arXiv subjects

Eran Sharon

Publications and source records attributed to Eran Sharon.

At least 19 recordsLinked to original sources

arXiv2026

Isometric Incompatibility in Growing Elastic Sheets

Geometric incompatibility, the inability of a material's rest state to be realized in Euclidean space, underlies shape formation in natural and synthetic thin sheets. Classical Gauss and Mainardi-Codazzi-Peterson (MCP) incompatibilities explain many patterns in nature, but they do not exhaust the mechanisms that frustrate thin elastic sheets. We identify a new incompatibility that forbids smooth stretching-free configurations, even when the rest state of the elastic sheet locally satisfies the Gauss and MCP compatibility conditions. We demonstrate this principle in a model of surface growth with positive Gaussian curvature, where a geometric horizon forms, leading to the onset of frustration. Experiments, simulations, and theory show that the sheet responds by nucleating periodic d-cone-like dimples. We show that this obstruction to stretching-free configurations is topological, and we point to open questions concerning the origin of frustration.

cond-mat.soft↗

arXiv2025

Confirming Wave Turbulence Predictions in Rotating Turbulence

Though highly impacting our lives, rotating turbulent flows are not well understood. These anisotropic three-dimensional disordered flows are governed by different nonlinear processes, each of which can be dominant in a different range of parameters. More than 20 years ago, Galtier used weak wave turbulence theory (WTT) to derive explicit predictions for the energy spectrum of rotating turbulence. The spectrum is an outcome of forward energy transfer by inertial waves, the linear modes of rotating fluid systems. This spectrum has not yet been observed in freely evolving flows. In this work, we show that the predicted WTT field does exist in steady rotating turbulence, alongside with the more energetic quasi two-dimensional turbulent field. By removing the 2D component from the steady state velocity field, we show that the remainder three-dimensional field consists of inertial waves and exactly obeys WTT predictions. Our analysis verifies the dependence of the energy spectrum on all four relevant parameters and provides limits, beyond which WTT predictions fail. These results provide a solid basis for new theoretical and experimental works focused on the coexistence of the quasi 2D field and the inertial waves field and on their interactions.

physics.flu-dyn↗

arXiv2025

Curved crack paths are predicted by elastic-charges

Predicting crack trajectories in brittle solids remains an open challenge in fracture mechanics due to the non-local nature of crack propagation and the way cracks modify their surrounding medium. Here, we develop a framework for analytically predicting crack trajectories, similar to predicting the motion of charged particles in external fields within Newtonian mechanics. We demonstrate that a crack can be described as a distribution of elastic charges, and within the framework of Linear Elastic Fracture Mechanics (LEFM), its interaction with the background stress can be approximated by a singular geometric charge at the crack tip. The cracks motion is then predicted as the propagation of this singular charge within the unperturbed stress field. We apply our approach to study crack trajectories near defects and validate it through experiments on flat elastomer sheets containing an edge dislocation. The experimental results show excellent agreement with theoretical predictions, including the convergence of curved crack trajectories toward a single focal point. We discuss future extension of our theory to the motion of multiple interacting cracks. Our findings highlight the potential of the elastic-charges approach to significantly advance classical fracture mechanics by enabling analytical solutions to problems traditionally requiring numerical methods.

cond-mat.soft↗

arXiv2024

Fast Radio Bursts and the radio perspective on multi-messenger gravitational lensing

Fast Radio Bursts (FRBs) are extragalactic millisecond-duration radio transients whose nature remains unknown. The advent of numerous facilities conducting dedicated FRB searches has dramatically revolutionised the field: hundreds of new bursts have been detected, and some are now known to repeat. Using interferometry, it is now possible to localise FRBs to their host galaxies, opening up new avenues for using FRBs as astrophysical probes. One promising application is studying gravitationally lensed FRBs. This review outlines the requirements for identifying a lensed FRB, taking into account their propagation effects and the importance of capturing the amplitude and phase of the signal. It also explores the different lens masses that could be probed with FRBs throughout the duration of an FRB survey, from stellar masses to individual galaxies. This highlights the unique cosmological applications of gravitationally lensed FRBs, including measurements of the Hubble constant and the compact object content of dark matter. Finally, we discuss future radio interferometers and the prospects for finding gravitationally lensed FRBs.

