It is exciting to see that this year’s Nobel Prize for physics goes to complex system studies. Fingering flow (wetting front instability) in unsaturated soils is a typical complex-system problem. The complex system is partially characterized by emergence and adaptation. For highly non-linear unsaturated flow, the emergent pattern is the fingering, and the corresponding adaptation principle is the optimality, such as the minimization of global flow resistance. Based on these ideas, I have mathematically demonstrated that the relatively permeability is a function of both saturation and water flux, while the traditional theory considers the relative permeability as a function of saturation only. The work was supported by experimental results and documented in a recent book Book Fluid Flow in the Subsurface: History, Generalization and Ap...
One key issue in applying the complex-system framework to unsaturated flow is to find a physical principle to describe the adaptation. To do that, does anyone have a more general principle than the minimization of the global flow resistance?
I'd like to attempt this probing question in layman's terms, as thoughts.
With regards emergence and adaptation, a principle of "boundaried flux" may better explain the effects of optimized balancing of transitional pressures.
I haven't read this "principle" stated anywhere yet, but it has gained relevance within the development of a theory I'm working on, which is called "Po1" (Pattern of One) and has manifested aspects of itself within the following case:
ttps://www.quantamagazine.org/mathematicians-prove-melting-ice-stays-smooth-20211006
The dynamics under consideration are the quantum states of the matter involved and their behaviour. When a complex-adaptive system's boundary is reached, and the transition region accessed, then departed again by crossing a boundary of an external complex-adaptive system, the flux of energy may initiate not only resistance, but a factor outcome of coherence as well.
Assuming no external stimuli other than a pure boundary transition for the same two systems - a simple case with instance value = 1, the dynamics should fit the Standard Model. The considered dynamic of the boundaried interaction, may well account for the optimal (not optimized) flow pressure calibration.
However, considering the quantum effects across all boundaries, in a standard expression - say for quantum entanglement - may well yield an assymetrical, optimized result. It may even point to possibilities of external manipulation in order to control flow across respective, boundaried topologies.
The way that I deals with the adaptation has been based on non-equilibrium thermodynamics (entropy production rate) that is still not fully developed yet. Under the condition of the minimization of global flow resistance for the steady-state subsurface flow problems, the entropy production rate can be at its minimum for a given flux boundary condition, and at its maximum for a given pressure boundary condition. (The entropy production rate is proportional to flux multiplied by energy gradient.) I was a little bit confused in my early studies and fortunately the final result is still correct.
Sagar Maitra Thanks for your contribution to the discussion. But your added references here are not really related to the discussion topic (fingering flow, complex system, and especially the adaptation principle).
This review paper shows my latest thinking on the subject. It demonstrates that the macroscopic theoretical results for fingering flow from optimality and from fractal flow pattern are similar. Some typical values of a key parameter are in a very narrow range, which is really good for practical applications. Further, the work clearly shows that there is hidden order out of seemingly disorders, a typical feature of a complex system.
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