Hyperasymptotic solutions for certain partial differential equations

We present the hyperasymptotic expansions for a certain group of solutions of the heat equation. We extend this result to a more general case of linear PDEs with constant coefficients. The generalisation is based on the method of Borel summability, which allows us to find integral representations of solutions for such PDEs.Comment: 17 page

3D freeform surfaces from planar sketches using neural networks

A novel intelligent approach into 3D freeform surface reconstruction from planar sketches is proposed. A multilayer perceptron (MLP) neural network is employed to induce 3D freeform surfaces from planar freehand curves. Planar curves were used to represent the boundaries of a freeform surface patch. The curves were varied iteratively and sampled to produce training data to train and test the neural network. The obtained results demonstrate that the network successfully learned the inverse-projection map and correctly inferred the respective surfaces from fresh curves

Autonomous on-board data processing and instrument calibration software for the SO/PHI

The extension of on-board data processing capabilities is an attractive option to reduce telemetry for scientific instruments on deep space missions. The challenges that this presents, however, require a comprehensive software system, which operates on the limited resources a data processing unit in space allows. We implemented such a system for the Polarimetric and Helioseismic Imager (PHI) on-board the Solar Orbiter (SO) spacecraft. It ensures autonomous operation to handle long command-response times, easy changing of the processes after new lessons have been learned and meticulous book-keeping of all operations to ensure scientific accuracy. This contribution presents the requirements and main aspects of the software implementation, followed by an example of a task implemented in the software frame, and results from running it on SO/PHI. The presented example shows that the different parts of the software framework work well together, and that the system processes data as we expect. The flexibility of the framework makes it possible to use it as a baseline for future applications with similar needs and limitations as SO/PHI.Comment: Conference: SPIE Astronomical Telescopes + Instrumentatio, Software and Cyberinfrastructure for Astronomy

Potential control under thin aqueous layers using a Kelvin Probe

Kelvin Probes can be modified to control as well as monitor potential. The design and operation of two different Kelvin Probe Potentiostats (KPPs) are described in this paper. One approach uses a permanent magnet and double coil to oscillate the needle at a fixed frequency, an AC backing potential, and software analysis and control schemes. This technique can also control the distance between the tip and sample, thereby tracking the topography of the sample. Both KPPs were used to make measurements on Type 304L stainless steel under thin layers of electrolyte. Cathodic polarization curves exhibited a limiting current density associated with oxygen reduction. The limiting current density varied with solution layer thickness over a finite range of thickness. Anodic polarization curves on 304L in a thin layer of chloride solution resulted in pitting corrosion. The breakdown potential did not vary with solution layer thickness. However, the thin layer was observed to increase in volume remarkably during pit growth owing to the absorption of water from the high humidity environment into the layer with ionic strength increased by the pit dissolution. The open circuit potential (OCP) and solution layer thickness were monitored during drying out of a thin electrolyte layer. Pitting corrosion initiated, as indicated by a sharp drop in the OCP, as the solution thinned and increased in concentration.This work was supported in part by the Office of Science and Technology and International (OST&I), Office of Civilian Radioactive Waste Management (OCRWM), US Department of Energy (DOE). The work is carried out as part of the DOE Multi-University Corrosion Cooperative under Cooperative Agreement DE-FC28-04RW12252

Biological Effects of Stellar Collapse Neutrinos

Massive stars in their final stages of collapse radiate most of their binding energy in the form of MeV neutrinos. The recoil atoms that they produce in elastic scattering off nuclei in organic tissue create radiation damage which is highly effective in the production of irreparable DNA harm, leading to cellular mutation, neoplasia and oncogenesis. Using a conventional model of the galaxy and of the collapse mechanism, the periodicity of nearby stellar collapses and the radiation dose are calculated. The possible contribution of this process to the paleontological record of mass extinctions is examined.Comment: gzipped PostScript (filename.ps.Z), 12 pages. Final version, Phys. Rev. Lett., in pres

Shape modeling technique KOALA validated by ESA Rosetta at (21) Lutetia

We present a comparison of our results from ground-based observations of asteroid (21) Lutetia with imaging data acquired during the flyby of the asteroid by the ESA Rosetta mission. This flyby provided a unique opportunity to evaluate and calibrate our method of determination of size, 3-D shape, and spin of an asteroid from ground-based observations. We present our 3-D shape-modeling technique KOALA which is based on multi-dataset inversion. We compare the results we obtained with KOALA, prior to the flyby, on asteroid (21) Lutetia with the high-spatial resolution images of the asteroid taken with the OSIRIS camera on-board the ESA Rosetta spacecraft, during its encounter with Lutetia. The spin axis determined with KOALA was found to be accurate to within two degrees, while the KOALA diameter determinations were within 2% of the Rosetta-derived values. The 3-D shape of the KOALA model is also confirmed by the spectacular visual agreement between both 3-D shape models (KOALA pre- and OSIRIS post-flyby). We found a typical deviation of only 2 km at local scales between the profiles from KOALA predictions and OSIRIS images, resulting in a volume uncertainty provided by KOALA better than 10%. Radiometric techniques for the interpretation of thermal infrared data also benefit greatly from the KOALA shape model: the absolute size and geometric albedo can be derived with high accuracy, and thermal properties, for example the thermal inertia, can be determined unambiguously. We consider this to be a validation of the KOALA method. Because space exploration will remain limited to only a few objects, KOALA stands as a powerful technique to study a much larger set of small bodies using Earth-based observations.Comment: 15 pages, 8 figures, 2 tables, accepted for publication in P&S

Regularity of Ornstein-Uhlenbeck processes driven by a L{\'e}vy white noise

The paper is concerned with spatial and time regularity of solutions to linear stochastic evolution equation perturbed by L\'evy white noise "obtained by subordination of a Gaussian white noise". Sufficient conditions for spatial continuity are derived. It is also shown that solutions do not have in general \cadlag modifications. General results are applied to equations with fractional Laplacian. Applications to Burgers stochastic equations are considered as well.Comment: This is an updated version of the same paper. In fact, it has already been publishe