Numerical approximation of phase field based shape and topology optimization for fluids

We consider the problem of finding optimal shapes of fluid domains. The fluid obeys the Navier--Stokes equations. Inside a holdall container we use a phase field approach using diffuse interfaces to describe the domain of free flow. We formulate a corresponding optimization problem where flow outside the fluid domain is penalized. The resulting formulation of the shape optimization problem is shown to be well-posed, hence there exists a minimizer, and first order optimality conditions are derived. For the numerical realization we introduce a mass conserving gradient flow and obtain a Cahn--Hilliard type system, which is integrated numerically using the finite element method. An adaptive concept using reliable, residual based error estimation is exploited for the resolution of the spatial mesh. The overall concept is numerically investigated and comparison values are provided

Shape optimization for surface functionals in Navier--Stokes flow using a phase field approach

We consider shape and topology optimization for fluids which are governed by the Navier--Stokes equations. Shapes are modelled with the help of a phase field approach and the solid body is relaxed to be a porous medium. The phase field method uses a Ginzburg--Landau functional in order to approximate a perimeter penalization. We focus on surface functionals and carefully introduce a new modelling variant, show existence of minimizers and derive first order necessary conditions. These conditions are related to classical shape derivatives by identifying the sharp interface limit with the help of formally matched asymptotic expansions. Finally, we present numerical computations based on a Cahn--Hilliard type gradient descent which demonstrate that the method can be used to solve shape optimization problems for fluids with the help of the new approach

Average transmission probability of a random stack

The transmission through a stack of identical slabs that are separated by gaps with random widths is usually treated by calculating the average of the logarithm of the transmission probability. We show how to calculate the average of the transmission probability itself with the aid of a recurrence relation and derive analytical upper and lower bounds. The upper bound, when used as an approximation for the transmission probability, is unreasonably good and we conjecture that it is asymptotically exact.Comment: 10 pages, 6 figure

Das Ernährungssystem Basel – Relevante Politiken, Institutionen und Akteure

Unsere Ernährung ist eng mit gesellschaftlichen Aspekten verknüpft. Von der Nahrungsmittelproduktion gehen erhebliche ökologische Wirkungen aus. Das Forschungsprojekt beleuchtet das Ernährungssystem in der Stadt näher und untersucht das Potential für eine nachhaltigere Gestaltung. Im ersten Projektteil wurden die Institutionen, Organisationen und Initiativen identifiziert, die im Ernährungssystem eine Rolle spielen und strategische und rechtliche Dokumente analysiert, die darauf Einfluss nehmen. Die Ergebnisse sind im Folgenden dargestellt. Das Ernährungssystem einer Stadtregion umfasst alle Prozesse, die Lebensmittel von der Produktion über Verarbeitung, Transport, Handel, Konsum bis zur Entsorgung von Lebensmittelresten (und Food Waste) in dieser Stadt durchlaufen, sowie alle Akteure und Institutionen, die diese Prozesse beeinflussen. Dieses System wird nicht nur von Rahmenbedingungen in der Stadt selbst beeinflusst, sondern ist eingebettet in übergeordnete Politiken und Strategien auf kantonaler und Bundesebene. Darüber hinaus ist das Ernährungssystem horizontal eingebettet in verschiedenste Politikfelder; in erster Linie Landwirtschaft, Gesundheit, Umwelt, Wirtschaft. Wie wir zeigen werden, sind aber noch weitere Politikfelder für das Ernährungssystem Basel relevant

NLO QCD and electroweak corrections to W+\gamma\ production with leptonic W-boson decays

We present a calculation of the next-to-leading-order electroweak corrections to W+\gamma\ production, including the leptonic decay of the W boson and taking into account all off-shell effects of the W boson, where the finite width of the W boson is implemented using the complex-mass scheme. Corrections induced by incoming photons are fully included and find particular emphasis in the discussion of phenomenological predictions for the LHC. The corresponding next-to-leading-order QCD corrections are reproduced as well. In order to separate hard photons from jets, a quark-to-photon fragmentation function a la Glover and Morgan is employed. Our results are implemented into Monte Carlo programs allowing for the evaluation of arbitrary differential cross sections. We present integrated cross sections for the LHC at 7TeV, 8TeV, and 14TeV as well as differential distributions at 14TeV for bare muons and dressed leptons. Finally, we discuss the impact of anomalous WW\gamma\ couplings.Comment: 33 pages latex, 16 figures, typos in Table 1 correcte

Social Factors in Aesthetics : Social Conformity Pressure and a Sense of Being Watched Affect Aesthetic Judgments

The present study is a first attempt to experimentally test the impact of two specific social factors, namely social conformity pressure and a sense of being watched, on participants’ judgments of the artistic quality of aesthetic objects. We manipulated conformity pressure with a test form in which a photograph of each stimulus was presented together with unanimously low (downward pressure) or high quality ratings (upward pressure) of three would-be previous raters. Participants’ sense of being watched was manipulated by testing each of them in two settings, one of which contained an eyespots stimulus. Both social factors significantly affected the participants’ judgments—unexpectedly, however, with conformity pressure only working in the downward direction and eyespots leading to an overall downward shift in participants’ judgments. Our findings indicate the relevance of including explicit and implicit social factors in aesthetics research, thus also reminding us of the limitations of overly reductionist approaches to investigating aesthetic perception and experience

Integrating Out Nuisance Parameters for Computationally More Efficient Bayesian Estimation : An Illustration and Tutorial

Funding We acknowledge support by the Open Access Publication Fund of Humboldt-Universität zu Berlin.Peer reviewedPublisher PD

Optical Control of Field-Emission Sites by Femtosecond Laser Pulses

We have investigated field emission patterns from a clean tungsten tip apex induced by femtosecond laser pulses. Strongly asymmetric modulations of the field emission intensity distributions are observed depending on the polarization of the light and the laser incidence direction relative to the azimuthal orientation of tip apex. In effect, we have realized an ultrafast pulsed field-emission source with site selectivity on the 10 nm scale. Simulations of local fields on the tip apex and of electron emission patterns based on photo-excited nonequilibrium electron distributions explain our observations quantitatively.Comment: 4 pages, submitted to Physical Review Letter