arXiv subjects

Edan Lerner

Publications and source records attributed to Edan Lerner.

At least 37 records · Page 2Linked to original sources

arXiv2023

Auxetic Granular Metamaterials

The flowing, jamming and avalanche behavior of granular materials is satisfyingly universal and vexingly hard to tune: a granular flow is typically intermittent and will irremediably jam if too confined. Here, we show that granular metamaterials made from particles with a negative Poisson's ratio yield more easily and flow more smoothly than ordinary granular materials. We first create a collection of auxetic grains based on a re-entrant mechanism and show that each grain exhibits a negative Poisson's ratio regardless of the direction of compression. Interestingly, we find that the elastic and yielding properties are governed by the high compressibility of granular metamaterials: at a given confinement they exhibit lower shear modulus, lower yield stress and more frequent, smaller avalanches than materials made from ordinary grains. We further demonstrate that granular metamaterials promote flow in more complex confined geometries, such as intruder and hopper geometries, even when the packing contains only a fraction of auxetic grains. Our findings blur the boundary between complex fluids and metamaterials and could help in scenarios that involve process, transport and reconfiguration of granular materials.

cond-mat.soft↗

arXiv2023

Scaling theory of critical strain-stiffening in disordered elastic networks

Disordered elastic networks provide a framework for describing a wide variety of physical systems, ranging from amorphous solids, through polymeric fibrous materials to confluent cell tissues. In many cases, such networks feature two widely separated rigidity scales and are nearly floppy, yet they undergo a dramatic stiffening transition when driven to sufficiently large strains. We present a complete scaling theory of the critical strain-stiffened state in terms of the small ratio between the rigidity scales, which is conceptualized in the framework of a singular perturbation theory. The critical state features quartic anharmonicity, from which a set of nonlinear scaling relations is derived. Scaling predictions for the macroscopic elastic modulus beyond the critical state are derived as well, revealing a previously unidentified characteristic strain scale. The predictions are quantitatively compared to a broad range of available numerical data on biopolymer network models and future research questions are discussed.

cond-mat.soft↗

arXiv2023

Boson-peak vibrational modes in glasses feature hybridized phononic and quasilocalized excitations

A hallmark of structural glasses and other disordered solids is the emergence of excess low-frequency vibrations, on top of the Debye spectrum $D_{\rm Debye}(ω)$ of phonons ($ω$ denotes the vibrational frequency), which exist in any solid whose Hamiltonian is translationally invariant. These excess vibrations -- a signature of which is a THz peak in the reduced density of states $D(ω)/D_{\rm Debye}(ω)$, known as the boson peak -- have resisted a complete theoretical understanding for decades. Here, we provide direct numerical evidence that vibrations near the boson peak consist of hybridizations of phonons with many quasilocalized excitations, the latter were recently shown to generically populate the low-frequency tail of the vibrational spectra of structural glasses quenched from a melt and of disordered crystals. Our results suggest that quasilocalized excitations exist up to and in the vicinity of the boson-peak frequency, and hence constitute fundamental building blocks of the excess vibrational modes in glasses.

cond-mat.soft↗

arXiv2023

The boson peak in the vibrational spectra of glasses

A hallmark of glasses is an excess of low-frequency, nonphononic vibrations, in addition to phonons. It is associated with the intrinsically nonequilibrium and disordered nature of glasses, and is generically manifested as a THz peak -- the boson peak -- in the ratio of the vibrational density of state (VDoS) and Debye's VDoS of phonons. Yet, the excess vibrations and the boson peak are not fully understood. Here, using reanalysis of experimental data, extensive computer simulations and a mean-field model, we show that the nonphononic part of the VDoS itself features both a universal power-law tail and a peak, entirely accounted for by quasi-localized nonphononic vibrations, whose existence was recently established. We explain the mild variation of the peak's frequency and magnitude with glasses' thermal history, along with the strong variation of the power-law tail. We also show that modes that populate the peak's region feature many coupled quasi-localized nonphononic vibrations, when their spatial structure is considered. Our results provide a unified physical picture of the low-frequency vibrational spectra of glasses, and in particular elucidate the origin, nature and properties of the boson peak.

