An experimental measurement of galactic cosmic radiation dose in conventional aircraft between San Francisco and London compared to theoretical values for conventional and supersonic aircraft

These direct measurements are in fair agreement with computations made using a program which considers both basic cosmic ray atmospheric physics and the focusing effect of the earth's magnetic field. These measurements also agree with those made at supersonic jet aircraft altitudes in Rb-57 aircraft. It is concluded that experiments and theory show that the doses received at conventional jet aircraft altitudes are slightly higher than those encountered in supersonic flights at much higher altitudes

The transition to conduction in diffusion-controlled gas breakdown

Measurements have been made of ultra-high-frequency (l80Mc/s) breakdown fields in hydrogen, nitrogen and neon, in a Rogowski-profiled spark gap, under conditions of pressure in which both the electron ambit and the mean-free-path were less than the gap width (0.494cm). The measurements were made with sustained fields and also with pulsed fields in overvolted conditions to obtain data on the variation of breakdown delays with overvoltage. The delays were measured by photographing an oscilloscope trace which displayed the gap voltage, and a range of 400 to 0.2 microseconds was observed with over voltages up to 100%. Breakdown was initiated during a pulse by irradiating the gas in the mid-gap region with a short (about 0.1 microsecond) burst of ultraviolet photons, A theory is proposed which determines the shape of the oscillograms, and hence gives breakdown delays. Good agreement was obtained between theoretical and experimental delays for hydrogen and nitrogen, but predicted delays were too short by factors up to ten for neon. A qualitative explanation is given for the anomalous results for neon. Maintaining voltages have been measured in hydrogen and nitrogen, as a function of the gas pressure, but were too low to measure in neon. In all three gases it is shown that the maintaining fields are consistent with losses by ambi-polar diffusion, although electrons which approach within one ambit of an electrode are driven into that electrode by the action of the field. Immediately after breakdown in overvolted conditions the voltage approached zero and then recovered to approach the maintaining voltage asymptotically. The recovery time- constants were of the order which might be expected if an initial excess electron population were being diminished by ambi-polar diffusion

Evolved stars in the Local Group galaxies. I. AGB evolution and dust production in IC 1613

We used models of thermally-pulsing asymptotic giant branch (AGB) stars, that also describe the dust-formation process in the wind, to interpret the combination of near- and mid-infrared photometric data of the dwarf galaxy IC 1613. This is the first time that this approach is extended to an environment different from the Milky Way and the Magellanic Clouds (MCs). Our analysis, based on synthetic population techniques, shows a nice agreement between the observations and the expected distribution of stars in the colour-magnitude diagrams obtained with JHK and Spitzer bands. This allows a characterization of the individual stars in the AGB sample in terms of mass, chemical composition, and formation epoch of the progenitors. We identify the stars exhibiting the largest degree of obscuration as carbon stars evolving through the final AGB phases, descending from 1-1.25Msun objects of metallicity Z=0.001 and from 1.5-2.5Msun stars with Z=0.002. Oxygen-rich stars constitute the majority of the sample (65%), mainly low mass stars (<2Msun) that produce a negligible amount of dust (<10^{-7}Msun/yr). We predict the overall dust-production rate from IC 1613, mostly determined by carbon stars, to be 6x10^{-7}Msun/yr with an uncertainty of 30%. The capability of the current generation of models to interpret the AGB population in an environment different from the MCs opens the possibility to extend this kind of analysis to other Local Group galaxies.Comment: 14 pages, 6 figures, accepted for publication on MNRA

Improving Quantum Query Complexity of Boolean Matrix Multiplication Using Graph Collision

The quantum query complexity of Boolean matrix multiplication is typically studied as a function of the matrix dimension, n, as well as the number of 1s in the output, \ell. We prove an upper bound of O (n\sqrt{\ell}) for all values of \ell. This is an improvement over previous algorithms for all values of \ell. On the other hand, we show that for any \eps < 1 and any \ell <= \eps n^2, there is an \Omega(n\sqrt{\ell}) lower bound for this problem, showing that our algorithm is essentially tight. We first reduce Boolean matrix multiplication to several instances of graph collision. We then provide an algorithm that takes advantage of the fact that the underlying graph in all of our instances is very dense to find all graph collisions efficiently

Derivation of the Blackbody Radiation Spectrum from a Natural Maximum-Entropy Principle Involving Casimir Energies and Zero-Point Radiation

