Direct Scattering for the Benjamin-Ono Equation with Rational Initial Data

We compute the scattering data of the Benjamin-Ono equation for arbitrary rational initial conditions with simple poles. Specifically, we obtain explicit formulas for the Jost solutions and eigenfunctions of the associated spectral problem, yielding an Evans function for the eigenvalues and formulas for the phase constants and reflection coefficient.Comment: 16 Pages, 2 Figure

pde2path - A Matlab package for continuation and bifurcation in 2D elliptic systems

pde2path is a free and easy to use Matlab continuation/bifurcation package for elliptic systems of PDEs with arbitrary many components, on general two dimensional domains, and with rather general boundary conditions. The package is based on the FEM of the Matlab pdetoolbox, and is explained by a number of examples, including Bratu's problem, the Schnakenberg model, Rayleigh-Benard convection, and von Karman plate equations. These serve as templates to study new problems, for which the user has to provide, via Matlab function files, a description of the geometry, the boundary conditions, the coefficients of the PDE, and a rough initial guess of a solution. The basic algorithm is a one parameter arclength continuation with optional bifurcation detection and branch-switching. Stability calculations, error control and mesh-handling, and some elementary time-integration for the associated parabolic problem are also supported. The continuation, branch-switching, plotting etc are performed via Matlab command-line function calls guided by the AUTO style. The software can be downloaded from www.staff.uni-oldenburg.de/hannes.uecker/pde2path, where also an online documentation of the software is provided such that in this paper we focus more on the mathematics and the example systems

pde2path - version 2.0: faster FEM, multi-parameter continuation, nonlinear boundary conditions, and periodic domains - a short manual

pdepath 2.0 is an upgrade of the continuation/bifurcation package pde2path for elliptic systems of PDEs over bounded 2D domains, based on the Matlab pdetoolbox. The new features include a more efficient use of FEM, easier switching between different single parameter continuations, genuine multi-parameter continuation (e.g., fold continuation), more efficient implementation of nonlinear boundary conditions, cylinder and torus geometries (i.e., periodic boundary conditions), and a general interface for adding auxiliary equations like mass conservation or phase equations for continuation of traveling waves. The package (library, demos, manuals) can be downloaded at www.staff.uni-oldenburg.de/hannes.uecker/pde2pat

Radiation Damage and Recovery Properties of Common Plastics PEN (Polyethylene Naphthalate) and PET (Polyethylene Terephthalate) Using a 137Cs Gamma Ray Source Up To 1 MRad and 10 MRad

Polyethylene naphthalate (PEN) and polyethylene teraphthalate (PET) are cheap and common polyester plastics used throughout the world in the manufacturing of bottled drinks, containers for foodstuffs, and fibers used in clothing. These plastics are also known organic scintillators with very good scintillation properties. As particle physics experiments increase in energy and particle flux density, so does radiation exposure to detector materials. It is therefore important that scintillators be tested for radiation tolerance at these generally unheard of doses. We tested samples of PEN and PET using laser stimulated emission on separate tiles exposed to 1 MRad and 10 MRad gamma rays with a 137Cs source. PEN exposed to 1 MRad and 10 MRad emit 71.4% and 46.7% of the light of an undamaged tile, respectively, and maximally recover to 85.9% and 79.5% after 5 and 9 days, respectively. PET exposed to 1 MRad and 10 MRad emit 35.0% and 12.2% light, respectively, and maximally recover to 93.5% and 80.0% after 22 and 60 days, respectively

Synchronization in the presence of time delays and inertia: Stability criteria

Linear stability of synchronized states in networks of delay-coupled oscillators depends on the type of interaction, the network, and oscillator properties. For inert oscillator response, found ubiquitously from biology to engineering, states with time-dependent frequencies can arise. These generate side bands in the frequency spectrum or lead to chaotic dynamics. The time delay introduces multistability of synchronized states and an exponential term in the characteristic equation. Stability analysis using the resulting transcendental characteristic equation is a difficult task and is usually carried out numerically. We derive criteria and conditions that enable fast and robust analytical linear stability analysis based on the system parameters. These apply to arbitrary network topologies, identical oscillators, and delays

Characterization of photomultiplier tubes in a novel operation mode for Secondary Emission Ionization Calorimetry

Hamamatsu single anode R7761 and multi-anode R5900-00-M16 Photomultiplier Tubes have been characterized for use in a Secondary Emission (SE) Ionization Calorimetry study. SE Ionization Calorimetry is a novel technique to measure electromagnetic shower particles in extreme radiation environments. The different operation modes used in these tests were developed by modifying the conventional PMT bias circuit. These modifications were simple changes to the arrangement of the voltage dividers of the baseboard circuits. The PMTs with modified bases, referred to as operating in SE mode, are used as an SE detector module in an SE calorimeter prototype, and placed between absorber materials (Fe, Cu, Pb, W, etc.). Here, the technical design of different operation modes, as well as the characterization measurements of both SE modes and the conventional PMT mode are reported

Conceptual designs study for a Personnel Launch System (PLS)

A series of conceptual designs for a manned, Earth to Low Earth Orbit transportation system was developed. Non-winged, low L/D vehicle shapes are discussed. System and subsystem trades emphasized safety, operability, and affordability using near-term technology. The resultant conceptual design includes lessons learned from commercial aviation that result in a safe, routine, operationally efficient system. The primary mission for this Personnel Launch System (PLS) would be crew rotation to the SSF; other missions, including satellite servicing, orbital sortie, and space rescue were also explored