cond-mat.dis-nn↗

arXiv2023

Self-oscillation and Synchronisation Transitions in Elasto-Active Structures

The interplay between activity and elasticity often found in active and living systems triggers a plethora of autonomous behaviors ranging from self-assembly and collective motion to actuation. Amongst these, spontaneous self-oscillations of mechanical structures is perhaps the simplest and most wide-spread type of non-equilibrium phenomenon. Yet, we lack experimental model systems to investigate the various dynamical phenomena that may appear. Here, we report self-oscillation and synchronization transitions in a centimeter-sized model system for one-dimensional elasto-active structures. By combining precision-desktop experiments of elastically coupled self-propelled particles with numerical simulations and analytical perturbative theory, we demonstrate that the dynamics of single chain follows a Hopf bifurcation. We show that this instability is controlled by a single non-dimensional elasto-active number that quantifies the interplay between activity and elasticity. Finally, we demonstrate that pairs of coupled elasto-active chains can undergo a synchronization transition: the oscillations phases of both chains lock when the coupling link is sufficiently stiff. Beyond the canonical case considered here, we anticipate our work to open avenues for the understanding and design of the self-organisation and response of active artificial and biological solids, e.g. in higher dimensions and for more intricate geometries.

cond-mat.soft↗

arXiv2023

Detecting low-energy quasilocalized excitations in computer glasses

Soft, quasilocalized excitations (QLEs) are known to generically emerge in a broad class of disordered solids, and to govern many facets of the physics of glasses, from wave attenuation to plastic instabilities. In view of this key role of QLEs, shedding light upon several open questions in glass physics depends on the availability of computational tools that allow to study QLEs' statistical mechanics. The latter is a formidable task since harmonic analyses are typically contaminated by hybridizations of QLEs with phononic excitations at low frequencies, obscuring a clear picture of QLEs' abundance, typical frequencies and other important micromechanical properties. Here we present an efficient algorithm to detect the field of quasilocalized excitations in structural computer glasses. The algorithm introduced takes a computer-glass sample as input, and outputs a library of QLEs embedded in that sample. We demonstrate the power of the new algorithm by reporting the spectrum of glassy excitations in two-dimensional computer glasses featuring a huge range of mechanical stability, which is inaccessible using conventional harmonic analyses due to phonon-hybridizations. Future applications are finally discussed.

cond-mat.soft↗

arXiv2023

Variability of mesoscopic mechanical disorder in disordered solids

Quantifying mechanical disorder in solids, either disordered crystals or glassy solids, and understanding its range of variability are of prime importance, e.g.~for discovering structure-properties relations. The bounds on the degree of mechanical fluctuations in disordered solids and how those depend on solids formation history remain unknown. Here, we study a broadly applicable quantifier of mesoscopic mechanical disorder $χ$, defined via the dimensionless fluctuations of the shear modulus, over a wide variety of disordered computer solids and upon varying different control parameters. $χ$ is intimately related to basic properties of disordered solids, such as elastic constants and plastic deformability, and can be experimentally extracted by wave-attenuation measurements. We find that a large variety of self-organized glassy solids, where disorder is an emergent property, appear to satisfy a generic lower bound on $χ$. On the other hand, we show that $χ$ is unbounded from above, and may diverge in systems driven towards the critical unjamming point. These results highlight basic properties of disordered solids and set the ground for systematically quantifying mechanical disorder across different systems.

cond-mat.dis-nn↗

arXiv2023

Anomalous linear elasticity of disordered networks

Continuum elasticity is a powerful tool applicable in a broad range of physical systems and phenomena. Yet, understanding how and on what scales material disorder may lead to the breakdown of continuum elasticity is not fully understood. We show, based on recent theoretical developments and extensive numerical computations, that disordered elastic networks near a critical rigidity transition, such as strain-stiffened fibrous biopolymer networks that are abundant in living systems, reveal an anomalous long-range linear elastic response below a correlation length. This emergent anomalous elasticity, which is non-affine in nature, is shown to feature a qualitatively different multipole expansion structure compared to ordinary continuum elasticity, and a slower spatial decay of perturbations. The potential degree of universality of these results, their implications (e.g. for cell-cell communication through biological extracellular matrices) and open questions are briefly discussed.

