Transmathematical High Performance Computing: The development of transmathematics and its application to the physical or computational sciences

High Performance Computing is essential to modern life. Indeed computer simulation of physical phenomena is now regarded as the fourth pillar of science, along with theory, observation, and experiment. Given the importance of computers to understanding physical phenomena, it is ironic that the von Neumann computer makes the physically impossible assumption that data can travel any distance in unit time - this implies faster than light travel - and forces von Neumann computers to become less efficient as they become faster and larger. By contrast dataflow computers are physically realistic and maintain their efficiency with increasing speed and size. Hence any sufficiently large program runs faster on a dataflow computer than on a von Neumann computer. In particular, slipstream computers, enabled by transmathematics, can complete execution of one or more compute-bound, in-line programs every clock tick - giving them a speed of many programs per clock tick! This gives them enormous advantages.PhD research proposals are invited on any aspect of the development of transmathematics or its application to the physical or computational sciences.