  The episodic dynamics of the magnetic eruption of a spinning black hole (BH)
accretion disks and its associated intense shapeup of their jets is studied via
three-dimensional general-relativistic magnetohydrodynamics (GRMHD). The
embedded magnetic fields in the disk get amplified by the magnetorotational
instability (MRI) so large as to cause an eruption of magnetic field
(recconection) and large chunks of matter episodically accrete toward the roots
of the jets upon such an event. We also find that the eruption events produce
intensive Alfv\'en pulses, which propagate through the jets. After the
eruption, the disk backs to the weakly magnetic states. Such disk activities
cause short time variabilities in mass accretion rate at the event horizon as
well as electromagnetic luminosity inside the jet. Since the dimensionless
strength parameter $a_0=eE/m_e \omega c$ of these Alfv\'en wave pulses is
extremely high for a substantial fraction of Eddington accretion rate accretion
flow onto a supermassive black hole, the Alfv\'en shocks turn into
ultrarelativistic $(a_0\gg 1)$ bow wake acceleration, manifesting into the
ultra-high energy cosmic rays and electrons which finally emit gamma-rays.
Since our GRMHD model has universality in its spatial and temporal scales, it
is applicable to a wide range of astrophysical objects ranging from those of
AGN (which is the primary target of this research), to micro-quasars.
Properties such as time variabilities of blazar gamma-ray flares and spectrum
observed by {\it Fermi} Gamma-ray Observatory are well explained by linear
acceleration of electrons by the bow wake.
