Related papers: "The Optiverse" and other sphere eversions
Space curve motion describes dynamics of material defects or interfaces, can be found in image processing or vortex dynamics. This article analyses some properties of space curves evolved by the curve shortening flow. In contrast to the…
This tutorial summarizes recent advances in the convex relaxation of the optimal power flow (OPF) problem, focusing on structural properties rather than algorithms. Part I presents two power flow models, formulates OPF and their relaxations…
We consider how transformation optics and invisibility cloaking can be used to construct models in subsets $\mathbb{R}^3$ with a varying metric, where the time-harmonic waves for a given angular wavenumber $k$, are equivalent to the waves…
We use global bifurcation techniques to establish the existence of arbitrarily many geometrically distinct nonplanar embedded smooth minimal 2-spheres in sufficiently elongated 3-dimensional ellipsoids of revolution. More precisely, we…
Using the idea of regularisation of singularities due to the variability of the fundamental constants in cosmology we study the cyclic universe models. We find two models of oscillating and non-singular mass density and pressure…
We describe gravitational lensing by a gravitational wave, in the regime in which multiple images of a light source are created. We adapt the vector formalism employed for ordinary gravitational lenses to the case of a non-stationary…
For a model convection-diffusion problem, we address the presence of oscillatory discrete solutions, and study difficulties in recovering standard approximation results for its solution. We justify the presence of non-physical oscillations…
We rigorously construct continuous curves of rotating vortex patch solutions to the two-dimensional Euler equations. The curves are large in that, as the parameter tends to infinity, the minimum along the interface of the angular fluid…
Bence-Merriman-Osher algorithm computes numerically mean curvature flow via solutions of heat equation iteratively initialized at the end of each short time interval. Inspired by the convergence proof of Evans of this algorithm where he…
Generation of few-cycle optical vortex pulses is challenging due to the large spectral bandwidths, as most vortex generation techniques are designed for monochromatic light. In this work, we use a spiral phase plate to generate few-cycle…
T. Borrvall and J. Petersson [Topology optimization of fluids in Stokes flow, International Journal for Numerical Methods in Fluids 41 (1) (2003) 77--107] developed the first model for topology optimization of fluids in Stokes flow. They…
Normalizing flows are a promising tool for modeling probability distributions in physical systems. While state-of-the-art flows accurately approximate distributions and energies, applications in physics additionally require smooth energies…
Optical flow estimation is a widely known problem in computer vision introduced by Gibson, J.J(1950) to describe the visual perception of human by stimulus objects. Estimation of optical flow model can be achieved by solving for the motion…
We formulate a method for computing Stokes flow past a highly deformed sphere with arbitrarily defined surface velocity. The fundamental ingredient is an explicit extrapolation operator extending a velocity field from the surface of a…
We propose an algorithm for evolving spiral curves on a planar domain by normal velocities depending on the so-called crystalline curvatures. The algorithm uses a minimizing movement approach and relies on a special level set method for…
The Poincar\'e sphere is a graphical representation in a three-dimensional space for the polarization of light. Similarly, an optical element with spatially varying birefringence can be represented by a surface on a four-dimensional…
We consider the problem of finding curves of minimum pointwise-maximum curvature, i.e., curves of minimax curvature, among planar curves of fixed length with prescribed endpoints and tangents at the endpoints. We reformulate the problem in…
We prove existence and uniqueness of the minimizer for the average geodesic distance to the points of a geodesically convex set on the sphere. This implies a corresponding existence and uniqueness result for an optimal algorithm for…
The aim of this note is to compare the averaged optimal coplanar transfer towards circular orbits when the costs are the transfer time transfer and the energy consumption. While the energy case leads to analyze a 2D Riemannian metric using…
This is an entry for the Gallery of Fluid Motion of the 65st Annual Meeting of the APS-DFD (fluid dynamics video). This video shows the motion of levitated liquid droplets. The levitation is produced by the vertical vibration of a liquid…