Stability of thin liquid films and sessile droplets under confinement

The stability of nonvolatile thin liquid films and of sessile droplets is strongly affected by finite size effects. We analyze their stability within the framework of density functional theory using the sharp kink approximation, i.e., on the basis of an effective interface Hamiltonian. We show that finite size effects suppress spinodal dewetting of films because it is driven by a long-wavelength instability. Therefore nonvolatile films are stable if the substrate area is too small. Similarly, nonvolatile droplets connected to a wetting film become unstable if the substrate area is too large. This instability of a nonvolatile sessile droplet turns out to be equivalent to the instability of a volatile drop which can attain chemical equilibrium with its vapor.Comment: 14 pages, 13 figure

An Inverse Problem for Localization Operators

A classical result of time-frequency analysis, obtained by I. Daubechies in 1988, states that the eigenfunctions of a time-frequency localization operator with circular localization domain and Gaussian analysis window are the Hermite functions. In this contribution, a converse of Daubechies' theorem is proved. More precisely, it is shown that, for simply connected localization domains, if one of the eigenfunctions of a time-frequency localization operator with Gaussian window is a Hermite function, then its localization domain is a disc. The general problem of obtaining, from some knowledge of its eigenfunctions, information about the symbol of a time-frequency localization operator, is denoted as the inverse problem, and the problem studied by Daubechies as the direct problem of time-frequency analysis. Here, we also solve the corresponding problem for wavelet localization, providing the inverse problem analogue of the direct problem studied by Daubechies and Paul.Comment: 18 pages, 1 figur

Pädiatrisches stumpfes thorakoabdominales Trauma: Damage-Control-Resuscitation-Therapie

Zusammenfassung: Die Primärversorgung von Kindern mit schwerem stumpfem Bauchtrauma und begleitender Azidose, Koagulopathie und Hypothermie (letale Trias) erfordert ein effizientes multidisziplinäres Therapieregime zur Reduktion der Mortalität. Ein 5,5Jahre alter Junge wurde auf einem Bergbauernhof zwischen Traktorhinterrad und Hoftorumrandung im Torsobereich eingequetscht. Es kam zu einer Milzruptur Grad IV, einer Leberruptur Grad III, einer Pankreaslazeration Grad III, einer beidseitigen Lungenkontusion und einem begleitenden Weichteiltrauma mit Rhabdomyolyse. Aufgrund des schweren Traumas mit Auftreten einer Koagulopathie und einer kombinierten metabolisch-respiratorischen Azidose erfolgten die Gabe von Blutprodukten anstelle der von Kristalloiden, Akzeptanz einer permissiven Hypotension, Stabilisierung der Körpertemperatur im Sinne einer Damage-Control-Resuscitation-Strategie sowie eine Milz erhaltende operative Versorgung mittels Laparotomie. Es wird ein mögliches Therapieregime für das pädiatrische schwere Trauma mit Massentransfusion (MT) diskutier

On orthogonal projections for dimension reduction and applications in augmented target loss functions for learning problems

The use of orthogonal projections on high-dimensional input and target data in learning frameworks is studied. First, we investigate the relations between two standard objectives in dimension reduction, preservation of variance and of pairwise relative distances. Investigations of their asymptotic correlation as well as numerical experiments show that a projection does usually not satisfy both objectives at once. In a standard classification problem we determine projections on the input data that balance the objectives and compare subsequent results. Next, we extend our application of orthogonal projections to deep learning tasks and introduce a general framework of augmented target loss functions. These loss functions integrate additional information via transformations and projections of the target data. In two supervised learning problems, clinical image segmentation and music information classification, the application of our proposed augmented target loss functions increase the accuracy

Convergence of simple adaptive Galerkin schemes based on h − h/2 error estimators

We discuss several adaptive mesh-refinement strategies based on (h − h/2)-error estimation. This class of adaptivemethods is particularly popular in practise since it is problem independent and requires virtually no implementational overhead. We prove that, under the saturation assumption, these adaptive algorithms are convergent. Our framework applies not only to finite element methods, but also yields a first convergence proof for adaptive boundary element schemes. For a finite element model problem, we extend the proposed adaptive scheme and prove convergence even if the saturation assumption fails to hold in general

