Goal: The goal of this project is to construct a quantum version of the cellular automata model for fluid flow discussed in “A New Kind of Science”. This will be done by considering all the possible outgoing directions in the collision between particles that conserve momentum. The starting point will be the hexagonal lattice. The properties of the micro-states and macro-states will be studied and compared with the “classical” model. Of interest is whether the Navier-Stokes equation describes the macroscopic behaviour of this model and the ways in which the “multiway graph” will behave .
Results: The simulations of three types of systems were accomplished: closed systems, open systems with periodic boundary conditions, and tubes in which the fluids were propagated. Three types of multiway graphs were observed: cyclic , tree-like and clustered graphs, the first one was associated with trivial cycles and the last two were associated with ‘random’ states. Causal invariance was only observed in the trivial ordered states. Additionally, a the states were analyzed from a macroscopic perspective by dividing the systems in bigger sections and averaging its properties (number of particles and linear momentum). By analyzing different pathways within the multiway graphs, it was observed that different branches shared similar macroscopic behaviour.
Future work: There is still a lot to explore in the fluid systems conformed by the rules specified above. Simulations with larger number of particles is of great interest to study the continuum limit, which can be compared with results obtained from Navier-Stokes equations.