= Solution
A <shock wave> is a thin, irreversible compression layer across which fluid <density>, <pressure>, <temperature> and <velocity> change rapidly, while conserved fluxes satisfy the <Rankine-Hugoniot conditions>. In the <shock frame>, a compressive hydrodynamic <shock> converts ordered upstream <kinetic energy> into downstream thermal <energy> and increases <entropy>. The upstream normal flow is supersonic; the downstream normal flow is subsonic for an ordinary gas-dynamic compression <shock>.
In an accreting <binary star>, a supersonic <stellar wind> can be captured by a compact companion and shocked. An <accretion stream> striking an <accretion disk>, an <accretion-disk boundary layer>, and a magnetically guided <accretion column> provide other sites where infall <energy> is dissipated and high-energy radiation is generated. <Shocks> heat and decelerate material; a disk also needs transport of <angular momentum> before its material can reach the compact star.
In <diffusive shock acceleration>, charged particles scatter from magnetic irregularities on both sides of a <shock> and repeatedly cross the converging flows. The average <energy> gain is first order in the <velocity> jump divided by the particle speed. Escape competes with acceleration, producing a nonthermal distribution rather than a single downstream <temperature>. <Supernova remnants> are important candidate sources of Galactic <cosmic rays>; <shocks> associated with <active galactic nuclei>, their jets and lobes, and <gamma-ray bursts> are candidate extragalactic accelerators. Ultrarelativistic energies require sufficient size, <magnetic field> and lifetime, and losses must not outpace acceleration. In particular a relativistic particle's <Larmor radius> must fit within the accelerator; the existence of a strong <shock> alone does not guarantee unlimited particle <energy>.
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