Vibrations and diverging length scales near the unjamming transition

Abstract

We numerically study the vibrations of jammed packings of particles interacting with finite-range, repulsive potentials at zero temperature. As the packing fraction $\varphi$ is lowered towards the onset of unjamming at ${\varphi }_c$, the density of vibrational states approaches a non-zero value in the limit of zero frequency. For $\varphi >{\varphi }_c$, there is a crossover frequency, ${\omega }^{\ast }$ below which the density of states drops towards zero. This crossover frequency obeys power-law scaling with $\varphi -{\varphi }_c$. Characteristic length scales, determined from the dominant wavevector contributing to the eigenmode at ${\omega }^{\ast }$, diverge as power-laws at the unjamming transition.

arXiv commentSubmitted to PRL, 4 pages + 7 .eps figures

References in corpus (7)

• Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder
• Random Packings of Frictionless Particles
• Harmonic Vibrational Excitations in Disordered Solids and the "Boson Peak"
• Continuum limit of amorphous elastic bodies: A finite-size study of low frequency harmonic vibrations
• Isostatic phase transition and instability in stiff granular materials
• Continuum limit of amorphous elastic bodies (II): Response to a point source
• Vibrations in glasses and Euclidean Random Matrix theory

Cited by in corpus (228)

• A density-independent glass transition in biological tissues
• Jammed Hard-Particle Packings: From Kepler to Bernal and Beyond
• Mean field theory of hard sphere glasses and jamming
• Jamming of Soft Particles: Geometry, Mechanics, Scaling and Isostaticity
• Critical Scaling of Shear Viscosity at the Jamming Transition
• Vibrational modes identify soft spots in a sheared disordered packing
• Effects of compression on the vibrational modes of marginally jammed solids
• Active Jamming: Self-propelled soft particles at high density
• Glass and Jamming Transitions: From Exact Results to Finite-Dimensional Descriptions
• Dynamical Heterogeneity close to the Jamming Transition in a Sheared Granular Material
• Hypoconstrained Jammed Packings of Nonspherical Hard Particles: Ellipses and Ellipsoids
• Continuum limit of the vibrational properties of amorphous solids
• Isostaticity, auxetic response, surface modes, and conformal invariance in twisted kagome lattices
• Continuum limit of amorphous elastic bodies (III): Three dimensional systems
• Finite-Size Scaling at the Jamming Transition
• Universal Spectrum of Normal Modes in Low-Temperature Glasses: an Exact Solution
• Minimal model of active colloids highlights the role of mechanical interactions in controlling the emergent behavior of active matter
• A unified framework for non-Brownian suspension flows and soft amorphous solids
• Low-frequency vibrations of soft colloidal glasses
• Non-linear susceptibility in glassy systems: a probe for cooperative dynamical length scales
• Jamming versus Glass Transitions
• Anharmonicity and quasi-localization of the excess low-frequency vibrations in jammed solids
• Stability at Random Close Packing
• Universal origin of boson peak vibrational anomalies in ordered crystals and in amorphous materials
• Floppy modes and non-affine deformations in random fiber networks
• Critical and non-critical jamming of frictional grains
• Basic Understanding of Condensed Phases of Matter via Packing Models
• Excess Vibrational Modes and the Boson Peak in Model Glasses
• Scaling of phononic transport with connectivity in amorphous solids
• The jamming transition as a paradigm to understand the loss landscape of deep neural networks
• Non-affine response: jammed packings versus spring networks
• Approach to jamming in an air-fluidized granular bed
• Soft Sphere Packings at Finite Pressure but Unstable to Shear
• Geometric interpretation of pre-vitrification in hard sphere liquids
• Jamming in finite systems: stability, anisotropy, fluctuations and scaling
• The distribution of forces affects vibrational properties in hard sphere glasses
• Structural signatures of the unjamming transition at zero temperature
• Heterogeneous Dynamics, Marginal Stability and Soft Modes in Hard Sphere Glasses
• Power-law scaling in granular rheology across flow geometries
• Shocks near Jamming
• Jammed frictionless discs: connecting local and global response
• Energy transport in jammed sphere packings
• Dynamic criticality at the jamming transition
• Normal Modes in Model Jammed Systems in Three Dimensions
