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We gauge the direct product of the Proca with the Dirac equation that describes the coupling to the electromagnetic field of the spin-cascade (1/2,3/2) residing in the four-vector spinor and analyze propagation of its wave fronts in terms of the Courant-Hilbert criteria. We show that the differential equation under consideration is unconditionally hyperbolic and the propagation of its wave fronts unconditionally causal. In this way we proof that the irreducible spin-cascade embedded within four-vector is free from the Velo-Zwanziger problem that plagues the Rarita-Schwinger description of spin-3/2. The proof extends also to the direct product of two Proca equations and implies causal propagation of the spin-cascade (0,1,2) within an electromagnetic environment.
We studied the shock propagation and its stability with the causal dissipative hydrodynamics in 1+1 dimensional systems. We show that the presence of the usual viscosity is not enough to stabilize the solution. This problem is solved by introducing a
By taking the spin and polarization of the electrons, positrons and photons into account in the strong-field QED processes of nonlinear Compton emission and pair production, we find that the growth rate of QED cascades in ultra-intense laser fields c
We provide a complete description of the angular distribution of gluons in a medium-induced QCD cascade. We identify two components in the distribution, a soft component dominated by soft multiple scatterings, and a hard component dominated by a few
A general theory of top-down cascades in complex networks is described which explains two similar types of perturbation amplifications in the complex networks of business supply chains (the `bullwhip effect) and ecological food webs (trophic cascades
We argue that atmospheric cascades can be regarded as example of the self-organized criticality and studied by using Levy flights and nonextensive approach. It allows us to understand the scale-invariant energy fluctuations inside cascades in a natural way.