The cat is out of the box!
I promise a thread 🧵when the paper gets accepted. It's about the thermodynamics of traffic flow near the critical density.
Next up is to show that the entropy of an urban network is the travel time!
1/n
The paper below by @jianxi_gao @LouisShekhtman and others reveals macroscopic emergent behavior in the Beijing urban network consistent with self-organized criticality. This changes everything.
pnas.org/doi/10.1073/pn…
Why? Because these observations support a 20-year-old conjecture by Nagel et al (2003) that traffic flow obeys the theory of gas-liquid phase transitions, possibly one of the best known theories in physics.
pubsonline.informs.org/doi/10.1287/op…
3/n
Therefore, near the critical density we will have power-law divergence behavior for most of the variables of interest and a fractal time-space network.
➡️ complex systems paradigm
@sfiscience
4/n
Nagel et al (2003) also note that to take advantage of the phase transition paradigm, one needs to know what is the control parameter; i.e. what is the interpretation of temperature T in the gas-liquid phase transitions:
5/n
The temperature was interpreted as the speed of vehicles in the two-fluid model of Prigogine and Herman (1979). Unfortunately, this does not produce fundamental diagrams that agree with observations (f=flow, rho=density):
6/n
In this paper I interpret the temperature as the **flow of vehicles**, based on the resemblance between the fundamental diagram of traffic flow in the liquid-gas coexistence curve for simple fluids. 77 fluids are presented below, along with the MFD for a few European cities:
7/n
This gives the following fundamental diagrams depending *only* on the order-parameter critical exponent β.
8a/n
The fit with data from UTD19 utd19.ethz.ch
8b/n
more fits with data from UTD19 utd19.ethz.ch
The values of the parameter 1.4<1/β<1.8 above are approximate and need further research. However, they give a strong indication that urban networks might be part of the Directed Percolation universality class, as suggested by @meeadsaberi @martikagv in pnas.org/doi/10.1073/pn…
10/n
Another possibility is that urban networks belong to the Manna universality class (1/β=1.577) describing systems systems naturally driven to the critical state: self-organized criticality.
en.wikipedia.org/wiki/Self-orga…
11/n
Yet another alternative, possibly not mutually exclusive with the above, is that urban networks belong to the #KPZ universality class (1/β=2) typically describing surface growth processes.
In the paper I show that this surface corresponds to Newell's traffic flow surface:
12/n
N(x,t) = Newell's traffic flow surface
= # of vehicles having past location x by time t
We already knew that traffic on a single link is in KPZ, even for multilane traffic including lane changes of course:
journals.aps.org/pre/abstract/1…
14/n: Scaling of traffic congestion
The data from the TTI urban mobility report (mobility.tamu.edu/umr/) reveals that delays scale *super-linearly* with the population of a city, with an exponent b=1.21.
15/n: Scaling of traffic congestion
The super-linear scaling above is not good news for #resiliency and #sustainability of our cities going forward, and it appears to have first been noted in the paper below:
nature.com/articles/srep0…
16/n: #Scaling of #traffic #congestion
I show that thanks to the 1:2:3 KPZ scaling, the slope 1.21 above is proportional to the transportation network #fractal dimension.
Thus, to improve the sustainability one should lower the connectivity of the network. Puzzling.
17/n Other implications:
Incorporate #complexity science course in #CEE education. Calculus and classical statistics cannot tackle fractals, chaos, power laws
Traffic management strategies seeking to maximize flow may be detrimental
Critical dynamics: microsimulation only
18/n, n=18.
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