A digital laboratory for the study of the evolution of chains of Open Atwood Machines (OAMs).
To the left is a screen grab of the main panel of OamLab. A selection of chains of HOAMs are shown in a kind of evolutionary horse race. Each circle, called a HOAM, represents a species of organism, and the collection of all organisms in the chain represent a trophic chain. The apex predators are to the far left, and the primary producers are at the far right. Each predator/prey interaction is controlled by a gene. The power-efficiency Goldilocks curve is the same for all such interactions. However, each interaction is located on a different part of the curve, so the power and efficiency of each chain is determined by the genes of each organism.
The yellowed circles represent the portion of the chain at which a current predator/prey interaction is currently in progress. When two halves of an OAM come together in this fashion, they form an OAM. The set of genes in predator and prey determine the speed and efficiency of transfer of still useful energy from the prey HOAM to the predator HOAM, and on down the chain to the next interaction. The set of genes in the entire chain determine the overall speed and efficiency of the trophic chain. Using fitness criteria based on speed, efficiency, or both, the most effective chains are preserved for the next horse race, and the least effective chains are discarded. Ultimately, the system converges to operate at efficiency of 0.62, the maximal point of the associated power-efficiency curve.
This is the original concave-downwards curve from the paper by H.T. Odum and R.C. Pinkerton of 1955. I now refer to such curves, having maximum power at an intermediate level of efficiency, as Goldilocks curves.
I realize that this is a rather bizarre approach - to use the dynamics of Atwood's Machine to represent the dynamics of a predator/prey interaction. But, H.T.Odum's view was that such Goldilocks curves are ubiquitous, and I reasoned that, as a test of his theories, any such Goldilocks curve will do. Since I know the mechanics of Atwood's Machine, that one was the best one to use. So, an HOAM is a half of an open Atwood Machine. Two halves, when brought together, form a single open Atwood Machine for which the correct dynamics can be applied.
In later studies, I have come to the conclusion that Odum's views on the importance of such power-efficiency curves is correct, and their ubiquity is correct, but NOT in the form of concave-downwards curves as shown in his paper of 1955, but as loops.
OamLab_V1.10.nlogo - This is the OamLab application, which will download if you click on the name. NetLogo is an interpreted language. The interpreter can be downloaded from Northwestern University, from this site here. OamLab was developed using NetLogo version 5.0.5. It may operate correctly on more recent releases.
It is also available from the NetLogo Modeling Commons site, or the OpenABM site:
You can download a number of files that explain the Newtonian mechanics of Atwood's Machine, and the operation of the OamLab application.
170330 NTF High-Level Design - OAM Lab R5.PDF - This is the closest I have to user documentation. It is a high level design document that was updated after the design was completed.
150101 NTF Atwood's Machine R4.PDF - In this diary note I investigate the Newtonian mechanics associated with Atwood's machine.
150418 NTF Three Shapes of AM Revisited R2.PDF - In this diary note I investigate the nature of the Goldilocks curves associated with the Atwood's Machine. It seems that there are two such Goldilocks curves. One exhibits maximum power at efficiency of 0.5, while the other exhibits maximum power at efficiency of 0.62. OamLab efficiency converges to an efficiency of 0.62. A third potential curve is NOT a Goldilocks curve (with maximum that is not too hot, and not too cold), and does not seem to be associated with any persistent dynamics.
151224 NTF ICBT and PowEff R7.PDF - In this note I do a rather "brute force" review of all possible combinations of power and efficiency inputs to generate Goldilocks curves. An example of a Goldilocks loop is shown to the right. The vast majority of Goldilocks curves form loops somewhat similar to this, rather than concave-downwards humps as originally shown in Odum's paper. I suspect the difference arises when you include friction in the analysis, which I did not do when looking at the Newtonian mechanics of Atwood's Machine. I should do that at some point.
Last Updated: April 2017