arXiv subjects

Hillel Aharoni

Publications and source records attributed to Hillel Aharoni.

11 recordsLinked to original sources

arXiv2026

Defect Topology in Colloidal Smectics

Colloidal smectics -- layered structures formed in dense suspensions of rod-like particles -- often exhibit grain boundaries, across which the layer orientation changes by $90^{\circ}$. Motivated by this feature, we develop a layer-based topological framework that treats orthogonal grain boundaries as constituents of the ground state rather than as exceptional defect structures. Extending the layer-based approach for ordinary smectics, we reduce the smectic structure to layers, half-layers, and domain walls. We classify the topology of defects and their combination rules based on this structure. In two dimensions, point defects are described by semi-directed cycle graphs. Although the disclination charge remains a valid topological invariant, it does not uniquely classify defects, as distinct graphs may share the same charge. In three dimensions, line defects are classified by their transverse graph structure, while point defects exhibit qualitatively different behavior. In particular, we show that the hedgehog disclination charge is not a topological invariant, but instead varies continuously under smooth deformations of the layer structure.

cond-mat.soft↗

arXiv2026

Unfrustrated Self-Morphing of Bulk Liquid Crystal Elastomers

Precise manipulation of shape-morphing responsive materials is crucial for applications in soft robotics and adaptive structures. While notable precision has been achieved in thin two-dimensional sheets, an accurate volumetric shape-morphing remains a major challenge due to geometric frustration, which inevitably generates complex, residual elastic stresses. In this work, we extend the geometric approach used for thin sheets to bulk Liquid Crystal Elastomers (LCEs). By examining their reference Ricci curvature, we formulate the minimal set of conditions required for a three-dimensional nematic director field to undergo stress-free, frustration-free deformations upon actuation. Through this mathematical framework, we identify two distinct classes of geometrically compatible bulk systems. The first class comprises twistless director fields that remain frustration-free across all temperatures, leading to holographic design principles demonstrated through "Planar" and "Smectic" LCE subfamilies. The second class features twisted configurations that exhibit unique, temperature-selective compatibility, leading to non-monotonic accumulation of internal elastic stresses that relax completely at a predefined target temperature. Our framework establishes a firm mathematical foundation for robust forward and inverse design protocols in bulk LCEs.

cond-mat.soft↗

arXiv2026

Inverse Design of Tightly Woven Smart Fabrics

We present a geometric framework for the inverse design of smart woven fabrics composed of non-uniformly shrinking threads. A sufficiently tight weaving structure imposes strong local criteria on the material deformation and reduces the local geometry to a single scalar degree of freedom. Control over this degree of freedom can be achieved through simple calibration for each specific material system, via either mechanical experiments or numerical simulations. This reduction allows us to inverse-design a woven smart fabric, that conforms to an arbitrary target geometry when actuated, by solving a nonlinear hyperbolic partial differential equation. We validate this approach by deriving the thread-level actuation required for specific target geometries. We present both exact analytic solutions for symmetric shapes and a numerical optimization method for arbitrary freeform surfaces. These results confirm the practicality of our framework in achieving programmable, complex three-dimensional shaping.

cond-mat.soft↗

arXiv2025

Inverse Design of Parameter-Controlled Disclination Paths

Topological defects, such as disclination lines in nematic liquid crystals, are fundamental to many physical systems and applications. In this work, we study the behavior of nematic disclinations in thin parallel-plate geometries with strong patterned planar anchoring. Building on prior models, we solve both the forward problem -- predicting disclination trajectories from given surface patterns -- and an extended inverse problem -- designing surface patterns to produce a tunable family of disclination curves under varying system parameters. We present an explicit calculation for pattern construction, analyze parameter limitations and stability constraints, and highlight experimental and technological applications.

cond-mat.soft↗

arXiv2023

Tunable Three-Dimensional Architecture of Nematic Disclination Lines

Disclinations lines play a key role in many physical processes, from the fracture of materials to the formation of the early universe. Achieving versatile control over disclinations is key to developing novel electro-optical devices, programmable origami, directed colloidal assembly, and controlling active matter. Here, we introduce a theoretical framework to tailor three-dimensional disclination architecture in nematic liquid crystals experimentally. We produce quantitative predictions for the connectivity and shape of disclination lines found in nematics confined between two thinly spaced glass substrates with strong planar anchoring. By drawing an analogy between nematic liquid crystals and magnetostatics, we find that: i) disclination lines connect defects with the same topological charge on opposite surfaces, and ii) disclination lines are attracted to regions of the highest twist. Using polarized light to pattern the in-plane alignment of liquid crystal molecules, we test these predictions experimentally and identify critical parameters that tune the disclination lines' curvature. We verify our predictions with computer simulations and find non-dimensional parameters enabling us to match experiments and simulations at different length scales. Our work provides a powerful method to understand and practically control defect lines in nematic liquid crystals.

