Publications

18.(2018). Geometric frustration and compatibility conditions for twodimensional director fields (vol 14, pg 424, 2018). Soft Matter. 14:(6)10681068.

17.(2018). Geometric frustration and compatibility conditions for twodimensional director fields. Soft Matter. 14:(3)424431. Abstract
Bent core (or banana shaped) liquidcrystalformingmolecules locally favor an ordered state of zero splay and constant bend. Such a state, however, cannot be realized in the plane and the resulting liquidcrystalline phase is frustrated and must exhibit some compromise of these two mutually contradicting local intrinsic tendencies. This constitutes one of the most wellstudied examples in which the intrinsic geometry of the constituents of a material gives rise to a geometrically frustrated assembly. Such geometric frustration is not only natural and ubiquitous but also leads to a striking variety of morphologies of ground states and exotic response properties. In this work we establish the necessary and sufficient conditions for two scalar functions, s and b to describe the splay and bend of a director field in the plane. We generalize these compatibility conditions for geometries with nonvanishing constant Gaussian curvature, and provide a reconstruction formula for the director field depending only on the splay and bend fields and their derivatives. Finally, we discuss optimal compromises for simple incompatible cases where the locally preferred values of the splay and bend cannot be simultaneously achieved.

16.(2015). Strong Resistance to Bending Observed for Nanoparticle Membranes. Nano Letters. 15:(10)67326737. Abstract
We demonstrate how gold nanopartide monolayers can be curled up into hollow scrolls that make it possible to extract both bending and stretching moduli from indentation by atomic force microscopy. We find a bending modulus that is 2 orders of magnitude larger than predicted by standard continuum elasticity, an enhancement we associate with nonlocal microstructural constraints. This finding opens up new opportunities for independent control of resistance to bending and stretching at the nanoscale.

15.(2015). Furrows in the wake of propagating dcones. Nature Communications. 6:7232. Abstract
A crumpled sheet of paper displays an intricate pattern of creases and pointlike singular structures, termed dcones. It is typically assumed that elongated creases form when ridges connecting two dcones fold beyond the material yielding threshold, and scarring is thus a byproduct of the folding dynamics that seek to minimize elastic energy. Here we show that rather than merely being the consequence of folding, plasticity can act as its instigator. We introduce and characterize a different type of crease that is inherently plastic and is formed by the propagation of a single point defect. When a preexisting dcone is strained beyond a certain threshold, the singular structure at its apex sharpens abruptly. The resulting focusing of strains yields the material just ahead of the singularity, allowing it to propagate, leaving a furrowlike scar in its wake. We suggest an intuitive fracture analogue to explain the creation of furrows.

14.(2015). NonEuclidean Ribbons. Journal of Elasticity. 119:(12)251261. Abstract
The classical theory of ribbons as developed by Sadowsky and Wunderlich has received much attention in recent years. It concerns the equilibrium conformations of thin and narrow ribbons whose intrinsic structure favors a rectangular and flat state. However, the intrinsic structure of naturally formed ribbons will often be more complicated; Spatial variations in the inplane distance metric can give rise to both geodesic curvature and Gaussian curvature, curving the ribbon in and out of its plane. Moreover, metric variation across the thickness of the ribbon may result in nontrivial reference normal curvatures. The resulting geometric structure is likely to have no zeroenergy (stressfree) realizations in Euclidean space. This paper presents a generalization of the Sadowsky functional, which measures the bending energy of narrow ribbons, for the case of incompatible ribbons (having no stressfree configuration). Specific solutions to special cases where the reference normal curvatures vanish, and for a naturally curved developable ribbon are presented and the resulting twiststretch relations are discussed.

