arXiv subjects

Edan Lerner

Publications and source records attributed to Edan Lerner.

At least 55 records · Page 3Linked to original sources

arXiv2021

Mechanical disorder of sticky-sphere glasses. II. Thermo-mechanical inannealability

Many structural glasses feature static and dynamic mechanical properties that can depend strongly on glass formation history. The degree of universality of this history-dependence, and what it is possibly affected by, are largely unexplored. Here we show that the variability of elastic properties of simple computer glasses under thermal annealing depends strongly on the strength of attractive interactions between the glasses' constituent particles -- referred to here as glass `stickiness'. We find that in stickier glasses the stiffening of the shear modulus with thermal annealing is strongly suppressed, while the thermal-annealing-induced softening of the bulk modulus is enhanced. Our key finding is that the characteristic frequency and density per frequency of soft quasilocalized modes becomes effectively invariant to annealing in very sticky glasses, the latter are therefore deemed `thermo-mechanically inannealable'. The implications of our findings and future research directions are discussed.

cond-mat.soft↗

arXiv2021

An energy-landscape-based crossover temperature in glass-forming liquids

The systematic identification of temperature scales in supercooled liquids that are key to understanding those liquids' underlying glass properties, and the latter's formation-history dependence, is a challenging task. Here we study the statistics of particles' squared displacements $δr^2$ between equilibrium liquid configurations at temperature $T$, and their underlying inherent states, using computer simulations of 11 different computer-glass-formers. We show that the relative fluctuations of $δr^2$ are nonmonotonic in $T$, exhibiting a maximum whose location defines the crossover temperature $T_{\small{\mathsf{X}}}$. Therefore, $T_{\small{\mathsf{X}}}$ marks the point of maximal heterogeneity during the process of tumbling down the energy landscape, starting from an equilibrium liquid state at temperature $T$, down to its underlying inherent state. We extract $T_{\small{\mathsf{X}}}$ for the 11 employed computer glasses, ranging from tetrahedral glasses to packings of soft elastic spheres, and demonstrate its usefulness in putting the elastic properties of different glasses on the same footing. Interestingly, we further show that $T_{\small{\mathsf{X}}}$ marks the crossover between two distinct regimes of the mean $\langleδr^2\rangle$: a high temperature regime in which $\langleδr^2\rangle$ scales approximately as $T^{0.5}$, and a deeply-supercooled regime in which $\langleδr^2\rangle$ scales approximately as $T^{1.3}$. Further research directions are discussed.

cond-mat.soft↗

arXiv2021

Note: Simple argument for emergent anisotropic stress correlations in disordered solids

It is now well-established that mechanical equilibrium in athermal disordered solids gives rise to anisotropic spatial correlations of the coarse-grained stress field that decay in space as $1/r^d$, where $r$ is the distance from the origin, and $d$ denotes the spatial dimension. In this note we present a simple, geometry based argument for the scaling form of the emergent spatial correlations of the stress field in disordered solids.

cond-mat.soft↗

arXiv2020

Low-frequency vibrational spectrum of mean-field disordered systems

We study a recently introduced and exactly solvable mean-field model for the density of vibrational states $\mathcal{D}(ω)$ of a structurally disordered system. The model is formulated as a collection of disordered anharmonic oscillators, with random stiffness $κ$ drawn from a distribution $p(κ)$, subjected to a constant field $h$ and interacting bilinearly with a coupling of strength $J$. We investigate the vibrational properties of its ground state at zero temperature. When $p(κ)$ is gapped, the emergent $\mathcal{D}(ω)$ is also gapped, for small $J$. Upon increasing $J$, the gap vanishes on a critical line in the $(h,J)$ phase diagram, whereupon replica symmetry is broken. At small $h$, the form of this pseudogap is quadratic, $\mathcal{D}(ω)\simω^2$, and its modes are delocalized, as expected from previously investigated mean-field spin glass models. However, we determine that for large enough $h$, a quartic pseudogap $\mathcal{D}(ω)\simω^4$, populated by localized modes, emerges, the two regimes being separated by a special point on the critical line. We thus uncover that mean-field disordered systems can generically display both a quadratic-delocalized and a quartic-localized spectrum at the glass transition.

