arXiv subjects

Gustavo Düring

Publications and source records attributed to Gustavo Düring.

At least 19 recordsLinked to original sources

arXiv2026

Bridging the Gap Between Avalanche Relaxation and Yielding Rheology

The yielding transition in amorphous materials, whether driven passively (simple shear) or actively, remains a fundamental open question in soft matter physics. While avalanche statistics at the critical point have been extensively studied, the emergence of the dynamic regime at yielding and the steady-state flow properties remain poorly understood. In particular, the significant variability observed in flow curves across different systems lacks a clear explanation. We determine, for the first time, the relationship between avalanche duration and size across the yielding transition, revealing how it evolves from quasistatic to dynamic flow regimes. This precise measurement is made using the Controlled Relaxation Time Model (CRTM), a new simulation framework that treats the relaxation time as a tunable parameter. CRTM reproduces known results in both limits and enables a direct analysis of the change of regime between them. Applying the model to different microscopic dynamics, we find that the existing scaling relation connecting critical exponents under flow holds for passive systems. However, active systems exhibit significant deviations, suggesting a missing ingredient in the current understanding of yielding.

cond-mat.soft↗

arXiv2026

Active Growth Layer Induced by Micromechanical Feedback Shapes Proliferating Cell Collectives

Proliferating cell collectives often develop an active growth layer near their boundary that regulates expansion and morphology, as observed in systems ranging from bacterial biofilms to epithelial tissues and tumor spheroids. While such layers have been attributed to diverse mechanisms, their microscopic origin remains unclear in many situations. Here, we show that micromechanical feedback alone provides a minimal mechanism for their emergence. We introduce a particle-based model of non-motile proliferating cells in which growth is locally inhibited by compressive stress, coupling division to mechanical interactions and generating an active growth layer without biochemical regulation. An emergent mechanical length scale, denoted by $χ$, sets the extent of the proliferative region and controls the system's behavior across scales, governing growth dynamics, morphology and organizing internal stress and velocity fields. Coarse-graining the model yields a continuum description with no adjustable parameters, providing a microscopic foundation for existing approaches. When the colony expands into a passive environment, we observe and characterize fingering instabilities driven purely by mechanical feedback. These instabilities can be tuned through the system geometry relative to $χ$, and leads to an exponential acceleration of colony growth, enhancing the collective growth rate. We further establish a correspondence with nutrient-depletion models, providing a route to study the statistical properties of expanding fronts within a minimal microscopic framework.

cond-mat.soft↗

arXiv2024

Self-Aligning Polar Active Matter

Self-alignment describes the property of a polar active unit to align or anti-align its orientation towards its velocity. In contrast to mutual alignment, where the headings of multiple active units tend to directly align to each other -- as in the celebrated Vicsek model --, self-alignment impacts the dynamics at the individual level by coupling the rotation and displacements of each active unit. This enriches the dynamics even without interactions or external forces, and allows, for example, a single self-propelled particle to orbit in a harmonic potential. At the collective level, self-alignment modifies the nature of the transition to collective motion already in the mean field description, and it can also lead to other forms of self-organization such as collective actuation in dense or solid elastic assemblies of active units. This has significant implications for the study of dense biological systems, metamaterials, and swarm robotics. Here, we review a number of models that were introduced independently to describe the previously overlooked property of self-alignment and identify some of its experimental realizations. Our aim is three-fold: (i)~underline the importance of self-alignment in active systems, especially in the context of dense populations of active units and active solids; (ii)~provide a unified mathematical and conceptual framework for the description of self-aligning systems; (iii)~discuss the common features and specific differences of the existing models of self-alignment. We conclude by discussing promising research avenues in which the concept of self-alignment could play a significant role.

