Related papers: Orange Peels and Fresnel Integrals
The Eynard-Orantin recursion formula provides an effective tool for certain enumeration problems in geometry. The formula requires a spectral curve and the recursion kernel. We present a uniform construction of the spectral curve and the…
Determining the relative brightness of the solar corona is one of the most critical stages in solar eclipse studies. For this purpose, images taken with different exposures and polarization angles in white-light observations are used. The…
Observations of the five confirmed optical pulsars indicate that the peak emission scales according to the magnetic field strength at the light cylinder. To the accuracy that such low number allows we show that this gives further…
Optical tweezers exploit light--matter interactions to trap particles ranging from single atoms to micrometer-sized eukaryotic cells. For this reason, optical tweezers are a ubiquitous tool in physics, biology, and nanotechnology. Recently,…
In this article we present an analytic solution of the famous problem of diffraction and interference of electrons through one and two slits (for simplicity, only the one-dimensional case is considered). In addition to exact formulas, we…
Presentation of folded documents is not an uncommon case in modern society. Digitizing such documents by capturing them with a smartphone camera can be tricky since a crease can divide the document contents into separate planes. To unfold…
In this paper, the evolution of a polygonal spiral curve by the crystalline curvature flow with a pinned center is considered with two view points, discrete model consist of an ODE system of facet lengths and a level set method. We…
We describe a self calibrating optical technique that allows to perform absolute measurements of scattering cross sections for the light scattered at extremely small angles. Very good performances are obtained by using a very simple optical…
Many common methods for data analysis rely on linear algebra. We provide new results connecting data analysis error to numerical accuracy, which leads to the first meaningful stopping criterion for two way spectral partitioning. More…
We show that the spectrum of a flow field can be extracted within a local region by straightforward filtering in physical space. We find that for a flow with a certain level of regularity, the filtering kernel must have a sufficient number…
The purpose of this note is to prove an Euler-type formula for partitions of the M\"obius strip. This formula was introduced in our joint paper with R.~Kiwan, "Courant-sharp property for Dirichlet eigenfunctions on the M\"obius strip"…
Thinning is the removal of contour pixels/points of connected components in an image to produce their skeleton with retained connectivity and structural properties. The output requirements of a thinning procedure often vary with…
We argue that once octonions are formulated as soft Lie algebras, they may be safely used and the non-associativity can be overcame. The necessary points are: (a) Fixing the direction of action by introducing the \delta operator. (b)…
A very simple model for cell swelling by osmosis is introduced, resulting in a parabolic free boundary problem. In case of radially symmetric initial conditions, it is shown that the model can be viewed as a gradient flow involving entropy,…
In this paper we present an algorithm for optical phase evaluation based on the wavelet transform technique. The main advantage of this method is that it requires only one fringe pattern. This algorithm is based on the use of a second…
This paper describes a method for the explicit reconstruction and visualization of various polarization ellipses from the intensities measured after a rotating polarizer. The state of polarization of a light beam is represented by the…
We transform a double integral into a second-order initial value problem, which we solve using Euler's method and Richardson extrapolation. For an example we consider, we achieve accuracy close to machine precision (1e-15). We also use the…
Conics and Cartesian ovals are very important curves in various fields of science. Also aspheric curves based on conics are useful in optics. Superconic curves recently suggested by A. Greynolds are extensions of both conics and Cartesian…
It is shown that space-time may possess the differentiability properties of manifolds as well as the ultraviolet finiteness properties of lattices. Namely, if a field's amplitudes are given on any sufficiently dense set of discrete points…
Optical tweezers are widely used for the manipulation of cells and their internal structures. However, the degree of manipulation possible is limited by poor control over the orientation of trapped cells. We show that it is possible to…