A Model-Based methodology to support the Space System Engineering (MBSSE)

International audienceThis paper presents a model based methodology that relies on the sound basis of the most recent and widespread applicable system engineering standards and model based practices, The methodology has been defined to support domain specific space system engineering standards and practices and assessed through the application on industrial case studies. A complementary formal verification approach has also been experimented

An Optimistic Planning Approach for the Aircraft Landing Problem

International audienceThe Aircraft Landing Problem consists in sequencing aircraft on the available runways and scheduling their landing times taking into consideration several operational constraints, in order to increase the runway capacity and/or to reduce delays.In this work we propose a new Mixed Integer Programming (MIP) model for sequencing and scheduling aircraft landings on a single or multiple independent runways incorporating safety constraints by means of separation between aircraft at runways threshold. Due to the NP-hardness of the problem, solving directly the MIP model for large realistic instances yields redhibitory computation times. Therefore, we introduce a novel heuristic search methodology based on Optimistic Planning that significantly improve the FCFS (First-Come First-Served) solution, and provides good-quality solutions inreasonable computational time. The solution approach is then tested on medium and large realistic instances generated from real-world traffic on Paris-Orly airport to show the benefit of our approach

Very Extended E8E_8 and A8A_8 at low levels, Gravity and Supergravity

We define a level for a large class of Lorentzian Kac-Moody algebras. Using this we find the representation content of very extended $A_{D-3}$ and $E_8$ (i.e. $E_{11}$) at low levels in terms of $A_{D-1}$ and $A_{10}$ representations respectively. The results are consistent with the conjectured very extended $A_8$ and $E_{11}$ symmetries of gravity and maximal supergravity theories given respectively in hep-th/0104081 and hep-th/0107209. We explain how these results provided further evidence for these conjectures.Comment: 16 pages, plain tex (equation 3.3 modified and one reference expanded

Formal Verification and Validation of AADL Models

International audienceSafety-critical systems are increasingly difficult to com- prehend due to their rising complexity. Methodologies, tools and modeling formalisms have been developed to overcome this. Component-based design is an im- portant paradigm that is shared by many of them

Detailed study of BBN implications of neutrino oscillation generated neutrino asymmetries in some four neutrino models

We re-examine the evolution of neutrino asymmetries in several four neutrino models. The first case involves the direct creation of $L_{\nu_e}$ by $\nu_e \leftrightarrow \nu_s$ oscillations. In the second case, we consider the mass hierarchy $m_{\nu_\tau} \gg m_{\nu_\mu}, m_{\nu_e}, m_{\nu_s}$ where $\nu_\tau \leftrightarrow \nu_s$ oscillations generate a large $L_{\nu_\tau}$ and some of this asymmetry is converted into $L_{\nu_e}$ by $\nu_{\tau} \leftrightarrow \nu_{e}$ oscillations. We estimate the implications for BBN for a range of cosmologically interesting $\delta m^2$ values. The present paper improves on previous published work by taking into account the finite repopulation rate and the time dependence of the distortions to the neutrino momentum distributions. The treatment of chemical decoupling is also improved.Comment: Expanded discussion on the sign of the neutrino asymmetr

Neutrino-Mixing-Generated Lepton Asymmetry and the Primordial 4^4He Abundance

It has been proposed that an asymmetry in the electron neutrino sector may be generated by resonant active-sterile neutrino transformations during Big Bang Nucleosynthesis (BBN). We calculate the change in the primordial $^4$He yield $Y$ resulting from this asymmetry, taking into account both the time evolution of the $\nu_e$ and $\bar\nu_e$ distribution function and the spectral distortions in these. We calculate this change in two schemes: (1) a lepton asymmetry directly generated by $\nu_e$ mixing with a lighter right-handed sterile neutrino $\nu_s$; and (2) a lepton asymmetry generated by a $\nu_\tau\leftrightarrow\nu_s$ or $\nu_\mu\leftrightarrow\nu_s$ transformation which is subsequently partially converted to an asymmetry in the $\nu_e\bar\nu_e$ sector by a matter-enhanced active-active neutrino transformation. In the first scheme, we find that the percentage change in $Y$ is between -1% and 9% (with the sign depending on the sign of the asymmetry), bounded by the Majorana mass limit m_{\nu_e}\la 1 eV. In the second scheme, the maximal percentage reduction in $Y$ is 2%, if the lepton number asymmetry in neutrinos is positive; Otherwise, the percentage increase in $Y$ is \la 5% for m^2_{\nu_\mu,\nu_\tau}-m^2_{\nu_s}\la 10^4 eV. We conclude that the change in the primordial $^4$He yield induced by a neutrino-mixing-generated lepton number asymmetry can be substantial in the upward direction, but limited in the downward direction.Comment: 15 pages, 7 figures, submitted to PR

