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Models & Model development

Models & Model development. ThermoTech key-note lecture by Tore Haug-Warberg Department of Chemical Engineering NTNU December 4, 2003. What is a model ?.

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Models & Model development

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  1. Models & Model development ThermoTech key-note lecture by Tore Haug-Warberg Department of Chemical Engineering NTNU December 4, 2003

  2. What is a model ? The model (i.e. the abstract concept) is used virtually everywhere e.g. in: Organization theory, economy, politics, planning, computer science, mathematics, physics, psychology, ... Several of these disciplines are represented in this room, and we should really look for a common definition to secure the planning of the ThermoTech project!

  3. Definitions Law: Regularities existing in objects and events - both observed and posited. Theory: Postulation system from which laws are deducible as theorems. Model : Set of constitutional equations turning a theory into a closed equation hierarchy. Gravity 2nd law

  4. Examples (I) Definitions are OK but examples are some-times better. Let’s have a closer look at the ideal gas (this is the most unifying non-trivial concept I can think of).

  5. Ideal gas (PV=NRT) Law : R. Boyle (1627-91), J. Charles (1746-1823) and A. Avogadro (1778-1850). Theory: J. C. Maxwell (1831-79), L. Boltzmann (1844-1906) and J. W. Gibbs (1839-1903) => statistical mechanics Model : L. Tisza (1961)

  6. Ideal gas law The works of Robert Boyle (1627-91), Jaques Charles (1746-1823) and Amedo Avogadro (1778-1850) indicated that PV=NRT is a good approximation for typical gases like air and air components, This investigation took about 150 years of pondering and experimental work!

  7. Ideal gas theory Statistical mechanics was founded by James Clerk Maxwell (1831-79), Ludwig Boltzmann (1844-1906) and Josiah Willard Gibbs (1839-1903): Ideal gas is reached by setting: U=0 (model)

  8. Ideal gas model Laszlo Tisza formulated in 1961 the Gibbsian thermodynamics as 4 postulates. Within this framework it can be shown that any pV equation-of-state must be on the form p=f(N/V,T). Hence, the simplest conceivable model is p=a(N/V)T. Note that parameter a cannot be resolved by thermodynamic theory alone => measurements (instantition problem)!

  9. Examples (II) James Clerk Maxwell formulated in 1876 the theory of electromagnetism which in fact is a closure (no models needed)

  10. Examples (III) Fluid mechanics: Constitutional models:

  11. Examples (IV) Thermodynamics phase equilibrium: Saul-Wagner 235-parameter model for water and steam:

  12. Paradigm A model can be “anything” from a simple statement U=0 to a set of equations with hundreds of parameters. The more advanced a theory is, the less complex the model needs to be: This follows from the requirement that

  13. Conclusion In mathematical “modeling” it is important to know where the theory stops and the modeling starts, and what are the assumptions and parameters: Constitutional models Assumptions Theory Simplification Parameters Simulation model Closure

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