cond-mat.soft↗

arXiv2022

Nonphononic spectrum of two-dimensional structural glasses

The scaling form and system-size dependence of the low-frequency wing of the nonphononic vibrational spectrum of two-dimensional structural glasses have been debated in recent literature. Here we provide numerical evidence that the prefactor $A_{\rm g}$ of the low-frequency nonphononic vibrational spectrum -- the latter grows from zero frequency ($ω\!=\!0$) as $A_{\rm g}ω^β$ -- is system-size dependent, and that the exponent $β$ exhibits a similar glass-formation-protocol and system-size dependence as seen in three-dimensional structural glasses.

cond-mat.soft↗

arXiv2022

Disordered crystals reveal soft quasilocalized glassy excitations

Structural glasses formed by quenching a melt are known to host a population of low-energy quasilocalized (nonphononic) excitations whose frequencies $ω$ follow a universal $\sim\!ω^4$ distribution as $ω\!\to\!0$, independently of the glass formation history, the interparticle interaction potential or spatial dimension. Here, we show that the universal quartic law of nonphononic excitations also holds in disordered crystals featuring finite long-range order, which is absent in their glassy counterparts. We thus establish that the degree of universality of the quartic law extends beyond structural glasses quenched from a melt. We further find that disordered crystals, whose level of disorder can be continuously controlled, host many more quasilocalized excitations than expected based on their degree of mechanical disorder -- quantified by the relative fluctuations of the shear modulus -- as compared to structural glasses featuring a similar degree of mechanical disorder. Finally, we show that the stability bound on nonlinear quasilocalized excitations -- previously established in structural glasses -- also holds in disordered crystals. Our results are related to glass-like anomalies experimentally observed in disordered crystals. More broadly, they constitute an important step towards tracing the essential ingredients necessary for the emergence of universal nonphononic excitations in disordered solids.

cond-mat.dis-nn↗

arXiv2021

Low-energy quasilocalized excitations in structural glasses

Glassy solids exhibit a wide variety of generic thermomechanical properties, ranging from universal anomalous specific heat at cryogenic temperatures to nonlinear plastic yielding and failure under external driving forces, which qualitatively differ from their crystalline counterparts. For a long time, it has been believed that many of these properties are intimately related to nonphononic, low-energy quasilocalized excitations (QLEs) in glasses. Indeed, recent computer simulations have conclusively revealed that the self-organization of glasses during vitrification upon cooling from a melt leads to the emergence of such QLEs. In this Perspective Article, we review developments over the past three decades towards understanding the emergence of QLEs in structural glasses, and the degree of universality in their statistical and structural properties. We discuss the challenges and difficulties that hindered progress in achieving these goals, and review the frameworks put forward to overcome them. We conclude with an outlook on future research directions and open questions.

cond-mat.soft↗

arXiv2021

Does mesoscopic elasticity control viscous slowing down in glassforming liquids?

