SOLUTION OF DIFFUSION-LIMITED AGGREGATION IN A NARROW CYLINDRICAL GEOMETRY

The diffusion Limited aggregation model (DLA) and the more general die lectric breakdown model (DBM) an solved exactly in a two-dimensional c ylindrical geometry with periodic boundary conditions of width 2. Our approach follows the exact evolution of the growing interface, using t he evolution matrix E, which is a temporal transfer matrix. The eigenv ector of this matrix with an eigenvalue of 1 represents the system's s teady state. This yields an estimate of the fractal dimension for DLA, which is in good agreement with simulations. The same technique is us ed to calculate the fractal dimension for various values of eta in the more general DBM. Our exact results are very close to the approximate results found by the fixed scale transformation approach. [S1063-651X (98)05010-7].