# Competitive random sequential adsorption of point and fixed-sized particles: analytical results

Source: [Competitive random sequential adsorption of point and fixed-sized particles: analytical results](<https://www.sota2.com/research/paper/68fa34291e209131ce896620>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T20:29:17.214Z

Authors: M. K. Hassan, J. Kurths

Published: 2001-06-09T08:23:26.000Z

## Abstract

We study the kinetics of competitive random sequential adsorption (RSA) of particles of binary mixture of points and fixed-sized particles within the mean-field approach. The present work is a generalization of the random car parking problem in the sense that it considers the case when either a car of fixed size is parked with probability q or the parking space is partitioned into two smaller spaces with probability (1-q) at each time event. This allows an interesting interplay between the classical RSA problem at one extreme (q=1), and the kinetics of fragmentation processes at the other extreme (q=0). We present exact analytical results for coverage for a whole range of q values, and physical explanations are given for different aspects of the problem. In addition, a comprehensive account of the scaling theory, emphasizing on dimensional analysis, is presented, and the exact expression for the scaling function and exponents are obtained.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/0106178>)

[PDF](<https://arxiv.org/pdf/cond-mat/0106178.pdf>)