensors
Rectangular Domain
Physical Motivations
Modelling the Physical System
Exact Solution of the Direct Problem
Sentinels for Inversion
Direct Method
Numerical Experiments
Sensitivity to the Size of the Observatory
Sentinels in a River
Oxygen Kinetics and Polluted Water
Convection-Dispersion-Reaction Equation
Exact Solution of the State Equation
Sentinels for a River (Evolution Regime)
Numerical Experiments
Our First Nonlinear Problem
Linear Case
Non-Linear Case
Non-Linear Problems
Position of the Problem
Sentinels of the Linearized Problem
Building the Generalized Inverse
Example
Dispersion Coefficients
Motivation
Linearized System
Linearized System Sentinels
Non-Linear Problem
Numerical Results
Position of a Source
Position of the Problem
Linearization
Sentinels of the Linearized Problem
Non-Linear Problem
Numerical Experiments
Unknown Position and Flow Rate
Sentinels of the Linearized Problem (1)
Sentinels of the Linearized Problem (2)
Moving Source
Recapitulation
Definitions
Inverse Problems
A Convergence Result
Gauss-Newton Method
Shallow Waters
The Movement of Tides: Saint-Venant Shallow Water Equations
Numerical Solution of Shallow Water Equations
Weak Formulation of the Problem
Reaction-Convection-Dispersion Equations
Sentinels
Appendix
Sentinels with a Given Sensibility and Duality
Duality
Existence of a Solution and Functional Spaces
References

Textul de pe ultima copertă

Inverse problems in pollution, where incomplete data forces the practitioner to work backwards from effects to determine causes, are a particularly challenging problem for environmental scientists and mathematicians. This useful guide explains how to solve inverse problems by measuring pollution concentration at a few points and - using the sentinel method - locate and identify pollutants, calculate the quantity of pollutant discharged, detect crises early, and more. This applications-oriented book also explains how to extend the method to other situations.