• Universal non-Debye scaling in the density of states of amorphous solids
• Heat transport in model jammed solids
• Localised soft modes and the supercooled liquid's irreversible passage through its configuration space
• Excitations of Ellipsoid Packings near Jamming
• Low-energy quasilocalized excitations in structural glasses
• Elasticity and Response in Nearly Isostatic Periodic Lattices
• Spatial structure of quasi-localized vibrations in nearly jammed amorphous solids
• Phonon transport and vibrational excitations in amorphous solids
• Soft modes and elasticity of nearly isostatic lattices: randomness and dissipation
• Topological persistence and dynamical heterogeneities near jamming
• Phonon gap and localization lengths in floppy materials
• Finite-Size-Scaling at the Jamming Transition: Corrections to Scaling and the Correlation Length Critical Exponent
• Elastic heterogeneity, vibrational states, and thermal conductivity across an amorphisation transition
• Exploring the jamming transition over a wide range of critical densities
• Jamming as a critical phenomenon: a field theory of zero-temperature grain packings
• Critical jamming of frictional grains in the generalized isostaticity picture
• Anomalous vibrational properties in the continuum limit of glasses
• Theory of the Structural Glass Transition: A Pedagogical Review
• Nonlinear modes disentangle glassy and Goldstone modes in structural glasses
• Constraints and vibrations in static packings of ellipsoidal particles
• Theory of the Jamming Transition at Finite Temperature
• Tuning Jammed Frictionless Disk Packings from Isostatic to Hyperstatic
• Continuum approach to wide shear zones in quasi-static granular matter
• Two diverging length scales in the structure of jammed packings
• Acoustic Probing of the Jamming Transition in an Unconsolidated Granular Medium
• Thermal fluctuations, mechanical response, and hyperuniformity in jammed solids
• Viscous forces and bulk viscoelasticity near jamming
• New jamming scenario: From marginal jamming to deep jamming
• On Variational Arguments for Vibrational Modes near Jamming
• Experimental study of the jamming transition at zero temperature
• Uniform Shock Waves in Disordered Granular Matter
• Stability of jammed packings I: the rigidity length scale
• Atomic-scale origin of dynamic viscoelastic response and creep in disordered solids
• Coherent potential approximation of random nearly isostatic kagome lattice
• Effective Medium Theory of Filamentous Triangular Lattice
• Spin-glass--like aging in colloidal and granular glasses
• Unjamming dynamics: the micromechanics of a seismic fault model
• Elastic Moduli and Vibrational Modes in Jammed Particulate Packings
• Excitation Chains at the Glass Transition
• Fluctuations, Jamming, and Yielding for a Driven Probe Particle in Disordered Disk Assemblies
• Mean-field model for the density of states of jammed soft spheres
• Marginally stable phases in mean-field structural glasses
• Beyond linear elasticity: Jammed solids at finite shear strain and rate
• Low-frequency vibrations of jammed packings in large spatial dimensions
• Free-then-freeze: transient learning degrees of freedom for introducing function in materials
• Floppiness, cutting, and freezing: Dynamic critical scaling near isostaticity
• Contact Changes near Jamming
• Relation of vibrational excitations and thermal conductivity to elastic heterogeneities in disordered solids
• Boson peak, elasticity, and glass transition temperature in polymer glasses: Effects of the rigidity of chain bending
• Unified theory of vibrational spectra in amorphous materials
• Critical scaling and aging in cooling systems near the jamming transition
• A review on shear jamming
• Memory of the Unjamming Transition during Cyclic Tiltings of a Granular Pile
• Achieving adjustable elasticity with non-affine to affine transition
• A random matrix definition of the boson peak
• Mechanical disorder of sticky-sphere glasses. I. Effect of attractive interactions
• A simple random matrix model for the vibrational spectrum of jammed packings
• Long wavelength structural anomalies in jammed systems
• Harmonic vibrational excitations in graded elastic networks: transition from phonons to gradons
• Rigidity percolation by next-nearest-neighbor braces on generic and regular isostatic lattices
• Vibrational properties of hard and soft spheres are unified at jamming
• Critical scalings and jamming in thermal colloidal systems
• Stability of jammed packings II: the transverse length scale
