Related papers: Shape and Fluctuations of Positively Curved Ribbon…

Ribbons are a class of slender structures whose length, width, and thickness are widely separated from each other. This scale separation gives a ribbon unusual mechanical properties in athermal macroscopic settings, e.g. it can bend without…

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…

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…

We study elastic ribbons subject to large, tensile pre-stress confined to a central region within the cross-section. These ribbons can buckle spontaneously to form helical shapes, featuring regions of alternating chirality (phases) that are…

We address the mechanics of an elastic ribbon subjected to twist and tensile load. Motivated by the classical work of Green and a recent experiment that discovered a plethora of morphological instabilities, we introduce a comprehensive…

The statistical mechanics of a ribbon polymer made up of two semiflexible chains is studied using both analytical techniques and simulation. The system is found to have a crossover transition at some finite temperature, from a type of short…

Using both experiments and finite element simulations, we explore the shape evolution of off-axis nematic elastomer ribbons as a function of temperature. The elastomers are prepared by cross-linking the mesogens with planar anchoring of the…

Twist stiffness and an asymmetric bending stiffness of a polymer or a polymer bundle is captured by the elastic ribbon model. We investigate the effects a ring geometry induces to a thermally fluctuating ribbon, finding bend-bend coupling…

Motivated by recent free-standing graphene experiments, we show how thermal fluctuations affect the mechanical properties of microscopically thin solid ribbons. A renormalization group analysis of flexural phonons reveals that elongated…

We analyze the thermal fluctuations of a narrow graphene nanoribbon. Using a continuum, membrane-like model we study the height-height correlation functions and the destabilization modes corresponding to two different boundaries conditions:…

The role of thermal fluctuations on the conformational dynamics of a single closed filament is studied. It is shown that, due to the interaction between charges and bending degrees of freedom, initially circular aggregates may undergo…

Helical ribbons arise in many biological and engineered systems, often driven by anisotropic surface stress, residual strain, and geometric or elastic mismatch between layers of a laminated composite. A full mathematical analysis is…

We investigate the statistical mechanics of long developable ribbons of finite width and very small thickness. The constraint of isometric deformations in these ribbon-like structures that follows from the geometric separation of scales…

A theoretical analysis of the effect of force and torque on spontaneously twisted, fluctuating elastic ribbons is presented. We find that when a filament with a straight center line and a spontaneously twisted noncircular cross section is…

A rich zoology of shapes emerges from a simple stretched and twisted elastic ribbon. Despite a lot of interest, all these shape are not understood, in particular the shape that prevails at large tension and twist and that emerges from a…

Ribbons are topological objects of biological and technological importance. Here, we study the folding of thick ribbons with hydrophobic surfaces in a bad solvent in regimes in which either the ribbon's thickness or the solvent molecule…

We consider an electron-phonon system in two and three dimensions on square, hexagonal and cubic lattices. The model is a modification of the standard Holstein model where the optical branch is appropriately curved in order to have a…

Crystalline sheets (e.g., graphene and transition metal dichalcogenides) liberated from a substrate are a paradigm for materials at criticality because flexural phonons can fluctuate into the third dimension. Although studies of static…

We present an analytical study of bent twisted ribbons. We first describe the elastic response of a ribbon within a purely mechanical framework. We then study the role of thermal fluctuations in modifying its elastic response. We predict…

We study the effects of thermal flucutations on thin elastic filaments with spontaneous curvature and torsion. We derive analytical expressions for the orientational correlation functions and for the persistence length of helices, and find…