Optimal Bidding in Wind Farm Management

We study the problem of wind farm management, in which the manager commits himself to deliver energy in some future time. He reduces the consequences of uncertainty by using a storage facility (a battery, for instance). We consider a simplified model in discrete time, in which the commitment is for the next period. We solve an optimal control problem to define the optimal bidding decision. Application to a real dataset is done, and the optimal size of the battery (or the overnight costs) for the wind farm is determined. We then describe a continuous time version involving a delay between the time of decision and the implementation

On Simulation of Manifold Indexed Fractional Gaussian Fields

To simulate fractional Brownian motion indexed by a manifold poses serious numerical problems: storage, computing time and choice of an appropriate grid. We propose an effective and fast method, valid not only for fractional Brownian fields indexed by a manifold, but for any Gaussian fields indexed by a manifold. The performance of our method is illustrated with different manifolds (sphere, hyperboloid).

Asymptotically efficient one-step stochastic gradient descent

A generic, fast and asymptotically efficient method for parametric estimation is described. It is based on the stochastic gradient descent on the loglikelihood function corrected by a single step of the Fisher scoring algorithm. We show theoretically and by simulations in the i.i.d. setting that it is an interesting alternative to the usual stochastic gradient descent with averaging or the adaptative stochastic gradient descent

On Simulation of Manifold Indexed Fractional Gaussian Fields

To simulate fractional Brownian motion indexed by a manifold poses serious numerical problems: storage, computing time and choice of an appropriate grid. We propose an effective and fast method, valid not only for fractional Brownian fields indexed by a manifold, but for any Gaussian fields indexed by a manifold. The performance of our method is illustrated with different manifolds (sphere, hyperboloid)

On Fractional Gaussian Random Fields Simulations

To simulate Gaussian fields poses serious numerical problems: storage and computing time. The midpoint displacement method is often used for simulating the fractional Brownian fields because it is fast. We propose an effective and fast method, valid not only for fractional Brownian fields, but for any Gaussian fields. First, our method is compared with midpoint for fractional Brownian fields. Second, the performance of our method is illustrated by simulating several Gaussian fields. The software FieldSim is an R package developed in R and C and that implements the procedures on which this paper focuses

Experimentelle Bestimmung der gebundenen Wirbellinien sowie des Strömungsverlaufs in der Umgebung der Hinterkante eines schlanken Deltaflügels

Es wird über Grenzschichtmessungen an einem scharfkantigen schlanken Deltaflügel (Seitenverhältnis [Lambda] = 1,0, Anstellwinkel [alpha] = 20,5°) mit turbulenten Grenzschichten berichtet. Aus den Geschwindigkeiten am Rand der Grenzschicht auf Ober- und Unterseite ergibt sich der Verlauf der gebundenen Wirbellinien in der tragenden Fläche. Ein Vergleich mit früheren Untersuchungen bei laminaren Grenzschichten zeigt den Einfluß des Grenzschichtcharakters auf die Wirbelbildung. Untersuchungen über den Verlauf der Strömung stromabwärts von der Hinterkante lassen erkennen, daß sich die von der Hinterkante ausgehende Wirbelschceht zu einem Wirbel aufrollt, dessen Drehsinn dem des Vorderkantenwirbels entgegengesetzt ist. Die Achse dieses Hinterkantenwirbels verläuft spiralförmig um die Achse des Vorderkantenwirlwls

Variety of stylolites morphologies and statistical characterization of the amount of heterogeneities in the rock

The surface roughness of several stylolites in limestones was measured using high resolution laser profilometry. The 1D signals obtained were statistically analyzed to determine the scaling behavior and calculate a roughness exponent, also called Hurst exponent. Statistical methods based on the characterization of a single Hurst exponent imply strong assumptions on the mathematical characteristics of the signal: the derivative of the signal (or local increments) should be stationary and have finite variance. The analysis of the measured stylolites show that these properties are not always verified simultaneously. The stylolite profiles show persistence and jumps and several stylolites are not regular, with alternating regular and irregular portions. A new statistical method is proposed here, based on a non-stationary but Gaussian model, to estimate the roughness of the profiles and quantify the heterogeneity of stylolites. This statistical method is based on two parameters: the local roughness (H) which describes the local amplitude of the stylolite, and the amount of irregularities on the signal (\mu), which can be linked to the heterogeneities initially present in the rock before the stylolite formed. Using this technique, a classification of the stylolites in two families is proposed: those for which the morphology is homogeneous everywhere and those with alternating regular and irregular portions