Replica Density Functional Study of One-Dimensional Hard Core Fluids in Porous Media

A binary quenched-annealed hard core mixture is considered in one dimension in order to model fluid adsorbates in narrow channels filled with a random matrix. Two different density functional approaches are employed to calculate adsorbate bulk properties and interface structure at matrix surfaces. The first approach uses Percus' functional for the annealed component and an explicit averaging over matrix configurations; this provides numerically exact results for the bulk partition coefficient and for inhomogeneous density profiles. The second approach is based on a quenched-annealed density functional whose results we find to approximate very well those of the former over the full range of possible densities. Furthermore we give a derivation of the underlying replica density functional theory.Comment: 22 pages, 11 figures, to be published in JS

A new diagnostic for ASDEX Upgrade edge ion temperatures by lithium-beam charge exchange recombination spectroscopy

This thesis work investigates the measurement of ion temperatures at the edge of a magnetically confined plasma used for fusion research at the ASDEX Upgrade tokamak operated by Max-Planck-Institut für Plasmaphysik in Garching. The tokamak is the most advanced concept in toroidal magnetic confinement fusion. The H-mode plasma regime, default scenario of the next step experiment ITER, is characterized by an edge transport barrier, which is not yet fully explained by theory. Experimentally measured edge ion temperature profiles will help to test and develop models for these barriers. Transport theory on a basic level is introduced as background and motivation for the new diagnostic. The standard model for an edge plasma instability named "edge localized mode" (ELM) observed in H-mode is described. The implementation of a new diagnostic for ion temperature measurements with high spatial resolution in the plasma edge region, its commissioning and the validation of the measurements comprises the main part of this work. The emission of line radiation induced by charge exchange processes between lithium atoms injected by a beam source and fully ionized impurities (of C and He) is observed with a detection system consisting of spectrometers and fast cameras. Due to the narrow beam (1 cm) and closely staggered optical fibers (6 mm), unprecedented spatial resolution of edge ion temperatures in all major plasma regimes of the ASDEX Upgrade tokamak was achieved. The spectral width of the line radiation (He II at 468.5 nm and C VI at 529.0 nm) contains information about the local ion temperature from thermal Doppler-broadening, which is the dominant broadening mechanism for these lines. The charge-exchange contribution to the total line radiation locally generated by the lithium is determined by gating the beam. Fitting a Gaussian model function to the local line radiation results in absolute line widths which can be directly converted into a temperature. The equilibration of impurities with the main plasma is fast enough that the assumption of nearly identical temperatures as the main plasma is justified. Corrections for systematic line broadening effects from collisional mixing and Zeeman broadening are incorporated by model calculations using existing routines for the involved atomic physics. Time resolution of the diagnostic is still not suffcient to resolve ELM events, but measuring between ELMs is possible if their frequency is low. L-mode plasmas with and without additional heating can be reliably diagnosed with a time resolution depending on the lithium beam intensity and plasma density, in best cases down to 100 ms. It was shown that diagnostic He puffing can be used to enhance the signal-to-noise ratio. Results from L-mode plasmas with electron heating show that ion temperatures can be significantly different from electron temperatures at the edge. For the verification of the new ion temperatures, comparison with data from already established diagnostics was done. In neutral beam heated L-mode and various H-mode plasmas the ion temperatures agree with those from a similar diagnostic measuring in the core using heating beams where both diagnostics overlap. They can be combined to form a complete ion temperature profile over the whole plasma radius. In a first application, transport coefficients have been determined by interpretative modeling for an ohmic plasma. In summary, a new method for measuring ion temperatures in the edge of a magnetically confined fusion plasma has been established. The results provide an important input to further understanding of transport in these plasmas

Data assimilation: mathematics for merging models and data

When you describe a physical process, for example, the weather on Earth, or an engineered system, such as a self-driving car, you typically have two sources of information. The first is a mathematical model, and the second is information obtained by collecting data. To make the best predictions for the weather, or most effectively operate the self-driving car, you want to use both sources of information. Data assimilation describes the mathematical, numerical and computational framework for doing just that

Density functional theory for colloidal mixtures of hard platelets, rods, and spheres

