Related papers: The Shape Parameter in the Shifted Surface Spline
Position representation is crucial for building position-aware representations in Transformers. Existing position representations suffer from a lack of generalization to test data with unseen lengths or high computational cost. We…
The ruled surface is a typical modeling surface in computer aided geometric design. It is usually given in the standard parametric form. However, it can also be in the forms than the standard one. For these forms, it is necessary to…
One-dimensional flexible objects are abundant in physics, from polymers to vortex lines to defect lines and many more. These objects structure their environment and it is natural to assume that the influence these objects exert on their…
This work presents a novel framework for spherical mesh parameterization. An efficient angle-preserving spherical parameterization algorithm is introduced, which is based on dynamic Yamabe flow and the conformal welding method with solid…
We present a general method for computing local parameterizations rooted at a point on a surface, where the surface is described only through a signed implicit function and a corresponding projection function. Using a two-stage process, we…
This paper presents a spline-based parameterisation framework for plane graphs. The plane graph is characterised by a collection of curves forming closed loops that fence-off planar faces which have to be parameterised individually. Hereby,…
The cosmic ray energy distributions contain spectral features, that is narrow energy regions where the slope of the spectrum changes rapidly. The identification and study of these features is of great importance to understand the…
Often, the unknown diffusivity in diffusive processes is structured by piecewise constant patches. This paper is devoted to efficient methods for the determination of such structured diffusion parameters by exploiting shape calculus. A…
This paper presents a description and analysis of a rational cubic spline FIF (RCSFIF) that has two shape parameters in each subinterval when it is defined implicitly. To be precise, we consider the iterated function system (IFS) with…
In this article we study the shape of a compact surface of constant mean curvature of Euclidean space whose boundary is contained in a round sphere. We consider the case that the boundary is prescribed or that the surface meets the sphere…
In a theoretical analysis, we generalise well known asymptotic results to obtain expressions for the rate of transfer of material from the surface of an arbitrary, rigid particle suspended in an open pathline flow at large P\'eclet number,…
A simple multi-physical system for the potential flow of a fluid through a shroud in which a mechanical component, like a turbine vane, is placed, is modeled mathematically. We then consider a multi criteria shape optimization problem, when…
Electromagnetic metasurfaces offer the capability to realize almost arbitrary power conserving field transformations. These field transformations are governed by the generalized sheet transition conditions, which relate the tangential…
The conchoid of a surface $F$ with respect to given fixed point $O$ is roughly speaking the surface obtained by increasing the radius function with respect to $O$ by a constant. This paper studies {\it conchoid surfaces of spheres} and…
Complex eigenfrequencies of the exterior of a scatterer are considered as signatures of the scatterer's shape. A parameter characterizing the ratio of the maximum transverse and longitudinal dimensions of a body is found.
We study the parameters range for the fixed point of a class of complex dynamics with the rational fractional function as $R_{n,a,c}(z)=z^n+\frac{a}{z^n}+c$, where $n=1,2,3,4$ is specified, $a$ and $c$ are two complex parameters. The…
Using contact dynamics simulations, we compare the effect of rolling resistance at the contacts in granular systems composed of disks with the effect of angularity in granular systems composed of regular polygonal particles. In simple shear…
Models for fluid deformable surfaces provide valid theories to describe the dynamics of thin fluidic sheets of soft materials. To use such models in morphogenesis and development requires to incorporate active forces. We consider active…
Order parameters based on spherical harmonics and Fourier coefficients already play a significant role in condensed matter research in the context of systems of spherical or point particles. Here, we extend these types of order parameter to…
We exhibit several transformations of surfaces in R^4. First, one that takes a flat surface and gets a surface with flat normal bundle; then, one that takes a surface with flat normal bundle and gets a flat surface; finally, a one-parameter…