cond-mat.soft↗

arXiv2022

Shape Morphing of Planar Liquid Crystal Elastomers

We consider planar liquid crystal elastomers: two dimensional objects made of anisotropic responsive materials, that upon activation remain flat however change their planar shape. We derive a closed form, analytical solution based on the implicit linearity featured by this subclass of deformations. Our solution provides the nematic director field on an arbitrary domain starting with two initial director curves. We discuss the different gauges choices for this problem, and the inclusion of disclinations in the nematic order. Finally, we propose several applications and useful design principles based on this theoretical framework.

cond-mat.soft↗

arXiv2019

Curved geometries from planar director fields - Solving the two-dimensional inverse problem

Thin nematic elastomers, composite hydrogels and plant tissues are among many systems that display uniform anisotropic deformation upon external actuation. In these materials, the spatial orientation variation of a local director field induces intricate global shape changes. Despite extensive recent efforts, to date, there is no general solution to the inverse design problem: how to design a director field that deforms exactly into a desired surface geometry upon actuation, or whether such a field exists. In this work, we phrase this inverse problem as a hyperbolic system of differential equations. We prove that the inverse problem is locally integrable, provide an algorithm for its integration, and derive bounds on global solutions. We classify the set of director fields that deform into a given surface, thus paving the way to finding optimized fields.

cond-mat.soft↗

arXiv2018

Aspects of Defect Topology in Smectic Liquid Crystals

We study the topology of smectic defects in two and three dimensions. We give a topological classification of smectic point defects and disclination lines in three dimensions. In addition we describe the combination rules for smectic point defects in two and three dimensions, showing how the broken translational symmetry of the smectic confers a path dependence on the result of defect addition.

cond-mat.soft↗

arXiv2017

Making Faces: Universal Inverse Design of Surfaces with Thin Nematic Elastomer Sheets

Programmable shape-shifting materials can take different physical forms to achieve multifunctionality in a dynamic and controllable manner. Although morphing a shape from 2D to 3D via programmed inhomogeneous local deformations has been demonstrated in various ways, the inverse problem -- programming a sheet to take an arbitrary desired 3D shape -- is much harder yet critical to realize specific functions. Here, we address this inverse problem in thin liquid crystal elastomer (LCE) sheets, where the shape is preprogrammed by precise and local control of the molecular orientation of the liquid crystal monomers. We show how blueprints for arbitrary surface geometries as well as local extrinsic curvatures can be generated using approximate numerical methods. Backed by faithfully alignable and rapidly lockable LCE chemistry, we precisely embed our designs in LCE sheets using advanced top-down microfabrication techniques. We thus successfully produce flat sheets that, upon thermal activation, take an arbitrary desired shape, such as a face. The general design principles presented here for creating an arbitrary 3D shape will allow for exploration of unmet needs in flexible electronics, metamaterials, aerospace and medical devices, and more.

cond-mat.soft↗

arXiv2017

Composite Dislocations in Smectic Liquid Crystals

Smectic liquid crystals are charcterized by layers that have a preferred uniform spacing and vanishing curvature in their ground state. Dislocations in the smectics play an important role in phase nucleation, layer reorientation, and dynamics. Typically modeled as possessing one line singularity, the layer structure of a dislocation leads to a diverging compression strain as one approaches the defect center, suggesting a large, elastically determined melted core. However, it has been observed that for large charge dislocations, the defect breaks up into two disclinations [C. E. Williams, Philos. Mag. 32, 313 (1975)]. Here we investigate the topology of the composite core. Because the smectic cannot twist, transformations between different disclination geometries are highly constrained. We demonstrate the geometric route between them and show that despite enjoying precisely the topological rules of the three-dimensional nematic, the additional structure of line disclinations in three-dimensional smectics localizes transitions to higher-order point singularities.

cond-mat.soft↗

arXiv2014

Two-dimensional defects in amorphous materials

We present a new definition of defects which is based on a Riemannian formulation of incompatible elasticity. Defects are viewed as local deviations of the material's reference metric field, $\bar{\mathfrak{g}}$, from a Euclidian metric. This definition allows the description of defects in amorphous materials and the formulation of the elastic problem, using a single field, $\bar{\mathfrak{g}}$. We provide a multipole expansion of reference metrics that represent a large family of two-dimensional (2D) localized defects. The case of a dipole, which corresponds to an edge dislocation is studied analytically, experimentally and numerically. The quadrupole term, which is studied analytically, as well as higher multipoles of curvature carry local deformations. These multipoles are good candidates for fundamental strain carrying entities in plasticity theories of amorphous materials and for a continuous modeling of recently developed meta-materials.

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