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The paper describes numerical experiments to investigate the selection of primary dendritic spacing lambda under transient conditions. The phase field method coupled to solutal diffusion is combined with a moving frame algorithm to enlarge the total calculation domain. For constant growth conditions of an Al-7%Si alloy, a range of lambda has been achieved depending on initial conditions. Quasistationary decrease of the solidification velocity leads to extinction of redundant trunks. Increasing the velocity leads to the formation of new trunks from ternary arms, but a striking incubation delay suggests a history-dependent spacing assignment. The results are compared to experimental and theoretical results. (C) 2002 Elsevier Science B.V. All rights reserved.