Narrow Results

We consider the problem of establishing gravity in cellular automata. In particular, when cellular automata states can be partitioned into empty, particle, and wall types, with the latter enclosing rectangular areas, we desire rules that will make the particles fall down and pile up on the bottom of each such area. We desire the rules to be both simple and time-efficient. We propose a block rule, and prove that it piles up particles on a grid of height h in time at most 3*h.

Simple one-dimensional models of blood flow are widely used in simulating the transport of blood around the human vasculature. However, the effects of gravity have only been previously examined briefly and the effects of changes in wall properties and their interaction with gravitational forces have not been investigated. Here the effects of both gravitational forces and local changes in wall stiffness on the one-dimensional flow through axisymmetric vessels are studied. The governing fluid dynamic equations are derived from the Navier-Stokes equations for an incompressible fluid and linked to a simple model of the vessel wall, derived here from an exponential stress-strain relationship. A closed form of the hyperbolic partial differential equations is found. The flow behavior is examined in both the steady state and for wave reflection at a junction between two sections of different wall stiffness. A significant change in wave reflection coefficient is found under the influence of gravity, particularly at low values of baseline non-dimensional wall stiffness.