Implementation and extension of the impulse transfer function method for future application to the space shuttle project. Volume 1: Analysis and correlation studies

Computer programming, data processing, and a correlation study that employed data collected in the first phase test were used to demonstrate that standard test procedures and equipment could be used to collect a significant number of transfer functions from tests of the Lunar Module test article LTA-11. The testing consisted of suspending the vehicle from the apex fittings of the outrigger trusses through a set of air springs to simulate the free-free state. Impulsive loadings were delivered, one at a time, at each of the landing gear's attachment points, in three mutually perpendicular directions; thus a total of 36 impulses were applied to the vehicle. Time histories of each pulse were recorded on magnetic tape along with 40 channels of strain gage response and 28 channels of accelerometer response. Since an automated data processing system was not available, oscillograph playbacks were made of all 2400 time histories as a check on the validity of the data taken. In addition, one channel of instrumentation was processed to determine its response to a set of forcing functions from a prior LTA-11 drop test. This prediction was compared with drop test results as a first measure of accuracy

Distributional properties of exponential functionals of Levy processes

We study the distribution of the exponential functional I(\xi,\eta)=\int_0^{\infty} \exp(\xi_{t-}) \d \eta_t, where $\xi$ and $\eta$ are independent L\'evy processes. In the general setting using the theories of Markov processes and Schwartz distributions we prove that the law of this exponential functional satisfies an integral equation, which generalizes Proposition 2.1 in Carmona et al "On the distribution and asymptotic results for exponential functionals of Levy processes". In the special case when $\eta$ is a Brownian motion with drift we show that this integral equation leads to an important functional equation for the Mellin transform of $I(\xi,\eta)$, which proves to be a very useful tool for studying the distributional properties of this random variable. For general L\'evy process $\xi$ ($\eta$ being Brownian motion with drift) we prove that the exponential functional has a smooth density on $\r \setminus \{0\}$, but surprisingly the second derivative at zero may fail to exist. Under the additional assumption that $\xi$ has some positive exponential moments we establish an asymptotic behaviour of \p(I(\xi,\eta)>x) as $x\to +\infty$, and under similar assumptions on the negative exponential moments of $\xi$ we obtain a precise asympotic expansion of the density of $I(\xi,\eta)$ as $x\to 0$. Under further assumptions on the L\'evy process $\xi$ one is able to prove much stronger results about the density of the exponential functional and we illustrate some of the ideas and techniques for the case when $\xi$ has hyper-exponential jumps.Comment: In this version we added a remark after Theorem 1 about extra conditions required for validity of equation (2.3

Theoretical and experimental study of AC loss in HTS single pancake coils

The electromagnetic properties of a pancake coil in AC regime as a function of the number of turns is studied theoretically and experimentally. Specifically, the AC loss, the coil critical current and the voltage signal are discussed. The coils are made of Bi2Sr2Ca2Cu3O10/Ag (BiSCCO) tape, although the main qualitative results are also applicable to other kinds of superconducting tapes, such as coated conductors. The AC loss and the voltage signal are electrically measured using different pick up coils with the help of a transformer. One of them avoids dealing with the huge coil inductance. Besides, the critical current of the coils is experimentally determined by conventional DC measurements. Furthermore, the critical current, the AC loss and the voltage signal are simulated, showing a good agreement with the experiments. For all simulations, the field dependent critical current density inferred from DC measurements on a short tape sample is taken into account.Comment: 22 pages, 15 figures; contents extended (sections 3.2 and 4); one new figure (figure 5) and two figures replaced (figures 3 and 8); typos corrected; title change