Weak-strong uniqueness for the Navier-Stokes equation for two fluids with surface tension

In the present work, we consider the evolution of two fluids separated by a sharp interface in the presence of surface tension - like, for example, the evolution of oil bubbles in water. Our main result is a weak-strong uniqueness principle for the corresponding free boundary problem for the incompressible Navier-Stokes equation: As long as a strong solution exists, any varifold solution must coincide with it. In particular, in the absence of physical singularities the concept of varifold solutions - whose global in time existence has been shown by Abels [2] for general initial data - does not introduce a mechanism for non-uniqueness. The key ingredient of our approach is the construction of a relative entropy functional capable of controlling the interface error. If the viscosities of the two fluids do not coincide, even for classical (strong) solutions the gradient of the velocity field becomes discontinuous at the interface, introducing the need for a careful additional adaption of the relative entropy.Comment: 104 page

The competitiveness situation of the EU meat processing and beverage manufacturing sectors

The status of competitiveness for the two most important food and beverage manufacturing sector s (meat processing and beverage manufacturing) in 13 EU countries is analysed empirically, using 1995 - 2002 Eurostat data. After a review of earlier agribusiness competitiveness studies an industial competitiveness index is proposed as a composite measure for multidimensional economic performance, covering profitability, productivity and output growth. The index approach enables relative competitiveness comparisons across industries, countries and over time. The results show that during 1999 - 2002 as compared to 1995 - 1998 for both sectors overall competitiveness in real terms slightly increased. At the same time, overall competitiveness seems to also have converged slightly across countries, implying that sector performance has become more similar. However, the two country rankings differ considerable as do the change patterns during the analysed period.European Union, competitiveness, meat processing, beverage manufacturing, index, International Relations/Trade, Livestock Production/Industries, F23, L66, Q13.,

Internet of Things: A Model for Cybersecurity Standards and the Categorisation of Devices

The networking of physical devices, including their infrastructure and data, is known as the Internet of Things. The number of networked devices is con- stantly increasing over the last years and is expected to continue to rise in the future. This also results in an increasing number of attacks on these devices which are considered potentially insecure. The reasons for the lack of cyber- security are diverse and lead, for example, to botnets and similar problems. Mandatory standards and guidelines can help to ensure cybersecurity re- gardless of a fast pace of development and a low price of the devices. In some areas, the development of these guidelines is already well advanced, ideally across countries as a European standard. However, problems with standardiza- tion are the different definitions of device categories and thus, the assignment of a device to a standard. Even in academia, definitions and categories for Internet of Things devices are ambiguous or completely lacking. This makes it difficult to find relevant publications. Therefore, a model of the Internet of Things was researched to solve these problems and define clear categories. The model divides the Internet of Things into categories, supplements the definitions with characteristics and distinguishes the different device types. The architectures and associated components are also considered. The model can be applied to all devices and available cybersecurity standards which is shown by mapping them to the model. The real-world applications are diverse and illustrated as different use cases. As digitalization evolves rapidly, the researched model is designed to adapt flexibly to new developments

The LRS Double Prism Assembly to be flown on the James Webb Space Telescope and Host galaxies of active galactic nuclei in the near infrared

The work presented in my thesis covers two aspects of modern astronomy: Observations and instrumentation. Part I of this thesis addresses the design, the development and the qualification of the Low Resolution Spectroscopy Double Prism Assembly (LRSDPA). From an instrumentational point of view, the purpose of the LRSDPA is to make an integration of two prisms, made of Germanium and Zincsulfide, into the imaging module of the mid infrared instrument of the James Webb Space Telescope possible. My design of the LRSDPA answers to several challenging specifications, joining together available envelope, mechanical, thermal, optical and alignment aspects. Both prisms are mounted separately onto a holder via a semi-kinematic interface. The Aluminium components of the demonstration, qualification and flight model all have been manufactured at the mechanical workshop of the 1st Institute of Physics. As it is demanded of all space equipment, the function and performance of the LRSDPA has to be thoroughly demonstrated. The qualification campaign that was conducted in collaboration with the Centre Spatial de Liège, has just been brought to a successful finish. A brief introduction to the James Webb Space Telescope and its mid infrared instrument are given in Chapters 1 and 2. Chapter 3 then describes in detail the scientific capabilities, the design and the qualification of the LRSDPA. The low resolution spectroscopy mode will provide prism slit spectroscopy at a resolution of R=100 and cover the wavelength range from 5µm-10µm. This mode is particularly aiming at spectroscopic analyses of very low surface brightness objects, such as the first light-emitting galaxies that re-ionized the universe shortly after the big bang. This scenario of re-ionization is supposed to happen shortly after the big bang, at redshifts of z=10-15. At these redshifts, the mid infrared wavelength domain gets in particular interesting, because it covers the rest-frame optical and near infrared wavelengths. Near infrared characteristics are also well suited to investigate key properties of host galaxies of active galactic nuclei (AGN), which constitute part II of my thesis. The study of host galaxies of quasi-stellar objects (QSO) is handicapped by the bright nucleus outshining its host, even with state-of-the-art telescopes. Untangling the host from the nucleus is easier for closer AGN, and in the near infrared wavelengths, the contrast in spectral energy distributions of active nucleus and host galaxy favor the detection of the host. For these reasons, we have created a nearby type I AGN sample optimized for near infrared studies, with a redshift limit of z<0.06. Chapter 4 gives a short introduction to the background motivating the selection of this sample. In Chapter 5, I present large scale, near infrared, seeing limited slit spectroscopy and imaging of nine of these AGN, carried out with ISAAC, mounted at the very large telescope (VLT) of the European Southern Observatory. Hydrogen recombination lines are observed in seven of the nine sources of which five show a broad component. In three sources, extended 1-0S(1) rotational-vibrational molecular hydrogen emission is detected. Stellar CO absorption is seen in four sources. In one of these objects, an upper limit of the central mass can be determined from the stellar velocity field. H- and Ks-band imaging allow me to determine the morphology class of the host galaxies. Colors (with supplementary J-band 2micron all sky survey images) show that the four galaxies with detected CO absorption are characterized by an overall strong stellar contribution. After removal of the nuclear point source, the host galaxies show colors typical for non-active spiral galaxies. In chapter 6, I analyze the central kiloparsec of another source included in this sample, HE 0036-5133, using adaptive optics and SINFONI, the integral field near infrared spectrograph of the VLT. This source is mostly famous for its extremely soft X-ray radiation and an X-ray outburst detected during the ROSAT all sky survey in 1990. With the help of different extinction maps and equivalent widths of various stellar absorption lines, the data reveals a deeply hidden nuclear bar and enhanced nuclear star formation, but no prominent sign of extreme QSO-like nuclear activity. In addition, the data supports that the origin of the soft X-ray core is caused by an absent hard X-ray source, rather than a deeply embedded hard X-ray source

Commissioning of the KATRIN Raman system and durability studies of optical coatings in glove box and tritium atmospheres

The aim of the Karlsruhe Tritium Neutrino (KATRIN) experiment is a neutrino mass measurement with a sensitivity of 0.2 eV/c2 (90% C.L.) by the investigation of tritium beta-spectrum. It requires the continuous monitoring of the isotopic composition of the tritium gas by Raman spectroscopy. The aim of this work was to design and commission the Raman system. Special emphasize was put on the metrological performance and reliable operation over the projected operating time of several years