cond-mat.soft↗

arXiv2024

Active Solids Model: Rigid Body Motion and Shape-changing Mechanisms

Active solids such as cell collectives, colloidal clusters, and active metamaterials exhibit diverse collective phenomena, ranging from rigid body motion to shape-changing mechanisms. The nonlinear dynamics of such active materials remains however poorly understood when they host zero-energy deformation modes and when noise is present. Here, we show that stress propagation in a model of active solids induces the spontaneous actuation of multiple soft floppy modes, even without exciting vibrational modes. By introducing an adiabatic approximation, we map the dynamics onto an effective Landau free energy, predicting mode selection and the onset of collective dynamics. These results open new ways to study and design living and robotic materials with multiple modes of locomotion and shape-change.

cond-mat.soft↗

arXiv2024

Elasticity of self-organized frustrated disordered spring networks

There have been some interesting recent advances in understanding the notion of mechanical disorder in structural glasses and the statistical mechanics of these systems' low-energy excitations. Here we contribute to these advances by studying a minimal model for structural glasses' elasticity in which the degree of mechanical disorder -- as characterized by recently introduced dimensionless quantifiers -- is readily tunable over a very large range. We comprehensively investigate a number of scaling laws observed for various macro-, meso- and microscopic elastic properties, and rationalize them using scaling arguments. Interestingly, we demonstrate that the model features the universal quartic glassy vibrational density of states as seen in many atomistic and molecular models of structural glasses formed by cooling a melt. The emergence of this universal glassy spectrum highlights the role of self-organization (towards mechanical equilibrium) in its formation, and elucidates why models featuring structural frustration alone do not feature the same universal glassy spectrum. Finally, we discuss relations to existing work in the context of strain-stiffening of elastic networks and of low-energy excitations in structural glasses, in addition to future research directions.

cond-mat.soft↗

arXiv2023

Avalanche properties at the yielding transition: from externally deformed glasses to active systems

We investigated the yielding phenomenon in the quasistatic limit using numerical simulations of soft particles. Two different deformation scenarios, simple shear (passive) and self-random force (active), and two interaction potentials were used. Our approach reveals that the exponents describing the avalanche distribution are universal within the margin of error, showing consistency between the passive and active systems. This indicates that any differences observed in the flow curves may have resulted from a dynamic effect on the avalanche propagation mechanism. The evolution time required to reach a steady state differs significantly between active and passive scenarios under similar conditions. However, we demonstrated that plastic avalanches under athermal quasistatic simulation dynamics display a similar scaling relationship between avalanche size and relaxation time, which cannot explain the different flow curves.

cond-mat.soft↗

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↗

arXiv2022

Path integral description and direct interaction approximation for elastic plate turbulence

In this work, we apply the Martin-Siggia-Rose path integral formalism to the equations of a thin elastic plate. Using a diagrammatic technique, we obtain the direct interaction approximation (DIA) equations to describe the evolutions of the correlation function and the response function of the fields. Consistent with previous results, we show that DIA equations for elastic plates can be derived from a non-markovian stochastic process and that in the weakly nonlinear limit, the DIA equations lead to the kinetic equation of wave turbulence theory. We expect that this approach will allow a better understanding of the statistical properties of wave turbulence and that DIA equations can open new avenues for understanding the breakdown of weakly nonlinear turbulence for elastic plates.

cond-mat.stat-mech↗

arXiv2021

Critical yielding rheology: from externally deformed glasses to active systems

In the last decade many research efforts have been focused on understanding the rheology of disordered materials, and several theoretical predictions have been put forward regarding their yielding behavior. Nevertheless, not many experiments nor molecular dynamics simulations were dedicated to testing those theoretical predictions. Here we use computer simulations to study the yielding transition under two different loading schemes: standard simple shear dynamics, and self-propelled, dense active systems. In the active systems a yielding transition is observed as expected, when the self-propulsion is increased. However, the range of self-propulsions in which a pure liquid regime exist appears to vanish upon approaching the so-called "jamming point" at which solidity of soft-sphere packings is lost. Such an "active yielding" transition shares similarities with the generic yielding transition for shear flows. A Herschel-Bulkley law is observed in both loading scenarios, with a clear difference in the critical scaling exponents between the two, suggesting the existent of different universality classes for the yielding transition under different driving conditions. In addition, we present direct measurements of length and time scales for both driving scenarios. A comparison with theoretical predictions from recent literature reveals poor agreement with our numerical results.

