Superposition Formulas for Darboux Integrable Exterior Differential Systems

In this paper we present a far-reaching generalization of E. Vessiot's analysis of the Darboux integrable partial differential equations in one dependent and two independent variables. Our approach provides new insights into this classical method, uncovers the fundamental geometric invariants of Darboux integrable systems, and provides for systematic, algorithmic integration of such systems. This work is formulated within the general framework of Pfaffian exterior differential systems and, as such, has applications well beyond those currently found in the literature. In particular, our integration method is applicable to systems of hyperbolic PDE such as the Toda lattice equations, 2 dimensional wave maps and systems of overdetermined PDE.Comment: 80 page report. Updated version with some new sections, and major improvements to other

The energy release in earthquakes, and subduction zone seismicity and stress in slabs

Energy release in earthquakes is discussed. Dynamic energy from source time function, a simplified procedure for modeling deep focus events, static energy estimates, near source energy studies, and energy and magnitude are addressed. Subduction zone seismicity and stress in slabs are also discussed

Using the Balance Function to study the charge correlations of hadrons

We present the recent Balance Function (BF) results obtained by the NA49 collaboration for the pseudo-rapidity dependence of non-identified charged particle correlations for two SPS energies. Experimental results indicate a clear centrality dependence only in the mid-rapidity region. The results of an energy dependence study of the BF throughout the whole SPS energy range will also be discussed. In addition, the correlation of identified hadrons is studied and presented for the first time. The study of hadron correlation has also been extended in order to cope with the high multiplicity environment that is expected to be seen at LHC. We will present the latest results from simulations concerning the extension of these studies to the ALICE experiment.Comment: To appear in the proccedings of the "Quark Confinement and Hadron Spectrum VII" conferenc

A system for synthetic vision and augmented reality in future flight decks

Rockwell Science Center is investigating novel human-computer interaction techniques for enhancing the situational awareness in future flight decks. One aspect is to provide intuitive displays that provide the vital information and the spatial awareness by augmenting the real world with an overlay of relevant information registered to the real world. Such Augmented Reality (AR) techniques can be employed during bad weather scenarios to permit flying in Visual Flight Rules (VFR) in conditions which would normally require Instrumental Flight Rules (IFR). These systems could easily be implemented on heads-up displays (HUD). The advantage of AR systems vs. purely synthetic vision (SV) systems is that the pilot can relate the information overlay to real objects in the world, whereas SV systems provide a constant virtual view, where inconsistencies can hardly be detected. The development of components for such a system led to a demonstrator implemented on a PC. A camera grabs video images which are overlaid with registered information. Orientation of the camera is obtained from an inclinometer and a magnetometer; position is acquired from GPS. In a possible implementation in an airplane, the on-board attitude information can be used for obtaining correct registration. If visibility is sufficient, computer vision modules can be used to fine-tune the registration by matching visual cues with database features. This technology would be especially useful for landing approaches. The current demonstrator provides a frame-rate of 15 fps, using a live video feed as background with an overlay of avionics symbology in the foreground. In addition, terrain rendering from a 1 arc sec. digital elevation model database can be overlaid to provide synthetic vision in case of limited visibility. For true outdoor testing (on ground level), the system has been implemented on a wearable computer

Scaling of transverse nuclear magnetic relaxation due to magnetic nanoparticle aggregation

The aggregation of superparamagnetic iron oxide (SPIO) nanoparticles decreases the transverse nuclear magnetic resonance (NMR) relaxation time T2 of adjacent water molecules measured by a Carr-Purcell-Meiboom-Gill (CPMG) pulse-echo sequence. This effect is commonly used to measure the concentrations of a variety of small molecules. We perform extensive Monte Carlo simulations of water diffusing around SPIO nanoparticle aggregates to determine the relationship between T2 and details of the aggregate. We find that in the motional averaging regime T2 scales as a power law with the number N of nanoparticles in an aggregate. The specific scaling is dependent on the fractal dimension d of the aggregates. We find T2 N^{-0.44} for aggregates with d=2.2, a value typical of diffusion limited aggregation. We also find that in two-nanoparticle systems, T2 is strongly dependent on the orientation of the two nanoparticles relative to the external magnetic field, which implies that it may be possible to sense the orientation of a two-nanoparticle aggregate. To optimize the sensitivity of SPIO nanoparticle sensors, we propose that it is best to have aggregates with few nanoparticles, close together, measured with long pulse-echo times.Comment: 20 pages, 3 figures, submitted to Journal of Magnetism and Magnetic Material

The equation of state of Mg_(0.6)Fe_(0.4)O to 200 GPa

New Hugoniot data on polycrystalline (avg.porosity 6.9%) samples of the magnesiowustite Mg_(0.6)Fe_(0.4)O are presented, covering the pressure range up to 200 GPa. When our data are fit by a single 3rd order Eulerian Hugoniot with K_0 constrained to its ultrasonic value of 161.5 GPa, the required isentropic pressure derivative K_0′ is 4.37 +/− 0.37. This value is significantly lower than the ultrasonic one of 6.18; existing isothermal compression data, however, are in agreement with our value rather than the ultrasonic one. Our data are adequately explained without phase transitions. There is some marginal evidence for a possible phase transition around 120 GPa. If such a transition indeed occurs it is probably of small volume change compared to the transition observed in FeO; we place an extreme upper bound of 3% on the density change such a transformation could involve and still be consistent with the data. Contrary to earlier hypotheses, we believe that a phase transition in magnesiowustite is not a likely explanation of the seismic effects in the D″ region of the lower mantle. The wustite transition may be a more complex phenomenon than initially supposed — perhaps an effect of nonstoichiometry localized to the iron-rich end of the solid solution series

Effects of electrical charging on the mechanical Q of a fused silica disk

We report on the effects of an electrical charge on mechanical loss of a fused silica disk. A degradation of Q was seen that correlated with charge on the surface of the sample. We examine a number of models for charge damping, including eddy current damping and loss due to polarization. We conclude that rubbing friction between the sample and a piece of dust attracted by the charged sample is the most likely explanation for the observed loss.Comment: submitted to Review of Scientific Instrument