Solving rank-constrained semidefinite programs in exact arithmetic

We consider the problem of minimizing a linear function over an affine section of the cone of positive semidefinite matrices, with the additional constraint that the feasible matrix has prescribed rank. When the rank constraint is active, this is a non-convex optimization problem, otherwise it is a semidefinite program. Both find numerous applications especially in systems control theory and combinatorial optimization, but even in more general contexts such as polynomial optimization or real algebra. While numerical algorithms exist for solving this problem, such as interior-point or Newton-like algorithms, in this paper we propose an approach based on symbolic computation. We design an exact algorithm for solving rank-constrained semidefinite programs, whose complexity is essentially quadratic on natural degree bounds associated to the given optimization problem: for subfamilies of the problem where the size of the feasible matrix is fixed, the complexity is polynomial in the number of variables. The algorithm works under assumptions on the input data: we prove that these assumptions are generically satisfied. We also implement it in Maple and discuss practical experiments.Comment: Published at ISSAC 2016. Extended version submitted to the Journal of Symbolic Computatio

Numerical simulation of spray coalescence in an eulerian framework : direct quadrature method of moments and multi-fluid method

The scope of the present study is Eulerian modeling and simulation of polydisperse liquid sprays undergoing droplet coalescence and evaporation. The fundamental mathematical description is the Williams spray equation governing the joint number density function f(v, u; x, t) of droplet volume and velocity. Eulerian multi-fluid models have already been rigorously derived from this equation in Laurent et al. (2004). The first key feature of the paper is the application of direct quadrature method of moments (DQMOM) introduced by Marchisio and Fox (2005) to the Williams spray equation. Both the multi-fluid method and DQMOM yield systems of Eulerian conservation equations with complicated interaction terms representing coalescence. In order to validate and compare these approaches, the chosen configuration is a self-similar 2D axisymmetrical decelerating nozzle with sprays having various size distributions, ranging from smooth ones up to Dirac delta functions. The second key feature of the paper is a thorough comparison of the two approaches for various test-cases to a reference solution obtained through a classical stochastic Lagrangian solver. Both Eulerian models prove to describe adequately spray coalescence and yield a very interesting alternative to the Lagrangian solver

VLBA Determination of the Distance to Nearby Star-forming Regions. IV. A Preliminary Distance to the Proto-Herbig AeBe Star EC 95 in the Serpens Core

Using the Very Long Base Array, we observed the young stellar object EC 95 in the Serpens cloud core at eight epochs from 2007 December to 2009 December. Two sources are detected in our field and are shown to form a tight binary system. The primary (EC 95a) is a 4-5 M_⊙ proto-Herbig AeBe object (arguably the youngest such object known), whereas the secondary (EC 95b) is most likely a low-mass T Tauri star. Interestingly, both sources are non-thermal emitters. While T Tauri stars are expected to power a corona because they are convective while they go down the Hayashi track, intermediate-mass stars approach the main sequence on radiative tracks. Thus, they are not expected to have strong superficial magnetic fields, and should not be magnetically active. We review several mechanisms that could produce the non-thermal emission of EC 95a and argue that the observed properties of EC 95a might be most readily interpreted if it possessed a corona powered by a rotation-driven convective layer. Using our observations, we show that the trigonometric parallax of EC 95 is π = 2.41 ± 0.02 mas, corresponding to a distance of 414.9^(+4.4)_ (–4.3) pc. We argue that this implies a distance to the Serpens core of 415 ± 5 pc and a mean distance to the Serpens cloud of 415 ± 25 pc. This value is significantly larger than previous estimates (d ~ 260 pc) based on measurements of the extinction suffered by stars in the direction of Serpens. A possible explanation for this discrepancy is that these previous observations picked out foreground dust clouds associated with the Aquila Rift system rather than Serpens itself

Effect of pine bark and compost on the biological denitrification process of non-hazardous landfill leachate: Focus on the microbiology

