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Thin sheets that are forced at their boundaries develop a variety of shapes aimed at minimising elastic energy by curving spontaneously in ways that break the symmetry of the sheet and the forcing. Characterising such buckling generally…
Gaseous layers (plastrons) trapped on the surfaces of immersed hydrophobic surfaces are critical for their function. Fibrillar morphologies offer a natural pathway, yet they are limited to a narrow range of liquid-surface systems and are…
Spectral Graph Neural Networks (GNNs) suffer from two critical limitations: poor performance on "heterophilic" graphs and performance collapse at high polynomial degrees (K), known as over-smoothing. Both issues stem from the static,…
Dense granular flows exhibit both surface deformation and secondary flows due to the presence of normal stress differences. Yet, a complete mathematical modelling of these two features is still lacking. This paper focuses on a steady…
A laterally confined thin elastic sheet lying on a liquid substrate displays regular undulations, called wrinkles, characterized by a spatially extended energy distribution and a well-defined wavelength $\lambda$. As the confinement…
The idea of working with a near-critical phase-separated liquid mixture whereby the surface tension becomes weak, has recently made the field of laser manipulation of liquid interfaces a much more convenient tool in practice. The…
Laguerre tessellations of macromolecules capture properties such as molecular interface surfaces, volumes and cavities. Explicit solvent molecular dynamics simulations of a macromolecule are slow as the number of solvent atoms considered…
Biomembranes play a central role in various phenomena like locomotion of cells, cell-cell interactions, packaging of nutrients, and in maintaining organelle morphology and functionality. During these processes, the membranes undergo…
In granular physics experiments, it is a persistent challenge to obtain the boundary stress measurements necessary to provide full a rheological characterization of the dynamics. Here, we describe a new technique by which the outer boundary…
Consider a surface, enclosing a fixed volume, described by a free-energy depending only on the local geometry; for example, the Canham-Helfrich energy quadratic in the mean curvature describes a fluid membrane. The stress at any point on…
Geometric continuum models for fluid lipid membranes are considered using classical field theory, within a covariant variational approach. The approach is cast as a higher-derivative Lagrangian formulation of continuum classical field…
We investigate equilibrium configurations for surface energies which contain the squared $L^2$ norm of the difference of the mean curvature H and the spontaneous curvature $c_o$ coupled with the elastic energy of the boundary curve, which…
Flexible slender structures such as rods, ribbons, plates, and shells exhibit extreme nonlinear responses bending, twisting, buckling, wrinkling, and self contact, that defy conventional simulation frameworks. Discrete Differential Geometry…
We present an analysis for a mixed finite element method for the bending problem of Koiter shell. We derive an error estimate showing that when the geometrical coefficients of the shell mid-surface satisfy certain conditions the finite…
The geometry of two-dimensional crystalline membranes dictates their mechanical, electronic and chemical properties. The local geometry of a surface is determined from the two invariants of the metric and the curvature tensors. Here we…
Modeling arbitrarily large deformations of surfaces smoothly embedded in three-dimensional space is challenging. The difficulties come from two aspects: the existing geometry processing or forward simulation methods penalize the difference…
We consider the rigorously derived thin shell membrane $\Gamma$-limit of a three-dimensional isotropic geometrically nonlinear Cosserat micropolar model and deduce full interior regularity of both the midsurface deformation…
This article is the second of a three-part series that derives a self-consistent theoretical framework of the electromechanics of arbitrarily curved lipid membranes. Existing continuum theories commonly treat lipid membranes as strictly…
Metasurfaces have attracted significant research interest owing to their unprecedented control over the spatial distributions of electromagnetic fields. Herein we propose the concept of metasurface tessellation to achieve reconfigurable…
This work presents a novel interpolation-free mesh adaptation technique for the Euler equations within the arbitrary Lagrangian Eulerian framework. For the spatial discretization, we consider a residual distribution scheme, which provides a…