# Random Sequential Adsorption on a Line: Mean-Field Theory of Diffusional Relaxation

Source: [Random Sequential Adsorption on a Line: Mean-Field Theory of Diffusional Relaxation](<https://www.sota2.com/research/paper/68fa298d1e209131ce8351e0>)

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

Data updated: 2025-10-24T12:57:27.719Z

Authors: Vladimir Privman, Mustansir Barma

Published: 1992-07-03T10:15:31.000Z

## Abstract

We develop a new fast-diffusion approximation for the kinetics of deposition of extended objects on a linear substrate, accompanied by diffusional relaxation. This new approximation plays the role of the mean-field theory for such processes and is valid over a significantly larger range than an earlier variant, which was based on a mapping to chemical reactions. In particular, continuum-limit off-lattice deposition is described naturally within our approximation. The criteria for the applicability of the mean-field theory are derived. While deposition of dimers, and marginally, trimers, is affected by fluctuations, we find that the k-mer deposition kinetics is asymptotically mean-field like for all k=4,5,..., where the limit k-\>infinity, when properly defined, describes deposition-diffusion kinetics in the continuum.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/9207004>)

[PDF](<https://arxiv.org/pdf/cond-mat/9207004.pdf>)