Updating constraint preconditioners for KKT systems in quadratic programming via low-rank corrections

This work focuses on the iterative solution of sequences of KKT linear systems arising in interior point methods applied to large convex quadratic programming problems. This task is the computational core of the interior point procedure and an efficient preconditioning strategy is crucial for the efficiency of the overall method. Constraint preconditioners are very effective in this context; nevertheless, their computation may be very expensive for large-scale problems, and resorting to approximations of them may be convenient. Here we propose a procedure for building inexact constraint preconditioners by updating a "seed" constraint preconditioner computed for a KKT matrix at a previous interior point iteration. These updates are obtained through low-rank corrections of the Schur complement of the (1,1) block of the seed preconditioner. The updated preconditioners are analyzed both theoretically and computationally. The results obtained show that our updating procedure, coupled with an adaptive strategy for determining whether to reinitialize or update the preconditioner, can enhance the performance of interior point methods on large problems.Comment: 22 page

Quantum limit of photothermal cooling

We study the problem of cooling a mechanical oscillator using the photothermal (bolometric) force. Contrary to previous attempts to model this system, we take into account the noise effects due to the granular nature of photon absorption. This allows us to tackle the cooling problem down to the noise dominated regime and to find reasonable estimates for the lowest achievable phonon occupation in the cantilever

Accuracy of a teleported trapped field state inside a single bimodal cavity

We propose a simplified scheme to teleport a superposition of coherent states from one mode to another of the same bimodal lossy cavity. Based on current experimental capabilities, we present a calculation of the fidelity that can be achieved, demonstrating accurate teleportation if the mean photon number of each mode is at most 1.5. Our scheme applies as well for teleportation of coherent states from one mode of a cavity to another mode of a second cavity, both cavities embedded in a common reservoir.Comment: 4 pages, 2 figures, in appreciation for publication in Physical Review

Ultraviolet relaxation dynamics in uracil: Time-resolved photoion yield studies using a laser-based thermal desorption source

Wavelength-dependent measurements of the RNA base uracil, undertaken with nanosecond ultraviolet laser pulses, have previously identified a fragment at m/z = 84 (corresponding to the C3H4N2O+ ion) at excitation wavelengths ≤232 nm. This has been interpreted as a possible signature of a theoretically predicted ultrafast ring-opening occurring on a neutral excited state potential energy surface. To further investigate the dynamics of this mechanism, and also the non-adiabatic dynamics operating more generally in uracil, we have used a newly built ultra-high vacuum spectrometer incorporating a laser-based thermal desorption source to perform time-resolved ion-yield measurements at pump wavelengths of 267 nm, 220 nm, and 200 nm. We also report complementary data obtained for the related species 2-thiouracil following 267 nm excitation. Where direct comparisons can be made (267 nm), our findings are in good agreement with the previously reported measurements conducted on these systems using cold molecular beams, demonstrating that the role of initial internal energy on the excited state dynamics is negligible. Our 220 nm and 200 nm data also represent the first reported ultrafast study of uracil at pump wavelengths 3(1ππ*) state. These measurements do not, however, provide any evidence for the appearance of the m/z = 84 fragment within the first few hundred picoseconds following excitation. This key finding indicates that the detection of this specific species in previous nanosecond work is not directly related to an ultrafast ring-opening process. An alternative excited state process, operating on a more extended time scale, remains an open possibility

On the age heterogeneity of the Pleiades, Hyades and Sirius moving groups

We investigate the nature of the classical low-velocity structures in the local velocity field, i.e. the Pleiades, Hyades and Sirius moving groups. After using a wavelet transform to locate them in velocity space, we study their relation with the open clusters kinematically associated with them. By directly comparing the location of moving group stars in parallax space to the isochrones of the embedded clusters, we check whether, within the observational errors on the parallax, all moving group stars could originate from the on-going evaporation of the associated cluster. We conclude that, in each moving group, the fraction of stars making up the velocity-space overdensity superimposed on the background is higher than the fraction of stars compatible with the isochrone of the associated cluster. These observations thus favour a dynamical (resonant) origin for the Pleiades, Hyades and Sirius moving groups.Comment: 8 pages, 8 figures, accepted for publication in A&

Detection limits of organic compounds achievable with intense, short-pulse lasers

Many organic molecules have strong absorption bands which can be accessed by ultraviolet short pulse lasers to produce efficient ionization. This resonant multiphoton ionization scheme has already been exploited as an ionization source in time-of-flight mass spectrometers used for environmental trace analysis. In the present work we quantify the ultimate potential of this technique by measuring absolute ion yields produced from the interaction of 267 nm femtosecond laser pulses with the organic molecules indole and toluene, and gases Xe, N2 and O2. Using multiphoton ionization cross sections extracted from these results, we show that the laser pulse parameters required for real-time detection of aromatic molecules at concentrations of one part per trillion in air and a limit of detection of a few attomoles are achievable with presently available commercial laser systems. The potential applications for the analysis of human breath, blood and tissue samples are discussed