Related papers: Fourth-order flows in surface modelling
A proof of convergence is given for a novel evolving surface finite element semi-discretization of Willmore flow of closed two-dimensional surfaces, and also of surface diffusion flow. The numerical method proposed and studied here…
We consider a RG flow in a general $\hat{su}(2)$ coset model perturbed by the least relevant field. The perturbing field as well as some particular fields of dimension close to one are constructed recursively in terms of lower level fields.…
We obtain explicit solutions of the mean curvature flow in some submanifolds of the Euclidean space. We give particularly an explicit solution of the flow of a hypersurface in the Lagrangian self-expander $L$ which is constructed in the…
These lecture notes aim to present some of the ideas behind the recent (conditional) existence and (weak-strong) uniqueness theory for mean curvature flow. Focusing on the simplest case of the evolution of a single closed hypersurface…
A numerical algorithm for mean curvature flow of closed mean convex surfaces with surgery is proposed. The method uses a finite element based mean curvature flow algorithm based on a coupled partial differential equation system which…
The main purpose of this short note is to point out that the negative gradient flow for the prescribed $\mathbf Q$-curvature problem on $S^n$ can be extended to handle the case that the $\mathbf Q$-curvature candidate $f$ may change signs.
An algorithm is proposed for generalized mean curvature flow of closed two-dimensional surfaces, which include inverse mean curvature flow, powers of mean and inverse mean curvature flow, etc. Error estimates are proven for semi- and full…
We study high codimension mean curvature flow of a submanifold $\mathcal{M}^n$ of dimension $n$ in Euclidean space $\mathbb{R}^{n+k}$ subject to the quadratic curvature condition $ |A|^{2}\leq c_n |H|^{2}, c _n = \min\{ \frac{4}{3n} ,…
The focus of this paper is to systematically study the influence of solid obstacle surface roughness in porous media on the microscale flow physics and report its effect on macroscale drag and Nusselt number. The Reynolds averaged flow…
We outline the main ideas behind the numerical modelling of soft-flowing crystals, with special attention to their application to microfluidic devices for the design of novel mesoscale porous materials.
In this paper, we present our general results about traversing flows on manifolds with boundary in the context of the flows on surfaces with boundary. We take advantage of the relative simplicity of $2D$-worlds to explain and popularize our…
Line fields on surfaces are a means to describe the nematic order that may pattern them. The least distorted nematic fields are called uniform, but they can only exist on surfaces with negative constant Gaussian curvature. To identify the…
The gravitational collapse in fourth order theories of gravity defined by an arbitrary action of the scalar curvature shows significant deviations with General Relativity. The presence of a new scalar mode produces a higher initial…
We present a collection of results on the evolution by curvature of networks of planar curves. We discuss in particular the existence of a solution and the analysis of singularities.
Earlier work of the first author examined two boundary value problems associated to the Gauss Curvature Flow on a surface of revolution generated by a positive, differentiable function on a compact interval. In this continuation, two…
In the domain of computer vision, optical flow stands as a cornerstone for unraveling dynamic visual scenes. However, the challenge of accurately estimating optical flow under conditions of large nonlinear motion patterns remains an open…
The flow of incompressible fluids through porous media plays a crucial role in many technological applications such as enhanced oil recovery and geological carbon-dioxide sequestration. The flow within numerous natural and synthetic porous…
Surface phase transitions in surfactant adsorption layers are known to affect the dynamic properties of foams and to induce surface nucleation in freezing emulsion drops. Recently, these transitions were found to play a role in several…
We present a metamodel for modeling control and data flows on subclass scales in object-oriented systems. UML Profiles were used as a representation mean and a complete metamodel definition was provided with an example of a diagram…
We consider mean curvature flow of an initial surface that is the graph of a function over some domain of definition in $R^n$. If the graph is not complete then we impose a constant Dirichlet boundary condition at the boundary of the…