cond-mat.dis-nn↗

arXiv2020

Mean-field model of interacting quasilocalized excitations in glasses

Structural glasses feature quasilocalized excitations whose frequencies $ω$ follow a universal density of states ${\cal D}(ω)\!\sim\!ω^4$. Yet, the underlying physics behind this universality is not fully understood. Here we study a mean-field model of quasilocalized excitations in glasses, viewed as groups of particles embedded inside an elastic medium and described collectively as anharmonic oscillators. The oscillators, whose harmonic stiffness is taken from a rather featureless probability distribution (of upper cutoff $κ_0$) in the absence of interactions, interact among themselves through random couplings (characterized by strength $J$) and with the surrounding elastic medium (an interaction characterized by a constant force $h$). We first show that the model gives rise to a gapless density of states ${\cal D}(ω)\!=\!A_{\rm g}\,ω^4$ for a broad range of model parameters, expressed in terms of the strength of stabilizing anharmonicity, which plays a decisive role in the model. Then -- using scaling theory and numerical simulations -- we provide a complete understanding of the non-universal prefactor $A_{\rm g}(h,J,κ_0)$, of the oscillators' interaction-induced mean square displacement and of an emerging characteristic frequency, all in terms of properly identified dimensionless quantities. In particular, we show that $A_{\rm g}(h,J,κ_0)$ is a nonmonotonic function of $J$ for a fixed $h$, varying predominantly exponentially with $-(κ_0 h^{2/3}\!/J^2)$ in the weak interactions (small $J$) regime -- reminiscent of recent observations in computer glasses -- and predominantly decaying as a power-law for larger $J$, in a regime where $h$ plays no role. We discuss the physical interpretation of the model and its possible relations to available observations in structural glasses, along with delineating some future research directions.

cond-mat.dis-nn↗

arXiv2020

Extracting the properties of quasilocalized modes in computer glasses: Long-range continuum fields, contour integrals and boundary effects

Low-frequency nonphononic modes and plastic rearrangements in glasses are spatially quasilocalized, i.e. feature a disorder-induced short-range core and known long-range decaying elastic fields. Extracting the unknown short-range core properties, potentially accessible in computer glasses, is of prime importance. Here we consider a class of contour integrals, performed over the known long-range fields, which are especially designed for extracting the core properties. We first show that in computer glasses of typical sizes used in current studies, the long-range fields of quasilocalized modes experience boundary effects related to the simulation box shape and the widely employed periodic boundary conditions. In particular, image interactions mediated by the box shape and the periodic boundary conditions induce fields' rotation and orientation-dependent suppression of their long-range decay. We then develop a continuum theory that quantitatively predicts these finite-size boundary effects and support it by extensive computer simulations. The theory accounts for the finite-size boundary effects and at the same time allows the extraction of the short-range core properties, such as their typical strain ratios and orientation. The theory is extensively validated in both 2D and 3D. Overall, our results offer a useful tool for extracting the intrinsic core properties of nonphononic modes and plastic rearrangements in computer glasses.

cond-mat.soft↗

arXiv2020

Robustness of Density of Low Frequency States in Amorphous Solids

Low frequency quasi-localized modes of amorphous glasses appear to exhibit universal density of states, depending on the frequencies as $D(ω) \sim ω^4$. To date various models of glass formers with short range binary interaction, and network glasses with both binary and ternary interactions, were shown to conform with this law. In this paper we examine granular amorphous solids with long-range electrostatic interactions, and find that they exhibit the same law. To rationalize this wide universality class we return to a model proposed by Gurevich, Parshin and Schober (GPS) and analyze its predictions for interaction laws with varying spatial decay, exploring this wider than expected universality class. Numerical and analytic results are provided for both the actual system with long range interaction and for the GPS model.

cond-mat.stat-mech↗

arXiv2020

Universality of the nonphononic vibrational spectrum across different classes of computer glasses

It has been recently established that the low-frequency spectrum of simple computer glass models is populated by soft, quasilocalized nonphononic vibrational modes whose frequencies $ω$ follow a gapless, universal distribution ${\cal D}(ω)\!\sim\!ω^4$. While this universal nonphononic spectrum has been shown to be robust to varying the glass history and spatial dimension, it has so far only been observed in simple computer glasses featuring radially-symmetric, pairwise interaction potentials. Consequently, the relevance of the universality of nonphononic spectra seen in simple computer glasses to realistic laboratory glasses remains unclear. Here we demonstrate the emergence of the universal $ω^4$ nonphononic spectrum in a broad variety of realistic computer glass models, ranging from tetrahedral network glasses with three-body interactions, through molecular glasses and glassy polymers, to bulk metallic glasses (BMGs). Taken together with previous observations, our results indicate that the low-frequency nonphononic vibrational spectrum of any glassy solid quenched from a melt features the universal $ω^4$ law, independently of the nature of its microscopic interactions.

