Introduction toSTELLA

Structural Thinking Experiential LearningLaboratory with Animation

Commerical ProductsGraphical Interface Differential Equation Solvers (GIDES)

PStella< Free run-time version

PBerkeley Madonna< Free run-time version< Solves “stiff” differential equations

PVisSim (Mathcad)PSimulink (Matlab)PSimilePModel Maker

Stella InterfaceStella “Layers” – Modeling

PConstructModel usingBuilding Blocks,Tools, Objects

POutputs

Layer Navigation

Map/Model ToggleChange to P2 (or else!)

Run Controller

Stella InterfaceStella “Layers” – Mapping

PTextPOutput Tables

and GraphsP Input using

Slides andDials

PPicturesPQuick Time

Movies

Stella InterfaceStella “Layers” – Equation

P Initial Values ofStocks

PConnectorInformation

PDifferentialEquationsRepresentingthe TimeDependence ofStocks

Stella InterfaceMenu / Icons

Stella InterfaceBuilding Blocks – Stocks

Value Undergoing a Change

Stella InterfaceBuilding Blocks – Flow

Change of Stock with Respect to Time

Stella InterfaceBuilding Blocks – Converter

ConstantsTransformation Equations

Stella InterfaceBuilding Blocks – Connectors

Links Building Blocks

Stella InterfaceTools – Hand

General Purpose Editing ToolCursor Pointer

Stella InterfaceTools – Dynamite

Delete (No “Undo”)

Stella InterfaceObjects – Graph Pad

Graphing Results

Stella InterfaceObjects – Table Pad

Spreadsheet-like Table of Results

Solving of Differential EquationsTaylor Series

Solving of Differential EquationsEuler Method

First 2 terms

Solving of Differential EquationsRunge-Kutta 2

First 3 Terms

Solving of Differential EquationsRunge-Kutta 4

First 5 Terms

Simple Model – Falling CalculatorSystem

y = heightyN = velocity = (acceleration)(time)yO = acceleration = g = 9.8 m s-2

Simple Model – Falling CalculatorStella Model

Simple Model – Falling CalculatorStella Model – Equation Layer

dCdt

kC

C Ckt

o

= −

= +

2

1 1

Simple Model – Falling CalculatorStella Model – Accuracy

PAir FrictionPBounce

Chemical KineticsSure looked like a natural fit to me!!

Kinetics ModelDimerization of Cyclopentadiene2nd Order Diels-Alder Reaction

2

Kinetics Model

Michaelis-MentonLen Soltzberg (Simmons College)

E + S º (ES)

(ES) 6 P + E

Oscillating ReactionsCriteria

PTwo or more coupled reactionsPAutocatalytic

Oscillating ReactionsBriggs-Rauscher

PH2O2

PKIO3 and H2SO4

PHOOCCH2COOH, MnSO4, starch

~15 s for each cycle

Oscillating ReactionsBelousov-Zhabotinskii

P 18 reversible stepsP 21 different chemical species

BrO3- + HBrO2 + H3O+ 6 2 BrO2 + 2 H2O

2 BrO2 + 2 Ce3+ + 2 H3O+ 6 2 HBrO2 + 2 Ce4+ + 2 H2O

A + Y 6 X + PX + Y 6 2PA + X 6 2X + 2Z2X 6 A + PB + Z 6 (f/2) Y

whereA = BrO3

-

X = HBrO2Z = Ce4+

P = HOBrB = organicY = Br -

Oregonator by Len Soltzberg (Simmons College)

Other ApplicationsRod Schluter (Formerly of CofC)

Acid/Base Equilibrium

H+ + OH- 6 H2O

D Tu

xe

dxD x( / )θ =−∫

313

3

( )

( )[ ]

U U RTD

C R Du

e

S R D e

A U RT e D

v u

u

u

− =

= −−

⎛⎝⎜

⎞⎠⎟

= − −⎡⎣⎢

⎤⎦⎥

− = − −

−

−

0

0

3

3 4 31

343

1

3 1

ln

ln

Other ApplicationsDebye Theory for Monatomic Crystals