astro-ph.HE↗

arXiv2024

4D Printing of Programmable Digital Metamaterials

Advances in 3D printing technology now enable the precise positioning of microscopic material voxels to form complex structures. Combined with emerging multi-material capabilities and printable responsive materials, this opens new possibilities for digital composite materials and 3D printing of shape-transforming structures, or 4D printing. Building upon these advancements, we devise a novel methodology for crafting digitized 4D-printed shape-transforming sheets. We 3D print responsive sheets composed of two layers, each consisting of active and passive voxels meticulously positioned to form thin structures that can be actuated on demand. Our approach solves a long-standing problem in the field, i.e., the independent and simultaneous programming of lateral geometry and reference curvature. This unprecedented control over the resulting shape unlocks new opportunities in synthetic shape-morphing materials, with potential applications in programmable mechanical properties and multi-material systems.

cond-mat.soft↗

arXiv2024

Direct measurement of energy transfer in strongly driven rotating turbulence

A short, abrupt increase in energy injection rate into steady strongly-driven rotating turbulent flow is used as a probe for energy transfer in the system. The injected excessive energy is localized in time and space and its spectra differ from those of the steady turbulent flow. This allows measuring energy transfer rates, in three different domains: In real space, the injected energy propagates within the turbulent field, as a wave packet of inertial waves. In the frequency domain, energy is transferred non-locally to the low, quasi-geostrophic modes. In wavenumber space, energy locally cascades toward small wavenumbers, in a rate that is consistent with two-dimensionsal (2D) turbulence models. Surprisingly however, the inverse cascade of energy is mediated by inertial waves that propagate within the flow with small, but non-vanishing frequency. Our observations differ from measurements and theoretical predictions of weakly driven turbulence. Yet, they show that in strongly-driven rotating turbulence, inertial waves play an important role in energy transfer, even at the vicinity of the 2D manifold.

physics.flu-dyn↗

arXiv2024

Locomotion of Active Sheets Driven by Curvature Modulation

The locomotion of flexible membrane-like organisms on top of curved surfaces appears in different contexts and scales. Still, such dynamics have not yet been quantitatively modeled and no realization of such motion in manmade systems has been achieved. We present an experimental and theoretical study of active gel ribbons surfing on a curved fluid-fluid interface via periodic modulation of their reference curvature. We derive a theoretical model, in which forces and torques emerge from curvature mismatch between the ribbon and the substrate. Analytic and numerical solutions of the equations of motion successfully predict the experimentally measured velocity profiles. We conclude by highlighting the relevance of this new, curvature-driven, mode of locomotion for a broad range of mechanical, as well as biological systems.

cond-mat.soft↗

arXiv2021

Geometric approach to mechanical design principles in continuous elastic sheets

Using a geometric formalism of elasticity theory we develop a systematic theoretical method for controlling and manipulating the mechanical response of slender solids to external loads. We formally express global mechanical properties associated with non-euclidean thin sheets, and interpret the expressions as inverse problem for designing desired mechanical properties. We show that by wisely designing geometric frustration, extreme mechanical properties can be encoded into a material using accessible experimental techniques. To test the methodology we derive a family of geometries that result with anomalous mechanical behavior such as tunable, an-harmonic, and even vanishing rigidities. The presented formalism can be discretized and thus opens a new pathway for the design of both continuum and discrete solids and structures.

