This paper introduces an optical measurement system for shock wave characteristics. The system works by mountinga metal plate attached to spring mounts against the shock wavefront. This set is sealed and can plot the shock wave pressure diagram by measuring plate's displacement, radiation and changing the reflection of light during shock wave conflict, and converting these optical data to volta...

We derive several new reformulations of the Hubeny-Rangamani-Takayanagi covariant holographic entanglement entropy formula. These include: (1) a minimax formula, which involves finding maximal-area achronal surface on timelike hypersurface homologous to D(A) (the boundary causal domain region A whose we are calculating) and minimizing over hypersurface; (2) max V-flow in maximize flux through d...