March 1971 wind tunnel tests of the Dorand DH 2011 jet flap rotor, volume 1

The results of wind tunnel tests, second series of tests performed in the NASA Ames 40 x 80 foot wind tunnel, of the DH 2011 jet-flap rotor are presented and analyzed. The tests have been focused on multicyclic effects and the capability of this rotor to reduce the vibratory loads and stresses in the blades. The reductions of the vibrations and stresses at tip speed ratio of 0.4 have attained 50%. The theory shows further reductions possible, reaching 80%. The results show that the performance characteristics after the modifications introduced since 1965 remained unchanged. The domain of investigation has been enlarged to include the tip speed ratios of 0.6 and 0.7. To analyze the complex aeroelastic phenomena a new analytical technique has been utilized to represent the mathematical model of the rotor. This technique, based on transfer matrices and transfer functions, appears very simple and it is believed that this analysis is applicable to many kinds of investigations involving large numbers of variables

March 1971 wind tunnel tests of the Dorand DH 2011 jet flap motor, volume 2

Wind tunnel tests were conducted of the Dorand DH 2011D jet flap rotor. The data recorded during the tests consist of: (1) multicyclic cam coefficients, (2) stress analysis, (3) vibratory loads, (4) Fourier analysis of flap deflection, and (5) blade bending stress. Data are presented in the form of tables and graphs

Subshifts, MSO Logic, and Collapsing Hierarchies

We use monadic second-order logic to define two-dimensional subshifts, or sets of colorings of the infinite plane. We present a natural family of quantifier alternation hierarchies, and show that they all collapse to the third level. In particular, this solves an open problem of [Jeandel & Theyssier 2013]. The results are in stark contrast with picture languages, where such hierarchies are usually infinite.Comment: 12 pages, 5 figures. To appear in conference proceedings of TCS 2014, published by Springe

Hastings' additivity counterexample via Dvoretzky's theorem

The goal of this note is to show that Hastings' counterexample to the additivity of minimal output von Neumann entropy can be readily deduced from a sharp version of Dvoretzky's theorem on almost spherical sections of convex bodies.Comment: 12 pages; v.2: added references, Appendix A expanded to make the paper essentially self-containe

On almost randomizing channels with a short Kraus decomposition

For large d, we study quantum channels on C^d obtained by selecting randomly N independent Kraus operators according to a probability measure mu on the unitary group U(d). When mu is the Haar measure, we show that for N>d/epsilon^2$, such a channel is epsilon-randomizing with high probability, which means that it maps every state within distance epsilon/d (in operator norm) of the maximally mixed state. This slightly improves on a result by Hayden, Leung, Shor and Winter by optimizing their discretization argument. Moreover, for general mu, we obtain a epsilon-randomizing channel provided N > d (\log d)^6/epsilon^2$. For d=2^k (k qubits), this includes Kraus operators obtained by tensoring k random Pauli matrices. The proof uses recent results on empirical processes in Banach spaces.Comment: We added some background on geometry of Banach space

Undecidable word problem in subshift automorphism groups

This article studies the complexity of the word problem in groups of automorphisms of subshifts. We show in particular that for any Turing degree, there exists a subshift whose automorphism group contains a subgroup whose word problem has exactly this degree

On the structure of the body of states with positive partial transpose

We show that the convex set of separable mixed states of the 2 x 2 system is a body of constant height. This fact is used to prove that the probability to find a random state to be separable equals 2 times the probability to find a random boundary state to be separable, provided the random states are generated uniformly with respect to the Hilbert-Schmidt (Euclidean) distance. An analogous property holds for the set of positive-partial-transpose states for an arbitrary bipartite system.Comment: 10 pages, 1 figure; ver. 2 - minor changes, new proof of lemma

Weak multiplicativity for random quantum channels

It is known that random quantum channels exhibit significant violations of multiplicativity of maximum output p-norms for any p>1. In this work, we show that a weaker variant of multiplicativity nevertheless holds for these channels. For any constant p>1, given a random quantum channel N (i.e. a channel whose Stinespring representation corresponds to a random subspace S), we show that with high probability the maximum output p-norm of n copies of N decays exponentially with n. The proof is based on relaxing the maximum output infinity-norm of N to the operator norm of the partial transpose of the projector onto S, then calculating upper bounds on this quantity using ideas from random matrix theory.Comment: 21 pages; v2: corrections and additional remark