Related papers: Bending of bilayers with general initial shapes
Experimental advances in the fabrication and characterization of few-layer materials stacked at a relative twist of small angle have recently shown the emergence of flat energy bands. As a consequence electron interactions become relevant,…
The free elastic flow is the $L^2$-gradient flow for Euler's elastic energy, or equivalently the Willmore flow with translation invariant initial data. In contrast to elastic flows under length penalisation or preservation, it is more…
We put forward a variational framework suitable for the study of curves whose energies depend on their bend and twist degrees of freedom. By employing the material curvatures to describe such elastic deformation modes, we derive the…
We present a study of the structural properties of the crystalline phases for a planar bilayer of particles interacting via repulsive Yukawa potentials in the weak screening region. The study is done with Monte Carlo computations and the…
Experimentally measuring the elastic properties of thin biological surfaces is non-trivial, particularly when they are curved. One technique that may be used is the indentation of a thin sheet of material by a rigid indenter, whilst…
Morphological change of bilayer membrane in vivo is not a spontaneous procedure but modulated by various types of proteins in general. Most of these modulations are associated with the localization of related proteins in the crowded lipid…
We develop a formalism that describes the bending and twisting of axoneme-like filament bundles. We obtain general formulas to determine the relative sliding between any arbitrary filaments in a bundle subjected to unconstrained…
Minimising the energy consumption associated with periodic motion is a priority common to a wide range of technologies and organisms - among them, many species of flying insect, for which flapping-wing flight is a life-essential mode of…
The purpose of this paper is to extend the Kitaev model to a general dimensional diamond crystal. We define the Hamiltonian by using representations of Clifford algebras. Then we compute the energy functions. We show that the energy…
The large deflections of cantilevered beams and plates are modeled and discussed. Traditional nonlinear elastic models (e.g., that of von Karman) employ elastic restoring forces based on the effect of stretching on bending, and these are…
We consider classical dynamical properties of a particle in a constant gravitational force and making specular reflections with circular, elliptic or oval boundaries. The model and collision map are described and a detailed study of the…
The paper presents a two-dimensional geometrically nonlinear formulation of a beam element that can accommodate arbitrarily large rotations of cross sections. The formulation is based on the integrated form of equilibrium equations, which…
We study the spontaneous out-of-plane bending of a planar untwisted ribbon composed of nematic polymer networks activated by a change in temperature. Our theory accounts for both stretching and bending energies, which compete to establish…
We discuss a discretization by polygonal lines of the Euler-Bernoulli bending energy and of Euler elasticae under clamped boundary conditions. We show Hausdorff convergence of the set of almost minimizers of the discrete bending energy to…
The electronic properties of the twisted InSe bilayer are studied by large-scale density functional theory. Spectral Function Unfolding reveals that the electronic structure of the twisted system can be described in terms of a combination…
Mechanical and elastic properties of materials are among the most fundamental quantities for many engineering and industrial applications. Here, we present a formulation that is efficient and accurate for calculating the elastic and bending…
Structure, function and dynamics of many biomolecular systems can be characterized by the energetic variational principle and the corresponding systems of partial differential equations (PDEs). This principle allows us to focus on the…
We propose a universal elastic energy for proteins, which depends only on the radius of gyration $R_{g}$ and the residue number $N$. It is constructed using physical arguments based on the hydrophobic effect and hydrogen bonding. Adjustable…
We present a nonequlibrium approach for the study of a flexible bilayer whose two components induce distinct curvatures. In turn, the two components are interconverted by an externally promoted reaction. Phase separation of the two species…
Numerically simulating deformations in thin elastic sheets is a challenging problem in computational mechanics due to destabilizing compressive stresses that result in wrinkling. Determining the location, structure, and evolution of…