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A core Course on Modeling. Introduction to Modeling 0LAB0 0LBB0 0LCB0 0LDB0 [email protected] [email protected] P.14. Structural and quantitative confidence in the lantern model. Contents Scaffolding Correct qualitative behavior V arying cat.-I quantities

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A core course on modeling

A core Course on Modeling

Introductionto Modeling

0LAB0 0LBB0 0LCB0 0LDB0

[email protected]

[email protected]

P.14


  • Structuralandquantitativeconfidence in the lantern model.

  • Contents

  • Scaffolding

  • Correct qualitativebehavior

  • Varying cat.-I quantities

  • Plottinggraphsusing the analysis tab

  • Correct asymptoticbehavior

  • Correct singularities

  • Convergence


  • Scaffolding.

  • Build extra features in the model, not neededfor the calculation of the cat.-II quantities, but toinspect the validity of the model.

  • Lanterns:

  • brightnessdistribution over the road

  • differencebetween max and min intensity

try!

try!


  • Scaffolding.

  • Build extra features in the model, not neededfor the calculation of the cat.-II quantities, but toinspect the validity of the model.

  • Lanterns:

  • brightnessdistribution over the road

  • differencebetween max and min intensity

try!

try!


  • Scaffolding.

  • Build extra features in the model, not neededfor the calculation of the cat.-II quantities, but toinspect the validity of the model.

  • Lanterns:

  • brightnessdistribution over the road

  • differencebetween max and min intensity

try!

try!


  • Correct qualitativebehavior.

  • Varying cat.-I quantities. Examples:

dL=25 m; h=5.5 m; p  2.4 kW

dL=25 m; h=12 m; p  2.4 kW: higherlanterns, solessfluctuations

dL=15 m; h=12 m; p  2.4 kW: lanterns closer together: verylittlefluctuations

dL=15 m; h=3 m; p  1 kW: shorterlanterns, soless energy/m

( 1/15 < 2.4/25) – but more fluctuations


  • Correct qualitativebehavior.

  • Plottinggraphsusing the analysis-tab. Examples:

Both maxIntandminInt are proportionalto P.

Sotheirdifferencealso

shouldbeproportionalto p.

Tallerlanternscause more blending lessfluctuations

Lanternsfurther apart givelargerfluctuations, solargerdifferencebetweenmaxIntandminInt.


  • Correct asymptoticbehavior.

  • If the street is long enough (100m) comparedto the height of the lanterns (2 ... 32 m) we expecttosee the boundaryeffectsseparatedfrom the regularbehavior:

h=2 m

h=4 m

hardlyany flat region

flat region?

h=8 m

flat region

flat region

flat region

h=16 m

h=32 m


  • Correct singularities.

  • IfdL is very large comparedto h, we canignoreaddingcontributions of multiple lanterns.

  • The maximum intensitycanthenbecalculated as p/h2:

  • p = 8069.5 W

  • h = 9.9 m

  • p/h2 = 82.3 W/m2

  • ACCEL gives 84 W/m2.

  • OK because of

  • contribution of

  • otherlanterns.


  • Correct convergence.

  • Suppose we increase performance bytakingfewerlanternsinto account.

  • allowsto set # lanternsto taken into account.

Thisversion of the model


  • Correct convergence.

  • Suppose we increase performance bytakingfewerlanternsinto account.

  • How few lanterns is enoughforreliableresult depends on regime

dL=25 m; nr. neighbours = 0

dL=25 m; nr. neighbours = 2

dL=25 m; nr. neighbours = 3  no noticeabledifference, soleftand right 2 lanterns is enough.


  • Correct convergence.

  • Suppose we increase performance bytakingfewerlanternsinto account.

  • How few lanterns is enoughforreliableresult depends on regime

dL=1 m; nr. neighbours = 0

dL=1 m; nr. neighbours = 5

dL=1 m; nr. neighbours = 10

dL=1 m; nr. neighbours = 20: graphstill looks not smooth, we presumablyneed more lanterns.


  • Summary:

  • Scaffoldingmaybeusefulto help ascertain the convincingness of the model;

  • Qualitativebehavor: think of configurationsthatcaneasilybeunderstood;

  • Asymptoticbehavior: can we separate ‘boundaryeffects’ thatcanbe ‘reasonedaway’;

  • Singularbehavior: are there cases where we can do the math even without a computer;

  • Convergence: do we take enough terms, steps, ... .


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