In an attempt to optimize the cost-efficiency of landfill leachate treatment by biological denitrification process, our study focused on finding low-cost alternatives to traditional expensive chemicals such as composted garden refuse and pine bark, which are both available in large amount in South African landfill sites. The overall objective was to assess the behaviour of the bacterial community in relation to each substrate while treating high strength landfill leachates. Denitrification processes in fixed bed reactors were simulated at laboratory scale using anaerobic batch tests with immature compost and pine bark. High strength leachate was simulated using a solution of water and nitrate at a concentration of 500 mg l−1. Results suggest that pine bark released large amounts of phenolic compounds and hydroxylated benzene rings, which both can delay the acclimatization time and inhibit the biological denitrification (only 30% efficiency). Furthermore, presence of potential pathogens like Enterobacter and Pantoea agglomerans prevents the applicability of the pine bark in full-scale operations. On the other hand, lightly composted garden refuse (CGR) offered an adequate substrate for the formation of a biofilm necessary to complete the denitrification process (total nitrate removal observed within 7 days). CGR further contributed to a rapid establishment of an active consortium of denitrifiers including Acinetobacter, Rhizobium, Thermomonas, Rheinheimera, Phaeospirillum and Flavobacterium. Clearly the original composition, nature, carbon to nitrogen ratio (C/N) and degree of maturity and stability of the substrates play a key role in the denitrification process, impacting directly on the development of the bacterial population and, therefore, on the long-term removal efficiency

Kinetic modelling of runaway electron avalanches in tokamak plasmas

Runaway electrons (REs) can be generated in tokamak plasmas if the accelerating force from the toroidal electric field exceeds the collisional drag force due to Coulomb collisions with the background plasma. In ITER, disruptions are expected to generate REs mainly through knock-on collisions, where enough momentum can be transferred from existing runaways to slow electrons to transport the latter beyond a critical momentum, setting off an avalanche of REs. Since knock-on runaways are usually scattered off with a significant perpendicular component of the momentum with respect to the local magnetic field direction, these particles are highly magnetized. Consequently, the momentum dynamics require a full 3-D kinetic description, since these electrons are highly sensitive to the magnetic non-uniformity of a toroidal configuration. A bounce-averaged knock-on source term is derived. The generation of REs from the combined effect of Dreicer mechanism and knock-on collision process is studied with the code LUKE, a solver of the 3-D linearized bounce-averaged relativistic electron Fokker-Planck equation, through the calculation of the response of the electron distribution function to a constant parallel electric field. This work shows that the avalanche effect can be important even in non-disruptive scenarios. RE formation through knock-on collisions is found to be strongly reduced when taking place off the magnetic axis, since trapped electrons cannot contribute to the RE population. The relative importance of the avalanche mechanism is investigated as a function of the key parameters for RE formation; the plasma temperature and the electric field strength. In agreement with theoretical predictions, the simulations show that in low temperature and E-field knock-on collisions are the dominant source of REs and can play a significant role for RE generation, including in non-disruptive scenarios.Comment: 23 pages, 12 figure

Compton telescope with coded aperture mask: Imaging with the INTEGRAL/IBIS Compton mode

Compton telescopes provide a good sensitivity over a wide field of view in the difficult energy range running from a few hundred keV to several MeV. Their angular resolution is, however, poor and strongly energy dependent. We present a novel experimental design associating a coded mask and a Compton detection unit to overcome these pitfalls. It maintains the Compton performance while improving the angular resolution by at least an order of magnitude in the field of view subtended by the mask. This improvement is obtained only at the expense of the efficiency that is reduced by a factor of two. In addition, the background corrections benefit from the coded mask technique, i.e. a simultaneous measurement of the source and background. This design is implemented and tested using the IBIS telescope on board the INTEGRAL satellite to construct images with a 12' resolution over a 29 degrees x 29 degrees field of view in the energy range from 200 keV to a few MeV. The details of the analysis method and the resulting telescope performance, particularly in terms of sensitivity, are presented