13.(2015). Confined disclinations: Exterior versus material constraints in developable thin elastic sheets. Physical Review E. 91:(2) Abstract
We examine the shape change of a thin disk with an inserted wedge of material when it is pushed against a plane, using analytical, numerical, and experimental methods. Such sheets occur in packaging, surgery, and nanotechnology. We approximate the sheet as having vanishing strain, so that it takes a conical form in which straight generators converge to a disclination singularity. Then, its shape is that which minimizes elastic bending energy alone. Real sheets are expected to approach this limiting shape as their thickness approaches zero. The planar constraint forces a sector of the sheet to buckle into the third dimension. We find that the unbuckled sector is precisely semicircular, independent of the angle delta of the inserted wedge. We generalize the analysis to include conical as well as planar constraints and thereby establish a law of corresponding states for shallow cones of slope is an element of and thin wedges. In this regime, the single parameter delta/is an element of(2) determines the shape. We discuss the singular limit in which the cone becomes a plane, and the unexpected slow convergence to the semicircular buckling observed in real sheets.

12.(2014). Why Do Sleeping Nematodes Adopt a HockeyStickLike Posture?. PLoS One. 9:(7) Abstract
A characteristic posture is considered one of the behavioral hallmarks of sleep, and typically includes functional features such as support for the limbs and shielding of sensory organs. The nematode C. elegans exhibits a sleeplike state during a stage termed lethargus, which precedes ecdysis at the transition between larval stages. A hockeysticklike posture is commonly observed during lethargus. What might its function be? It was previously noted that during lethargus, C. elegans nematodes abruptly rotate about their longitudinal axis. Plausibly, these `` flips'' facilitate ecdysis by assisting the disassociation of the old cuticle from the new one. We found that bodyposture during lethargus was established using a stereotypical motor program and that body bends during lethargus quiescence were actively maintained. Moreover, flips occurred almost exclusively when the animals exhibited a single body bend, preferentially in the anterior or mid section of the body. We describe a simple biomechanical model that imposes the observed lengths of the longitudinally directed bodywall muscles on an otherwise passive elastic rod. We show that this minimal model is sufficient for generating a rotation about the anteriorposterior body axis. Our analysis suggests that posture during lethargus quiescence may serve a developmental role in facilitating flips and that the control of body wall muscles in anterior and posterior body regions are distinct.

11.(2014). Realspace renormalization in statistical mechanics. Reviews of Modern Physics. 86:(2)647669. Abstract
This review compares the conceptualization and practice of early realspace renormalization group methods with the conceptualization of more recent realspace transformations based on tensor networks. For specificity, it focuses upon two basic methods: the "potentialmoving" approach most used in the period 1975 1980 and the "rewiring method" as it has been developed in the last five years. The newer method, part of a development called the tensor renormalization group, was originally based on principles of quantum entanglement. It is specialized for computing approximations for tensor products constituting, for example, the free energy or the ground state energy of a large system. It can attack a wide variety of problems, including quantum problems, which would otherwise be intractable. The older method is formulated in terms of spin variables and permits a straightforward construction and analysis of fixed points in rather transparent terms. However, in the form described here it is unsystematic, offers no path for improvement, and of unknown reliability. The new method is formulated in terms of index variables which may be considered as linear combinations of the statistical variables. Free energies emerge naturally, but fixed points are more subtle. Further, physical interpretations of the index variables are often elusive due to a gauge symmetry which allows only selected combinations of tensor entries to have physical significance. In applications, both methods employ analyses with varying degrees of complexity. The complexity is parametrized by an integer called chi (or D in the recent literature). Both methods are examined in action by using them to compute fixed points related to Ising models for small values of the complexity parameter. They behave quite differently. The old method gives a reasonably good picture of the fixed point, as measured, for example, by the accuracy of the measured critical indices. This happens at low values of chi, but there i

10.(2014). OrientationDependent Handedness and Chiral Design. Physical Review X. 4:(1) Abstract
Chirality occupies a central role in fields ranging from biological selfassembly to the design of optical metamaterials. The definition of chirality, as given by Lord Kelvin, associates chirality with the lack of mirror symmetry: the inability to superpose an object on its mirror image. While this definition has guided the classification of chiral objects for over a century, the quantification of handed phenomena based on this definition has proven elusive, if not impossible, as manifest in the paradox of chiral connectedness. In this work, we put forward a quantification scheme in which the handedness of an object depends on the direction in which it is viewed. While consistent with familiar chiral notions, such as the righthand rule, this framework allows objects to be simultaneously right and left handed. We demonstrate this orientation dependence in three different systemsa biomimetic elastic bilayer, a chiral propeller, and optical metamaterialand find quantitative agreement with chirality pseudotensors whose form we explicitly compute. The use of this approach resolves the existing paradoxes and naturally enables the design of handed metamaterials from symmetry principles.