The dramatic slowing down of relaxation dynamics of liquids approaching the glass transition remains a highly debated problem, where the crux of the puzzle resides in the elusive increase of the activation barrier $ΔE(T)$ with decreasing temperature $T$. A class of theoretical frameworks -- known as elastic models -- attribute this temperature dependence to the variations of the liquid's macroscopic elasticity, quantified by the high-frequency shear modulus $G_\infty(T)$. While elastic models find some support in a number of experimental studies, these models do not take into account the spatial structures, length scales, and heterogeneity associated with structural relaxation in supercooled liquids. Here, we propose that viscous slowing down is controlled by a mesoscopic elastic stiffness $κ(T)$, defined as the characteristic stiffness of response fields to local dipole forces in the liquid's underlying inherent states. First, we show that $κ(T)$ -- which is intimately related to the energy and length scales characterizing quasilocalized, nonphononic excitations in glasses -- increases more strongly with decreasing $T$ than the macroscopic inherent state shear modulus $G(T)$ in several computer liquids. Second, we show that the simple relation $ΔE(T)\proptoκ(T)$ holds remarkably well for some computer liquids, implying a direct connection between the liquid's underlying mesoscopic elasticity and enthalpic energy barriers. On the other hand, we show that for other computer liquids, the above relation fails. Finally, we provide strong evidence that what distinguishes computer liquids in which the $ΔE(T) \propto κ(T)$ relation holds, from those in which it does not, is that the latter feature highly granular potential energy landscapes, where many sub-basins separated by low activation barriers exist. [Rest of abstract abridged]

cond-mat.soft↗

arXiv2021

Bond-space operator disentangles quasi-localized and phononic modes in structural glasses

The origin of several emergent mechanical and dynamical properties of structural glasses is often attributed to populations of localized structural instabilities, coined quasilocalized modes (QLMs). Under a restricted set of circumstances, glassy QLMs can be revealed by analyzing computer glasses' vibrational spectra in the harmonic approximation. However, this analysis has limitations due to system-size effects and hybridization processes with low energy phononic excitations (plane waves) that are omnipresent in elastic solids. Here we overcome these limitations by exploring the spectrum of a linear operator defined on the space of particle interactions (bonds) in a disordered material. We find that this bond-force-response operator offers a unique interpretation of QLMs in glasses, and cleanly recovers some of their important statistical and structural features. The analysis presented here reveals the dependence of the number density (per frequency) and spatial extent of QLMs on material preparation protocol (annealing). Finally, we discuss future research directions and possible extensions of this work.

cond-mat.dis-nn↗

arXiv2021

A unified quantifier of mechanical disorder in solids

Mechanical disorder in solids, which is generated by a broad range of physical processes and controls various material properties, appears in a wide variety of forms. Defining unified and measurable dimensionless quantifiers, allowing quantitative comparison of mechanical disorder across widely different physical systems, is therefore an important goal. Two such coarse-grained dimensionless quantifiers (among others) appear in the literature, one is related to the spectral broadening of discrete phononic bands in finite-size systems (accessible through computer simulations) and the other is related the spatial fluctuations of the shear modulus in macroscopically large systems. The latter has been recently shown to determine the amplitude of wave attenuation rates in the low-frequency limit (accessible through laboratory experiments). Here, using two alternative and complementary theoretical approaches linked to the vibrational spectra of solids, we derive a basic scaling relation between the two dimensionless quantifiers. This scaling relation, which is supported by simulational data, shows that the two apparently distinct quantifiers are in fact intrinsically related, giving rise to a unified quantifier of mechanical disorder in solids. We further discuss the obtained results in the context of the unjamming transition taking place in soft sphere packings at low confining pressures, in addition to their implications for our understanding of the low-frequency vibrational spectra of disordered solids in general, and in particular those of glassy systems.

cond-mat.soft↗

arXiv2021

Brittle to ductile transitions in glasses: Roles of soft defects and loading geometry

Understanding the fracture toughness of glasses is of prime importance for science and technology. We study it here using extensive atomistic simulations in which the interaction potential, glass transition cooling rate and loading geometry are systematically varied, mimicking a broad range of experimentally accessible properties. Glasses' nonequilibrium mechanical disorder is quantified through $A_{\rm g}$, the dimensionless prefactor of the universal spectrum of nonphononic excitations, which measures the abundance of soft glassy defects that affect plastic deformability. We show that while a brittle-to-ductile transition might be induced by reducing the cooling rate, leading to a reduction in $A_{\rm g}$, iso-$\!A_{\rm g}$ glasses are either brittle or ductile depending on the degree of Poisson contraction under unconstrained uniaxial tension. Eliminating Poisson contraction using constrained tension reveals that iso-$\!A_{\rm g}$ glasses feature similar toughness, and that varying $A_{\rm g}$ under these conditions results in significant toughness variation. Our results highlight the roles played by both soft defects and loading geometry (which affects the activation of defects) in the toughness of glasses.

