Thin film dynamics on a vertically rotating disk partially immersed in a liquid bath

The axisymmetric flow of a thin liquid film is considered for the problem of a vertically rotating disk that is partially immersed in a liquid bath. A model for the fully three-dimensional free-boundary problem of the rotating disk, that drags a thin film out of the bath is set up. From this, a dimension-reduced extended lubrication approximation that includes the meniscus region is derived. This problem constitutes a generalization of the classic drag-out and drag-in problem to the case of axisymmetric flow. The resulting nonlinear fourth-order partial differential equation for the film profile is solved numerically using a finite element scheme. For a range of parameters steady states are found and compared to asymptotic solutions. Patterns of the film profile, as a function of immersion depth and angular velocity are discussed.Comment: 31 pages, 19 figures accepted: Applied Mathematical Modellin

Quantitative estimates of discrete harmonic measures

A theorem of Bourgain states that the harmonic measure for a domain in ℝ d is supported on a set of Hausdorff dimension strictly less thand [2]. We apply Bourgain's method to the discrete case, i.e., to the distribution of the first entrance point of a random walk into a subset of ℤ d ,d≥2. By refining the argument, we prove that for allβ>0 there existsρ(d,β)N(d,β), anyx ∈ ℤ d , and anyA ⊂ {1, ,n} d •{y∈ℤ whereν A,x (y) denotes the probability thaty is the first entrance point of the simple random walk starting atx intoA. Furthermore,ρ must converge tod asβ →

Identification and model based assessment of the potential water retention caused by land-use changes

International audienceThe extreme summer flood in the Elbe River watershed initiated a debate on the role of forest conversion and afforestation as measures for preventive flood protection. To quantify the effect of forest conversion and afforestation on flood runoff from catchments reliable model calculations are essential. The article overviews the present state of our work and provides an example for a model- based assessment of potential water retention caused by land-use changes in a catchment in the Central Ore Mountains (Saxony, Germany). The potential of flood control by land-use management measures is highly dependant on the site-specific soil and relief conditions and the rainfall event characteristics. The pre-event soil moisture is distinctly lower under forest land-use. Furthermore, infiltration, percolation in the subsoil is increased. These effects exist for small/medium-scale events whereas they become marginal for extreme events

Slip-controlled thin film dynamics

In this study, we present a novel method to assess the slip length and the viscosity of thin films of highly viscous Newtonian liquids. We quantitatively analyse dewetting fronts of low molecular weight polystyrene melts on Octadecyl- (OTS) and Dodecyltrichlorosilane (DTS) polymer brushes. Using a thin film (lubrication) model derived in the limit of large slip lengths, we can extract slip length and viscosity. We study polymer films with thicknesses between 50 nm and 230 nm and various temperatures above the glass transition. We find slip lengths from 100 nm up to 1 micron on OTS and between 300 nm and 10 microns on DTS covered silicon wafers. The slip length decreases with temperature. The obtained values for the viscosity are consistent with independent measurements.Comment: 4 figure

Mentale Modelle der Führenden : Semantische Analyse des Sprechens über Changeprozesse

Diese Studie ist eine Single-Case-Studie, welche die Initialphase der Modernisierung einer nordrhein-westfälischen Staatsverwaltungsbehörde untersucht. Es werden mentale Modelle der Führenden anhand von Interviews identifiziert, wobei insbesondere Metaphern und Frames als Indikatoren für mentale Modelle in den Fokus rücken. Die Grundidee ist, dass Veränderungsprozesse nur dann gelingen, wenn mentale Modelle (Grundannahmen, Überzeugungen, Erklärungszusammenhänge) sowie die damit verbundenen Sprach- und Interaktionsmuster reflektiert, verändert und konsensfähig gemacht werden. Die Studie ist im Bereich der angewandten Linguistik verortet. Sie verbindet kognitionssemantische und metaphernanalytische Methoden und diskutiert die Erkenntnisse im Kontext vom transformationalen und organisationalen Veränderungslernen

Quantitative estimates of discrete harmonic measures

A theorem of Bourgain states that the harmonic measure for a domain in $\R^d$ is supported on a set of Hausdorff dimension strictly less than $d$ \cite{Bourgain}. We apply Bourgain's method to the discrete case, i.e., to the distribution of the first entrance point of a random walk into a subset of $\Z ^d$, $d\geq 2$. By refining the argument, we prove that for all \b>0 there exists \rho (d,\b)N(d,\b), any $x \in \Z^d$, and any $A\subset \{1,..., n\}^d$ | \{y\in\Z^d\colon \nu_{A,x}(y) \geq n^{-\b} \}| \leq n^{\rho(d,\b)}, where $\nu_{A,x} (y)$ denotes the probability that $y$ is the first entrance point of the simple random walk starting at $x$ into $A$. Furthermore, $\rho$ must converge to $d$ as \b \to \infty.Comment: 16 pages, 2 figures. Part (B) of the theorem is ne

Nonlinear photoluminescence spectra from a quantum dot-cavity system: Direct evidence of pump-induced stimulated emission and anharmonic cavity-QED

We investigate the power-dependent photoluminescence spectra from a strongly coupled quantum dot-cavity system using a quantum master equation technique that accounts for incoherent pumping, pure dephasing, and fermion or boson statistics. Analytical spectra at the one-photon correlation level and the numerically exact multi-photon spectra for fermions are presented. We compare to recent experiments on a quantum dot-micropiller cavity system and show that an excellent fit to the data can be obtained by varying only the incoherent pump rates in direct correspondence with the experiments. Our theory and experiments together show a clear and systematic way of studying stimulated-emission induced broadening and anharmonic cavity-QED.Comment: We have reworked our previous arXiv paper and submitted this latest version for peer revie