cond-mat.soft↗

arXiv2020

Nonlinear quasilocalized excitations in glasses. I. True representatives of soft spots

Structural glasses formed by quenching a melt possess a population of soft quasilocalized excitations --- often called `soft spots' --- that are believed to play a key role in various thermodynamic, transport and mechanical phenomena. Under a narrow set of circumstances, quasilocalized excitations assume the form of vibrational (normal) modes, that are readily obtained by a harmonic analysis of the multi-dimensional potential energy. In general, however, direct access to the population of quasilocalized modes via harmonic analysis is hindered by hybridizations with other low-energy excitations, e.g.~phonons. In this series of papers we re-introduce and investigate the statistical-mechanical properties of a class of low-energy quasilocalized modes --- coined here \emph{nonlinear quasilocalized excitations} (NQEs) --- that are defined via an anharmonic (nonlinear) analysis of the potential energy landscape of a glass, and do not hybridize with other low-energy excitations. In this first paper, we review the theoretical framework that embeds a micromechanical definition of NQEs. We demonstrate how harmonic quasilocalized modes hybridize with other soft excitations, whereas NQEs properly represent soft spots without hybridization. We show that NQEs' energies converge to the energies of the softest, non-hybridized harmonic quasilocalized modes, cementing their status as true representatives of soft spots in structural glasses. Finally, we perform a statistical analysis of the mechanical properties of NQEs, which results in a prediction for the distribution of potential energy barriers that surround typical inherent states of structural glasses, as well as a prediction for the distribution of local strain thresholds to plastic instability.

cond-mat.soft↗

arXiv2020

Finite-size effects in the nonphononic density of states in computer glasses

The universal form of the density of nonphononic, quasilocalized vibrational modes of frequency $ω$ in structural glasses, ${\cal D}(ω)$, was predicted theoretically decades ago, but only recently revealed in numerical simulations. In particular, it has been recently established that, in generic computer glasses, ${\cal D}(ω)$ increases from zero frequency as $ω^4$, independent of spatial dimension and of microscopic details. However, in [E. Lerner, and E. Bouchbinder, Phys. Rev. E 96, 020104(R) (2017)] it was shown that the preparation protocol employed to create glassy samples may affect the form of their resulting ${\cal D}(ω)$: glassy samples rapidly quenched from high temperature liquid states were shown to feature ${\cal D}(ω)\!\sim\!ω^β$ with $β\!<\!4$, presumably limiting the degree of universality of the $ω^4$ law. Here we show that exponents $β\!<\!4$ are only seen in small glassy samples quenched from high-temperatue liquid states --- whose sizes are comparable to or smaller than the size of the disordered core of soft quasilocalized vibrations --- while larger glassy samples made with the same protocol feature the universal $ω^4$ law. Our results demonstrate that observations of $β\!<\!4$ in the nonphononic density of states stem from finite-size effects, and we thus conclude that the $ω^4$ law should be featured by any sufficiently large glass quenched from a melt.

cond-mat.soft↗

arXiv2020

Pinching a glass reveals key properties of its soft spots

It is now well established that glasses feature quasilocalized nonphononic excitations --- coined "soft spots"---, which follow a universal $ω^4$ density of states in the limit of low frequencies $ω$. All glass-specific properties, such as the dependence on the preparation protocol or composition, are encapsulated in the non-universal prefactor of the universal $ω^4$ law. The prefactor, however, is a composite quantity that incorporates information both about the number of quasilocalized nonphononic excitations and their characteristic stiffness, in an apparently inseparable manner. We show that by pinching a glass, i.e. by probing its response to force dipoles, one can disentangle and independently extract these two fundamental pieces of physical information. This analysis reveals that the number of quasilocalized nonphononic excitations follows a Boltzmann-like law in terms of the parent temperature from which the glass is quenched. The latter, sometimes termed the fictive (or effective) temperature, plays important roles in non-equilibrium thermodynamic approaches to the relaxation, flow and deformation of glasses. The analysis also shows that the characteristic stiffness of quasilocalized nonphononic excitations can be related to their characteristic size, a long sought-for length scale. These results show that important physical information, which is relevant for various key questions in glass physics, can be obtained through pinching a glass.