• Relationship between vibrations and dynamical heterogeneity in a model glass former: extended soft modes but local relaxation
• Vibrational density of states and specific heat in glasses from random matrix theory
• Phonon Dispersion and Elastic Moduli of Two-Dimensional Disordered Colloidal Packings of Soft Particles with Frictional Interactions
• Sponge-like rigid structures in frictional granular packings
• Entropy favors heterogeneous structures of networks near the rigidity threshold
• On the study of force-balance percolation
• Universal relaxation dynamics of sphere packings below jamming
• Evolution of covalent networks under cooling: contrasting the rigidity window and jamming scenarios
• Polymer Glass-Formation in Variable Dimension
• Anomalous diffusion and stretched exponentials in heterogeneous glass-forming liquids: Low-temperature behavior
• Sparse random matrices and vibrational spectra of amorphous solids
• Stress relaxation above and below the jamming transition
• Softening of Granular Packings with Dynamic Forcing
• Sounds of Failure: Passive Acoustic Measurements of Excited Vibrational Modes
• Direct link between boson-peak modes and dielectric $\alpha$-relaxation in glasses
• Disordered Solids Without Well-Defined Transverse Phonons: The Nature of Hard Sphere Glasses
• Instabilities of jammed packings of frictionless spheres under compression
• Nonlocal elasticity near jamming
• Shear shocks in fragile networks
• Evidence for marginal stability in emulsions
• Exact mean field inference in asymmetric kinetic Ising systems
• Non-local effects reflect the jamming criticality in granular flows of frictionless particles
• Finite size analysis of zero-temperature jamming transition under applied shear stress
• Jamming by growth
• Contact nonlinearities and linear response in jammed particulate packings
• Rotational sound in disordered granular materials
• Force networks and the dynamic approach to jamming in sheared granular media
• Penrose Tilings as Jammed Solids
• Role of disorder in determining the vibrational properties of mass-spring networks
• Shear induced solidification of athermal systems with weak attraction
• Dynamical compressibility of dense granular shear flows
• A dynamical relation between dual finite temperature classical and zero temperature quantum systems: quantum critical jamming and quantum dynamical heterogeneities
• The Glass-like Structure of Globular Proteins and the Boson Peak
• Density of states in random lattices with translational invariance
• On $k$-Core Percolation in Four Dimensions
• Linear Viscoelastic Response of the Vertex Model with Internal and External Dissipation: Normal Modes Analysis
• On the study of jamming percolation
• Jamming Mechanisms and Density Dependence in a Kinetically-Constrained Model
• Normal stresses, contraction, and stiffening in sheared elastic networks
• Realizing negative Poisson's ratio in unstressed spring networks
• Dynamics of k-core percolation in a random graph
• Force Percolation Transition of Jammed Granular Systems
• Growing length scale in gravity-driven dense granular flow
• Disorder-induced vibrational anomalies from crystalline to amorphous solids
• A unified quantifier of mechanical disorder in solids
• Randomness-Induced Redistribution of Vibrational Frequencies in Amorphous Solids
• Contact Changes of Sheared Systems: Scaling, Correlations, and Mechanisms
• Jamming as a Multicritical Point
• Dynamic length scales in athermal, shear-driven, jamming of frictionless disks in two dimensions
• A small subset of normal modes mimics the properties of dynamical heterogeneity in a model supercooled liquid
• Scaling Theory for the Frictionless Unjamming Transition
• The relation between stretched-exponential relaxation and the vibrational density of states in glassy disordered systems
• Jamming Criticality of Near-Crystals
• Force heterogeneities in particle assemblies: From order to disorder
• Higher order corrections to the effective potential close to the jamming transition in the perceptron model
• Unjamming in models with analytic pairwise potentials
• Critical scaling for yield is independent from distance to isostaticity
• Anomalous Stress Fluctuations in Athermal Two Dimensional Amorphous Solids
• Mean field theory of jamming of nonspherical particles
• Anomalous linear elasticity of disordered networks
• Mechanical and Vibrational Properties of Three-Dimensional Dimer Packings Near the Jamming Transition
