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Munoz, V., Asenjo, F. A., Dominguez, M., Lopez, R. A., Valdivia, J. A., Vinas, A., et al. (2014). Largeamplitude electromagnetic waves in magnetized relativistic plasmas with temperature. Nonlinear Process Geophys., 21(1), 217–236.
Abstract: Propagation of largeamplitude waves in plasmas is subject to several sources of nonlinearity due to relativistic effects, either when particle quiver velocities in the wave field are large, or when thermal velocities are large due to relativistic temperatures. Wave propagation in these conditions has been studied for decades, due to its interest in several contexts such as pulsar emission models, laserplasma interaction, and extragalactic jets. For largeamplitude circularly polarized waves propagating along a constant magnetic field, an exact solution of the fluid equations can be found for relativistic temperatures. Relativistic thermal effects produce: (a) a decrease in the effective plasma frequency (thus, waves in the electromagnetic branch can propagate for lower frequencies than in the cold case); and (b) a decrease in the upper frequency cutoff for the Alfven branch (thus, Alfven waves are confined to a frequency range that is narrower than in the cold case). It is also found that the Alfven speed decreases with temperature, being zero for infinite temperature. We have also studied the same system, but based on the relativistic Vlasov equation, to include thermal effects along the direction of propagation. It turns out that kinetic and fluid results are qualitatively consistent, with several quantitative differences. Regarding the electromagnetic branch, the effective plasma frequency is always larger in the kinetic model. Thus, kinetic effects reduce the transparency of the plasma. As to the Alfven branch, there is a critical, nonzero value of the temperature at which the Alfven speed is zero. For temperatures above this critical value, the Alfven branch is suppressed; however, if the background magnetic field increases, then Alfven waves can propagate for larger temperatures. There are at least two ways in which the above results can be improved. First, nonlinear decays of the electromagnetic wave have been neglected; second, the kinetic treatment considers thermal effects only along the direction of propagation. We have approached the first subject by studying the parametric decays of the exact wave solution found in the context of fluid theory. The dispersion relation of the decays has been solved, showing several resonant and nonresonant instabilities whose dependence on the wave amplitude and plasma temperature has been studied systematically. Regarding the second subject, we are currently performing numerical 1D particle in cell simulations, a work that is still in progress, although preliminary results are consistent with the analytical ones.

Toledo, P. A., Riquelme, S. R., & Campos, J. A. (2015). Earthquake source parameters that display the first digit phenomenon. Nonlinear Process Geophys., 22(5), 625–632.
Abstract: We study the main parameters of earthquakes from the perspective of the first digit phenomenon: the nonuniform probability of the lower first digit different from O compared to the higher ones. We found that source parameters like coseismic slip distributions at the fault and coseismic inland displacements show first digit anomaly. We also found the tsunami runups measured after the earthquake to display the phenomenon. Other parameters found to obey first digit anomaly are related to the aftershocks: we show that seismic moment liberation and seismic waiting times also display an anomaly. We explain this finding by invoking a selforganized criticality framework. We demonstrate that critically organized automata show the first digit signature and we interpret this as a possible explanation of the behavior of the studied parameters of the Tohoku earthquake.
