Equilibrium. Stable equilibrium (negative feedback)

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Presentation transcript:

Equilibrium

Stable equilibrium (negative feedback)

Unstable equilibrium (positive feedback),

At Equilibrium: Inflows=Outflows

80 gal/min 120 gal ???

Assume Equilibrium: Inflows=Outflows 80 gal/min 120 gal 80 gal/min

At Equilibrium: Inflows=Outflows 80 gal/min 120 gal 20 gal/min Is water level a)rising b)Falling c)Staying the same

At Equilibrium: Inflows=Outflows 80 gal/min 120 gal 20 gal/min Is water level a)rising b)Falling c)Staying the same

At Equilibrium: Inflows=Outflows 80 gal/min 120 gal 80 gal/min Is water level a)rising b)Falling c)Staying the same

At Equilibrium: Inflows=Outflows 80 gal/min 120 gal 80 gal/min Is water level a)rising b)Falling c)Staying the same

At Equilibrium: Inflows=Outflows 80 gal/min 120 gal 140 gal/min Is water level a)rising b)Falling c)Staying the same

At Equilibrium: Inflows=Outflows 80 gal/min 120 gal 140 gal/min Is water level a)rising b)Falling c)Staying the same

At Equilibrium: Inflows=Outflows Is water level a)rising b)Falling c)Staying the same =2 min 8 gal/min 20 gal ??=_________

At Equilibrium: Inflows=Outflows Is water level a)rising b)Falling c)Staying the same =2 min 8 gal/min 20 gal ??=_10 gal/min________

At Equilibrium: Inflows=Outflows Is water level a)rising b)Falling c)Staying the same =2 min 8 gal/min 16 gal ??=_________

At Equilibrium: Inflows=Outflows Is water level a)rising b)Falling c)Staying the same =2 min 8 gal/min 16 gal ??=__8 gal/min_______

At Equilibrium: Inflows=Outflows Is water level a)rising b)Falling c)Staying the same =2 min 8 gal/min 12 gal ??=_________

At Equilibrium: Inflows=Outflows Is water level a)rising b)Falling c)Staying the same =2 min 8 gal/min 12 gal ??=___6 gal/min_____

At Equilibrium: Inflows=Outflows Is pollutant level a)rising b)Falling c)Staying the same 8 ppm/yr 12 ppm =.2 (1/yr) ??=_________

At Equilibrium: Inflows=Outflows Is pollutant level a)rising b)Falling c)Staying the same 8 ppm/yr 12 ppm =.2 (1/yr) ??=__2.4 ppm/yr____

At Equilibrium: Inflows=Outflows Is pollutant level a)rising b)Falling c)Staying the same 8 ppm/yr ?? =.2 (1/yr) 8 ppm/yr What is the lifetime?

At Equilibrium: Inflows=Outflows Is pollutant level a)rising b)Falling c)Staying the same 8 ppm/yr ??= 40 ppm =.2 (1/yr) 8 ppm/yr What is the lifetime? Lifetime=1/(DecayConstant)=5 yr

Whenever the net flow = -k*stock you get exponential decay to zero** Summary (exponential decay/Goal seeking) Sometimes we like to use the concept of lifetime (decay time constant) instead of decay rate constant. Here k is the decay rate constant.

Whenever the net flow = inflow-k*stock you get exponential decay to a Goal, Xeq Summary (exponential decay/Goal seeking) The Goal is the value of X (the stock) that makes the net flow zero Inflow=outflow Inflow=k*stock at equilibrium Here X is any stock.

Ceq=Inflow*lifetime Ceq=Inflow/(DecayRateConstant) Outflow=Content/(lifetime) Outflow=DecayRateConstant*Content Summary (exponential decay/Goal seeking)