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Particle acceleration in ultra-relativistic oblique shock waves

We perform Monte Carlo simulations of diffusive shock acceleration at highly relativistic oblique shock waves. High upstream flow Lorentz gamma factors are used, which are relevant to models of ultra relativistic particle shock acceleration in Active Galactic Nuclei (AGN) central engines and relativistic jets and Gamma Ray Burst (GRB) fireballs. We investigate numerically the acceleration properties -in the ultra relativistic flow regime of $Γ\sim 10-10^{3}$- such as angular distribution, acceleration time constant, particle energy gain versus number of crossings and spectral shapes. We perform calculations for sub-luminal and super-luminal shocks, using two different approaches respectively. The $Γ^{2}$ energization for the first crossing cycle and the significantly large energy gain for subsequent crossings as well as the high 'speed up' factors found, are important in supporting the Vietri and Waxman models on GRB ultra-high energy cosmic ray, neutrino, and gamma-ray output.