ExponentialDecline

Exponential decline of connected stock

Diagram

Information

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ExponentialDecline will drain the connected stock into a sink with infinite capacity at a rate that is determined at any time as the product of the current amount in the connected stock and the fractional rate given. The rate can either be given as a constant parameter fractionalRate or as a real input u, making it variable in time.

Notes

By default it is assumed, that the rate given is a continously compounding rate (isCCR = true). If this is not case, the rate will be converted using the →ForceOfInterest converter.

The effective rate of decline(e.g the product of the rate and amount in stock) must never be negative, as filling the connected stock is prohibited. Should the rate of outflow from the stock become negative, it will be set to zero.

Exponential decline processes have a constant half-life (e.g., the time it takes to to shrink by 50%) which can be found by dividing log(2) ≈ 0.69 by the continuously compounding fractional rate (or by log(1+rate) if the rate is not a continuously compounding rate).

Parameters (3)

fractionalRate	Value: unspecified Type: Rate (1/s) Description: Constant fractional rate to be used if chosen
isCCR	Value: true Type: Boolean Description: = true, if the factional rate given is assumed to be a continuously compounding rate else the rate will be converted
hasConstantRate	Value: false Type: Boolean Description: = true, if the constant fractional rate is used instead of the real input u

fractionalRate

Value: unspecified

Type: Rate (1/s)

Description: Constant fractional rate to be used if chosen

isCCR

Value: true

Type: Boolean

Description: = true, if the factional rate given is assumed to be a continuously compounding rate else the rate will be converted

hasConstantRate

Value: false

Type: Boolean

Description: = true, if the constant fractional rate is used instead of the real input u

Connectors (5)

	y	Type: RealOutput Description: Rate information
	y1	Type: RealOutput Description: Rate information
	y2	Type: RealOutput Description: Rate information
	massPort	Type: FlowPort Description: Inflow to or outflow from connected stock
	u	Type: RealInput Description: Fractional rate given as exogenous input

Components (5)

	decreasing	Type: ProportionalTransition Description: Rate of transition is proportional to the amount in stock A
	cloud	Type: Cloud Description: System boundary
	parFractionalRate	Type: ConstantConverter Description: Constant rate (optional)
	indicatedRate	Type: PassThrough Description: Indicated fractional rate
	convertedRate	Type: ForceOfInterest Description: Continuously compounding rate