9.(2013). ThreeDimensional Geometry of the HeinekeMikulicz Strictureplasty. Inflammatory Bowel Diseases. 19:(4)704711. Abstract
Background: The objective of this study was to assess the regional geometry of the HeinekeMikulicz (HM) strictureplasty. The HM intestinal strictureplasty is commonly performed for the treatment of stricturing Crohn's disease of the small intestine. This procedure shifts relatively normal proximal and distal tissue to the point of narrowing and thus increases the luminal diameter. The overall effect on the regional geometry of the HM strictureplasty, however, has not been previously described in detail. Methods: HM strictureplasties were created in latex tubing and cast with an epoxy resin. The resultant casts of the lumens were then imaged using computed tomography. Using 3dimensional vascular reconstruction software, the crosssectional areas were determined and the surface geometry was examined. Results: The HM strictureplasty, while increasing the lumen at the point of the stricture, also results in a counterproductive luminal narrowing proximal and distal to the strictureplasty. Within the model used, crosssectional area was diminished 25% to 50% below baseline. This effect is enhanced when 2 strictureplasties are placed in close proximity to each other. Conclusions: The HM strictureplasty results in alterations in the regional geometry that may result in a compromise of the lumen proximal and distal to the location of the strictureplasty. When 2 HM strictureplasties are created in close proximity to each other, care should be undertaken to assure that the lumen of the intervening segment is adequate. (Inflamm Bowel Dis 2013;19:704711)

8.(2013). The metric description of elasticity in residually stressed soft materials. Soft Matter. 9:(34)81878197. Abstract
Living tissue, polymeric sheets and environmentally responsive gel are often described as elastic media. However, when plants grow, plastic sheets deform irreversibly and hydrogels swell differentially the different material elements within an object change their rest lengths often resulting in objects that possess no stressfree configuration making the standard elastic description inappropriate. In this paper we review an elastic framework based on Riemannian geometry devised to describe such objects lacking a stressfree configuration. In this framework the growth or irreversible deformation are associated with the change of a reference Riemannian metric that prescribes local distances within the body, and the elastic problem is one of optimal embedding. We discuss and resolve points of controversy regarding the Riemannian metric formulation. We give examples for dimensionally reduced theories, such as plates and shells theories, which arise naturally and discuss the relation between geometric frustration and residual stress.

7.(2011). Geometry and Mechanics in the Opening of Chiral Seed Pods. Science. 333:(6050)17261730. Abstract
We studied the mechanical process of seed pods opening in Bauhinia variegate and found a chiralitycreating mechanism, which turns an initially flat pod valve into a helix. We studied configurations of strips cut from pod valve tissue and from composite elastic materials that mimic its structure. The experiments reveal various helical configurations with sharp morphological transitions between them. Using the mathematical framework of "incompatible elasticity," we modeled the pod as a thin strip with a flat intrinsic metric and a saddlelike intrinsic curvature. Our theoretical analysis quantitatively predicts all observed configurations, thus linking the pod's microscopic structure and macroscopic conformation. We suggest that this type of incompatible strip is likely to play a role in the selfassembly of chiral macromolecules and could be used for the engineering of synthetic selfshaping devices.

6.(2011). Hyperbolic nonEuclidean elastic strips and almost minimal surfaces. Physical Review E. 83:(4) Abstract
We study equilibrium configurations of thin and elongated nonEuclidean elastic strips with hyperbolic twodimensional reference metrics (a) over bar which are invariant along the strip. In the vanishing thickness limit energy minima are obtained by minimizing the integral of the mean curvature squared among all isometric embeddings of (a) over bar. For narrow strips these minima are very close to minimal surfaces regardless of the specific form of the metric. We study the properties of these "almost minimal" surfaces and find a rich range of threedimensional stable configurations. We provide some explicit solutions as well as a framework for the incorporation of additional forces and constraints.

