A method and apparatus for distributing time and frequency information to a plurality of studios such that the studios can then use the time and frequency information frequency and timelock their studio components to the global reference. An axis of rotation, an angle of rotation and a displacement vector are calculated in order to arrive at an exact congruence of the positioning image of the testpiece with the ideal reference image. A first opening 10k on the upstream side of the color change valve 4 is provided at a position close to the inner wall of a through hole h constituted as a part of the circulation piping 3 so that no space is allowed between the inner wall and the first opening 10k. The valve has a first portion directly secured to the bottom surface and a second portion that extends from the first portion. For each time step, the model predicts the incremental growth of the branch tips and the pressure and flow rate distribution in the system by solving the governing equations and satisfying the boundary conditions at the fracture tips, wellbore and connected branch joints. Element Mb comprises Be, Mg, Ca, Sr, Ba, or a combination thereof.