cond-mat.soft↗

arXiv2021

Euclidean Frustrated Ribbons

Geometrical frustration in thin sheets is ubiquitous across scales in biology and becomes increasingly relevant in technology. Previous research identified the origin of the frustration as the violation of Gauss's \emph{Theorema Egregium}. Such "Gauss frustration" exhibits rich phenomenology; it may lead to mechanical instabilities, anomalous mechanics and shape-morphing abilities that can be harnessed in engineering systems. Here we report a new type of geometrical frustration, one that is as general as Gauss frustration. We show that its origin is the violation of Mainardi-Codazzi-Peterson compatibility equations and that it appears in Euclidean sheets. Combining experiments, simulations and theory, we study the specific case of a Euclidean ribbon with radial and geodesic curvatures. Experiments, conducted using different materials and techniques, reveal shape transitions, symmetry breaking and spontaneous stress focusing. These observations are quantitatively rationalized using analytic solutions and geometrical arguments. We expect this frustration to play a significant role in natural and engineering systems, specifically in slender 3D printed sheets.

cond-mat.soft↗

arXiv2021

Hierarchy of Geometrical Frustration in Elastic Ribbons: shape-transitions and energy scaling obtained from a general asymptotic theory

Geometrically frustrated elastic ribbons exhibit, in many cases, significant changes in configuration depending on the relation between their width and thickness. We show that the existence of such a transition, and the scaling at which it occurs, strongly depend on the system considered. Using an asymptotic approach, treating the width as a small parameter, we find the leading energy terms resulting from the frustration and predict the existence and scaling of the shape transition. We study in detail 5 different types of frustrated ribbons with a different morphological dependence on ribbon's width: a sharp shape-transition at a critical width, a moderate transition with an intermediate regime, and no transition at all. We show that the predictions of our approach match experimental results from two different experimental systems: prestressed rubber bilayers and 4D printed thermoplastics, in a wide variety of geometric settings.

cond-mat.soft↗

arXiv2019

On the Packing of Stiff Rods on Ellipsoids Part I -- Geometry

We suggest a geometrical mechanism for the ordering of slender filaments inside non-isotropic containers, using cortical microtubules in plant cells and packing of viral genetic material inside capsids as concrete examples. We show analytically how the shape of the cell affects the ordering of phantom, non-self-avoiding, stiff rods. We find that for oblate cells the preferred orientation is along the equator, while for prolate spheroids with an aspect ratio close to one, the orientation is along the principal (long axis). Surprisingly, at high enough aspect ratio, a configurational phase transition occurs, and the rods no longer point along the principal axis, but at an angle to it, due to high curvature at the poles. We discuss some of the possible effects of self avoidance, using energy considerations. These results are relevant to other packing problems as well, such as spooling of filament in the industry or spider silk inside water droplets.

cond-mat.soft↗

arXiv2019

Oscillating membranes: modeling and controlling autonomous shape-transforming sheets

Living organisms have mastered the dynamic control of internal stresses to perform an array of functions, such as change shape and locomote. State-of-the-art attempts to replicate this ability in synthetic materials are rudimentary in comparison. Here we present the first experimental realization of a self-oscillating gel in a thin sheet configuration. We show that internal signaling produces stresses that drive lifelike shape changes, that the material's response is accurately modelled with the theory of non-Euclidean elasticity and that the internal signaling can be programmed with light. Together, our results demonstrate a complete route for developing fully autonomous soft machines.

cond-mat.soft↗

arXiv2018

Shape and Fluctuations of Positively Curved Ribbons

We study the shape and shape fluctuations of positively curved ribbons, with a flat reference metric and a sphere-like reference curvature. Such incompatible geometry is likely to occur in many self assembled materials and other experimental systems. Such ribbons exhibit a sharp transition between rigid ring and an anomalously soft spring as a function of their width. As a result, the temperature dependence of these ribbons' shape is unique, exhibiting a non-monotonic dependence of the persistence and Kuhn lengths on the temperature and width. We map the possible configuration phase space and show the existence of three phases- at high temperatures it is the Ideal Chain phase, where the ribbon is well described by classical models (e.g- worm like chain model); The second phase, for cold and narrow ribbons, is the Plain Ergodic phase - a ribbon in this phase might be thought of as made out of segments that gyrate within an oblate spheroid with extreme aspect ratio; The third phase, for cold, wide ribbons, is a direct result of the residual stress caused by the incompatibility, called Random Structured phase. A ribbon in this phase behaves on large scales as an Ideal Chain, however the segments of this chain are not straight, rather they may have different shapes, mainly helices (both left and right handed) of various pitches.

