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High Energy, Nuclear, Particle Physics
Could the 3D percolation model explain Regge-Trajectories?
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[QUOTE="Anashim, post: 6069256, member: 646863"] There is something relevant that I did not mention. In (paywalled, the last two papers): [URL]https://www.nature.com/collections/rxsztdqblr/[/URL] it is experimentally checked that the directed percolation models describe well the critical transition from laminar to turbulent flow. However, the model only works in a narrow neighbourhood of the critical condition. The problem is that the incompressible Navier Stokes equations are Galileo-invariant, not Lorentz-invariant. This disease may be somewhat "cured" doing a "pseudo-relativistic" correction. Please, bear in mind that the incompressible Navier-Stokes equations approximation breaks down as Mach's number approaches 1 from (well) below. Instead of considering the critical opertator: $$p_c:=\frac{|\mathbb{Re}-\mathbb{Re}_c|}{\mathbb{Re}_c}\propto \frac{|U-U_c|}{U_c}$$ where ##Re## denotes Reynold's number, ##c## critical condition and ##U## the reference velocity, you can use, instead: $$p_c:=\frac{|\mathbb{Re}-\mathbb{Re}_c|}{\mathbb{Re}_c\Big [1+\frac{\mathbb{Re}\mathbb{Re}_c}{\mathbb{Re}_m^2}\Big ]}\propto \frac{|U-U_c|}{U_c\Big [1+\frac{UU_c}{U_m^2}\Big ]}$$ where ##m## denotes the speed of sound condition (Mach's number=1). In this way, the validity of the percolation model may be extended deep into the turbulence region. The speed of sound may play here a similar roled to the speed of light in relativity. Poincare's invariance must be somehow restored if incompressible Navier-Stokes equations and hadron interactions are to be mutually related by the same Universality Class model. Now, I'm finally done with this issue. [/QUOTE]
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Could the 3D percolation model explain Regge-Trajectories?
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