• Mechanical response of an inclined frictional granular layer approaching unjamming
• Phase transition in the binary mixture of jammed particles with large size dispersity
• Origin of Corrections to Mean-field at the Onset of Unjamming
• Vibrational properties of two-dimensional dimer packings near the jamming transition
• Localization in random bipartite graphs: numerical and empirical study
• Model Energy Landscapes of Low-Temperature Fluids: Dipolar Hard Spheres
• Sound damping in frictionless granular materials: The interplay between configurational disorder and inelasticity
• Jamming and Unusual Charge Density Fluctuations of Strange Metals
• Universal behaviour of the glass and the jamming transitions in finite dimensions
• Microscopic elasticity of complex systems
• Scaling regimes and fluctuations of observables in computer glasses approaching the unjamming transition
• Strain fluctuations and elastic moduli in disordered solids
• Shape driven confluent rigidity transition in curved biological tissues
• Designing the pressure-dependent shear modulus using tessellated granular metamaterials
• Novel elastic instability of amorphous solids in finite spatial dimensions
• Stress-dependent normal mode frequencies from the effective mass of granular matter
• Level statistics and Anderson delocalization in two-dimensional granular materials
• One-dimensional Kac model of dense amorphous hard spheres
• Universal scaling for disordered viscoelastic matter near the onset of rigidity
• Grains unchained: local fluidization of a granular packing by focused ultrasound
• Diffusion in jammed particle packs
• Structural and mechanical characteristics of sphere packings near the jamming transition: From fully amorphous to quasi-ordered structures
• Two-scale scenario of rigidity percolation of sticky particles
• Mechanical properties of jammed packings of frictionless spheres under applied shear stress
• Phonons and elasticity in critically coordinated lattices
• Active Jamming at Criticality
• Thermalized connectivity networks of jammed packings
• Structured randomness: Jamming of soft discs and pins
• Spectral responses in granular compaction
• Jamming is a first-order transition with quenched disorder in amorphous materials sheared by cyclic quasistatic deformations
• Jamming in confined geometry: Criticality of the jamming transition and implications of structural relaxation in confined supercooled liquids
• Phonon transport properties of particulate physical gels
• Long-Range Correlations in Elastic Moduli and Local Stresses at the Unjamming Transition
• Effective medium theory for viscoelasticity of soft jammed solids
• Emergence of linear elasticity from the atomistic description of matter
• The connection between polymer collapse and the onset of jamming
• Protein folding as a jamming transition
• Jamming transition and normal modes of polydispersed soft particle packing
• From crystal to amorphopus: a novel route towards unjamming in soft disk packings
• Force network analysis of jammed solids
• Particle-scale origin of quadrupolar non-affine displacement fields in granular solids
• Vibrational density of states of amorphous solids with long-ranged power-law correlated disorder in elasticity
• Vibrational similarities in jamming-unjamming of polycrystalline and disordered granular packings
• A real-space renormalization group for jamming
• Jamming on curved surfaces
• Signal Transmissibility in Marginal Granular Materials
• Unearthing the anticrystal: criticality in the linear response of disordered solids
• Force propagation in isostatic granular packs
• Singular perturbation near mode-coupling transition
• Experimental measurements of the granular density of modes via impact
• Critical fluctuations of elastic moduli in jammed solids
• Jamming in Perspective
• Structural, mechanical, and vibrational properties of particulate physical gels
• Understanding the Low-Frequency Modes in Disordered Systems at Single-Particle Level
• Particle pinning as a method to manipulate marginal stability
• A comparison of jamming behavior in systems composed of dimer- and ellipse-shaped particles
• Quantum structure of glasses and the boson peak: a theory of vibrations
• Shear flow of frictional spheroids: Comparison between elongated and flattened particles
• Frequency-dependent attenuation and elasticity in unconsolidated earth materials: effect of damping
• Following the evolution of metastable glassy states under external perturbations: compression and shear-strain