Recent progress in tidal modeling

Recent contributions to tidal theory during the last five years are reviewed. Specific areas where recent progress has occurred include: the action of mean wind and dissipation on tides, interactions of other waves with tides, the use of TGCM in tidal studies. Furthermore, attention is put on the nonlinear interaction between semidiurnal and diurnal tides. Finally, more realistic thermal excitation and background wind and temperature models have been developed in the past few years. This has led to new month-to-month numerical simulations of the semidiurnal tide. Some results using these models are presented and compared with ATMAP tidal climatologies

Plasma diagnostic of a solar prominence from hydrogen and helium resonance lines

We present the first comparison of profiles of H et He resonance lines observed by SUMER with theoretical profiles computed with our non-LTE radiative transfer code. We use the H I Lyman-beta, H I Lyman-epsilon, and He I 584 A lines. Our code allows us to obtain the plasma parameters in prominences in conjunction with a multi-line, multi-element set of observations. The plasma temperature in the prominence core is ~ 8600 K and the pressure is 0.03 dyn/cm^2. The Ly-beta line is formed in a higher temperature region (more than 11000 K).Comment: 2 pages, 2 color figures. Proceedings of SF2A, Semaine de l'Astrophysique Francaise, Journees de la SF2A 2006, Pari

Effect of motions in prominences on the helium resonance lines in the extreme ultraviolet

<b>Context</b>: Extreme ultraviolet resonance lines of neutral and ionised helium observed in prominences are difficult to interpret as the prominence plasma is optically thick at these wavelengths. If mass motions are taking place, as is the case in active and eruptive prominences, the diagnostic is even more complex. <b>Aims</b>: We aim at studying the effect of radial motions on the spectrum emitted by moving prominences in the helium resonance lines and at facilitating the interpretation of observations, in order to improve our understanding of these dynamic structures. <b>Methods</b>: We develop our non-local thermodynamic equilibrium radiative transfer code formerly used for the study of quiescent prominences. The new numerical code is now able to solve the statistical equilibrium and radiative transfer equations in the non-static case by using velocity-dependent boundary conditions for the solution of the radiative transfer problem. This first study investigates the effects of different physical conditions (temperature, pressure, geometrical thickness) on the emergent helium radiation. <b>Results</b>: The motion of the prominence plasma induces a Doppler dimming effect on the resonance lines of HE i and HE ii. The velocity effects are particularly important for the HE ii λ 304 Å line as it is mostly formed by resonant diffusion of incident radiation under prominence conditions. The HE i resonance lines at 584 and 537 Å also show some sensitivity to the motion of the plasma, all the more when thermal emission is not too important in these lines. We also show that it is necessary to consider partial redistribution in frequency for the scattering of the incident radiation. Conclusions.This set of helium lines offers strong diagnostic possibilities that can be exploited with the SOHO spectrometers and with the EIS spectrometer on board the Hinode satellite. The addition of other helium lines and of lines from other elements (in particular hydrogen) in the diagnostics will further enhance the strength of the method

Partial redistribution effects in the formation of hydrogen lines in quiescent prominences

Departures from complete frequency redistribution (CRD) in hydrogen lines are investigated for solar prominences. Partial redistribution effects (PRD) are found both in the wings (their already known lowering) and in the central part of the L alpha line; a new feature is evidenced here: the partially coherent scattering in the near wings of the line leads to a double-peaked profile mirroring the incident solar radiation. With a low density model, we obtain a good agreement with OSO 8 observed profiles. On the contrary, the PRD computed L beta profile (lower density, no reversal) departs from the observed one, a result which calls for more progress in terms of non-LTE transfer and modelling

Diagnostics of active and eruptive prominences through hydrogen and helium lines modelling

In this study we show how hydrogen and helium lines modelling can be used to make a diagnostic of active and eruptive prominences. One motivation for this work is to identify the physical conditions during prominence activation and eruption. Hydrogen and helium lines are key in probing different parts of the prominence structure and inferring the plasma parameters. However, the interpretation of observations, being either spectroscopic or obtained with imaging, is not straightforward. Their resonance lines are optically thick, and the prominence plasma is out of local thermodynamic equilibrium due to the strong incident radiation coming from the solar disk. In view of the shift of the incident radiation occurring when the prominence plasma flows radially, it is essential to take into account velocity fields in the prominence diagnostic. Therefore we need to investigate the effects of the radial motion of the prominence plasma on hydrogen and helium lines. The method that we use is the resolution of the radiative transfer problem in the hydrogen and helium lines out of local thermodynamic equilibrium. We study the variation of the computed integrated intensities in H and He lines with the radial velocity of the prominence plasma. We can confirm that there exist suitable lines which can be used to make a diagnostic of the plasma in active and eruptive prominences in the presence of velocity fields.Comment: 5 pages, 4 colour figure

ACCPM with a nonlinear constraint and an active set strategy to solve nonlinear multicommodity flow problems

This paper proposes an implementation of a constrained analytic center cutting plane method to solve nonlinear multicommodity flow problems. The new approach exploits the property that the objective of the Lagrangian dual problem has a smooth component with second order derivatives readily available in closed form. The cutting planes issued from the nonsmooth component and the epigraph set of the smooth component form a localization set that is endowed with a self-concordant augmented barrier. Our implementation uses an approximate analytic center associated with that barrier to query the oracle of the nonsmooth component. The paper also proposes an approximation scheme for the original objective. An active set strategy can be applied to the transformed problem: it reduces the dimension of the dual space and accelerates computations. The new approach solves huge instances with high accuracy. The method is compared to alternative approaches proposed in the literatur

Automatic Formulation of Stochastic Programs Via an Algebraic Modeling Language

This paper presents an open source tool that automatically generates the so-called deterministic equivalent in stochastic programming. The tool is based on the algebraic modeling language ampl. The user is only required to provide the deterministic version of the stochastic problem and the information on the stochastic process, either as scenarios or as a transitions-based event tre

Confidence level solutions for stochastic programming

We propose an alternative approach to stochastic programming based on Monte-Carlo sampling and stochastic gradient optimization. The procedure is by essence probabilistic and the computed solution is a random variable. The associated objective value is doubly random, since it depends on two outcomes: the event in the stochastic program and the randomized algorithm. We propose a solution concept in which the probability that the randomized algorithm produces a solution with an expected objective value departing from the optimal one by more than $\epsilon$ is small enough. We derive complexity bounds for this process. We show that by repeating the basic process on independent sample, one can significantly sharpen the complexity bounds