Abstract
The relaxation process to a scaling state which is a nonequilibrium steady state in evolving cellular structures, such as soap froths and grain systems, is investigated by computer simulation of the vertex model and phenomenology in two dimensions. Our results are as follows: (i) This relaxation is hierarchical, that is, the average size of a cell (the characteristic length of the system) relaxes rapidly at an early stage and then topological quantities associated with the shape of cells relax slowly at a late stage. (ii) The latter slow relaxation is well described by the stretched exponential function. (iii) The time exponent β of the stretched exponential function is related to the power γ of the distribution for the time interval of the topological change in the form γ= 1 + β.
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