The quantum dynamics of several characteristic simple situations in the dynamics of ultracold Bose gases will be systematically studied for a broad range of their basic parameters, with particular emphasis on the incoherent particles and the possibility of their stimulated growth into coherent phase grains. Situations include supersonic flow past an obstacle, collisions of BECs, reflection of a BEC from a barrier, and interaction of obstacles and vortices. The aim is to produce quantitative maps of their behaviour as a function of basic scaled parameters such as velocity, obstacle dimensions, and duration. To date, knowledge of these simple dynamical situations is mostly limited to isolated parameter choices, whereas this project objective is to make the coverage broad, comprehensive and continuous. This has many practical applications to understanding of more complex/realistic situations that can be broken up into the simpler elements, and is timely given the increase in BEC dynamics experiments in the last 2-3 years. Simulations with phase-space methods of the first-principles, c-field, and Bogoliubov variety are essential for broad coverage. This matches and will build on the existing extensive and deep experience of the researcher in developing and using such methods, obtained during the EIF fellowship. Finalisation of the stochastic time-adaptive Bogoliubov simulation method roughly developed then is necessary and planned. 3 years of research at the Polish Academy of Sciences in Warsaw is planned. It is already home to several world experts on Bose gas dynamics, and several other expert groups are in Warsaw and Poland, so professional integration will be thorough, and EU-wide scientific integration will increase. The project work will be used to obtain a habilitation, necessary to obtain a permanent independent research position in the Polish system.