cond-mat.soft↗

arXiv2021

Auxetic behavior on demand: a three steps recipe for new designs

Despite their outstanding mechanical properties, with many industrial applications, a rational and systematic design of new and controlled auxetic materials remains poorly developed. Here a unified framework is established to describe bidimensional perfect auxetics with potential use in the design of new materials. Perfect auxetics are characterized by a Poisson's ratio $ν=-1$ over a finite strain range and can be modeled as materials composed of rotating rigid units. Inspired by a natural connection between these rotating rigid units with an antiferromagnetic spin system, here are unveiled the conditions for the emergence of a non-trivial floppy mode responsible for the auxetic behavior. Furthermore, this model paves a simple pathway for the design of new auxetic materials, based on three simple steps, which set the sufficient connectivity and geometrical constraints for perfect auxetics. In particular, a new exotic crystal, a Penrose quasi-crystal and the long desired isotropic auxetic material are designed and constructed for the first time. Using 3D printed materials, finite element methods and this rigid unit model, the auxetic behavior of these designs is shown to be robust under small disturbances in the structure, though the Poisson's ratio value relies on system's details, approaching $-1$ close to the ideal case.

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↗

arXiv2018

Elastic Weak Turbulence: from the vibrating plate to the drum

Weak wave turbulence has been observed on a thin elastic plate in previous work. Here we report theoretical, experimental and numerical studies of wave turbulence in a thin elastic plate submitted to increasing tension. When increasing the tension (or decreasing the bending stiffness of the plate) the plate evolves progressively from a plate into an elastic membrane as in drums. We start from the plate and increase the tension in experiments and numerical simulations. We observe that the system remains in a state of weak turbulence of weakly dispersive waves. This observation is in contrast with what has been observed in water waves when decreasing the water depth, which also changes the waves from dispersive to weakly dispersive. The weak turbulence observed in the deep water case evolves into a solitonic regime. Here no such transition is observed for the stretched plate. We then apply the weak turbulence theory to the membrane case and show with numerical simulations that indeed the weak turbulence framework remains valid for the membrane and no formation of singular structures (shocks) should be expected in contrast with acoustic wave turbulence.

cond-mat.stat-mech↗

arXiv2018

A Kolmogorov spectrum for strongly vibrating plates

In fluid turbulence, energy is transferred from a scale to another by an energy cascade that depends only on the energy dissipation rate. It leads by dimensional arguments to the Kolmogorov 1941 (K41) spectrum. Remarkably the normal modes of vibrations in elastic plates manifests an energy cascade with the same K41 spectrum in the fully non-linear regime. Moreover, the elastic deformations present large "eddies" together with a myriad of small "crumpling eddies", such that folds, developable cones, and more complex stretching structures, in close analogy with spots, swirls, vortices and other structures in hydrodynamic turbulence. We characterize the energy cascade, the validity of the constant energy dissipation rate over the scales and the role of intermittency via the correlation functions.

nlin.CD↗

arXiv2017

An exact result in strong wave turbulence of thin elastic plates

An exact result concerning the energy transfers between non-linear waves of thin elastic plate is derived. Following Kolmogorov's original ideas in hydrodynamical turbulence, but applied to the Föppl-von Kármán equation for thin plates, the corresponding Kármán-Howarth-Monin relation and an equivalent of the $\frac{4}{5}$-Kolmogorov's law is derived. A third-order structure function involving increments of the amplitude, velocity and the Airy stress function of a plate, is proven to be equal to $-\varepsilon\, \ell$, where $\ell$ is a length scale in the inertial range at which the increments are evaluated and $\varepsilon$ the energy dissipation rate. Numerical data confirm this law. In addition, a useful definition of the energy fluxes in Fourier space is introduced and proven numerically to be flat in the inertial range. The exact results derived in this Letter are valid for both, weak and strong wave-turbulence. They could be used as a theoretical benchmark of new wave-turbulence theories and to develop further analogies with hydrodynamical turbulence.