cond-mat.soft↗

arXiv2021

A simple and broadly-applicable definition of shear transformation zones

Plastic deformation in amorphous solids is known to be carried by stress-induced localized rearrangements of a few tens of particles, accompanied by the conversion of elastic energy to heat. Despite their central role in determining how glasses yield and break, the search for a simple and generally applicable definition of the precursors of those plastic rearrangements -- the so-called shear transformation zones (STZs) -- is still ongoing. Here we present a simple definition of STZs -- based solely on the harmonic approximation of a glass' energy. We explain why and demonstrate directly that our proposed definition of plasticity carriers in amorphous solids is more broadly applicable compared to anharmonic definitions put forward previously. Finally, we offer an open-source library that analyzes low-lying STZs in computer glasses and in laboratory materials such as dense colloidal suspensions for which the harmonic approximation is accessible. Our results constitute a physically motivated methodological advancement towards characterizing mechanical disorder in glasses, and understanding how they yield.

cond-mat.soft↗

arXiv2021

Elastic moduli fluctuations predict wave attenuation rates in glasses

The disorder-induced attenuation of elastic waves is central to the universal low-temperature properties of glasses. Recent literature offers conflicting views on both the scaling of the wave attenuation rate $Γ(ω)$ in the low-frequency limit ($ω\!\to\!0$), and on its dependence on glass history and properties. A theoretical framework -- termed Fluctuating Elasticity Theory (FET) -- predicts low-frequency Rayleigh scattering scaling in $d$ spatial dimensions, $Γ(ω)\!\sim\!γ\,ω^{d+1}$, where $γ\!=\!γ(V_{\rm c})$ quantifies the coarse-grained spatial fluctuations of elastic moduli, involving a correlation volume $V_{\rm c}$ that remains debated. Here, using extensive computer simulations, we show that $Γ(ω)\!\sim\!γ\,ω^3$ is asymptotically satisfied in two dimensions ($d\!=\!2$) once $γ$ is interpreted in terms of ensemble -- rather than spatial -- averages, where $V_{\rm c}$ is replaced by the system size. In so doing, we also establish that the finite-size ensemble-statistics of elastic moduli is anomalous and related to the universal $ω^4$ density of states of soft quasilocalized modes. These results not only strongly support FET, but also constitute a strict benchmark for the statistics produced by coarse-graining approaches to the spatial distribution of elastic moduli.

cond-mat.soft↗

arXiv2021

Mechanical disorder of sticky-sphere glasses. I. Effect of attractive interactions

Recent literature indicates that attractive interactions between particles of a dense liquid play a secondary role in determining its bulk mechanical properties. Here we show that, in contrast with their apparent unimportance to the bulk mechanics of dense liquids, attractive interactions can have a major effect on macro- and microscopic elastic properties of glassy solids. We study several broadly-applicable dimensionless measures of stability and mechanical disorder in simple computer glasses, in which the relative strength of attractive interactions -- referred to as `glass stickiness' -- can be readily tuned. We show that increasing glass stickiness can result in the decrease of various quantifiers of mechanical disorder, on both macro- and microscopic scales, with a pair of intriguing exceptions to this rule. Interestingly, in some cases strong attractions can lead to a reduction of the number density of soft, quasilocalized modes, by up to an order of magnitude, and to a substantial decrease in their core size, similar to the effects of thermal annealing on elasticity observed in recent works. Contrary to the behavior of canonical glass models, we provide compelling evidence indicating that the stabilization mechanism in our sticky-sphere glasses stems predominantly from the self-organized depletion of interactions featuring large, \emph{negative} stiffnesses. Finally, we establish a fundamental link between macroscopic and microscopic quantifiers of mechanical disorder, which we motivate via scaling arguments. Future research directions are discussed.

cond-mat.soft↗