Related papers: An energetically consistent surface correction met…
Topological defects are ubiquitous on surfaces with orientational order fields. Here, we study equilibrium states generated by the feedback between geometry and nematic order on fluid membranes with an integer topological defect. When the…
A stationary rotating surface is a compact surface in Euclidean space whose mean curvature $H$ at each point $x$ satisfies $2H(x)=a r^2+b$, where $r$ is the distance from $x$ to a fixed straight-line $L$, and $a$ and $b$ are constants.…
We obtain improved local well-posedness results for the Lorentzian timelike minimal surface equation. In dimension $d=3$, for a surface of arbitrary co-dimension, we show a gain of $1/3$ derivative regularity compared to a generic equation…
Surface matching usually provides significant deformations that can lead to structural failure due to the lack of physical policy. In this context, partial surface matching of non-linear deformable bodies is crucial in engineering to govern…
We study a mathematical model for deformation of glued elastic bodies in 2D or 3D, which is a linear elasticity system with adhesive force on the glued surface. We reveal a variational structure of the model and prove the unique existence…
The presence of corners in the computational domain, in general, reduces the regularity of solutions of parabolic problems and diminishes the convergence properties of the finite element approximation introducing a so-called "pollution…
We describe a novel fluctuating-surface current formulation of radiative heat transfer between bodies of arbitrary shape that exploits efficient and sophisticated techniques from the surface-integral-equation formulation of classical…
This paper investigates the rigidity of bordered polyhedral surfaces. Using the variational principle, we show that bordered polyhedral surfaces are determined by boundary value and discrete curvatures on the interior edges. As a corollary,…
This paper presents an analytical model of punctual elastic contact between a rigid body of arbitrary geometry and a plane surface. A simple analytical model is developed in order to evaluate the contact force knowing the volume of…
We propose an approach to measure surface elastic constants of soft solids. Generally, this requires one to probe interfacial mechanics at around the elastocapillary length scale, which is typically microscopic. Deformations of microscopic…
The floating body approach to affine surface area is adapted to a holomorphic context providing an alternate approach to Fefferman's invariant hypersurface measure.
Ab initio thermodynamics is a widespread, computationally efficient approach to predict the stable configuration of a surface in contact with a surrounding (gas or liquid) environment. In a prevalent realization of this approach, this…
We present a novel parametric finite element approach for simulating the surface diffusion of curves and surfaces. Our core strategy incorporates a predictor-corrector time-stepping method, which enhances the classical first-order temporal…
The position-based dynamics (PBD) algorithm is a popular and versatile technique for real-time simulation of deformable bodies, but is only applicable to forces that can be expressed as linearly compliant constraints. In this work, we…
Patterned surfaces with large effective slip lengths, such as super-hydrophobic surfaces containing trapped gas bubbles, have the potential to reduce hydrodynamic drag. Based on lubrication theory, we analyze an approach of a hydrophilic…
This paper develops and benchmarks an immersed peridynamics method to simulate the deformation, damage, and failure of hyperelastic materials within a fluid-structure interaction framework. The immersed peridynamics method describes an…
We consider fully discrete embedded finite element approximations for a shallow water hyperbolic problem and its reduced-order model. Our approach is based on a fixed background mesh and an embedded reduced basis. The Shifted Boundary…
We present a posteriori error estimates for a recently developed atomistic/continuum coupling method, the Consistent Energy-Based QC Coupling method. The error estimate of the deformation gradient combines a residual estimate and an a…
In this paper, the convergence of the solutions for a discretized linear state-based static peridynamic system to the corresponding continuous solution is analytically proven. To obtain an implementable model, we further apply…
Accurate representation of interfaces and flux exchange is vital for coupled multiphysics simulations across a broad range of applications. Currently, coupling approaches are limited by the underlying discretization or to specific physical…