Related papers: "The Optiverse" and other sphere eversions
Sphere eversions have been described so far by either pictures with minimal topological complexity, numerical evolution or complex equations. We write down relatively simple explicit formulas for the whole eversion, both analytic and…
We give linear-time quasiconvex programming algorithms for finding a Moebius transformation of a set of spheres in a unit ball or on the surface of a unit sphere that maximizes the minimum size of a transformed sphere. We can also use…
The problem of a disc or cylinder initially rolling with slipping on a surface and subsequently transitioning to rolling without slipping is often cited in textbooks. The following experiment serves to clearly demonstrate the transition…
We present a (possibly) new sphere eversion based on the contractibility* of a certain subset of the space of immersions of the circle in the plane. (*: by strong deformation retraction)
The staid subject of exact static spherically symmetric perfect fluid solutions of Einstein's equations has been reinvigorated in the last decade. We now have several solution generating techniques which give rise to new exact solutions.…
A spherical droplet is given an initial rotation in the streamwise direction and is impulsively accelerated by a uniform free stream. Numerical results for the deformation and dynamics of the droplet are obtained by utilising a finite…
Given an observed gravitational lens mirage produced by a foreground deflector (cf. galaxy, quasar, cluster,...), it is possible via numerical lens inversion to retrieve the real source image, taking full advantage of the magnifying power…
This paper focus on the theoretical analysis and simulation of electromagnetic wave transforms, which is widely encountered in teaching physics. When the electromagnetic wave is not consistent with the shape of the object, it is often…
We define two transforms between minimal surfaces with non-circular ellipse of curvature in the 5-sphere, and show how this enables us to construct, from one such surface, a sequence of such surfaces. We also use the transforms to show how…
We address the question of constructing simple inviscid vortex models which optimally approximate realistic flows as solutions of an inverse problem. Assuming the model to be incompressible, inviscid and stationary in the frame of reference…
We present a unified treatment of the abstract problem of finding the best approximation between a cone and spheres in the image of affine transformations. Prominent instances of this problem are phase retrieval and source localization. The…
We show that every quadrangulation of the sphere can be transformed into a $4$-cycle by deletions of degree-$2$ vertices and by $t$-contractions at degree-$3$ vertices. A $t$-contraction simultaneously contracts all incident edges at a…
An evolution of a spherical region, subjected to uniform buoyancy force, is investigated. Incompressibility and axial symmetry are assumed, together with a buoyancy discontinuity at the boundary. The boundary turns into a vortex sheet and…
The motion of noncircular two-dimensional vortices is shown to depend on a form of coupling between vortex ellipticity and the gradient of fluid density. The approach is based on the perspective that an elliptic vortex can be described as…
The standard simplex in R^n, also known as the probability simplex, is the set of nonnegative vectors whose entries sum up to 1. They frequently appear as constraints in optimization problems that arise in machine learning, statistics, data…
We introduce an extension of the convex potentials for finite frames (e.g. the frame potential defined by Benedetto and Fickus) in the framework of Bessel sequences of integer translates of finite sequences in $L^2(\R^k)$. We show that…
We construct an idealized universe for didactic purposes. This universe is assumed to consist of absolute Euclidean space and to be filled with a classical medium which allows for sound waves. A known solution to the wave equation…
We study propagation of high-frequency electromagnetic waves in a curved spacetime. We demonstrate how a modification of the standard geometric optics allows one to include the helicity dependent corrections into the equations of motion of…
A numerical scheme for computing arc-length parametrized curves of low bending energy that are confined to convex domains is devised. The convergence of the discrete formulations to a continuous model and the unconditional stability of an…
Optical force can enable precise manipulations of small particles for various applications. It is well known that an isotropic lossless dielectric sphere is only subject to forward optical force under the illumination of an electromagnetic…