Stability of jammed packings II: the transverse length scale

Schoenholz, Samuel S.; Goodrich, Carl P.; Kogan, Oleg; Liu, Andrea J.; Nagel, Sidney R.

doi:10.1039/c3sm51096d

Cited by 31 publications

(43 citation statements)

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“…1(e). It has been argued that the vanishing of the characteristic frequency at point J implies two possible diverging length scales, associated with the transverse and longitudinal excitations, respectively [24,25,29]. Here we show that ω L IR > 0 at point J, so the length of Ω L (k) and Γ L (k) by plotting Ω L p −1/2 and πΓ L p −1/2 against kp −1/3 , which is however not the case in Fig.…”

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confidence: 99%

Disordered Solids without Well-Defined Transverse Phonons: The Nature of Hard-Sphere Glasses

et al. 2015

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We probe the Ioffe-Regel limits of glasses with repulsions near the zero-temperature jamming transition by measuring the dynamical structure factors. At zero temperature, the transverse IoffeRegel frequency vanishes at the jamming transition with a diverging length, but the longitudinal one does not, which excludes the existence of a diverging length associated with the longitudinal excitations. At low temperatures, the transverse and longitudinal Ioffe-Regel frequencies approach zero at the jamming-like transition and glass transition, respectively. As a consequence, glasses between the glass transition and jamming-like transition, which are hard sphere glasses in the low temperature limit, can only carry well-defined longitudinal phonons and have an opposite pressure dependence of the ratio of the shear modulus to the bulk modulus from glasses beyond the jamminglike transition.PACS numbers: 63.50. Lm,64.70.pv,61.43.Bn Upon compression, colloidal systems undergo the glass transition when the relaxation time (or the viscosity) exceeds the measurable value [1][2][3]. In the absence of the thermal energy, the compression leads to the jamming transition of packings of repulsive particles with the sudden formation of rigidity and static force networks [4,5]. Although the initial jamming phase diagram [4] proposes that the glass transition of purely repulsive systems collapses with the jamming transition in the zero temperature (T = 0) limit, or equivalently in the hard sphere limit [6], recent studies have evidenced that the T = 0 or hard sphere glass transition happens at a packing fraction φ g0 lower than the critical value φ j0 of the T = 0 jamming transition at the so-called point J [7][8][9][10][11][12].The departure of φ g0 from φ j0 leaves φ ∈ (φ g0 , φ j0 ) a special region. At T = 0, the systems in this region are unjammed and unable to sustain the shear or compression. However, they are by definition glasses when being thermally excited, because particles are unable to diffuse freely. While glasses are believed to be mechanically rigid solids, it seems perplexing that the systems in (φ g0 , φ j0 ) are rigid in the glass perspective but not in the T = 0 jamming perspective, which makes T = 0 singular.For soft and repulsive spheres, recent simulations have indicated that the glass transition temperature T g is proportional to the pressure p and vanishes at φ g0 [6][7][8][9]. Both colloidal experiments and simulations have also shown that inside the glass regime, at fixed temperature, there exists a crossover pressure p j at which the first peak of the pair distribution function reaches the maximum height g max 1 [7,8,[13][14][15], reminiscing the structural signature of the T = 0 jamming transition [16]. At such a crossover, the pressure dependence of the temperatureand vanishes at φ j0 [7,8]. In other words, when compressed at a fixed low temperature, the system undergoes the glass transition first and then the emergence of g max 1 .The whole picture is reproduced here as well in Fig. 3.A recent study ha...

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Disordered Solids without Well-Defined Transverse Phonons: The Nature of Hard-Sphere Glasses

et al. 2015

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“…1 as LΔZ ν , where ν is a correlation length exponent. We see that the resulting length scale, ξ ∼ ΔZ −ν , has ν = ψ=2 = 1=2, which has the same scaling as ℓ T (14,18). Interestingly, ref.…”

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“…The jamming transition marks the onset of rigidity in athermal sphere packings and was originally proposed as a zero-temperature transition (2,3) for soft repulsive spheres in a nonequilibrium "jamming phase diagram" (4) of varying packing density and applied shear. Many studies have documented behaviors characteristic of critical phenomena near the jamming transition, including power law scaling (2,3,5) and scaling collapses (6-13) of numerous properties, with the expression of quantities in terms of scaling functions, diverging length scales (6,(14)(15)(16)(17)(18)(19), and finite-size scaling (10,12,20). Theories have been developed to individually understand and relate some of these power laws (15,16,21,22), but a unified scaling theory has been lacking.…”

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Scaling ansatz for the jamming transition

Goodrich

Liu

Sethna

2016

Proc. Natl. Acad. Sci. U.S.A.

