Stability and Capsizing of Ships in Random Sea – a Survey

This report is a survey of methods of stochastic and nonlinear dynamics in ship stability. After a brief introduction we describe the sea as a stationary random field. We then derive the general equations of motion of a ship from ‘first principles’, specializing to the case of the equations of motion for roll, heave and sway using strip theory from which eventually the ‘archetypal’ nonlinear random differential equation for the roll motion follows. This determines in particular how and where the stochasticity of the sea enters the equation. We then analyze simple nonlinear models of ship motion by means of the theory of random dynamical systems which amounts to studying invariant measures, Lyapunov exponents, random attractors and their (random) domain of attraction and to using stochastic bifurcation theory to describe qualitative changes.     

ORBKIT: A modular python toolbox for cross‐platform postprocessing of quantum chemical wavefunction data

ORBKIT is a toolbox for postprocessing electronic structure calculations based on a highly modular and portable Python architecture. The program allows computing a multitude of electronic properties of molecular systems on arbitrary spatial grids from the basis set representation of its electronic wavefunction, as well as several grid‐independent properties. The required data can be extracted directly from the standard output of a large number of quantum chemistry programs. ORBKIT can be used as a standalone program to determine standard quantities, for example, the electron density, molecular orbitals, and derivatives thereof. The cornerstone of ORBKIT is its modular structure. The existing basic functions can be arranged in an individual way and can be easily extended by user‐written modules to determine any other derived quantity. ORBKIT offers multiple output formats that can be processed by common visualization tools (VMD, Molden, etc.). Additionally, ORBKIT possesses routines to order molecular orbitals computed at different nuclear configurations according to their electronic character and to interpolate the wavefunction between these configurations. The program is open‐source under GNU‐LGPLv3 license and freely available at https://github.com/orbkit/orbkit/ . This article provides an overview of ORBKIT with particular focus on its capabilities and applicability, and includes several example calculations. © 2016 Wiley Periodicals, Inc.     

Exact Boundary Controllability on a Tree-Like Network of Nonlinear Planar Timoshenko Beams

This paper concerns a system of equations describing the vibrations of a planar network of nonlinear Timoshenko beams.The authors derive the equations and appropriate nodal conditions,determine equilibrium solutions and,using the methods of quasilinear hyperbolic systems,prove that for tree-like networks the natural initial-boundary value problem admits semi-global classical solutions in the sense of Li [Li,T.T.,Controllability and Observability for Quasilinear Hyperbolic Systems,AIMS Ser.Appl.Math.,vol 3,American Institute of Mathematical Sciences and Higher Education Press,2010] existing in a neighborhood of the equilibrium solution.The authors then prove the local exact controllability of such networks near such equilibrium configurations in a certain specified time interval depending on the speed of propagation in the individual beams.     

Stand und Entwicklungstendenzen auf Dem Gebiet Der Isotopen- und Strahlentechnik

Die Ionisationsgasanalyse ist eine gasanalytische Methode, die anf der Änderung der durch Ionisation von Atomen oder Molekülen hervorgerufenen Leitfähigkeit von Gasen beruht. Ausgehend von einer allgemeinen Charakterisierung der anf diesem Verfahren basierenden Ionisationsdetektoren (Elektroneneinfang-, Aerosolionisations-, Ionisierungsquerschnitts und Edelgasdetektoren) werden deren Theorie, Eigenschaften, Hauptanwendungsgebiet und Entwicklungsmöglichkeiten aufgezeigt und diskutiert.     

Die unipotenten charaktere von 2F4(q2)

.Alle endlichen Gruppen vom Lie-Typ besitzen eine ausgezeichnete Menge von irreduziblen komplexen Charakteren, die von Lusztig eingeführten unipotenten Charaktere. Diese werden fülr einen vorgegebenen Typ unabhängig vom zugrunde liegenden Körper klassifiziert. Aufgrund der ebenfalls von Lusztig bewiesenen Jordan-Zerlegung der irreduziblen komplexen Charaktere laiit sich die Charaktertafel einer jeden endlichen Gruppe G vom Lie-Typ im wesentlichen zusammenbauen, wenn man die unipotenten Charaktere der halbeinfachen Anteile der Zentralisatoren aller halbeinfachen Elemente in G kennt. Das Problem der Berechnung der Charaktertafel ist somit zurückgeführt auf die Bestimmung aller Werte der unipotenten Charaktere der einfachen Gruppen vom Lie-Typ.