Two-dimensional systems of elongated particles: From diluted to dense

Abstract

This chapter is devoted to the analysis of jamming and percolation behavior of two-dimensional systems of elongated particles. We consider both continuous and discrete spaces (with the special attention to the square lattice), as well the systems with isotropically deposited and aligned particles. Overviews of different analytical and computational methods and main results are presented.

arXiv comment47 pages, 22 figures, 167 references; to be published in Order, Disorder and Criticality: Advanced Problems of Phase Transition Theory, Volume 6, October 2020, World Scientific https://doi.org/10.1142/11711

References in corpus (40)

• Jammed Hard-Particle Packings: From Kepler to Bernal and Beyond
• A fast Monte Carlo algorithm for site or bond percolation
• Efficient Monte Carlo algorithm and high-precision results for percolation
• Recent advances in percolation theory and its applications
• Continuum Percolation Thresholds in Two Dimensions
• Recent advances and open challenges in percolation
• Fundamental challenges in packing problems: from spherical to non-spherical particles
• Precise Algorithm to Generate Random Sequential Addition of Hard Hyperspheres at Saturation
• Robust Algorithm to Generate a Diverse Class of Dense Disordered and Ordered Sphere Packings via Linear Programming
• Percolation and jamming in random sequential adsorption of linear segments on square lattice
• Distance of closest approach of two arbitrary hard ellipses in 2D
• Finite-Size-Scaling at the Jamming Transition: Corrections to Scaling and the Correlation Length Critical Exponent
• Adsorption of Line Segments on a Square Lattice
• Percolation of linear $k$-mers on square lattice: from isotropic through partially ordered to completely aligned state
• A Monte-Carlo Analysis of Percolation of Line-Segments on a Square Lattice
• Random sequential adsorption of partially oriented linear $k$-mers on square lattice
• Jamming in two-dimensional packings
• Continuum random sequential adsorption of polymer on a flat and homogeneous surface
• Impact of defects on percolation in random sequential adsorption of linear k-mers on square lattice
• Random packing of regular polygons and star polygons on a flat two-dimensional surface
• Shape universality classes in the random sequential addition of non-spherical particles
• Percolation and jamming of random sequential adsorption samples of large linear $k$-mers on a square lattice
• Dimer coverings on the Sierpinski gasket with possible vacancies on the outmost vertices
• Clustering in vibrated monolayers of granular rods
• Jamming and percolation in random sequential adsorption of straight rigid rods on a two-dimensional triangular lattice
• Jammed systems of oriented needles always percolate on square lattices
• Modelling of interacting dimer adsorption
• Random Sequential Adsorption of Oriented Superdisks
• Jamming and percolation in generalized models of random sequential adsorption of linear $k$-mers on a square lattice
• Random sequential adsorption and diffusion of dimers and k-mers on a square lattice
• Anisotropy in electrical conductivity of two-dimensional films containing aligned rodlike particles: continuous and lattice models
• Reversible Random Sequential Adsorption of Dimers on a Triangular Lattice
• Jamming and percolation properties of random sequential adsorption with relaxation
• Percolation thresholds for discorectangles: numerical estimation for a range of aspect ratios
• Random sequential adsorption on Euclidean, fractal and random lattices
• Connectedness percolation of hard convex polygonal rods and platelets
• A microscopic 2D lattice model of dimer granular compaction with friction
• Nonstandard Convergence to Jamming in Random Sequential Adsorption: The Case of Patterned One-Dimensional Substrates
• Diffusion dynamics and steady states of systems of hard rods on the square lattice
• Irreversible Deposition of Line Segment Mixtures on a Square Lattice: Monte Carlo Study

Cited by in corpus (5)

• Random sequential adsorption of partially ordered discorectangles onto a continuous plane
• Connectedness percolation in the random sequential adsorption packings of elongated particles
• Confinement effects on the random sequential adsorption packings of elongated particles in a slit
• Percolation connectivity in deposits obtained using competitive random sequential adsorption of binary disk mixtures
• Invariant percolation properties in random isotropic systems of conductive discorectangles on a plane: From disks to sticks