5.(2010). The mechanics of nonEuclidean plates. Soft Matter. 6:(22)56935704. Abstract
NonEuclidean plates are plates ("stacks" of identical surfaces) whose twodimensional intrinsic geometry is not Euclidean, i.e. cannot be realized in a flat configuration. They can be generated via different mechanisms, such as plastic deformation, natural growth or differential swelling. In recent years there has been a concurrent theoretical and experimental progress in describing and fabricating nonEuclidean plates (NEP). In particular, an effective plate theory was derived and experimental methods for a controlled fabrication of responsive NEP were developed. In this paper we review theoretical and experimental works that focus on shape selection in NEP and provide an overview of this new field. We made an effort to focus on the governing principles, rather than on details and to relate the main observations to known mechanical behavior of ordinary plates. We also point out to open questions in the field and to its applicative potential.

4.(2009). Buckling transition and boundary layer in nonEuclidean plates. Physical Review E. 80:(1) Abstract
NonEuclidean plates are thin elastic bodies having no stressfree configuration, hence exhibiting residual stresses in the absence of external constraints. These bodies are endowed with a threedimensional reference metric, which may not necessarily be immersible in physical space. Here, based on a recently developed theory for such bodies, we characterize the transition from flat to buckled equilibrium configurations at a critical value of the plate thickness. Depending on the reference metric, the buckling transition may be either continuous or discontinuous. In the infinitely thin plate limit, under the assumption that a limiting configuration exists, we show that the limit is a configuration that minimizes the bending content, among all configurations with zero stretching content (isometric immersions of the midsurface). For small but finite plate thickness, we show the formation of a boundary layer, whose size scales with the square root of the plate thickness and whose shape is determined by a balance between stretching and bending energies.

3.(2007). Spontaneous buckling of elastic sheets with a prescribed nonEuclidean metric. Physica DNonlinear Phenomena. 235:(12)2932. Abstract
We present an experimental study of the threedimensional (3D) configurations that result from nonuniform lateral growth/shrinking of thin elastic sheets. We build gel sheets that undergo inducible differential shrinking. The nonuniform shrinking prescribes a nonEuclidean metric on a disc, and thus a nonzero Gaussian curvature. To minimize their elastic energy the free sheets form threedimensional structures that approximate the imposed metric. We show how both large scale buckling and wrinklingtype structures can be generated, depending on the nature of possible embeddings of the imposed metric in Euclidean space. (c) 2007 Elsevier B.V. All rights reserved.

2.(2007). Shaping of elastic sheets by prescription of nonEuclidean metrics. Science. 315:(5815)11161120. Abstract
The connection between a surface's metric and its Gaussian curvature ( Gauss theorem) provides the base for a shaping principle of locally growing or shrinking elastic sheets. We constructed thin gel sheets that undergo laterally nonuniform shrinkage. This differential shrinkage prescribes nonEuclidean metrics on the sheets. To minimize their elastic energy, the free sheets form threedimensional structures that follow the imposed metric. We show how both largescale buckling and multiscale wrinkling structures appeared, depending on the nature of possible embeddings of the prescribed metrics. We further suggest guidelines for how to generate each type of feature.

1.(2005). Hydrodynamic singularities and clustering in a freely cooling inelastic gas. Physical Review Letters. 94:(8) Abstract
We employ hydrodynamic equations to follow the clustering instability of a freely cooling dilute gas of inelastically colliding spheres into a welldeveloped nonlinear regime. We simplify the problem by dealing with a onedimensional coarsegrained flow. We observe that at a late stage of the instability the shear stress becomes negligibly small, and the gas flows solely by inertia. As a result the flow formally develops a finitetime singularity, as the velocity gradient and the gas density diverge at some location. We argue that flow by inertia represents a generic intermediate asymptotic of unstable free cooling of dilute inelastic gases.