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How much complexity is too much?. “you should try to make things as simple as possible, but not too simple” A. Einstein. “All modeling is a gross simplification of the real system.” G. Whelan. “Don’t work any harder than you have to.” K. Castleton. Talking Points.

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## How much complexity is too much?

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**How much complexity is too much?**“you should try to make things as simple as possible, but not too simple” A. Einstein “All modeling is a gross simplification of the real system.” G. Whelan “Don’t work any harder than you have to.” K. Castleton**Talking Points**• Who is Karl Castleton and “What does he do?” • The ADVECTIVE, DISPERSIVE, and DECAY equation. • Intuition about the system • Intuition about the equation • Semi-Analytical techniques • Numerical techniques • Conclusions**Who is Karl Castleton**• Mesa State Graduate: A.A.S. 1987, B.S. 1992 Computer Science and Mathematics • Washington State University: M.S. Computer Science 1997 • Works at Pacific Northwest National Laboratory • Master Project solved the advective, dispersive, decay equation by three different methods**The “Equation”**• Used in Civil Engineering, Environmental, Pharmaceutical, System Biological modeling • Is a partial differential equation • A number of analytical solutions for simplified cases • Flow, spreading, and degrading**Intuition about the system**Dz Uy Ux Ux C Uy Dx Dx Dz**Intuition about the equation**• Plug flow • Spreading in three dimensions • Degradation, decay within the cell • Simplification can yield analytical results**Semi-Analytical Techniques**• Take the mathematics as far as it can go and then use a computer to put you over the top. • Reduce the model to a system that has an analytical result for instantaneous release. • Convolute the instantaneous release with input forcing function.**Numerical Techniques**• Just implement the equation • “Easy” to implement • Code can be very close to equation • Can consume a lot of computer resources • Does allow for a variety of values**Conclusion**• There are many ways to solve a modeling question • Use no more or less than you need • Do not always use the same tool/technique • Do not work any harder than you have to.

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