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We study the non-monotonic force-extension behaviour of helical ribbons using a new model for inextensible elastic strips. Unlike previous rod models our model predicts hysteresis behaviour for low-pitch ribbons of arbitrary material…

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…

Observed under the polarizing microscope, the B7bis phase in the banana compound D14F3 [J.P. Bedel et al, Liq. Cryst., 27, 1411 (2000)] displays two types of textures of defects, namely (a): helical ribbons, that nucleate in large…

We combine experiments with simulations to investigate the fluid-structure interaction of a flexible helical rod rotating in a viscous fluid, under low Reynolds number conditions. Our analysis takes into account the coupling between the…

We use computer simulations and scaling arguments to investigate statistical and structural properties of a semiflexible ribbon composed of isosceles triangles. We study two different models, one where the bending energy is calculated from…

Patterns and forms adopted by Nature, such as the shape of living cells, the geometry of shells and the branched structure of plants, are often the result of simple dynamical paradigms. Here we show that a growing self-interacting string…

Torsional-space Monte Carlo simulations of flexible molecules are usually based on the assumption that all values of dihedral angles have equal probability in the absence of atomic interactions. In the present paper it is shown that this…

We present a general theory for the equilibrium structure of cylindrical tubules and helical ribbons of chiral lipid membranes. This theory is based on a continuum elastic free energy that permits variations in the direction of molecular…

The goal of this paper is twofold. First we prove a rigidity estimate, which generalises the theorem on geometric rigidity of Friesecke, James and M\"uller to 1-forms with non-vanishing exterior derivative. Second we use this estimate to…

In this paper we derive the general equilibrium equations of a polymer chain with a noncircular cross section by the variation of the free energy functional. From the equilibrium equation of the elastic ribbon we derive analytically the…

This paper extends on a recent work where it was shown that forces dependent on the helical structure may cause two DNA molecules to spontaneously braid [R. Cortini et Al, Biophys. J. 101, 875 (2011)]. Here, bending fluctuations of DNA…

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 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…

Protein folding is a universal process, very fast and accurate, which works consistently (as it should be) in a wide range of physiological conditions. The present work is based on three premises, namely: ($i$) folding reaction is a process…

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 introduce a construction of multiscale tight frames on general domains. The frame elements are obtained by spectral filtering of the integral operator associated with a reproducing kernel. Our construction extends classical wavelets as…

The effects of turbulence in the very local interstellar medium (VLISM) have been proposed by Giacalone & Jokipii (2015) to be important in determining the structure of the Interstellar Boundary Explorer (IBEX) ribbon via particle trapping…

Topology is an important determinant of the behavior of a great number of condensed-matter systems, but until recently has played a minor role in elasticity. We develop a theory for the deformations of a class of twisted non-Euclidean…

It is believed that, much like a cat's cradle, the cytoskeleton can be thought of as a network of strings under tension. We show that both regular and random bond-disordered networks having bonds that buckle upon compression exhibit a…

Using a {\it collective} Monte Carlo algorithm we study the low-temperature and long-distance properties of two systems of two-dimensional classical tops. Both systems have the same spin-wave dynamics (low-temperature behavior) as a large…