Related papers: Fourth-order flows in surface modelling
Using the fractional discrete Laplace operator for triangle meshes, we introduce a fractional combinatorial Calabi flow for discrete conformal structures on surfaces, which unifies and generalizes Chow-Luo's combinatorial Ricci flow for…
We study the dynamics of orientational phase ordering in fluid membranes. Through numerical simulation we find an unusually slow coarsening of topological texture, which is limited by subdiffusive propagation of membrane curvature. The…
The purpose of this paper is, first, to give an algorithm that enables to obtain the lines of curvature on parametric hypersurfaces in Euclidean 4-space, and then, to obtain the curvatures of such lines by using the extended Darboux frame…
This work represents an application of constant mean curvature graphs (as solutions of the mean curvature PDE) to non-linear non-Darcy flows in porous media. It relates time invariant pressure distribution graphs to graphs of constant mean…
This text is an introduction to dilation surfaces. We attempt to expose some geometric and dynamical aspects of the subject: moduli spaces, directional foliations and the Teichm\"uller flow.
We analyse second order (in Riemann curvature) geometric flows (un-normalised) on locally homogeneous three manifolds and look for specific features through the solutions (analytic whereever possible, otherwise numerical) of the evolution…
Over the last few decades, phase-field equations have found increasing applicability in a wide range of mathematical-scientific fields (e.g. geometric PDEs and mean curvature flow, materials science for the study of phase transitions) but…
Drop deformation in shear flow is determined up to second order theory in Ca while considering kinetic effects on surfactants distributions in steady state. Surfactants inside the drop are adsorbed faster than those on the surface leading…
We give biLipschitz models for the Ricci flow on some 4-manifolds (minimal surfaces of general type), exhibiting a combination of expanding and static behavior.
We first give a general introduction to the mean curvature flow, and then discuss fundamental results established over the last 10 years that yield a precise theory for the flow through singularities in $\mathbb{R}^3$. With the aim of…
Optimal-order uniform-in-time $H^1$-norm error estimates are given for semi- and full discretizations of mean curvature flow of surfaces in arbitrarily high codimension. The proposed and studied numerical method is based on a parabolic…
Embedding diagrams have been used extensively to visualize the properties of curved space in Relativity. We introduce a new kind of embedding diagram based on the {\it extrinsic} curvature (instead of the intrinsic curvature). Such an…
We report electron microscopy observations of the surface plastic flow in polishing of rough metal surfaces with a controlled spherical asperity structure. We show that asperity--abrasive sliding contacts exhibit viscous behavior, where the…
We extend the concept of optical flow to a dynamic non-Euclidean setting. Optical flow is traditionally computed from a sequence of flat images. It is the purpose of this paper to introduce variational motion estimation for images that are…
Shallow flow or thin liquid film models are used for a wide range of physical and engineering problems. Shallow flow models allow capturing the free surface of the fluid with little effort and reducing the three-dimensional problem to a…
An evolving surface finite element discretisation is analysed for the evolution of a closed two-dimensional surface governed by a system coupling a generalised forced mean curvature flow and a reaction--diffusion process on the surface,…
Modeling the mechanics of fluid in complex scenes is vital to applications in design, graphics, and robotics. Learning-based methods provide fast and differentiable fluid simulators, however most prior work is unable to accurately model how…
Numerical simulations of a model of plane Couette flow focusing on its in-plane spatio-temporal properties are used to study the dynamics of turbulent spots.
We give two examples of surfaces with canonical map of degree 4 onto a canonical surface.
Quaternions are an important tool to describe the orientation of a molecule. This paper considers the use of quaternions in matching two conformations of a molecule, in interpolating rotations, in performing statistics on orientational…