1,474 research outputs found
Icosahedron designs
It is known from the work of Adams and Bryant that icosahedron designs of order v exist for v ≡ 1 (mod 60) as well as for v = 16. Here we prove that icosahedron designs exist if and only if v ≡ 1, 16, 21 or 36 (mod 60), wit
Quasi-Static Nonlinear Analysis of a Celestial Icosahedron Shaped Vacuum Lighter Than Air Vehicle
Due to the many drawbacks associated with a traditional lighter than air vehicle (LTAV), there is a desire for a LTAV which generates lift from an internal vacuum. To date, two feasible designs (the icosahedron and the hexakis icosahedron) for this so called vacuum lighter than air vehicle (VLTAV) have been studied at the Air Force Institute of Technology (AFIT). This research looks to show the feasibility of a new design for a VLTAV, the celestial icosahedron. This research includes a boundary condition study which proves the symmetric nature of the celestial icosahedron\u27s frame with laterally constrained and unconstrained vertices. This research also presents three feasible designs of various structural diameters (0.8001, 1.2192, and 0.7576 meters) for the celestial icosahedron
Panoramic optical and near-infrared SETI instrument: optical and structural design concepts
We propose a novel instrument design to greatly expand the current optical
and near-infrared SETI search parameter space by monitoring the entire
observable sky during all observable time. This instrument is aimed to search
for technosignatures by means of detecting nano- to micro-second light pulses
that could have been emitted, for instance, for the purpose of interstellar
communications or energy transfer. We present an instrument conceptual design
based upon an assembly of 198 refracting 0.5-m telescopes tessellating two
geodesic domes. This design produces a regular layout of hexagonal collecting
apertures that optimizes the instrument footprint, aperture diameter,
instrument sensitivity and total field-of-view coverage. We also present the
optical performance of some Fresnel lenses envisaged to develop a dedicated
panoramic SETI (PANOSETI) observatory that will dramatically increase sky-area
searched (pi steradians per dome), wavelength range covered, number of stellar
systems observed, interstellar space examined and duration of time monitored
with respect to previous optical and near-infrared technosignature finders.Comment: 14 pages, 5 figures, 3 table
McLaren's Improved Snub Cube and Other New Spherical Designs in Three Dimensions
Evidence is presented to suggest that, in three dimensions, spherical
6-designs with N points exist for N=24, 26, >= 28; 7-designs for N=24, 30, 32,
34, >= 36; 8-designs for N=36, 40, 42, >= 44; 9-designs for N=48, 50, 52, >=
54; 10-designs for N=60, 62, >= 64; 11-designs for N=70, 72, >= 74; and
12-designs for N=84, >= 86. The existence of some of these designs is
established analytically, while others are given by very accurate numerical
coordinates. The 24-point 7-design was first found by McLaren in 1963, and --
although not identified as such by McLaren -- consists of the vertices of an
"improved" snub cube, obtained from Archimedes' regular snub cube (which is
only a 3-design) by slightly shrinking each square face and expanding each
triangular face. 5-designs with 23 and 25 points are presented which, taken
together with earlier work of Reznick, show that 5-designs exist for N=12, 16,
18, 20, >= 22. It is conjectured, albeit with decreasing confidence for t >= 9,
that these lists of t-designs are complete and that no others exist. One of the
constructions gives a sequence of putative spherical t-designs with N= 12m
points (m >= 2) where N = t^2/2 (1+o(1)) as t -> infinity.Comment: 16 pages, 1 figur
Rolling quantum dice with a superconducting qubit
One of the key challenges in quantum information is coherently manipulating
the quantum state. However, it is an outstanding question whether control can
be realized with low error. Only gates from the Clifford group -- containing
, , and Hadamard gates -- have been characterized with high
accuracy. Here, we show how the Platonic solids enable implementing and
characterizing larger gate sets. We find that all gates can be implemented with
low error. The results fundamentally imply arbitrary manipulation of the
quantum state can be realized with high precision, providing new practical
possibilities for designing efficient quantum algorithms.Comment: 8 pages, 4 figures, including supplementary materia
Geometric Entanglement of Symmetric States and the Majorana Representation
Permutation-symmetric quantum states appear in a variety of physical
situations, and they have been proposed for quantum information tasks. This
article builds upon the results of [New J. Phys. 12, 073025 (2010)], where the
maximally entangled symmetric states of up to twelve qubits were explored, and
their amount of geometric entanglement determined by numeric and analytic
means. For this the Majorana representation, a generalization of the Bloch
sphere representation, can be employed to represent symmetric n qubit states by
n points on the surface of a unit sphere. Symmetries of this point distribution
simplify the determination of the entanglement, and enable the study of quantum
states in novel ways. Here it is shown that the duality relationship of
Platonic solids has a counterpart in the Majorana representation, and that in
general maximally entangled symmetric states neither correspond to anticoherent
spin states nor to spherical designs. The usability of symmetric states as
resources for measurement-based quantum computing is also discussed.Comment: 10 pages, 8 figures; submitted to Lecture Notes in Computer Science
(LNCS
Choice of Measurement Sets in Qubit Tomography
Optimal generalized measurements for state estimation are well understood.
However, practical quantum state tomography is typically performed using a
fixed set of projective measurements and the question of how to choose these
measurements has been largely unexplored in the literature. In this work we
develop theoretical asymptotic bounds for the average fidelity of pure qubit
tomography using measurement sets whose axes correspond to vertices of Platonic
solids. We also present complete simulations of maximum likelihood tomography
for mixed qubit states using the Platonic solid measurements. We show that
overcomplete measurement sets can be used to improve the accuracy of
tomographic reconstructions.Comment: 13 Pages, 6 figure
Interconvertible soft articles
Rugged, soft, interconvertible articles constructed from soft, resilient members, which articles adopt a substantially different geometry upon an interior to exterior interconversion. The articles of the invention provide a significant visual effect and are useful as educational aids, magician's props, and toys.Published versio
- …