相关论文: Forceless Sadowsky strips are spherical
The equilibrium shape of a thin, elastic, inextensible ribbon minimizes its bending energy. It has been shown that, as the width of the ribbon tends to zero, the bending energy Gamma-converges to the so called Sadowsky functional. In this…
We present a new one-dimensional model for elastic strips based on a nondevelopable ruled surface. An auxiliary field regularizes the Sadowsky narrow-strip model to allow nonzero twist with vanishing curvature. The energy exhibits the…
Differential growth processes play a prominent role in shaping leaves and biological tissues. Using both analytical and numerical calculations, we consider the shapes of closed, elastic strips which have been subjected to an inhomogeneous…
Ribbons are long narrow strips possessing three distinct material length scales (thickness, width, and length) which allow them to produce unique shapes unobtainable by wires or filaments. For example when a ribbon has half a twist and is…
We consider an inextensible, semiflexible polymer or worm-like chain which is confined in the transverse direction by a parabolic potential and subject to a longitudinal force at the ends, so that the polymer is stretched out and…
We consider thin plates whose energy density is a quadratic function of the difference between the second fundamental form of the deformed configuration and a "natural" curvature tensor. This tensor either denotes the second fundamental…
Recently a significant interest in ferromagnetic curved thin films has appeared. In particular, thin spherical shells are currently of great interest due to their capability to support skyrmion solutions which can be stabilized by curvature…
A \Gamma-convergence result involving the elastic energy of a narrow inextensible ribbon is established. A non-dimensional form of the elastic energy is reduced to a one-dimensional integral over the centerline of the ribbon with the aspect…
We investigate morphologies of semiflexible polymer rings, such as circular DNA, which are adsorbed onto topographically or chemically structured substrate surfaces. We classify all equilibrium morphologies for two striped surface…
This paper presents a new method for modelling the dynamic behaviour of developable ribbons, two dimensional strips with much smaller width than length. Instead of approximating such surface with a general triangle mesh, we characterize it…
By means of a variational approach we rigorously deduce three one-dimensional models for elastic ribbons from the theory of von K\'arm\'an plates, passing to the limit as the width of the plate goes to zero. The one-dimensional model found…
We study in this article the mathematical properties of a class of orbital-free kinetic energy functionals. We prove that these models are linearly stable but nonlinearly unstable, in the sense that the corresponding kinetic energy…
Interplay between structure and function in atomically thin crystalline nanoribbons is sensitive to their conformations yet the ability to prescribe them is a formidable challenge. Here, we report a novel paradigm for controlled nucleation…
We elucidate the elastic behavior of a wormlike chain in 3D under compression and provide exact solutions for the experimentally accessible force-extension relation in terms of generalized spheroidal wave functions. In striking contrast to…
This paper establishes isomorphisms for the Laplace operator in weighted Sobolev spaces (WSS). These spaces are similar to standard Sobolev spaces, but they are endowed with weights prescribing functions growth or decay at infinity.…
Efforts to modulate the electronic properties of atomically thin crystalline nanoribbons requires precise control over their morphology. Here, we perform atomistic simulations on freestanding graphene nanoribbons (GNRs) to first identify…
Natural slender structures, such as plant leaves, petals, and tendrils, often exhibit complex three-dimensional (3D) morphologies-including twisting, helical coiling, and saddle-bending-driven by differential growth. The resulting internal…
A coarse grained model for flexible polymers end-grafted to repulsive spherical nanoparticles is studied for various chain lengths and grafting densities under good solvent conditions, by Molecular Dynamics methods and density functional…
We construct fractional Sobolev spaces on arbitrary time scales, both in one dimension and on product time scales. In 1D, we define $W^{\alpha(\cdot),p}_{\mathrm{rd}}(\mathcal I)$ through a variable-order Gagliardo-type seminorm and prove…
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…