MIP-based instantaneous control of mixed-integer PDE-constrained gas transport problems

We study the transient optimization of gas transport networks including both discrete controls due to switching of controllable elements and nonlinear fluid dynamics described by the system of isothermal Euler equations, which are partial differential equations in time and 1-dimensional space. This combination leads to mixed-integer optimization problems subject to nonlinear hyperbolic partial differential equations on a graph. We propose an instantaneous control approach in which suitable Euler discretizations yield systems of ordinary differential equations on a graph. This networked system of ordinary differential equations is shown to be well-posed and affine-linear solutions of these systems are derived analytically. As a consequence, finite-dimensional mixed-integer linear optimization problems are obtained for every time step that can be solved to global optimality using general-purpose solvers. We illustrate our approach in practice by presenting numerical results on a realistic gas transport network.     

Nonparametric inference of gradual changes in the jump behaviour of time-continuous processes

In applications the properties of a stochastic feature often change gradually rather than abruptly, that is: after a constant phase for some time they slowly start to vary. In this paper we discuss statistical inference for the detection and the localization of gradual changes in the jump characteristic of a discretely observed Ito semimartingale. We propose a new measure of time variation for the jump behaviour of the process. The statistical uncertainty of a corresponding estimate is analysed by deriving new results on the weak convergence of a sequential empirical tail integral process and a corresponding multiplier bootstrap procedure.     

Development and test of a numerical model for pulse thermography in civil engineering

Pulse thermography of concrete structures is used in civil engineering for detecting voids, honeycombing and delamination. Quantitatively realistic numerical 3D simulation is difficult due to the arising boundary layer at the heated surface and unreliable information about material parameters and environmental conditions. We address both issues by a semi-analytic reformulation of the heat transport problem and by parameter identification. Numerical results are compared with measurements of a test specimen.     

Characterization of active phosphorus surface sites at synthetic carbonate-free fluorapatite using single-pulse 1H, 31P, and 31P CP MAS NMR

The chemically active phosphorus surface sites defined as PO(x), PO(x)H, and PO(x)H2, where x = 1, 2, or 3, and the bulk phosphorus groups of PO4(3-) at synthetic carbonate-free fluorapatite (Ca5(PO4)3F) have been studied by means of single-pulse 1H,31P, and 31P CP MAS NMR. The changes in composition and relative amounts of each surface species are evaluated as a function of pH. By combining spectra from single-pulse 1H and 31P MAS NMR and data from 31P CP MAS NMR experiments at varying contact times in the range 0.2-3.0 ms, it has been possible to distinguish between resonance lines in the NMR spectra originating from active surface sites and bulk phosphorus groups and also to assign the peaks in the NMR spectra to the specific phosphorus species. In the 31P CP MAS NMR experiments, the spinning frequency was set to 4.2 kHz; in the single-pulse 1H MAS NMR experiments, the spinning frequency was 10 kHz. The 31P CP MAS NMR spectrum of fluorapatite at pH 5.9 showed one dominating resonance line at 2.9 ppm assigned to originate from PO4(3-) groups and two weaker shoulder peaks at 5.4 and 0.8 ppm which were assigned to the unprotonated PO(x) (PO, PO2-, and PO3(2-)) and protonated PO(x)H (PO2H and PO3H-) surface sites. At pH 12.7, the intensity of the peak representing unprotonated PO(x) surface sites has increased 1.7% relative to the bulk peak, while the intensity of the peaks of the protonated species PO(x)H have decreased 1.4% relative to the bulk peak. At pH 3.5, a resonance peak at -4.5 ppm has appeared in the 31P CP MAS NMR spectrum assigned to the surface species PO(x)H2 (PO3H2). The results from the 1H MAS and 31P CP MAS NMR measurements indicated that H+, OH-, and physisorbed H2O at the surface were released during the drying process at 200 degrees C.     

Analytical relation between effective mode field area and waveguide dispersion in microstructure fibers

For optical fibers exhibiting a radially symmetric refractive index profile, there exists an analytical relation that connects waveguide dispersion and the Petermann-II mode field radius. We extend the usefulness of this relation to the nonradially symmetric case of microstructure fibers in the anomalous dispersion regime, yielding a simple relation between dispersion and effective mode field area. Assuming a Gaussian mode distribution, we derive a fundamental upper limit for the effective mode field area that is required to obtain a certain amount of anomalous waveguide dispersion. This relation is demonstrated to show excellent agreement for fiber designs suited for supercontinuum generation and soliton lasers in the near infrared.     

Interaction-induced resonance in conductance and thermopower of quantum wires

We study the effect of electron-electron interaction on the transport properties of short clean quantum wires adiabatically connected to reservoirs. Interactions lead to resonances in a multichannel wire at particular values of the Fermi energy. We investigate in detail the resonance in a two-channel wire. The (negative) conductance correction peaks at the resonance, and decays exponentially as the Fermi energy is tuned away, the resonance width being given by the temperature. Likewise, the thermopower shows a characteristic structure, which is surprisingly well approximated by the so-called Mott formula. Finally, fourfold splitting of the resonance in a magnetic field provides a unique signature of the effect.     

Zinsmodelle für Versicherungen – Diskussion der Anforderungen und Vergleich der Modelle von Hull-White und Cairns

Applications of term structure models in insurance mathematics are characterized by the usage of interest rates of various times to maturity, by the long lifetimes of insurance products and typically by long-term guarantees over the lifetime of the product such as a guaranteed minimal return. For term structure models in insurance, the main requirement is their ability to realistically implement these aspects over long time periods. Due to the lack of observable market data for most products, analysis of term structure models for insurance purposes is difficult. As a consequence, one first has to rely on the evaluation of the theoretical properties of term structure models with respect to their applicability in insurance and second one has to rely on comparisons to certain benchmark models. This in turn implies significant problems regarding a comparable implementation of models, in particular considering calibration and modeling of interest rate shocks.     

Adjoint-based sensitivity analysis of quantities of interest of complex combustion models

An adjoint-based approach for the sensitivity analysis of complex reaction mechanisms is presented. It builds purely on the evaluation of the governing equations. No adjoint equations have to be derived explicitly. Instead, the required adjoint operator is constructed numerically. The approach can be utilised for various kinetic models and in existing codes with minimal implementation effort. All dependencies on the state and on model parameters are fully evaluated without simplifications. Sensitivities are calculated more efficiently and more robustly compared with the often-used brute-force method. The approach is demonstrated for a homogeneous (zero-dimensional) reactor with different complex reaction mechanisms including several reaction types.