A safety margin and flight reference system and display for powered-lift aircraft

A study was conducted to explore the feasibility of a safety margin and flight reference system for those powered-lift aircraft which require a backside piloting technique. The main objective was to display multiple safety margin criteria as a single variable which could be tracked both manually and automatically and which could be monitored in order to derive safety margin status. The study involved a pilot-in-the-loop analysis of several system concepts and a simulator experiment to evaluate those concepts showing promise. A system was ultimately configured which yielded reasonable compromises in controllability, status information content, and the ability to regulate safety margins at some expense of the allowable low speed flight path envelope

An evaluation of the spatial resolution of soil moisture information

Rainfall-amount patterns in the central regions of the U.S. were assessed. The spatial scales of surface features and their corresponding microwave responses in the mid western U.S. were investigated. The usefulness for U.S. government agencies of soil moisture information at scales of 10 km and 1 km. was ascertained. From an investigation of 494 storms, it was found that the rainfall resulting from the passage of most types of storms produces patterns which can be resolved on a 10 km scale. The land features causing the greatest problem in the sensing of soil moisture over large agricultural areas with a radiometer are bodies of water. Over the mid-western portions of the U.S., water occupies less than 2% of the total area, the consequently, the water bodies will not have a significant impact on the mapping of soil moisture. Over most of the areas, measurements at a 10-km resolution would adequately define the distribution of soil moisture. Crop yield models and hydrological models would give improved results if soil moisture information at scales of 10 km was available

Discrete concavity and the half-plane property

Murota et al. have recently developed a theory of discrete convex analysis which concerns M-convex functions on jump systems. We introduce here a family of M-concave functions arising naturally from polynomials (over a field of generalized Puiseux series) with prescribed non-vanishing properties. This family contains several of the most studied M-concave functions in the literature. In the language of tropical geometry we study the tropicalization of the space of polynomials with the half-plane property, and show that it is strictly contained in the space of M-concave functions. We also provide a short proof of Speyer's hive theorem which he used to give a new proof of Horn's conjecture on eigenvalues of sums of Hermitian matrices.Comment: 14 pages. The proof of Theorem 4 is corrected

Computing the Mertens and Meissel-Mertens constants for sums over arithmetic progressions

We give explicit numerical values with 100 decimal digits for the Mertens constant involved in the asymptotic formula for $\sum\limits_{\substack{p\leq x p\equiv a \bmod{q}}}1/p$ and, as a by-product, for the Meissel-Mertens constant defined as $\sum_{p\equiv a \bmod{q}} (\log(1-1/p)+1/p)$, for $q \in \{3$, ..., $100\}$ and $(q, a) = 1$.Comment: 12 pages, 6 table

On the comparison of volumes of quantum states

This paper aims to study the \a-volume of \cK, an arbitrary subset of the set of $N\times N$ density matrices. The \a-volume is a generalization of the Hilbert-Schmidt volume and the volume induced by partial trace. We obtain two-side estimates for the \a-volume of \cK in terms of its Hilbert-Schmidt volume. The analogous estimates between the Bures volume and the \a-volume are also established. We employ our results to obtain bounds for the \a-volume of the sets of separable quantum states and of states with positive partial transpose (PPT). Hence, our asymptotic results provide answers for questions listed on page 9 in \cite{K. Zyczkowski1998} for large $N$ in the sense of \a-volume. \vskip 3mm PACS numbers: 02.40.Ft, 03.65.Db, 03.65.Ud, 03.67.M

Complex critical exponents for percolation transitions in Josephson-junction arrays, antiferromagnets, and interacting bosons

We show that the critical behavior of quantum systems undergoing a percolation transition is dramatically affected by their topological Berry phase $2\pi\rho$. For irrational $\rho$, we demonstrate that the low-energy excitations of diluted Josephson-junctions arrays, quantum antiferromagnets, and interacting bosons are spinless fermions with fractal spectrum. As a result, critical properties not captured by the usual Ginzburg-Landau-Wilson description of phase transitions emerge, such as complex critical exponents, log-periodic oscillations and dynamically broken scale-invariance.Comment: revised version accepted for publication in Phys. Rev. Let

Cheat Sensitive Quantum Bit Commitment

We define cheat sensitive cryptographic protocols between mistrustful parties as protocols which guarantee that, if either cheats, the other has some nonzero probability of detecting the cheating. We give an example of an unconditionally secure cheat sensitive non-relativistic bit commitment protocol which uses quantum information to implement a task which is classically impossible; we also describe a simple relativistic protocol.Comment: Final version: a slightly shortened version of this will appear in PRL. Minor corrections from last versio

On the communication cost of entanglement transformations

We study the amount of communication needed for two parties to transform some given joint pure state into another one, either exactly or with some fidelity. Specifically, we present a method to lower bound this communication cost even when the amount of entanglement does not increase. Moreover, the bound applies even if the initial state is supplemented with unlimited entanglement in the form of EPR pairs, and the communication is allowed to be quantum mechanical. We then apply the method to the determination of the communication cost of asymptotic entanglement concentration and dilution. While concentration is known to require no communication whatsoever, the best known protocol for dilution, discovered by Lo and Popescu [Phys. Rev. Lett. 83(7):1459--1462, 1999], requires a number of bits to be exchanged which is of the order of the square root of the number of EPR pairs. Here we prove a matching lower bound of the same asymptotic order, demonstrating the optimality of the Lo-Popescu protocol up to a constant factor and establishing the existence of a fundamental asymmetry between the concentration and dilution tasks. We also discuss states for which the minimal communication cost is proportional to their entanglement, such as the states recently introduced in the context of ``embezzling entanglement'' [W. van Dam and P. Hayden, quant-ph/0201041].Comment: 9 pages, 1 figure. Added a reference and some further explanations. In v3 some arguments are given in more detai

Entanglement Swapping Chains for General Pure States

We consider entanglement swapping schemes with general (rather than maximally) entangled bipartite states of arbitary dimension shared pairwise between three or more parties in a chain. The intermediate parties perform generalised Bell measurements with the result that the two end parties end up sharing a entangled state which can be converted into maximally entangled states. We obtain an expression for the average amount of maximal entanglement concentrated in such a scheme and show that in a certain reasonably broad class of cases this scheme is provably optimal and that, in these cases, the amount of entanglement concentrated between the two ends is equal to that which could be concentrated from the weakest link in the chain.Comment: 18 pages, 5 figure

Origin of the tetragonal-to-orthorhombic (nematic) phase transition in FeSe: a combined thermodynamic and NMR study

The nature of the tetragonal-to-orthorhombic structural transition at $T_s\approx90$ K in single crystalline FeSe is studied using shear-modulus, heat-capacity, magnetization and NMR measurements. The transition is shown to be accompanied by a large shear-modulus softening, which is practically identical to that of underdoped Ba(Fe,Co)$_2$As$_2$, suggesting very similar strength of the electron-lattice coupling. On the other hand, a spin-fluctuation contribution to the spin-lattice relaxation rate is only observed below $T_s$. This indicates that the structural, or "nematic", phase transition in FeSe is not driven by magnetic fluctuations