The directed percolation dynamical universality class is characterized by just three independent critical exponents. These exponents are (in a 3d space):
$$\beta=\beta'=0.813(9)$$
$$\nu_\perp=0.584(5)$$
$$\nu_\parallel=1.110(10)$$
The latter two numbers are in close agreement with the (soft)...
The exchange of soft Pomerons (and Reggeons) (##\alpha_R(0)=0.55## and ##\alpha_P(0)=1.08##) seem to describe total hadron-hadron cross sections pretty well in the Regge limit. See, for example:
https://arxiv.org/abs/hep-ph/9209205
In this limit, QCD is of very little use since the exchanged...
Choking mass flow seems to reflect the fact that fluid momentum density has a maximum value (in stationary conditions) equal to ##\rho_* c_*## where ##\rho_*## is the critical mass density and ##c_*## is the critical velocity, which is closely related to the speed of sound (see...
I am not a mathematician, but in Field Theory long-range correlations are always associated with massless propagators. Propagators is something I would immediately associate with a wave equation (i.e. an hyperbolic PDE, not an elliptic one). I'm sorry, but I cannot be more specific, as I said...
Well this is leading me nowhere again.
This is what I think:
Vortex shedding introduces a NATURAL time scale.
The speed of sound is the maximum velocity at which information travels inside the fluid.
Assume that the incoming fluid velocity increases: the natural time scale decreases and...
In:
"Fluid Dynamics", Chapter 3 (Turbulence), Section 26,
Landau and Lifchitz analyze the problem of the stability of a steady flow past a body of finite size.
The fluid is assumed to be incompressible and they reach the conclusion that perturbations that deviate from steady flows start to...
For reference:Nature's monograph on transition to turbulence and Directed Percolation models (paywalled):
https://www.nature.com/collections/rxsztdqblr/I am very confused. Letter number (5) of Nature's monograph on turbulence shows NO sign of turbulence density saturation and the agreement...
Typical critical Reynolds ##\mathbb{Re}_c## are so low compared to sound Reynolds ##\mathbb{ Re}_m## in usual incompressible fluids that it is pretty sure that the "pseudo-relativistic" corrections do not play any role in the deviations from critical behaviour deep inside the turbulent phase...
If everything I said in the previous posts turns out to be true (I am going to the the calculations to see if the hypotheses hold true), a trivial consequence would be that:
$$p_c:=\frac{U_c}{U_m}$$
is a universal number. It would only depend on the spatial dimension ##d## number of the...
There is something relevant that I did not mention.
In (paywalled, the last two papers):
https://www.nature.com/collections/rxsztdqblr/
it is experimentally checked that the directed percolation models describe well the critical transition from laminar to turbulent flow. However, the model...
Regge-theory succesfully explains the latest LHC ##pp## elastic scattering experimental results and total cross-sections:
https://arxiv.org/pdf/1711.03288
https://arxiv.org/abs/1808.08580
Three different Regge-trajectories are needed: one Reggeon, one (soft) Pomeron and one Odderon. The...
The idea of using statistical physics models (including critical dynamics described by different universality classes) to solve QCD problems in different asymptotic cases is, apparently, well known:
https://arxiv.org/pdf/hep-ph/0609161.pdf
https://arxiv.org/pdf/hep-ph/0401052.pdf...
What I am about to write is purely speculative. They are just a set of ideas that some researchers are working with and some ideas that I have in mind. They are just phenomenological models that try to fit the experimental hadronic interactions and speculations of my own. If any of these models...