A geometry-based density functional theory is presented for mixtures of hard spheres, hard needles and hard platelets; both the needles and the platelets are taken to be of vanishing thickness. Geometrical weight functions that are characteristic for each species are given and it is shown how convolutions of pairs of weight functions recover each Mayer bond of the ternary mixture and hence ensure the correct second virial expansion of the excess free energy functional. The case of sphere-platelet overlap relies on the same approximation as does Rosenfeld's functional for strictly two-dimensional hard disks. We explicitly control contributions to the excess free energy that are of third order in density. Analytic expressions relevant for the application of the theory to states with planar translational and cylindrical rotational symmetry, e.g. to describe behavior at planar smooth walls, are given. For binary sphere-platelet mixtures, in the appropriate limit of small platelet densities, the theory differs from that used in a recent treatment [L. Harnau and S. Dietrich, Phys. Rev. E 71, 011504 (2004)]. As a test case of our approach we consider the isotropic-nematic bulk transition of pure hard platelets, which we find to be weakly first order, with values for the coexistence densities and the nematic order parameter that compare well with simulation results.Comment: 39 pages, 8 figure

Untersuchung komplexer Bohrgarnituren mit integriertem, schaltbarem Erweiterungswerkzeug

Es wird gezeigt, dass die angestrebte Steuerung der Lastverteilung auf Pilotmeißel und Erweiterungswerkzeug durch den Einsatz eines hydraulischen Thrusters im Pilotstrang erreicht werden kann. Das zur Steuerung bestehende operative Fenster einer solchen Bohrgarnitur ist jedoch im Allgemeinen klein und bedarf für jeden Einsatzfall einer detaillierten Vorausplanung. Ein entsprechender Berechnungsansatz zur Simulation der Vorgänge in einer komplexen Bohrgarnitur mit schaltbarem Erweiterungswerkzeug wurde entwickelt und getestet. Er stützt sich auf die Bingham-Gleichung für die Bohrgeschwindigkeit, die für die speziellen Belange der vorliegenden Untersuchung modifiziert wurde. Die Einflüsse individueller operativer und konstruktiver Parameter auf das Steuerverhalten der komplexen Bohrgarnitur wurden eingehend untersucht. Die Auswertung der Ergebnisse führte zu allgemeinen Planungs- und Einsatzempfehlungen

Implementation of a siRNA Screen for Prostate Tumour Cell Lines Using Living Cell Arrays

Prostate cancer is one of the most common causes of death in men. In this work a siRNA screen of around 1500 cancer-relevant genes was performed using 3 different cell lines (VCaP, LAPC-4, RWPE-1). A novel technique, the living cell array, was initiated in order to obtain information about the biology of Androgeninduced growth in prostate tumour cell lines. This technique is based on the principal of reverse transfection [1] and genes are knocked down by siRNAs. The cells on the living cell array were set under stress by reduction of the androgens in the media while the proliferation and apoptosis were quantified. The statistical analysis of the data implicates the success of the screen and shows that this method is suitable for large-scale experiments.Prostatakrebs ist neben Lungenkrebs eine der häufigsten Todesursachen bei Männern. In dieser Arbeit wurden 1500 potenziell tumorrelevante Gene in drei Zelllinien (VCaP, LAPC-4, RWPE-1) gescreent. Dafür wurde eine neue Technik, die Lebendzellarrays, genutzt, um Informationen über die Biologie Androgen-unabhängiger Prostatazellen zu gewinnen. Die Lebendzellarrays basieren auf dem Prinzip der reversen Transfektion [1], und in Folge werden die mRNAs der gewünschten Gene durch spezifische »silencer RNAs« (siRNAs) ausgeschaltet. Die Zellen wurden parallel sowohl in normalem Medium untersucht als auch mit androgen-reduziertem Medium unter Stress gesetzt. Das Wachstum der Prostatazellen wurde mittels Markern für Proliferation und Apoptose beobachtet. Die Daten der Screens wurden mit Hilfe statistischer Verfahren evaluiert. Die Lebendzellarrays konnten erfolgreich für einen umfangreichen SiRNA-screen angewendet werden