Fast and Accurate Computation of Orbital Collision Probability for Short-Term Encounters

International audienceThis article provides a new method for computing the probability of collision between two spherical space objects involved in a short-term encounter under Gaussian-distributed uncertainty. In this model of conjunction, classical assumptions reduce the probability of collision to the integral of a two-dimensional Gaussian probability density function over a disk. The computational method presented here is based on an analytic expression for the integral, derived by use of Laplace transform and D-finite functions properties. The formula has the form of a product between an exponential term and a convergent power series with positive coefficients. Analytic bounds on the truncation error are also derived and are used to obtain a very accurate algorithm. Another contribution is the derivation of analytic bounds on the probability of collision itself, allowing for a very fast and - in most cases - very precise evaluation of the risk. The only other analytical method of the literature - based on an approximation - is shown to be a special case of the new formula. A numerical study illustrates the efficiency of the proposed algorithms on a broad variety of examples and favorably compares the approach to the other methods of the literature

Non-linear stability in photogravitational non-planar restricted three body problem with oblate smaller primary

We have discussed non-linear stability in photogravitational non-planar restricted three body problem with oblate smaller primary. By photogravitational we mean that both primaries are radiating. We normalised the Hamiltonian using Lie transform as in Coppola and Rand (1989). We transformed the system into Birkhoff's normal form. Lie transforms reduce the system to an equivalent simpler system which is immediately solvable. Applying Arnold's theorem, we have found non-linear stability criteria. We conclude that $L_6$ is stable. We plotted graphs for $(\omega_1, D_2).$ They are rectangular hyperbola.Comment: Accepted for publication in Astrophysics & Space Scienc

Modulated Amplitude Waves in Bose-Einstein Condensates

We analyze spatio-temporal structures in the Gross-Pitaevskii equation to study the dynamics of quasi-one-dimensional Bose-Einstein condensates (BECs) with mean-field interactions. A coherent structure ansatz yields a parametrically forced nonlinear oscillator, to which we apply Lindstedt's method and multiple-scale perturbation theory to determine the dependence of the intensity of periodic orbits (``modulated amplitude waves'') on their wave number. We explore BEC band structure in detail using Hamiltonian perturbation theory and supporting numerical simulations.Comment: 5 pages, 4 figs, revtex, final form of paper, to appear in PRE (forgot to include \bibliography command in last update, so this is a correction of that; the bibliography is hence present again

Differences between patients', physicians' and pharmacists' preferences for treatment products in haemophilia : a discrete choice experiment

The provision of health care to patients with haemophilia through replacement of the deficient coagulation factor is the result of a complex interaction between patients, physicians and policy makers, each carrying their individual sets of preferences. Preferences of patients, physicians and pharmacists towards perceived viral safety, risk of inhibitor development, infusion frequency during prophylaxis, pharmaceutical dosage form, distribution modes and price were evaluated by conjoint analysis, using a discrete choice experiment. Overall 178 patients', 69 physicians and 58 pharmacists completed the study. Patients, physicians and pharmacists displayed preferences: (i) similar in direction and strength for risk of inhibitors and frequency of prophylaxis, (ii) similar in direction, but not in strength for perceived viral safety and price, with patients showing lower strength compared with physicians and pharmacists, and (iii) dissimilar in direction and/or strength for: (i) dosage form, which tested important only for pharmacists and (ii) distribution mode, which tested important for patients and physicians only. Our study provides evidence of the differences between different stakeholders in the preferences towards haemophilia replacement therapy, indicating that different opinions should be taken into account when planning optimal care