The slow viscous ow past a rectangular array of parallel circular cylinders is studied. The method of eigenfunction expansions and matching between two domains is used to obtain the ow. Permeabilities in the three principal directions are determined. Approximate formulas are derived.

A non-trivial cluster growth model, equivalent to the lattice-free Eden-C model, is proposed. The model is constructed by randomly adding contiguous circles without overlapping. Large-scale computer simulations show the interior density is constant at 0.650, while the boundary is fractal, with a thickness proportional to the 0.396 power of the mean radius.

An off-lattice Eden cluster growth model is introduced and implemented in two and three dimensions, using both a flat substrate with periodic boundary conditions and a radial geometry. Large-scale simulations are conducted to investigate the kinetic roughening. In the radial geometry, both the origin and center of mass are used to measure surface width, and growth exponent estimates in two dimensions verify previous findings that the choice of origin or center of mass does affect the growth exponent. The growth exponent for the surface of the off-lattice radial clusters in three dimensions is found to be approximately 1 10 . The results are used to discuss the universality of the selfaffine scaling of three-dimensional Eden growth in both flat substrate and radial geometries.

A heavy cable spans two points in space. There exists an optimum cable length such that the maximum tension is minimized. If the two end points are at the same level, the optimum length is 1.258 times the distance between the ends. The optimum lengths for end points of different heights are also found.