Related papers: A disk-covering problem with application in optica…
In this paper we investigate the parameterized complexity of the task of counting and detecting occurrences of small patterns in unit disk graphs: Given an $n$-vertex unit disk graph $G$ with an embedding of ply $p$ (that is, the graph is…
Optical interferometric imaging enables astronomical observation at extremely high angular resolution. The necessary optical information for imaging, such as the optical path differences and visibilities, is easy to extract from fringes…
We calculate simulated images of disks perturbed by embedded small planets. These 10-50 M_Earth bodies represent the growing cores of giant planets. We examine scattered light and thermal emission from these disks over a range of…
Imaging circumstellar disks in the near-infrared provides unprecedented information about the formation and evolution of planetary systems. However, current post-processing techniques for high-contrast imaging using ground-based telescopes…
(abridged) Debris disks around main sequence stars are produced by the erosion and evaporation of unseen parent bodies. AU Microscopii (GJ 803) is a compelling object to study in the context of disk evolution across different spectral…
Two dimensional particle disks in proximity to a planet are numerically integrated to determine when a planet in a circular orbit can truncate a particle disk. Collisions are treated by giving each particle a series of velocity…
We study the problems of covering or partitioning a polygon $P$ (possibly with holes) using a minimum number of small pieces, where a small piece is a connected sub-polygon contained in an axis-aligned unit square. For covering, we seek to…
Pupil-mapping is a technique whereby a uniformly-illuminated input pupil, such as from starlight, can be mapped into a non-uniformly illuminated exit pupil, such that the image formed from this pupil will have suppressed sidelobes, many…
Detecting the angles and orbits of remote targets precisely has been playing crucial roles in astrophysical research. Due to the resolution limitations imposed by the Airy disk in a single telescope, optical interferometric schemes with at…
Determination of refractive index of micro-disks of a calcinated ($1100^\circ$C in air) photo-resist SZ2080$^\mathrm{TM}$ was carried out using transmission and reflection spectroscopy. Interference fringes at specific…
We have identified four circumstellar disks with a deficit of dust emission from their inner 15-50 AU. All four stars have F-G spectral type, and were uncovered as part of the Spitzer Space Telescope ``Cores to Disks'' Legacy Program…
In the past few years, several disks with inner holes that are empty of small dust grains have been detected and are known as transitional disks. Recently, Spitzer has identified a new class of "pre-transitional disks" with gaps; these…
In this article, we study the intersection (or union) of the convex hull of N confocal paraboloids (or ellipsoids) of revolution. This study is motivated by a Minkowski-type problem arising in geometric optics. We show that in each of the…
This paper is concerned with a study of the classical isoperimetric problem modified by an addition of a non-local repulsive term. We characterize existence, non-existence and radial symmetry of the minimizers as a function of mass in the…
We present a scheme for achieving macroscopic quantum superpositions in optomechanical systems by using single photon postselection and detecting them with nested interferometers. This method relieves many of the challenges associated with…
Inside a fixed bounded domain $\Omega$ of the plane, we look for the best compact connected set $K$, of given perimeter, in order to maximize the first Dirichlet eigenvalue $\lambda_1(\Omega\setminus K)$. We discuss some of the qualitative…
Intersection graphs of planar geometric objects such as intervals, disks, rectangles and pseudo-disks are well studied. Motivated by various applications, Butman et al. in SODA 2007 considered algorithmic questions in intersection graphs of…
The Gemini Planet Imager (GPI) has excelled in imaging debris disks in the near-infrared. The GPI Exoplanet Survey (GPIES) imaged twenty-four debris disks in polarized $H$-band light, while other programs observed half of these disks in…
We consider the isoperimetric problem in planar sectors with density $r^{p}$, and with density $a>1$ inside the unit disk and $1$ outside. We characterize solutions as a function of sector angle. We also solve the isoperimetric problem in…
We consider the problem of packing a family of disks "on a shelf", that is, such that each disk touches the $x$-axis from above and such that no two disks overlap. We prove that the problem of minimizing the distance between the leftmost…