cond-mat.soft↗

arXiv2016

Isometric immersions, energy minimization and self-similar buckling in non-Euclidean elastic sheets

The edges of torn plastic sheets and growing leaves often display hierarchical buckling patterns. We show that this complex morphology (i) emerges even in zero strain configurations, and (ii) is driven by a competition between the two principal curvatures, rather than between bending and stretching. We identify the key role of branch-point (or "monkey-saddle") singularities in generating complex wrinkling patterns in isometric immersions, and show how they arise naturally from minimizing the elastic energy.

cond-mat.soft↗

arXiv2015

Elasticity and Fluctuations of Frustrated Nano-Ribbons

We derive a reduced quasi-one-dimensional theory of geometrically frustrated elastic ribbons. Expressed in terms of geometric properties alone, it applies to ribbons over a wide range of scales, allowing the study of their elastic equilibrium, as well as thermal fluctuations. We use the theory to account for the twisted-to-helical transition of ribbons with spontaneous negative curvature, and the effect of fluctuations on the corresponding critical exponents. The persistence length of such ribbons changes non-monotonically with the ribbon's width, dropping to zero at the transition. This and other statistical properties qualitatively differ from those of non-frustrated fluctuating filaments.

cond-mat.soft↗

arXiv2015

Elastic interactions between 2D geometric defects

In this paper, we introduce a methodology applicable to a wide range of localized two-dimensional sources of stress. This methodology is based on a geometric formulation of elasticity. Localized sources of stress are viewed as singular defects---point charges of the curvature associated with a reference metric. The stress field in the presence of defects can be solved using a scalar stress function that generalizes the classical Airy stress function to the case of materials with nontrivial geometry. This approach allows the calculation of interaction energies between various types of defects. We apply our methodology to two physical systems: shear-induced failure of amorphous materials and the mechanical interaction between contracting cells.

cond-mat.soft↗

arXiv2015

The plane stress state of residually stressed bodies: a stress function approach

The stressed state of flattened thin elastic sheet, as well as that of translationally symmetric 3D solids, are effectively 2D problems. This paper study equilibrium state-of-stress in metrically-incompatible 2D elastic materials. The solution is represented by a scalar stress function, generalizing the Airy stress function, which is determined by geometric compatibility conditions. We develop a perturbative approximation method for solving this stress function, valid for any constitutive relation. We apply the method for the case of a Hookean solid to solve prototypical examples in which the classical Airy approach is either inaccurate or inapplicable. Results are shown to agree well with numerical results obtained in previous works.

cond-mat.soft↗

arXiv2015

Isometric immersions and self-similar buckling in Non-Euclidean elastic sheets

The edge of torn elastic sheets and growing leaves often form a hierarchical buckling pattern. Within non-Euclidean plate theory this complex morphology can be understood as low bending energy isometric immersions of hyperbolic Riemannian metrics. With this motivation we study the isometric immersion problem in strip and disk geometries. By finding explicit piecewise smooth solutions of hyperbolic Monge-Ampere equations on a strip, we show there exist periodic isometric immersions of hyperbolic surfaces in the small slope regime. We extend these solutions to exact isometric immersions through resummation of a formal asymptotic expansion. In the disc geometry we construct self-similar fractal-like isometric immersions for disks with constant negative curvature. The solutions in both the strip and disc geometry qualitatively resemble the patterns observed experimentally and numerically in torn elastic sheets, leaves and swelling hydrogels. For hyperbolic non-Euclidean sheets, complex wrinkling patterns are thus possible within the class of finite bending energy isometric immersions. Further, our results identify the key role of the degree of differentiability (regularity) of the isometric immersion in determining the global structure of a non-Euclidean elastic sheet in 3-space.

cond-mat.soft↗