By numerical calculation, the Planck spectrum with zero-point radiation is shown to satisfy a natural maximum-entropy principle whereas alternative choices of spectra do not. Specifically, if we consider a set of conducting-walled boxes, each with a partition placed at a different location in the box, so that across the collection of boxes the partitions are uniformly spaced across the volume, then the Planck spectrum correspond to that spectrum of random radiation (having constant energy kT per normal mode at low frequencies and zero-point energy (1/2)hw per normal mode at high frequencies) which gives maximum uniformity across the collection of boxes for the radiation energy per box. The analysis involves Casimir energies and zero-point radiation which do not usually appear in thermodynamic analyses. For simplicity, the analysis is presented for waves in one space dimension.Comment: 11 page

Hydrodynamic reductions of the heavenly equation

We demonstrate that Pleba\'nski's first heavenly equation decouples in infinitely many ways into a triple of commuting (1+1)-dimensional systems of hydrodynamic type which satisfy the Egorov property. Solving these systems by the generalized hodograph method, one can construct exact solutions of the heavenly equation parametrized by arbitrary functions of a single variable. We discuss explicit examples of hydrodynamic reductions associated with the equations of one-dimensional nonlinear elasticity, linearly degenerate systems and the equations of associativity.Comment: 14 page

Quantum Algorithms for Matrix Products over Semirings

In this paper we construct quantum algorithms for matrix products over several algebraic structures called semirings, including the (max,min)-matrix product, the distance matrix product and the Boolean matrix product. In particular, we obtain the following results. We construct a quantum algorithm computing the product of two n x n matrices over the (max,min) semiring with time complexity O(n^{2.473}). In comparison, the best known classical algorithm for the same problem, by Duan and Pettie, has complexity O(n^{2.687}). As an application, we obtain a O(n^{2.473})-time quantum algorithm for computing the all-pairs bottleneck paths of a graph with n vertices, while classically the best upper bound for this task is O(n^{2.687}), again by Duan and Pettie. We construct a quantum algorithm computing the L most significant bits of each entry of the distance product of two n x n matrices in time O(2^{0.64L} n^{2.46}). In comparison, prior to the present work, the best known classical algorithm for the same problem, by Vassilevska and Williams and Yuster, had complexity O(2^{L}n^{2.69}). Our techniques lead to further improvements for classical algorithms as well, reducing the classical complexity to O(2^{0.96L}n^{2.69}), which gives a sublinear dependency on 2^L. The above two algorithms are the first quantum algorithms that perform better than the $\tilde O(n^{5/2})$-time straightforward quantum algorithm based on quantum search for matrix multiplication over these semirings. We also consider the Boolean semiring, and construct a quantum algorithm computing the product of two n x n Boolean matrices that outperforms the best known classical algorithms for sparse matrices. For instance, if the input matrices have O(n^{1.686...}) non-zero entries, then our algorithm has time complexity O(n^{2.277}), while the best classical algorithm has complexity O(n^{2.373}).Comment: 19 page

On the nature of the most obscured C-rich AGB stars in the Magellanic Clouds

The stars in the Magellanic Clouds with the largest degree of obscuration are used to probe the highly uncertain physics of stars in the asymptotic giant branch (AGB) phase of evolution. Carbon stars in particular, provide key information on the amount of third dredge-up (TDU) and mass loss. We use two independent stellar evolution codes to test how a different treatment of the physics affects the evolution on the AGB. The output from the two codes are used to determine the rates of dust formation in the circumstellar envelope, where the method used to determine the dust is the same for each case. The stars with the largest degree of obscuration in the LMC and SMC are identified as the progeny of objects of initial mass $2.5-3~M_{\odot}$ and $\sim 1.5~M_{\odot}$, respectively. This difference in mass is motivated by the difference in the star formation histories of the two galaxies, and offers a simple explanation of the redder infrared colours of C-stars in the LMC compared to their counterparts in the SMC. The comparison with the Spitzer colours of C-rich AGB stars in the SMC shows that a minimum surface carbon mass fraction $X(C) \sim 5\times 10^{-3}$ must have been reached by stars of initial mass around $1.5~M_{\odot}$. Our results confirm the necessity of adopting low-temperature opacities in stellar evolutionary models of AGB stars. These opacities allow the stars to obtain mass-loss rates high enough ($\gtrsim 10^{-4}M_{\odot}/yr$) to produce the amount of dust needed to reproduce the Spitzer coloursComment: 14 pages, 5 figures, 1 table; accepted for publication in MNRAS Main Journa

Strong low-frequency quantum correlations from a four-wave mixing amplifier

We show that a simple scheme based on nondegenerate four-wave mixing in a hot atomic vapor behaves like a near-perfect phase-insensitive optical amplifier, which can generate bright twin beams with a measured quantum noise reduction in the intensity difference of more than 8 dB, close to the best optical parametric amplifiers and oscillators. The absence of a cavity makes the system immune to external perturbations, and the strong quantum noise reduction is observed over a large frequency range.Comment: 4 pages, 4 figures. Major rewrite of the previous version. New experimental results and further analysi