Variational Estimates using a Discrete Variable Representation

The advantage of using a Discrete Variable Representation (DVR) is that the Hamiltonian of two interacting particles can be constructed in a very simple form. However the DVR Hamiltonian is approximate and, as a consequence, the results cannot be considered as variational ones. We will show that the variational character of the results can be restored by performing a reduced number of integrals. In practice, for a variational description of the lowest n bound states only n(n+1)/2 integrals are necessary whereas D(D+1)/2 integrals are enough for the scattering states (D is the dimension of the S matrix). Applications of the method to the study of dimers of He, Ne and Ar, for both bound and scattering states, are presented.Comment: 30 pages, 7 figures. Minor changes (title modified, typos corrected, 1 reference added). To be published in PR

Activity Identification and Local Linear Convergence of Douglas--Rachford/ADMM under Partial Smoothness

Convex optimization has become ubiquitous in most quantitative disciplines of science, including variational image processing. Proximal splitting algorithms are becoming popular to solve such structured convex optimization problems. Within this class of algorithms, Douglas--Rachford (DR) and alternating direction method of multipliers (ADMM) are designed to minimize the sum of two proper lower semi-continuous convex functions whose proximity operators are easy to compute. The goal of this work is to understand the local convergence behaviour of DR (resp. ADMM) when the involved functions (resp. their Legendre-Fenchel conjugates) are moreover partly smooth. More precisely, when both of the two functions (resp. their conjugates) are partly smooth relative to their respective manifolds, we show that DR (resp. ADMM) identifies these manifolds in finite time. Moreover, when these manifolds are affine or linear, we prove that DR/ADMM is locally linearly convergent. When $J$ and $G$ are locally polyhedral, we show that the optimal convergence radius is given in terms of the cosine of the Friedrichs angle between the tangent spaces of the identified manifolds. This is illustrated by several concrete examples and supported by numerical experiments.Comment: 17 pages, 1 figure, published in the proceedings of the Fifth International Conference on Scale Space and Variational Methods in Computer Visio

The first INTEGRAL-OMC catalogue of optically variable sources

The Optical Monitoring Camera (OMC) onboard INTEGRAL provides photometry in the Johnson V-band. With an aperture of 50 mm and a field of view of 5deg x 5deg, OMC is able to detect optical sources brighter than V~18, from a previously selected list of potential targets of interest. After more than nine years of observations, the OMC database contains light curves for more than 70000 sources (with more than 50 photometric points each). The objectives of this work have been to characterize the potential variability of the objects monitored by OMC, to identify periodic sources and to compute their periods, taking advantage of the stability and long monitoring time of the OMC. To detect potential variability, we have performed a chi-squared test, finding 5263 variable sources out of an initial sample of 6071 objects with good photometric quality and more than 300 data points each. We have studied the periodicity of these sources using a method based on the phase dispersion minimization technique, optimized to handle light curves with very different shapes.In this first catalogue of variable sources observed by OMC, we provide for each object the median of the visual magnitude, the magnitude at maximum and minimum brightness in the light curve during the window of observations, the period, when found, as well as the complete intrinsic and period-folded light curves, together with some additional ancillary data.Comment: Accepted by Astronomy & Astrophysics; 13 pages, 16 figures. Figures' resolution has been degraded to fit astro-ph constraint

New Measure of the Dissipation Region in Collisionless Magnetic Reconnection

A new measure to identify a small-scale dissipation region in collisionless magnetic reconnection is proposed. The energy transfer from the electromagnetic field to plasmas in the electron's rest frame is formulated as a Lorentz-invariant scalar quantity. The measure is tested by two-dimensional particle-in-cell simulations in typical configurations: symmetric and asymmetric reconnection, with and without the guide field. The innermost region surrounding the reconnection site is accurately located in all cases. We further discuss implications for nonideal MHD dissipation

State Estimation for Kite Power Systems with Delayed Sensor Measurements

We present a novel estimation approach for airborne wind energy systems with ground-based control and energy generation. The estimator fuses measurements from an inertial measurement unit attached to a tethered wing and position measurements from a camera as well as line angle sensors in an unscented Kalman filter. We have developed a novel kinematic description for tethered wings to specifically address tether dynamics. The presented approach simultaneously estimates feedback variables for a flight controller as well as model parameters, such as a time-varying delay. We demonstrate the performance of the estimator for experimental flight data and compare it to a state-of-the-art estimator based on inertial measurements

Predictive Control of Autonomous Kites in Tow Test Experiments

In this paper we present a model-based control approach for autonomous flight of kites for wind power generation. Predictive models are considered to compensate for delay in the kite dynamics. We apply Model Predictive Control (MPC), with the objective of guiding the kite to follow a figure-of-eight trajectory, in the outer loop of a two level control cascade. The tracking capabilities of the inner-loop controller depend on the operating conditions and are assessed via a frequency domain robustness analysis. We take the limitations of the inner tracking controller into account by encoding them as optimisation constraints in the outer MPC. The method is validated on a kite system in tow test experiments.Comment: The paper has been accepted for publication in the IEEE Control Systems Letters and is subject to IEEE Control Systems Society copyright. Upon publication, the copy of record will be available at http://ieeexplore.ieee.or