cond-mat.soft↗

arXiv2020

Statistical mechanics of local force dipole responses in computer glasses

Soft quasilocalized modes (QLMs) are universally featured by structural glasses quenched from a melt, and are supposedly involved in a number of glassy anomalies such as the low temperature scaling of their thermal conductivity and specific heat, and sound attenuation at intermediate frequencies. In computer glasses, QLMs may assume the form of harmonic vibrational modes under a narrow set of circumstances, however direct access to their full distribution over frequency is hindered by hybridizations of QLMs with other low-frequency modes (e.g.~phonons). Previous studies to overcome this issue have demonstrated that the response of a glass to local force dipoles serves as a good proxy for its QLMs; we therefore study here the statistical-mechanical properties of the responses to local force dipoles in computer glasses, over a large range of glass stabilities and in various spatial dimensions, with the goal of revealing properties of the yet-inaccessible full distribution of QLMs' frequencies. We find that, as opposed to the spatial-dimension-independent universal distribution of QLMs' frequencies $ω$ (and, consequently, also of their stiffness $κ\!=\!ω^2$), the distribution of stiffnesses associated with responses to local force dipoles features a (weak) dependence on spatial dimension. We rationalize this dependence by introducing a lattice model that incorporates both the real-space profiles of QLMs --- associated with dimension-dependent long-range elastic fields --- and the universal statistical properties of their frequencies. Finally, we discuss possible connections between our findings and basic aspects of the glass transition problem, and to finite-size effects in plastic activity of ultrastable glasses.

cond-mat.soft↗

arXiv2019

Mechanical properties of simple computer glasses

Recent advances in computational glass physics enable the study of computer glasses featuring a very wide range of mechanical and kinetic stabilities. The current literature, however, lacks a comprehensive data set against which different computer glass models can be quantitatively compared on the same footing. Here we present a broad study of the mechanical properties of several popular computer glass forming models. We examine how various dimensionless numbers that characterize the glasses' elasticity and elasto-plasticity vary under different conditions --- in each model and across models --- with the aim of disentangling the model-parameter-, external-parameter- and preparation-protocol-dependencies of these observables. We expect our data set to be used as an interpretive tool in future computational studies of elasticity and elasto-plasticity of glassy solids.

cond-mat.soft↗

arXiv2019

Rigidity and auxeticity transitions in networks with strong bond-bending interactions

A widely-studied model for gels or biopolymeric fibrous materials are networks with central force interactions, such as Hookean springs. Less commonly studied are materials whose mechanics are dominated by non-central force interactions such as bond-bending potentials. Inspired by recent experimental advancements in designing colloidal gels with tunable interactions, we study the micro- and macroscopic elasticity of two-dimensional planar graphs with strong bond bending potentials, in addition to weak central forces. We introduce a theoretical framework that allows us to directly investigate the limit in which the ratio of characteristic central-force to bending stiffnesses vanishes. In this limit we show that a generic isostatic point exists at $z_c=4$, coinciding with the isostatic point of frames with central force interactions in two dimensions. We further demonstrate the emergence of a stiffening transition when the coordination is increased towards the isostatic point, which shares similarities with the strain-induced stiffening transition observed in biopolymeric fibrous materials, and coincides with an auxeticity transition above which the material's Poisson's ratio approaches -1 when bond-bending interactions dominate.

cond-mat.soft↗

arXiv2019

Wave attenuation in glasses: Rayleigh and generalized-Rayleigh scattering scaling

