259,709 research outputs found
Optimization of graded multilayer designs for astronomical x-ray telescopes
We developed a systematic method for optimizing the design of depth-graded multilayers for astronomical hard-x-ray and soft-γ-ray telescopes based on the instrument’s bandpass and the field of view. We apply these methods to the design of the conical-approximation Wolter I optics employed by the balloon-borne High Energy Focusing Telescope, using W/Si as the multilayer materials. In addition, we present optimized performance calculations of mirrors, using other material pairs that are capable of extending performance to photon energies above the W K-absorption edge (69.5 keV), including Pt/C, Ni/C, Cu/Si, and Mo/Si
Efficient approximate unitary t-designs from partially invertible universal sets and their application to quantum speedup
At its core a -design is a method for sampling from a set of unitaries in
a way which mimics sampling randomly from the Haar measure on the unitary
group, with applications across quantum information processing and physics. We
construct new families of quantum circuits on -qubits giving rise to
-approximate unitary -designs efficiently in
depth. These quantum circuits are based on a relaxation of technical
requirements in previous constructions. In particular, the construction of
circuits which give efficient approximate -designs by Brandao, Harrow, and
Horodecki (F.G.S.L Brandao, A.W Harrow, and M. Horodecki, Commun. Math. Phys.
(2016).) required choosing gates from ensembles which contained inverses for
all elements, and that the entries of the unitaries are algebraic. We reduce
these requirements, to sets that contain elements without inverses in the set,
and non-algebraic entries, which we dub partially invertible universal sets. We
then adapt this circuit construction to the framework of measurement based
quantum computation(MBQC) and give new explicit examples of -qubit graph
states with fixed assignments of measurements (graph gadgets) giving rise to
unitary -designs based on partially invertible universal sets, in a natural
way. We further show that these graph gadgets demonstrate a quantum speedup, up
to standard complexity theoretic conjectures. We provide numerical and
analytical evidence that almost any assignment of fixed measurement angles on
an -qubit cluster state give efficient -designs and demonstrate a quantum
speedup.Comment: 25 pages,7 figures. Comments are welcome. Some typos corrected in
newest version. new References added.Proofs unchanged. Results unchange
Tapered laminate designs for new non-crimp fabric architectures
Non-Crimp Fabric (NCF) materials are now available in a range of areal weights and layer architectures, including 0/45, 0/−45, 45/−45 and 0/90, which correspond to the standard ply orientations employed in traditional UD material lay-ups. The benefit of NCF material is generally associated with increased deposition rate, but this advantage may be offset by reduced design freedoms when a specific form of mechanical coupling behaviour is required, layer terminations must be introduced and/or thermal warping distortion eliminated.
This article investigates the extent to which new NCF architectures can be tailored to achieve warp free tapered laminates with mechanical Extension-Shearing Bending-Twisting coupling, by single axis (longitudinal) deposition of all ply angles; thus avoiding ply discontinuities that may be introduce in large component manufacture. Lamination parameter design spaces are used to demonstrate the extent of the feasible solutions both before and after applying a laminate tapering scheme
Designing experiments for an application in laser and surface Chemistry
We consider the design used to collect data for a Second Harmonic Generation (SHG) experiment, where the behaviour of interfaces between two phases, for example the surface of a liquid, is investigated. These studies have implications in surfactants, catalysis, membranes and electrochemistry. Ongoing work will be described in designing experiments to investigate nonlinear models used to represent the data, relating the intensity of the SHG signal to the polarisation angles of the polarised light beam. The choice of design points and their effect on parameter estimates is investigated. Various designs and the current practice of using equal-spaced levels are investigated, and their relative merits compared on the basis of the overall aim of the chemical study
New bounds for equiangular lines
A set of lines in is called equiangular if the angle between
each pair of lines is the same. We address the question of determining the
maximum size of equiangular line sets in , using semidefinite
programming to improve the upper bounds on this quantity. Improvements are
obtained in dimensions . In particular, we show that the
maximum number of equiangular lines in is for all and is 344 for This provides a partial resolution of the
conjecture set forth by Lemmens and Seidel (1973).Comment: Minor corrections; added one new reference. To appear in "Discrete
Geometry and Algebraic Combinatorics," A. Barg and O. R. Musin, Editors,
Providence: RI, AMS (2014). AMS Contemporary Mathematics serie
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