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Monitoring Protein Adsorption with Solid-state Nanopores
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Large deviations in one-dimensional random sequential adsorption.

P L Krapivsky1

  • 1Department of Physics, Boston University, Boston, Massachusetts 02215, USA.

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|January 20, 2021
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Summary
This summary is machine-generated.

We studied random sequential adsorption (RSA) models on a lattice, finding that the occupation number statistics are solvable for a minimal case (b=1). A perturbation method was developed to calculate variance for all b, offering insights into jammed systems.

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Materials Science

Background:

  • Random sequential adsorption (RSA) is a fundamental process where particles deposit irreversibly and randomly.
  • The process terminates when the system reaches a jammed state, preventing further particle addition.
  • Lattice-based RSA models introduce specific site-availability rules, influencing packing density and system dynamics.

Purpose of the Study:

  • To analyze lattice RSA models with specific site-availability constraints (at least b neighbors unoccupied).
  • To compute the full counting statistics of the occupation number for the minimal model (b=1).
  • To develop a general method for calculating occupation number cumulants and variance for any b.

Main Methods:

  • Analysis of lattice RSA models with a site-selection rule based on unoccupied neighboring sites.
  • Exact computation of full counting statistics for the b=1 case, reduced to a solvable Riccati equation.
  • Development of a perturbation procedure to determine occupation number cumulants for arbitrary b.

Main Results:

  • The full counting statistics for the b=1 lattice RSA model were exactly determined.
  • A Riccati equation was identified as the key to solving the b=1 case.
  • A perturbation method was established, enabling the calculation of occupation number variance for all values of b.

Conclusions:

  • The study provides a detailed analysis of lattice RSA models with neighbor-exclusion rules.
  • The derived methods offer a pathway to understand the statistical properties of jammed systems in these models.
  • The variance of the occupation number was successfully computed for all b, contributing to the understanding of packing fractions in disordered systems.