Optimal switching threshold in the algorithm for simulating Random Sequential Adsorption by the Auxiliary List Method
Authors: УльяновМ.В. УльяновМ.В. , УразовС.О. УразовС.О. 
Published: July 2023

Рассмотрена задача определения оптимального порога переключения в методе вспомогательных списков, обеспечивающего эффективную по времени реализацию случайной последовательной адсорбции при осаждении ортогонально ориентированных линейных объектов на квадратную двумерную решетку. Изложены результаты теоретического анализа алгоритма метода вспомогательных списков на основе аппроксимаций функций концентрации свободных ячеек по экспериментальным данным. На основании теоретических результатов и экспериментального исследования сформулировано простое, в аспекте программных реализаций, условие переключения на формирование списков ячеек, доступных для осаждения.

The article considers the problem of determining the optimal switching threshold in the algorithm for modelling random sequential adsorption by the auxiliary list method in order to increase the time efficiency of program implementation. Random sequential adsorption is a process where particles are randomly and irreversibly deposited on a substrate without overlapping with previously adsorbed particles. Random sequential adsorption is a useful model for many physical, chemical, and biological processes. A square lattice consisting of cells is often used to represent a substrate. The article considers an algorithm for modelling the deposition of linear particles occupying several consecutive cells on a square lattice. To study the features and kinetics of the random sequential adsorption and determine the characteristics of the coating, it is necessary to find statistically significant data through simulation of the deposition of particles on a lattice, both for different lattice sizes and for different particle lengths. The need to obtain large samples generates the requirement for the time efficiency of the software implementation of random sequential adsorption simulation. Due to the inverse exponential dependence of the growth of the lattice coating concentration with particles on the simulation time, direct simulation of the jamming state on a computer is a laborious task. Technically, this problem can be solved by various methods, in particular, by switching at a certain concentration of deposited particles to auxiliary lists of cells available for adsorption by particles. There are known results on the experimental determination of the threshold for switching to the formation of lists stage, but the question theoretically remains open at what concentration the use of lists becomes effective. The article is devoted to the presentation of the results of theoretical analysis of the algorithm of the auxiliary list method based on approximations of the concentration functions of free cells according to experimental data. The results obtained agree with the experimentally determined switching threshold. Based on theoretical results and experimental research, a simple, in terms of software implementation, condition for switching to the formation of lists of cells available for adsorption is formulated.