Related papers: A disk-covering problem with application in optica…
Transitional discs are a class of circumstellar discs around young stars with extensive clearing of dusty material within their inner regions on 10s of au scales. One of the primary candidates for this kind of clearing is the formation of…
With the present and soon-to-be breakthrough of optical interferometry, countless objects shall be within reach of interferometers; yet, most of them are expected to remain only marginally resolved with hectometric baselines. In this paper,…
Given a set ${\cal D}$ of unit disks in the Euclidean plane, we consider (i) the {\it discrete unit disk cover} (DUDC) problem and (ii) the {\it rectangular region cover} (RRC) problem. In the DUDC problem, for a given set ${\cal P}$ of…
Incoming optical interferometers will allow spectro-imaging at high angular resolution. Non-homothetic Fizeau concept combines good sensitivity and high spectral resolution capabilities. However, one critical issue is the design of the beam…
Zernike polynomials are a basis of orthogonal polynomials on the unit disk that are a natural basis for representing smooth functions. They arise in a number of applications including optics and atmospheric sciences. In this paper, we…
A pattern of interpolation nodes on the disk is studied, for which the interpolation problem is theoretically unisolvent, and which renders a minimal numerical condition for the collocation matrix when the standard basis of Zernike…
We consider the planar two-center problem for a convex polygon: given a convex polygon in the plane, find two congruent disks of minimum radius whose union contains the polygon. We present an $O(n\log n)$-time algorithm for the two-center…
The problem of covering random points in a plane with sets of a given shape has several practical applications in communications and operations research. One especially prominent application is the coverage of randomly-located points of…
We investigate the possibility to find evidence for planets in circumstellar disks by infrared and submillimeter interferometry. We present simulations of a circumstellar disk around a solar-type star with an embedded planet of 1 Jupiter…
We have obtained millimeter wavelength photometry, high-resolution optical spectroscopy and adaptive optics near-infrared imaging for a sample of 26 Spitzer-selected transition circumstellar disks. All of our targets are located in the…
The detection and characterisation of extra-solar planets is a major theme driving modern astronomy, with the vast majority of such measurements being achieved by Doppler radial-velocity and transit observations. Another technique -- direct…
An image-based technique for measuring the complex field in the pupil of an imaging system is presented. Two point source images, one with a small modification introduced in the pupil, are combined using a simple and non-iterative…
In this paper we consider the problem of locating $k$ obnoxious facilities (congruent disks of maximum radius) amidst $n$ demand points (existing repulsive facility sites) ordered from left to right in the plane so that none of the existing…
Millimetre-compact dust disks are thought to have efficient radial drift of icy dust pebbles, which has been hypothesised to produce an enhanced cold ($T<$400 K) H$_2$O reservoir in their inner disks. Mid-infrared spectral surveys, now with…
Interferometry has brought many new constraints in optical astronomy in the recent years. A major leap in this field is the opening of large interferometric facilities like the Very Large Telescope Interferometer and the Keck Interferometer…
Given a point set P in 2D, the problem of finding the smallest set of unit disks that cover all of P is NP-hard. We present a simple algorithm for this problem with an approximation factor of 25/6 in the Euclidean norm and 2 in the max…
We present an H-band image of the light scattered from circumstellar dust around the nearby (10 pc) young M star AU Microscopii (AU Mic, GJ 803, HD 197481), obtained with the Keck adaptive optics system. We resolve the disk both vertically…
Oblique plane microscopy is a method enabling light-sheet fluorescence imaging through a single microscope objective lens by focusing on a tilted plane within the sample. To focus the fluorescence emitted by the oblique plane on a camera,…
The percolation threshold and wrapping probability $R_{\infty}$ for the two-dimensional problem of continuum percolation on the surface of a Klein bottle have been calculated by the Monte Carlo method with the Newman--Ziff algorithm for…
We study a nonlocal perimeter functional inspired by the Minkowski content, whose main feature is that it interpolates between the classical perimeter and the volume functional. This problem is related by a generalized coarea formula to a…