Dual Linearised Gravity in Arbitrary Dimensions

We construct dual formulation of linearised gravity in first order tetrad formalism in arbitrary dimensions within the path integral framework following the standard duality algorithm making use of the global shift symmetry of the tetrad field. The dual partition function is in terms of the (mixed symmetric) tensor field $\Phi_{[\nu_{1}\nu_{2}...\nu_{d-3}]\nu}$ in {\it frame-like} formulation. We obtain in d-dimensions the dual Lagrangian in a closed form in terms of field strength of the dual frame-like field. Next by coupling a source with the (linear) Riemann tensor in d-dimensions, dual generating functional is obtained. Using this an operator mapping between (linear) Riemann tensor and Riemann tensor corresponding to the dual field is derived and we also discuss the exchange of equations of motion and Bianchi identity.Comment: 14 pages, typos corrected, Published version: Class. Quantum Grav. 22(2005)538

Temperature Fluctuations and Abundances in HII Galaxies

There is evidence for temperature fluctuations in Planetary Nebulae and in Galactic HII regions. If such fluctuations occur in the low-metallicity, extragalactic HII regions used to probe the primordial helium abundance, the derived 4He mass fraction, Y_P, could be systematically different from the true primordial value. For cooler, mainly high-metallicity HII regions the derived helium abundance may be nearly unchanged but the oxygen abundance could have been seriously underestimated. For hotter, mainly low-metallicity HII regions the oxygen abundance is likely accurate but the helium abundance could be underestimated. The net effect is to tilt the Y vs. Z relation, making it flatter and resulting in a higher inferred Y_P. Although this effect could be large, there are no data which allow us to estimate the size of the temperature fluctuations for the extragalactic HII regions. Therefore, we have explored this effect via Monte Carlos in which the abundances derived from a fiducial data set are modified by \Delta-T chosen from a distribution with 0 < \Delta-T < \Delta-T_max where \Delta-T_max is varied from 500K to 4000K. It is interesting that although this effect shifts the locations of the HII regions in Y vs. O/H plane, it does not introduce any significant additional dispersion.Comment: 11 pages, 9 postscript figures; submitted to the Ap

Rational invariants of even ternary forms under the orthogonal group

In this article we determine a generating set of rational invariants of minimal cardinality for the action of the orthogonal group $\mathrm{O}_3$ on the space $\mathbb{R}[x,y,z]_{2d}$ of ternary forms of even degree $2d$. The construction relies on two key ingredients: On one hand, the Slice Lemma allows us to reduce the problem to dermining the invariants for the action on a subspace of the finite subgroup $\mathrm{B}_3$ of signed permutations. On the other hand, our construction relies in a fundamental way on specific bases of harmonic polynomials. These bases provide maps with prescribed $\mathrm{B}_3$-equivariance properties. Our explicit construction of these bases should be relevant well beyond the scope of this paper. The expression of the $\mathrm{B}_3$-invariants can then be given in a compact form as the composition of two equivariant maps. Instead of providing (cumbersome) explicit expressions for the $\mathrm{O}_3$-invariants, we provide efficient algorithms for their evaluation and rewriting. We also use the constructed $\mathrm{B}_3$-invariants to determine the $\mathrm{O}_3$-orbit locus and provide an algorithm for the inverse problem of finding an element in $\mathbb{R}[x,y,z]_{2d}$ with prescribed values for its invariants. These are the computational issues relevant in brain imaging.Comment: v3 Changes: Reworked presentation of Neuroimaging application, refinement of Definition 3.1. To appear in "Foundations of Computational Mathematics

Time Variations in the Scale of Grand Unification

We study the consequences of time variations in the scale of grand unification, $M_U$, when the Planck scale and the value of the unified coupling at the Planck scale are held fixed. We show that the relation between the variations of the low energy gauge couplings is highly model dependent. It is even possible, in principle, that the electromagnetic coupling $\alpha$ varies, but the strong coupling $\alpha_3$ does not (to leading approximation). We investigate whether the interpretation of recent observations of quasar absorption lines in terms of time variation in $\alpha$ can be accounted for by time variation in $M_U$. Our formalism can be applied to any scenario where a time variation in an intermediate scale induces, through threshold corrections, time variations in the effective low scale couplings.Comment: 14 pages, revtex4; Updated observational results and improved statistical analysis (section IV); added reference