Related papers: An energetically consistent surface correction met…
A shape sensitive, variational approach for the matching of surfaces considered as thin elastic shells is investigated. The elasticity functional to be minimized takes into account two different types of nonlinear energies: a membrane…
Background: The generation of potential energy surfaces is a critical step in theoretical models aiming to understand and predict nuclear fission. Discontinuities frequently arise in these surfaces in unconstrained collective coordinates,…
One primary objective in submanifold geometry is to discover fascinating and significant classical examples of $H_1$. In this paper which relies on the theory we established in [Adv. Math. 405 (2022), 08514, 50 pages, arXiv:2101.11780] and…
In this report we describe a mesh editing system that we implemented that uses a natural stretching and bending energy defined over smooth surfaces. As such, this energy behaves uniformly under various mesh resolutions. All of the elements…
In this paper we analyze a fully discrete numerical scheme for solving a parabolic PDE on a moving surface. The method is based on a diffuse interface approach that involves a level set description of the moving surface. Under suitable…
Solid-state dewetting (SSD), a widespread phenomenon in solid-solid-vapor system, could be used to describe the accumulation of solid thin films on the substrate. In this work, we consider the sharp interface model for axisymmetric SSD with…
The thermodynamics and mechanics of the surface of a deformable body are studied here, following and refining the general approach of Gibbs. It is first shown that the 'local' thermodynamic variables of the state of the surface are only the…
We present a spectrally accurate embedded boundary method for solving linear, inhomogeneous, elliptic partial differential equations (PDE) in general smooth geometries, focusing in this manuscript on the Poisson, modified Helmholtz, and…
A wide range of natural and industrial processes involve heat and mass transport in porous media. In some important cases the transported substance may undergo phase change, e.g. from liquid to solid and vice versa in the case of freezing…
The immersed peridynamics (IPD) method is a fluid-structure interaction (FSI) model to simulate fluid-driven material damage and failure of an immersed structure, in which a peridynamic (PD) constitutive correspondence model is employed…
The structure equations for a surface are introduced and two required results based on the Codazzi equations are obtained from them. Important theorems pertaining to isometric surfaces are stated and a theorem of Bonnet is obtained. A…
A class of peridynamic material models known as constitutive correspondence models provide a bridge between classical continuum mechanics and peridynamics. These models are useful because they allow well-established local constitutive…
The identification of coherent structures from experimental or numerical data is an essential task when conducting research in fluid dynamics. This typically involves the construction of an empirical mode base that appropriately captures…
In this work, we aim to develop energy-stable parametric finite element approximations for a sharp-interface model with strong surface energy anisotropy, which is derived from the first variation of an energy functional composed of…
Active contour models based on local region fitting energy can segment images with intensity inhomogeneity effectively, but their segmentation results are easy to error if the initial contour is inappropriate. In this paper, we present a…
Peridynamics (PD) is a non-local continuum formulation. The original version of PD was restricted to bond-based interactions. Bond-based PD is geometrically exact and its kinematics are similar to classical continuum mechanics (CCM).…
We present a new approach for the mechanically consistent modelling and simulation of fluid-structure interactions with contact. The fundamental idea consists of combining a relaxed contact formulation with the modelling of seepage through…
A recently developed Eulerian finite element method is applied to solve advection-diffusion equations posed on hypersurfaces. When transport processes on a surface dominate over diffusion, finite element methods tend to be unstable unless…
A rigorous and powerful theoretical framework is proposed to obtain systems of orthogonal functions (or shape modes) to represent optical surfaces. The method is general so it can be applied to different initial shapes and different…
Soft interfaces can mediate interactions between particles bound to them. The force transmitted through the surface geometry on a particle may be expressed as a closed line integral of the surface stress tensor around that particle. This…