Related papers: Elasticity and Fluctuations of Frustrated Nano-Rib…
We examine the effects of thermal fluctuations on thin elastic filaments with non-circular cross-section and arbitrary spontaneous curvature and torsion. Analytical expressions for orientational correlation functions and for the persistence…
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…
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…
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 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…
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…
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…
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:…
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 investigate the effect of thermal fluctuations on the mechanical properties of nanotubes by employing tools from statistical physics. For 2D sheets it was previously shown that thermal fluctuations effectively renormalize elastic moduli…
Helical objects are often implemented in electronic or mechanical micro-systems, requiring a precise understanding of their mechanical properties. While helices formed by cylindrical filaments have been intensely investigated, little is…
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…
The effects of thermal elastic fluctuations in rubber materials are examined. It is shown that, due to an interplay with the incompressibility constraint, these fluctuations qualitatively modify the large-deformation stress-strain relation,…
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…
Thermal fluctuations can play an important role in the buckling of elastic objects at small scales, such as polymers or nanotubes. In this paper, we study the finite-temperature buckling transition of an extensible rod by analyzing…
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…
The nonlinear dynamics of an elastic filament that is forced to rotate at its base is studied by hydrodynamic simulation techniques; coupling between stretch, bend, twist elasticity and thermal fluctuations is included. The…
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 develop a novel biased Monte-Carlo simulation technique to measure the force-extension curves and the distribution function of the extension of fluctuating filaments stretched by external force. The method is applicable for arbitrary…
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…