Jamming in Systems Composed of Frictionless Ellipse-Shaped Particles

Abstract

We study the structural and mechanical properties of jammed ellipse packings, and find that the nature of the jamming transition in these systems is fundamentally different from that for spherical particles. Ellipse packings are generically hypostatic with more degrees of freedom than constraints. The spectra of low energy excitations possess two gaps and three distinct branches over a range of aspect ratios. In the zero compression limit, the energy of the modes in the lowest branch increases {\it quartically} with deformation amplitude, and the density of states possesses a $\delta$-function at zero frequency. We identify scaling relations that collapse the low-frequency part of the spectra for different aspect ratios. Finally, we find that the degree of hypostaticity is determined by the number of quartic modes of the packing.

4 pages, 4 figures

References in corpus (9)

• Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder
• Random Packings of Frictionless Particles
• Geometric origin of excess low-frequency vibrational modes in amorphous solids
• Jamming transition in emulsions and granular materials
• Continuum limit of amorphous elastic bodies: A finite-size study of low frequency harmonic vibrations
• Hypoconstrained Jammed Packings of Nonspherical Hard Particles: Ellipses and Ellipsoids
• Entropy and Temperature of a Static Granular Assembly
• Understanding the Frequency Distribution of Mechanically Stable Disk Packings
• Stresses in isostatic granular systems and emergence of force chains

Cited by in corpus (77)

• Jammed Hard-Particle Packings: From Kepler to Bernal and Beyond
• Jamming of Soft Particles: Geometry, Mechanics, Scaling and Isostaticity
• Hyperuniform States of Matter
• Stress-strain behavior and geometrical properties of packings of elongated particles
• Finite-Size Scaling at the Jamming Transition
• Stability at Random Close Packing
• Granular materials composed of shape-anisotropic grains
• Extraction of Force-Chain Network Architecture in Granular Materials Using Community Detection
• The packing of granular polymer chains
• The jamming transition as a paradigm to understand the loss landscape of deep neural networks
• Non-affine response: jammed packings versus spring networks
• Jamming in finite systems: stability, anisotropy, fluctuations and scaling
• Jammed frictionless discs: connecting local and global response
• Excitations of Ellipsoid Packings near Jamming
• Hypostatic jammed packings of frictionless nonspherical particles
• Phonon gap and localization lengths in floppy materials
• Jammed frictional tetrahedra are hyperstatic
• Universality of jamming of non-spherical particles
• Critical jamming of frictional grains in the generalized isostaticity picture
• Local origin of global contact numbers in frictional ellipsoid packings
• Constraints and vibrations in static packings of ellipsoidal particles
• Tuning Jammed Frictionless Disk Packings from Isostatic to Hyperstatic
• Particle-scale reversibility in athermal particulate media below jamming
• Non-universal Voronoi cell shapes in amorphous ellipsoid packings
• Organizing Principles for Dense Packings of Nonspherical Hard Particles: Not All Shapes Are Created Equal
• Emergent SO(3) Symmetry of the Frictionless Shear Jamming Transition
• Exact Constructions of a Family of Dense Periodic Packings of Tetrahedra
• Athermal jamming of soft frictionless Platonic solids
• Experimental study of the jamming transition at zero temperature
• Stability of jammed packings I: the rigidity length scale
• Jamming of semiflexible polymers
• Elastic Moduli and Vibrational Modes in Jammed Particulate Packings
• Hard ellipses: Equation of state, structure and self-diffusion
• Jamming in Granular Polymers
• The structural, vibrational, and mechanical properties of jammed packings of deformable particles in three dimensions
• Effects of particle-size ratio on jamming of binary mixtures
• Isostaticity of Constraints in Jammed Systems of Soft Frictionless Platonic Solids
• Variable-cell method for stress-controlled jamming of athermal, frictionless grains
• Jamming in Systems With Quenched Disorder
• Dynamics of Sheared Ellipses and Circular Disks: Effects of Particle Shape
• Machine Learning Characterization of Structural Defects in Amorphous Packings of Dimers and Ellipses
• Rotational and Translational Phonon Modes in Glasses Composed of Ellipsoidal Particles
• Compression Driven Jamming of Athermal Frictionless Spherocylinders in Two Dimensions
• Bridging particle deformability and collective response in soft solids
• Geometrical families of mechanically stable granular packings
• Compression- and Shear-Driven Jamming of U-Shaped Particles in Two Dimensions
• Rods are less fragile than spheres: Structural relaxation in dense liquids composed of anisotropic particles
• Jamming by growth
• Jamming graphs: A local approach to global mechanical rigidity
• Relaxation dynamics in a binary hard-ellipse liquid
• Shear response of granular packings compressed above jamming onset
• Shear-Driven Flow of Athermal, Frictionless, Spherocylinder Suspensions in Two Dimensions: Stress, Jamming, and Contacts
• Jamming transition in non-spherical particle systems: pentagons vs. disks
• Scaling Theory for the Frictionless Unjamming Transition
• Mean field theory of jamming of nonspherical particles
• Anisotropic Particles Strengthen Granular Pillars under Compression
• Mechanical and Vibrational Properties of Three-Dimensional Dimer Packings Near the Jamming Transition
• Vibrational properties of two-dimensional dimer packings near the jamming transition
• Athermal shearing of frictionless cross-shaped particles of varying aspect ratio
• Scaling theory of critical strain-stiffening in disordered elastic networks
• Designing the pressure-dependent shear modulus using tessellated granular metamaterials
• Bottom stresses of static packing of granular chains
• Effects of spherical confinement and backbone stiffness on flexible polymer jamming
• Infinitesimal asphericity changes the universality of the jamming transition
• Densest versus jammed packings of bent-core trimers
• Densest vs. jammed packings of 2D bent-core trimers
• Mechanical response of packings of non-spherical particles: A case study of 2D packings of circulo-lines
• Perspective: A Phase Diagram for Deep Learning unifying Jamming, Feature Learning and Lazy Training
• Structured randomness: Jamming of soft discs and pins
• Theory of rigidity and numerical analysis of density of states of two-dimensional amorphous solids with dispersed frictional grains in the linear response regime
• Packings of frictionless spherocylinders
• Protein folding as a jamming transition
• Mixing properties of bi-disperse ellipsoid assemblies: Mean-field behaviour in a granular matter experiment
• Measure of distance and overlap between two arbitrary ellipses on a sphere
• Testing mean-field theory for jamming of non-spherical particles: Contact number, gap distribution, and vibrational density of states
• Translational and rotational velocities in shear-driven jamming of ellipsoidal particles
• A comparison of jamming behavior in systems composed of dimer- and ellipse-shaped particles