A generatingfunctionology approach to a problem of Wilf

Wilf posed the following problem: determine asymptotically as $n\to\infty$ the probability that a randomly chosen part size in a randomly chosen composition of n has multiplicity m. One solution of this problem was given by Hitczenko and Savage. In this paper, we study this question using the techniques of generating functions and singularity analysis.Comment: 12 page

Giant anharmonicity suppresses superconductivity in AlH3_3 under pressure

The anharmonic self energy of two zone boundary phonons were computed to lowest order for AlH$_3$ in the $Pm\bar 3n$ structure at 110 GPa. The wavevector and branch index corresponding to these modes are situated in a region of phase space providing most of the electron-phonon coupling. The self energies are found to be very large and the anharmonic contribution to the linewidth of one of the modes studied could be distinguished from the electron-phonon linewidth. It is found that anharmonicity suppresses the electron-phonon coupling parameter $\lambda$, providing a possible explanation for the disagreement between experiment and previous theoretical studies of superconductivity in this system.Comment: 10 pages, 4 figure

Compressive Pattern Matching on Multispectral Data

We introduce a new constrained minimization problem that performs template and pattern detection on a multispectral image in a compressive sensing context. We use an original minimization problem from Guo and Osher that uses $L_1$ minimization techniques to perform template detection in a multispectral image. We first adapt this minimization problem to work with compressive sensing data. Then we extend it to perform pattern detection using a formal transform called the spectralization along a pattern. That extension brings out the problem of measurement reconstruction. We introduce shifted measurements that allow us to reconstruct all the measurement with a small overhead and we give an optimality constraint for simple patterns. We present numerical results showing the performances of the original minimization problem and the compressed ones with different measurement rates and applied on remotely sensed data.Comment: Published in IEEE Transactions on Geoscience and Remote Sensin

The Software behind the Higgs Boson Discovery

In this column, David Rousseau describes the enormous software development effort associated with teasing out evidence for the elusive Higgs boson, a cornerstone of the Standard Model. In keeping with previous Impact columns, everything about this is huge but the application is unique

Using off-diagonal confinement as a cooling method

In a recent letter [Phys. Rev. Lett. 104, 167201 (2010)] we proposed a new confining method for ultracold atoms on optical lattices, based on off-diagonal confinement (ODC). This method was shown to have distinct advantages over the conventional diagonal confinement (DC) that makes use of a trapping potential, including the existence of pure Mott phases and highly populated condensates. In this paper we show that the ODC method can also lead to temperatures that are smaller than with the conventional DC method, depending on the control parameters. We determine these parameters using exact diagonalizations for the hard-core case, then we extend our results to the soft-core case by performing quantum Monte Carlo (QMC) simulations for both DC and ODC systems at fixed temperatures, and analysing the corresponding entropies. We also propose a method for measuring the entropy in QMC simulations.Comment: 6 pages, 6 figure

Wigner islands with electrons over helium

We present here the first experimental study of Wigner islands formed by electrons floating over helium. Electrons are trapped electrostatically in a mesoscopic structure covered with a helium film, behaving as a quantum dot. By removing electrons one by one, we are able to find the addition spectrum, i.e. the energy required to add (or extract) one electron from the trap with occupation number $N$. Experimental addition spectra are compared with Monte Carlo simulations for the actual trap geometry, confirming the ordered state of electrons over helium in the island.Comment: 12 pages, 13 figures, draft pape

Polaron relaxation in ferroelectric thin films

We report a dielectric relaxation in ferroelectric thin films of the ABO3 family. We have compared films of different compositions with several growth modes: sputtering (with and without magnetron) and sol-gel. The relaxation was observed at cryogenic temperature (T<100K) for frequencies from 100Hz up to 10MHz. This relaxation activation energy is always lower than 200meV. It is very similar to the polaron relaxation that we reported in the parent bulk perovskites. Being independent of the materials size, morphology and texture, this relaxation can be a useful probe of defects in actual integrated capacitors with no need for specific shapin

Flash ionization of the partially ionized wind of the progenitor of SN 1987A

The H II region created by the progenitor of SN 1987A was further heated and ionized by the supernova flash. Prior to the flash, the temperature of the gas was 4000 - 5000 K, and helium was neutral, while the post-flash temperature was only slightly less than 10^5 K, with the gas being ionized to helium-like ionization stages of C, N and O. We have followed the slow post-flash cooling and recombination of the gas, as well as its line emission, and find that the strongest lines are N V 1240 and O VI 1034. Both these lines are good probes for the density of the gas, and suitable instruments to detect the lines are STIS on HST and FUSE, respectively. Other lines which may be detectable are N IV] 1486 and [O III] 5007, though they are expected to be substantially weaker. The relative strength of the oxygen lines is found to be a good tracer of the color temperature of the supernova flash. From previous observations, we put limits on the hydrogen density, n_H, of the H II region. The early N V 1240 flux measured by IUE gives an upper limit which is n_H ~ 180 \eta^{-0.40} cm^{-3}, where \eta is the filling factor of the gas. The recently reported emission in [O III] 5007 at 2500 days requires n_H = (160\pm12) \eta^{-0.19} cm^{-3}, for a supernova burst similar to that in the 500full1 model of Ensman & Burrows (1992). For the more energetic 500full2 burst the density is n_H = (215\pm15) \eta^{-0.19} cm^{-3}. These values are much higher than in models of the X-ray emission from the supernova (n_H ~ 75 cm^{-3}), and it seems plausible that the observed [O III] emission is produced primarily elsewhere than in the H II region. We also discuss the type of progenitor consistent with the H II region. In particular, it seems unlikely that its spectral type was much earlier than B2 Ia.Comment: LaTeX, 23 pages including 4 figures. To appear in ApJ (Main Journal