MIMO Grid Impedance Identification of Three-Phase Power Systems: Parametric vs. Nonparametric Approaches

A fast and accurate grid impedance measurement of three-phase power systems is crucial for online assessment of power system stability and adaptive control of grid-connected converters. Existing grid impedance measurement approaches typically rely on pointwise sinusoidal injections or sequential wideband perturbations to identify a nonparametric grid impedance curve via fast Fourier computations in the frequency domain. This is not only time-consuming, but also inaccurate during time-varying grid conditions, while on top of that, the identified nonparametric model cannot be immediately used for stability analysis or control design. To tackle these problems, we propose to use parametric system identification techniques (e.g., prediction error or subspace methods) to obtain a parametric impedance model directly from time-domain current and voltage data. Our approach relies on injecting wideband excitation signals in the converter's controller and allows to accurately identify the grid impedance in closed loop within one injection and measurement cycle. Even though the underlying parametric system identification techniques are well-studied in general, their utilization in a grid impedance identification setup poses specific challenges, is vastly underexplored, and has not gained adequate attention in urgent and timely power systems applications. To this end, we demonstrate in numerical experiments how the proposed parametric approach can accomplish a significant improvement compared to prevalent nonparametric methods.Comment: 7 pages, 7 figure

Rotational state-changing collisions between N2+_2^+ and Rb at low energies

We present a theoretical study of rotationally elastic and inelastic collisions between molecular nitrogen ions and Rb atoms in the sub-Kelvin temperature regime prevalent in ion-atom hybrid trapping experiments. The cross sections for rotational excitation and de-excitation collisions were calculated using quantum-scattering methods on ab-initio potential energy surfaces for the energetically lowest singlet electronic channel of the system. We find that the rotationally inelastic collision rates are at least an order of magnitude smaller than the charge-exchange rates found in this system, rendering inelastic processes a minor channel under the conditions of typical hybrid trapping experiments.Comment: 6 pages, 5 figures, Computational study of rotational state changing collision

Cascade Failure in a Phase Model of Power Grids

We propose a phase model to study cascade failure in power grids composed of generators and loads. If the power demand is below a critical value, the model system of power grids maintains the standard frequency by feedback control. On the other hand, if the power demand exceeds the critical value, an electric failure occurs via step out (loss of synchronization) or voltage collapse. The two failures are incorporated as two removal rules of generator nodes and load nodes. We perform direct numerical simulation of the phase model on a scale-free network and compare the results with a mean-field approximation.Comment: 7 pages, 2 figure

A high-quality annually laminated sequence from Lake Belau, Northern Germany: Revised chronology and its implications for palynological and tephrochronological studies

The annually laminated record of Lake Belau offers an exceptional opportunity to investigate with high temporal resolution Holocene environmental change, aspects of climate history and human impact on the landscape. A new chronology based on varve counts, 14C-datings and heavy metal history has been established, covering the last 9400 years. Based on multiple varve counting on two core sequences, the easily countable laminated section spans about 7850 varve years (modelled age range c. 9430 to 1630 cal. BP). Not all of the record is of the same quality but approximately 69% of the varves sequence is classified to be of high quality and only c. 5% of low quality. The new chronology suggests dates generally c. 260 years older than previously assumed for the laminated section of the record. The implications for the vegetation and land-use history of the region as well as revised datings for pollen stratigraphical events are discussed. Tephra analysis allowed the identification of several cryptotephra layers. New dates for volcanic eruptions are presented for the Lairg B event (c. 6848 cal. BP, 2s range 6930–6713 cal. BP), the Hekla 4 event (c. 4396 cal. BP, 2s range 4417–4266 cal. BP), and Hekla 3 eruption (c. 3095 cal. BP, 2s range 3120–3068 cal. BP)