TY - JOUR

T1 - DIFFUSION MODELS ON TRIANGULATED SURFACES

AU - Ampilova, N.

PY - 2021/12/22

Y1 - 2021/12/22

N2 - Diffusion processes occur in many scientific areas; they are especially important in chemistry, biology and medicine. Most of the mathematical models that describe diffusion are nonlinear Partial Differential Equations, which do not have analytical solutions and numerical methods require large computing resources. There is a growing interest in the structures (fractal clusters) generated by diffusion processes, and the search for new models has intensified. The important method complementary to mathematical models is imitation modeling in which the space mobility of the particles of a substance is directly modeled. There are two directions in such an approach: an imitation of random walks of particles; and cellular automata modeling. In this work, for the modeling of the fractal cluster growth on triangulated surfaces, we implement algorithms based on random walk. We use classical variants of Diffusion Limited Aggregation (DLA) and Reaction Limited Aggregation (RLA) models. It is shown that, in the framework of the classical Cluster Aggregation (CCA) model, fractal cluster on a triangulated surface cannot be correctly constructed without additional assumptions about the cluster restructuring. The software is written in Python; it may be used by both researchers and students as a tool for the modeling of complex processes.

AB - Diffusion processes occur in many scientific areas; they are especially important in chemistry, biology and medicine. Most of the mathematical models that describe diffusion are nonlinear Partial Differential Equations, which do not have analytical solutions and numerical methods require large computing resources. There is a growing interest in the structures (fractal clusters) generated by diffusion processes, and the search for new models has intensified. The important method complementary to mathematical models is imitation modeling in which the space mobility of the particles of a substance is directly modeled. There are two directions in such an approach: an imitation of random walks of particles; and cellular automata modeling. In this work, for the modeling of the fractal cluster growth on triangulated surfaces, we implement algorithms based on random walk. We use classical variants of Diffusion Limited Aggregation (DLA) and Reaction Limited Aggregation (RLA) models. It is shown that, in the framework of the classical Cluster Aggregation (CCA) model, fractal cluster on a triangulated surface cannot be correctly constructed without additional assumptions about the cluster restructuring. The software is written in Python; it may be used by both researchers and students as a tool for the modeling of complex processes.

KW - триангулируемая поверхность

KW - диффуззия

KW - модель диффузии ограниченной агрегацией

M3 - Article

VL - 23

SP - 11

EP - 22

JO - JOURNAL OF APPLIED ELECTROMAGNETISM

JF - JOURNAL OF APPLIED ELECTROMAGNETISM

SN - 1109-1606

IS - 2

ER -