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We propose a Widom-like scaling ansatz for the critical jamming transition. Our ansatz for the elastic energy shows that the scaling of the energy, compressive strain, shear strain, system size, pressure, shear stress, bulk modulus, and shear modulus are all related to each other via scaling relations, with only three independent scaling exponents. We extract the values of these exponents from already known numerical or theoretical results, and we numerically verify the resulting predictions of the scaling theory for the energy and residual shear stress. We also derive a scaling relation between pressure and residual shear stress that yields insight into why the shear and bulk moduli scale differently. Our theory shows that the jamming transition exhibits an emergent scale invariance, setting the stage for the potential development of a renormalization group theory for jamming.jamming transition | scaling ansatz | nonequilibrium critical phenomena T he existence of criticality at the jamming transition suggests that universal physics underlies rigidity in disordered solids ranging from glasses to granular materials (1). The jamming transition marks the onset of rigidity in athermal sphere packings and was originally proposed as a zero-temperature transition (2, 3) for soft repulsive spheres in a nonequilibrium "jamming phase diagram" (4) of varying packing density and applied shear. Many studies have documented behaviors characteristic of critical phenomena near the jamming transition, including power law scaling (2, 3, 5) and scaling collapses (6-13) of numerous properties, with the expression of quantities in terms of scaling functions, diverging length scales (6,(14)(15)(16)(17)(18)(19), and finite-size scaling (10,12,20). Theories have been developed to individually understand and relate some of these power laws (15,16,21,22), but a unified scaling theory has been lacking. Here, we develop such a theory by proposing a scaling ansatz for the jamming critical point in terms of the fields originally identified by the jamming phase diagram, namely density and shear.The critical point scaling ansatz introduced by Widom (23) in the 1960s was a key advance in the theory of critical phenomena that set the stage for the development of the renormalization group. The ansatz writes the state functions near continuous equilibrium phase transitions in terms of power law ratios of the control parameters. By positing a scaling function for the free energy, it exploits the fact that quantities, such as the specific heat, magnetization, and susceptibility, are derivatives of the free energy to derive relations not only among their scaling exponents but among their scaling functions. Thus, the scaling ansatz provides a unified and comprehensive description of systems exhibiting what later was realized to be an emergent scale invariance.Unlike most systems exhibiting a dynamical scale invariance, we find that a jammed system can also be viewed as a material with critical properties that are determined by a state function, analo...

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“…Finally, similar scalings have been related to stability under compression [23] and shear [24]. Before considering how modes with different frequency contribute to the nonaffine response, we analyse the density of states.…”

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confidence: 99%

Nonaffinity in amorphous solids close to the jamming transition

Arévalo

Ciamarra

2017

EPJ Web Conf.

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Abstract. Nonaffinity is known to be an integral part of the response of amorphous solids. Its role is particularly relevant in particulate systems close to their jamming transition, where it dominates the elastic response. Thus, to determine the elastic properties of amorphous solids it is essential to rationalize the features of their nonaffine response. Via numerical simulations we investigate the relation between the non affine response and the vibrational properties of model amorphous materials. We show that, contrary to previous speculations, modes below the Boson peak are those mostly responsible for the nonaffine response.

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Stability of jammed packings II: the transverse length scale

Cited by 31 publications

References 22 publications

Disordered Solids without Well-Defined Transverse Phonons: The Nature of Hard-Sphere Glasses

Disordered Solids without Well-Defined Transverse Phonons: The Nature of Hard-Sphere Glasses

Scaling ansatz for the jamming transition

Nonaffinity in amorphous solids close to the jamming transition

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