Related papers: Self-avoiding fluid deformable surfaces
The paper studies a finite element method for computing transport and diffusion along evolving surfaces. The method does not require a parametrization of a surface or an extension of a PDE from a surface into a bulk outer domain. The…
The Helfrich energy is commonly used to model the elastic bending energy of lipid bilayers in membrane mechanics. The governing differential equations for certain geometric characteristics of the shape of the membrane can be obtained by…
Phase transition problems on curved surfaces can lead to a panopticon of fascinating patterns. In this paper we consider finite element approximations of phase field models with a spatially inhomogeneous and anisotropic surface energy…
Manipulation of small-scale particles across streamlines is the elementary task of microfluidic devices. Many such devices operate at very low Reynolds numbers and deflect particles using arrays of obstacles, but a systematic quantification…
We apply the boundary-element method to Stokes flows with helical symmetry, such as the flow driven by an immersed rotating helical flagellum. We show that the two-dimensional boundary integral method can be reduced to one dimension using…
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…
We develop a new optimisation technique that combines multiresolution subdivision surfaces for boundary description with immersed finite elements for the discretisation of the primal and adjoint problems of optimisation. Similar to wavelets…
Liquid crystals with molecules constrained to the tangent bundle of a curved surface show interesting phenomena resulting from the tight coupling of the elastic and bulk free energies of the liquid crystal with geometric properties of the…
Viscoelastic surface rheology plays an important role in multiphase systems. A typical example is the actin cortex which surrounds most animal cells. It shows elastic properties for short time scales and behaves viscous for longer time…
The presence of surfactants alters the dynamics of viscous drops immersed in an ambient viscous fluid. This is specifically true at small scales, such as in applications of droplet based microfluidics, where the interface dynamics become of…
One of the main challenges in numerically solving partial differential equations is finding a discretisation for the computational domain that balances the accurate representation of the underlying field with computational efficiency.…
We propose a particle-based method to simulate thin-film fluid that jointly facilitates aggressive surface deformation and vigorous tangential flows. We build our dynamics model from the surface tension driven Navier-Stokes equation with…
Vesicles and many biological membranes are made of two monolayers of lipid molecules and form closed lipid bilayers. The dynamical behaviour of vesicles is very complex and a variety of forms and shapes appear. Lipid bilayers can be…
Incompressible fluids on curved surfaces are considered with respect to the interplay between topology, geometry and fluid properties using a surface vorticity-stream function formulation, which is solved using parametric finite elements.…
We prove a microlocal lower bound on the mass of high energy eigenfunctions of the Laplacian on compact surfaces of negative curvature, and more generally on surfaces with Anosov geodesic flows. This implies controllability for the…
We present an immersed boundary method to simulate the creeping motion of a rigid particle in a fluid described by the Stokes equations discretized thanks to a finite element strategy on unfitted meshes, called Phi-FEM, that uses the…
We present a numerical method to deal efficiently with large numbers of particles in incompressible fluids. The interactions between particles and fluid are taken into account by a physically motivated ansatz based on locally defined drag…
We consider shape optimization problems subject to elliptic partial differential equations. In the context of the finite element method, the geometry to be optimized is represented by the computational mesh, and the optimization proceeds by…
The paper is devoted to the numerical solution of elastoplastic constitutive initial value problems. An improved form of the implicit return-mapping scheme for nonsmooth yield surfaces is proposed that systematically builds on a…
We present a single, unified, multi-scale model to study the attachment\detachment dynamics of two deforming, near spherical cells, coated with binding ligands and subject to a slow, homogeneous shear flow in a viscous fluid medium. The…