COMP155Computer SimulationOctober 13, 2008Odum’s Energy Diagrams Developed in context of Ecological Sciences Systems are modeled by the storage and by the storage and transformation of energy in the systemmajority of today’s figures are borrowed from this book.Modeling Ecosystems Odum introduced a graphical model to support the expression of ecosystem modelsA Simple Systema) examples of water tanks storing waterb)energy systems diagramb)energy systems diagramc) growth of storage after starting with an initially small valueSimulation of Dynamic Systemsdiagram mathematics programThis is an example of“Euler Integration”Equivalent Stella ModelSymbolic EquivalentsEnergy System ComponentsEnergy Laws 1stlaw: Conservation of Energy energy flowing into a system must be accounted for in outflows or in storage within the system 2ndlaw: Increasing Entropy dispersed energy cannot do any more work and leaves the system degradedheat sink represents lose of degraded energyEnergy PathwaysEnergy Pathways Since everything (including information) has some available energy associated with it, there is energy flow on all pathwaysFlows are pushed by forcesFlows are pushed by forces physical force, chemical concentration, voltage 2 a force come from outside system (source) or from inside system (storage)Flow of Material Materials flow on some pathways, but not allFlow of Money Money generally circulates in the opposite direction from energy and materialsStorage Flows must all be of same type typical use energystorage materials storageInteractions (Production Process) Interactions are used to combine different types of things to produce something newInteractionsAmplifier Constant gain amplifiers have a high energy source, and a low energy control signal. Example: a voice into a microphone is a low energy control signal, electrical power is the high energy sourceAmplifier reproduction:  low energy control: number of rabbits high energy source: available foodExchangeLoop-limited Converter The loop-limited converterrepresents a subsystem in which the amount of material being recycled ismaterial being recycled islimited Because the recycling limits the production, output diminishes as input increases examples: enzymes, catalystsLoop-limited ConverterComposite Symbols Consumer, Producer, Box and Switch are composite symbols may or may not show internal structureproducer miscellaneous boxconsumer switchExample Producersproduction as transformation of one inputproduction as a product production as a product of two inputsproduction with autocatalytic use of two inputsExample Consumersconsumption as transformation of one inputConsumption as a product of two inputsof two inputsconsumption with autocatalytic use of two inputsExample SwitchesQuantifying Models Add numbers (or equation) to flows on energy diagrams to quantify the modelthis represents the system in a steady state(flows are constant)Variable Flows Variable flows are indicated by equationsDiagrams to Equations Differential equations can be read directly from the diagramsQKJdtdQ1−=Diagrams to EquationsRKJR0−=KRKGKJdtd 543−−+= GKRKdtdG21−=Converting to Stella: example 1one stock, two flowsInflow: constant Joutflow: influenced by store Q and constant K1Stella Model for Tankinflow: Joutflow: K1*Qequations for Q setup by StellaConversion to Stella: example 2Conversion to Stella: example 2Conversion to Stella: example 3Conversion to Stella: example 3Conversion to Stella: example 3Summary Energy Notation:  focused on transformations and store: natural components in ecological scienceSystem DynamicsSystem Dynamics focused on stocks and flows less obvious meaning easier translation to implementationTransformity (next time?)transformity: then amount of energy of one type required to make one joule of another typeof another