Monotonicity properties of k(eff) with shape change and with nesting

It was found that, contrary to expectations based on physical intuition, k( eff) can both increase and decrease when changing the shape of an initially regular critical system, while preserving its volume. Physical intuition w ould only allow for a decrease of k(eff) when the surface/volume ratio incr eases. The unexpected behaviour of increasing k(eff) was found through nume rical investigation. For a convincing demonstration of the possibility of t he non-monotonic behaviour, a simple geometrical proof was constructed. Thi s latter proof, in turn, is based on the assumption that k(eff) can only in crease (or stay constant) in the case of nesting, i.e. when adding extra vo lume to a system. Since we found no formal proof of the nesting theorem for the general case, we close the paper by a simple formal proof of the monot onic behaviour of k(eff) by nesting. (C) 2001 Elsevier Science Ltd. All rig hts reserved.