  Many similar phenomena occur in astrophysical systems with spatial and mass
scales different by many orders of magnitudes. For examples, collimated
outflows are produced from the Sun, proto-stellar systems, gamma-ray bursts,
neutron star and black hole X-ray binaries, and supermassive black holes;
various kinds of flares occur from the Sun, stellar coronae, X-ray binaries and
active galactic nuclei; shocks and particle acceleration exist in supernova
remnants, gamma-ray bursts, clusters of galaxies, etc. In this report I
summarize briefly these phenomena and possible physical mechanisms responsible
for them. I emphasize the importance of using the Sun as an astrophysical
laboratory in studying these physical processes, especially the roles magnetic
fields play in them; it is quite likely that magnetic activities dominate the
fundamental physical processes in all of these systems.
  As a case study, I show that X-ray lightcurves from solar flares, black hole
binaries and gamma-ray bursts exhibit a common scaling law of non-linear
dynamical properties, over a dynamical range of several orders of magnitudes in
intensities, implying that many basic X-ray emission nodes or elements are
inter-connected over multi-scales. A future high timing and imaging resolution
solar X-ray instrument, aimed at isolating and resolving the fundamental
elements of solar X-ray lightcurves, may shed new lights onto the fundamental
physical mechanisms, which are common in astrophysical systems with vastly
different mass and spatial scales. Using the Sun as an astrophysical
laboratory, "Applied Solar Astrophysics" will deepen our understanding of many
important astrophysical problems.
