Related papers: "The Optiverse" and other sphere eversions
Topological techniques are used to study the motions of systems of point vortices in the infinite plane, in singly-periodic arrays, and in doubly-periodic lattices. The reduction of each system using its symmetries is described in detail.…
We present a systematic derivation of three mathematical models of increasing complexity for optical design, based on Hamilton's characteristic functions and conservation of luminous flux, and briefly explain the connection with the…
Estimating motion in videos is an essential computer vision problem with many downstream applications, including controllable video generation and robotics. Current solutions are primarily trained using synthetic data or require tuning of…
Representing complex shapes with simple primitives in high accuracy is important for a variety of applications in computer graphics and geometry processing. Existing solutions may produce suboptimal samples or are complex to implement. We…
We study the problem of recovering the initial data of the two dimensional wave equation from values of its solution on the boundary $\partial \Om$ of a smooth convex bounded domain $\Om \subset \R^2$. As a main result we establish…
The problem of optimization of a cycle of tangential deformations of the surface of a spherical object (microsquirmer) self-propelling in a viscous fluid at low Reynolds numbers is represented in a noncanonical Hamiltonian form. The…
Vector optical vortices exhibit complex polarisation patterns due to the interplay between spin and orbital angular momenta. Here we demonstrate, both analytically and with simulations, that certain polarisation features of optical vortex…
Approximating a function with a finite series, e.g., involving polynomials or trigonometric functions, is a critical tool in computing and data analysis. The construction of such approximations via now-standard approaches like least squares…
We investigate a mean curvature flow obtained via elliptic regularization, and prove that it is not only a Brakke flow, but additionally a generalized BV flow proposed by Stuvard and Tonegawa. In particular, we show that the change in…
Energy minimization has been an intensely studied core problem in computer vision. With growing image sizes (2D and 3D), it is now highly desirable to run energy minimization algorithms in parallel. But many existing algorithms, in…
During the upstroke of a normal eye blink, the upper lid moves and paints a thin tear film over the exposed corneal and conjunctival surfaces. This thin tear film may be modeled by a nonlinear fourth-order PDE derived from lubrication…
It is well known that a superfluid rotates by forming an array of quantized vortices. A relativistic formulation for superfluid vortex dynamics is required for a range of problems in astrophysics and cosmology, from neutron star interiors…
We introduce some new experiments where light diffraction is demonstrated with simple elements: white light diffraction with a coin, construction of a diffractive lens by holography, diffraction properties in digital discs and an…
We consider an inverse problem for the linear one-dimensional wave equation with variable coefficients consisting in determining an unknown source term from a boundary observation. A method to obtain approximations of this inverse problem…
This is the first of several monographs to be devoted to the optics of accelerated systems. They are being published for the benefit of those who may wish to have another way of looking at kineoptical problems, and also to demonstrate that…
Using the observed time and spatial intervals defined originally by Einstein and the observation frame in the vierbein formalism, we propose that in curved spacetime, for a wave received in laboratories, the observed frequency is the…
We experimentally generate cylindrically polarized wavepackets with transverse orbital angular momentum, demonstrating the coexistence of spatiotemporal optical vortex with spatial polarization singularity. The results in this paper extend…
Stellar seismic inversions have proved to be a powerful technique for probing the internal structure of stars, and paving the way for a better understanding of the underlying physics by revealing some of the shortcomings in current stellar…
A nonlocal curvature flow is introduced to evolve locally convex curves in the plane. It is proved that this flow with any initial locally convex curve has a global solution, keeping the local convexity and the elastic energy of the…
A new modulus of smoothness based on the Euler angles is introduced on the unit sphere and is shown to satisfy all the usual characteristic properties of moduli of smoothness, including direct and inverse theorem for the best approximation…