Related papers: Sharp interfaces in two dimensional free boundary …
We discuss the sharp interface limit of a diffuse interface model for a two-phase flow of two partly miscible viscous Newtonian fluids of different densities, when a certain parameter \epsilon>0 related to the interface thickness tends to…
A potential motion of ideal incompressible fluid with a free surface and infinite depth is considered in two-dimensional geometry. A time-dependent conformal mapping of the lower complex half-plane of the auxiliary complex variable $w$ into…
The method of boundary curve reparametrization is applied to construction of the approximate analytical conformal mapping of the unit disk onto an arbitrary given finite domain with a boundary smooth at every point but fininte number of…
The Ohta-Kawasaki model for diblock-copolymers is well known to the scientific community of diffuse-interface methods. To accurately capture the long-time evolution of the moving interfaces, we present a derivation of the corresponding…
Multiphase flows are commonly found in chemical engineering processes such as distillation columns, bubble columns, fluidized beds and heat exchangers. The physical boundaries of domains in numerical simulations of multiphase flows are…
We present an hybrid VOF/embedded boundary method allowing to model two-phase flows in presence of solids with arbitrary shapes. The method relies on the coupling of existing methods: a geometric Volume of fluid (VOF) method to tackle the…
This paper addresses challenges in flexibly modeling multimodal data that lie on constrained spaces. Such data are commonly found in spatial applications, such as climatology and criminology, where measurements are restricted to a…
We propose a novel 3D shape correspondence method based on the iterative alignment of so-called smooth shells. Smooth shells define a series of coarse-to-fine shape approximations designed to work well with multiscale algorithms. The main…
A suitable measure for the similarity of shapes represented by parameterized curves or surfaces is the Fr\'echet distance. Whereas efficient algorithms are known for computing the Fr\'echet distance of polygonal curves, the same problem for…
Multiphase flows are characterized by sharp moving interfaces, separating different fluids or phases. In many cases the dynamics of the interface determines the behavior of the flow. In a coarse, or reduced order model, it may therefore be…
The quantitative characterization of the microstructure of random heterogeneous media in $d$-dimensional Euclidean space $\mathbb{R}^d$ via a variety of $n$-point correlation functions is of great importance, since the respective infinite…
Efficient simulation of Darcy flow in highly heterogeneous porous media requires iterative solvers that remain robust under large permeability contrasts and mixed boundary conditions. Spectral coarse spaces in two-level overlapping Schwarz…
The roughness properties of two-dimensional fracture surfaces as created by the slow failure of random fuse networks are considered and compared to yield surfaces of perfect plasticity with similar disorder. By studying systems up to a…
We study obstacle problems governed by two distinct types of diffusion operators involving interacting free boundaries. We obtain a somewhat surprising coupling property, leading to a comprehensive analysis of the free boundary. More…
We consider an open, bounded, simply connected (Lipschitz) domain in $\mathbb{R}^d$, which contains a closed polyhedral surface or polygonal contour, referred to as the interface. From this interface, forces are exerted in the normal…
We present a novel area matching algorithm for merging two different 2D grid maps. There are many approaches to address this problem, nevertheless, most previous work is built on some assumptions, such as rigid transformation, or similar…
This paper proposes a composable fine-tuning method that integrates graph structural priors with modular adapters to address the high computational cost and structural instability faced by large-scale pre-trained models in multi-task…
We present a cost-efficient and versatile method to map an unknown 3D freeform surface using only sparse measurements while the end-effector of a robotic manipulator moves along the surface. The geometry is locally approximated by a plane,…
New finite element methods are proposed for elliptic interface problems in one and two dimensions. The main motivation is not only to get an accurate solution but also an accurate first order derivative at the interface (from each side).…
Josephson junctions in a two-dimensional electron gas with spin-orbit coupling are a promising candidate to realize topological superconductivity. While it is known that the geometry of the junction strongly influences the size of the…