cond-mat.stat-mech↗

arXiv2017

Wave turbulence in vibrating plates : the effect of damping

The effect of damping in the wave turbulence regime for thin vibrating plates is studied. An experimental method, allowing measurements of dissipation in the system at all scales, is first introduced. Practical experimental devices for increasing the dissipation are used. The main observable consequence of increasing the damping is a significant modification in the slope of the power spectral density, so that the observed power laws are not in a pure inertial regime. However, the system still displays a turbulent behavior with a cut-off frequency that is determined by the injected power which does not depend on damping. By using the measured damping power-law in numerical simulations, similar conclusions are drawn out.

nlin.CD↗

arXiv2017

Statistics and properties of low-frequency vibrational modes in structural glasses

Low-frequency vibrational modes play a central role in determining various basic properties of glasses, yet their statistical and mechanical properties are not fully understood. Using extensive numerical simulations of several model glasses in three dimensions, we show that in systems of linear size $L$ sufficiently smaller than a crossover size $L_{D}$, the low-frequency tail of the density of states follows $D(ω)\!\sim\!ω^4$ up to the vicinity of the lowest Goldstone mode frequency. We find that the sample-to-sample statistics of the minimal vibrational frequency in systems of size $L\!<\!L_D$ is Weibullian, with scaling exponents in excellent agreement with the $ω^4$ law. We further show that the lowest frequency modes are spatially quasi-localized, and that their localization and associated quartic anharmonicity are largely frequency-independent. The effect of preparation protocols on the low-frequency modes is elucidated and a number of glassy lengthscales are briefly discussed.

cond-mat.soft↗

arXiv2017

Phases of higher spin black holes: Hawking-Page, transitions between black holes and a critical point

We study the thermodynamic phase diagram of three-dimensional $sl(N;\mathbb{R})$ higher spin black holes. By analyzing the semi-classical partition function we uncover a rich structure that includes Hawking-Page transitions to the AdS$_3$ vacuum, first order phase transitions among black hole states, and a second order critical point. Our analysis is explicit for $N=4$ but we extrapolate some of our conclusions to arbitrary $N$. In particular, we argue that even $N$ is stable in the ensemble under consideration but odd $N$ is not.

hep-th↗

arXiv2016

Effect of particle collisions in dense suspension flows

We study non-local effects associated with particle collisions in dense suspension flows, in the context of the affine solvent model known to capture various aspects of the jamming transition. We show that an individual collision changes significantly the velocity field on a characteristic volume $Ω_c\sim 1/δz$ that diverges as jamming is approached, where $δz$ is the deficit in coordination number required to jam the system. Such an event also affects the contact forces between particles on that same volume $Ω_c$, but this change is modest in relative terms, of order $f_{coll}\sim \bar{f}^{0.8}$, where $\bar{f}$ is the typical contact force scale. We then show that the requirement that coordination is stationary (such that a collision has a finite probability to open one contact elsewhere in the system) yields the scaling of the viscosity (or equivalently the viscous number) with coordination deficit $δz$. The same scaling result was derived in [E.~DeGiuli, G.~Düring, E.~Lerner, and M.~Wyart, Phys.~Rev.~E {\bf 91}, 062206 (2015)] via different arguments making an additional assumption. The present approach gives a mechanistic justification as to why the correct finite size scaling volume behaves as $1/δz$, and can be used to recover a marginality condition known to characterize the distributions of contact forces and gaps in jammed packings.

cond-mat.stat-mech↗