The attenuation of long-wavelength phonons (waves) by glassy disorder plays a central role in various glass anomalies, yet it is neither fully characterized, nor fully understood. Of particular importance is the scaling of the attenuation rate $Γ(k)$ with small wavenumbers $k\!\to\!0$ in the thermodynamic limit of macroscopic glasses. Here we use a combination of theory and extensive computer simulations to show that the macroscopic low-frequency behavior emerges at intermediate frequencies in finite-size glasses, above a recently identified crossover wavenumber $k_\dagger$, where phonons are no longer quantized into bands. For $k\!<\!k_\dagger$, finite-size effects dominate $Γ(k)$, which is quantitatively described by a theory of disordered phonon bands. For $k\!>\!k_\dagger$, we find that $Γ(k)$ is affected by the number of quasilocalized nonphononic excitations, a generic signature of glasses that feature a universal density of states. In particular, we show that in a frequency range in which this number is small, $Γ(k)$ follows a Rayleigh scattering scaling $\sim\!k^{d+1}$ ($d$ is the spatial dimension), and that in a frequency range in which this number is sufficiently large, the recently observed generalized-Rayleigh scaling of the form $\sim\!k^{d+1}\log\!{(k_0/k)}$ emerges ($k_0\!>k_\dagger$ is a characteristic wavenumber). Our results suggest that macroscopic glasses --- and, in particular, glasses generated by conventional laboratory quenches that are known to strongly suppress quasilocalized nonphononic excitations --- exhibit Rayleigh scaling at the lowest wavenumbers $k$ and a crossover to generalized-Rayleigh scaling at higher $k$. Some supporting experimental evidence from recent literature is presented.

cond-mat.soft↗

arXiv2019

Characterizing nonaffinity upon decompression of soft-sphere packings

Athermal elastic moduli of soft sphere packings are known to exhibit universal scaling properties near the unjamming point, most notably the vanishing of the shear-to-bulk moduli ratio $G/B$ upon decompression. Interestingly, the smallness of $G/B$ stems from the large nonaffinity of deformation-induced displacements under shear strains, compared to insignificant nonaffinity of displacements under compressive strains. In this work we show using numerical simulations that the relative weights of the affine and nonaffine contributions to the bulk modulus, and their dependence on the proximity to the unjamming point, can qualitatively differ between different models that feature the same generic unjamming phenomenology. In canonical models of unjamming we observe that the ratio of the nonaffine to total bulk moduli $B_{na}/B$ approaches a constant upon decompression, while in other, less well-studied models, it vanishes. We show that the vanishing of $B_{na}/B$ in non-canonical models stems from the emergence of an invariance of net (zero) forces on the constituent particles to compressive strains at the onset of unjamming. We provide a theoretical scaling analysis that fully explains our numerical observations, and allows to predict the scaling behavior of $B_{na}/B$ upon unjamming, given the functional form of the pairwise interaction potential.

cond-mat.soft↗

arXiv2019

Micromechanical theory of strain-stiffening of biopolymer networks

Filamentous bio-materials such as fibrin or collagen networks exhibit an enormous stiffening of their elastic moduli upon large deformations. This pronounced nonlinear behavior stems from a significant separation between the stiffnesses scales associated with bending vs. stretching the material's constituent elements. Here we study a simple model of such materials - floppy networks of hinged rigid bars embedded in an elastic matrix - in which the effective ratio of bending to stretching stiffnesses vanishes identically. We introduce a theoretical framework and build upon it to construct a numerical method with which the model's micro- and macro-mechanics can be carefully studied. Our model, numerical method and theoretical framework allow us to robustly observe and fully understand the critical properties of the athermal strain-stiffening transition that underlies the nonlinear mechanical response of a broad class of biomaterials.

cond-mat.soft↗

arXiv2019

Non-reciprocal robotic metamaterials

Non-reciprocal transmission of motion is potentially highly beneficial to a wide range of applications, ranging from wave guiding, to shock and vibration damping and energy harvesting. To date, large levels of non-reciprocity have been realized using broken spatial or temporal symmetries, yet only in the vicinity of resonances or using nonlinearities, thereby nonreciprocal transmission remains limited to narrow ranges of frequencies or input magnitudes and sensitive to attenuation. Here, we devise a novel type of robotic mechanical metamaterials wherein we use local control loops to break reciprocity at the level of the interactions between the unit cells. We show theoretically that first-of-their-kind asymmetric standing waves at all frequencies and unidirectionally amplified propagating waves emerge. We demonstrate experimentally and numerically that this property leads to tunable, giant, broadband and attenuation-free non-reciprocal performances, namely a level of 50dB non-reciprocal isolation over 3.5 decades in frequency, as well as one-way amplification of pulses.

physics.app-ph↗