Gérald Gurtner

Physics, Networks and Agent-Based Models

Physical networks

Most of the results presented here can be found in these two papers and my phd thesis.

My background in physics have involved a lot of work revolving around networks. In particular, I have studied networks transporting physical quantities like charge, mass or forces.

Why?

Well, because transport networks are organized to their function in nature. But linking their form to their function in not always obvious. Consider this issue. Your blood vessels — essentially, pipes — form a network which is able to transport vital nutriments from their source (let’s say the lungs) to their different destinations (you organs). Now, the sap of trees is flowing through pipes forming a network able to transport vital nutriments from their sources (let’s say the roots) to their destination. It sounds similar doesn’t it? Same function, same form? Well, then why trees have a reticulated network in their leaves — i.e. a network where the branches divide and merge — whereas your blood network is a branched network — without merging?

The quick answer is that these two types of networks do not meet the same requirements. Indeed, it is possible to show (add ref…) that a reticulated network is not optimal from the point of view of the energy dissipation due to the passage of liquid through the veins/channel/pipes/whatever. Why does this form has been selected through evolution then? The answer is not straightforward, but one can for instance think that the leaves are quite fragile. Thus, if they lose a vital part (near to the branch), all of the rest will die. This is true for humans too, but losing a blood vessel near the source — the heart — is much harder, because it is well protected. Hence, the leaves seem to have made a compromise between optimization and robustness — a compromise that the mammals did not do because their vessels were more protected.

This illustrates the fact that network are a results of their environment, and that their structure can meet different needs.

Next: How?

 

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