TY - JOUR

T1 - Solution of diffusion limited aggregation in a narrow cylindrical geometry

AU - Kol, Boaz

AU - Aharony, Amnon

PY - 1998

Y1 - 1998

N2 - The diffusion limited aggregation model (DLA) and the more general dielectric breakdown model (DBM) are solved exactly in a two-dimensional cylindrical geometry with periodic boundary conditions of width 2. Our approach follows the exact evolution of the growing interface, using the evolution matrix [formula presented] which is a temporal transfer matrix. The eigenvector of this matrix with an eigenvalue of 1 represents the system’s steady state. This yields an estimate of the fractal dimension for DLA, which is in good agreement with simulations. The same technique is used to calculate the fractal dimension for various values of [formula presented] in the more general DBM. Our exact results are very close to the approximate results found by the fixed scale transformation approach.

AB - The diffusion limited aggregation model (DLA) and the more general dielectric breakdown model (DBM) are solved exactly in a two-dimensional cylindrical geometry with periodic boundary conditions of width 2. Our approach follows the exact evolution of the growing interface, using the evolution matrix [formula presented] which is a temporal transfer matrix. The eigenvector of this matrix with an eigenvalue of 1 represents the system’s steady state. This yields an estimate of the fractal dimension for DLA, which is in good agreement with simulations. The same technique is used to calculate the fractal dimension for various values of [formula presented] in the more general DBM. Our exact results are very close to the approximate results found by the fixed scale transformation approach.

UR - http://www.scopus.com/inward/record.url?scp=0032185903&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.58.4716

DO - 10.1103/PhysRevE.58.4716

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AN - SCOPUS:0032185903

SN - 1063-651X

VL - 58

SP - 4716

EP - 4729

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

IS - 4

ER -