Construction of a Kohn-Sham Iteration Scheme in Time-Dependent Lattice Density-Functional Theory

In the present thesis, a rigorous mathematical formulation of time-dependent density-functional theory for lattice systems is derived, serving a formally exact approach towards solving time-dependent many-particle Schrödinger problems. After introducing the necessary mathematical foundations, a one-to-one mapping from external potentials onto electronic densities obtained by solving the Schrödinger equation is introduced. Its properties and the related Banach spaces of scalar potentials and electronic densities are discussed in detail. It allows to precisely formulate the Kohn-Sham Iteration scheme, mapping a given many-particle to an effective single-particle Schrödinger problem, both generating the exact same density. Employing the Banach fixed point theorem, the Kohn-Sham Iteration scheme is proven to be convergent depending on the chosen initial density.In der hier vorliegenden Arbeit wird ein mathematisches Framework zeitabhängiger Dichte-Funktional-Theorie für quantenmechanische Gitter-Systeme entwickelt. Dies erlaubt einen formal exakten Ansatz für die Lösung der zugehörigen Vielteilchen-Schrödinger-gleichung. Beginnend mit der Diskussion relevanter mathematischer Konzepte, wird eine eins-zu-eins Abbildung zwischen externen Potentialen und zugehörigen, sich aus der Lösung der Schrödingergleichung ergebenden elektronischen Dichten definiert. Selbige, und die zugehörig betrachteten Banachräume externer Potentiale und elektronischer Dichten werden im Hinblick auf die Einführung des sog. Kohn-Sham Iterationsschemas näher untersucht. Das Schema ermöglicht, im Falle von Konvergenz, ein gegebenes interagierendes Vielteilchen-Schrödingerproblem eindeutig auf ein, die selbe Dichte generierendes effektives Einteilchen-Schrödingerproblem zurückzuführen. Unter Verwendung des Banach Fixpunkt Satzes zeigt sich, dass das Kohn-Sham Iterationsschema, abhängig von der gewählten Anfangsdichte, konvergiert

Construction of a Kohn-Sham Iteration Scheme in Time-Dependent Lattice Density-Functional Theory

In the present thesis, a rigorous mathematical formulation of time-dependent density-functional theory for lattice systems is derived, serving a formally exact approach towards solving time-dependent many-particle Schrödinger problems. After introducing the necessary mathematical foundations, a one-to-one mapping from external potentials onto electronic densities obtained by solving the Schrödinger equation is introduced. Its properties and the related Banach spaces of scalar potentials and electronic densities are discussed in detail. It allows to precisely formulate the Kohn-Sham Iteration scheme, mapping a given many-particle to an effective single-particle Schrödinger problem, both generating the exact same density. Employing the Banach fixed point theorem, the Kohn-Sham Iteration scheme is proven to be convergent depending on the chosen initial density.In der hier vorliegenden Arbeit wird ein mathematisches Framework zeitabhängiger Dichte-Funktional-Theorie für quantenmechanische Gitter-Systeme entwickelt. Dies erlaubt einen formal exakten Ansatz für die Lösung der zugehörigen Vielteilchen-Schrödinger-gleichung. Beginnend mit der Diskussion relevanter mathematischer Konzepte, wird eine eins-zu-eins Abbildung zwischen externen Potentialen und zugehörigen, sich aus der Lösung der Schrödingergleichung ergebenden elektronischen Dichten definiert. Selbige, und die zugehörig betrachteten Banachräume externer Potentiale und elektronischer Dichten werden im Hinblick auf die Einführung des sog. Kohn-Sham Iterationsschemas näher untersucht. Das Schema ermöglicht, im Falle von Konvergenz, ein gegebenes interagierendes Vielteilchen-Schrödingerproblem eindeutig auf ein, die selbe Dichte generierendes effektives Einteilchen-Schrödingerproblem zurückzuführen. Unter Verwendung des Banach Fixpunkt Satzes zeigt sich, dass das Kohn-Sham Iterationsschema, abhängig von der gewählten Anfangsdichte, konvergiert

Grief, disorientation, and futurity

AbstractThis paper seeks to develop a phenomenological account of the disorientation of grief, specifically the relationship between disorientation and the breakdown in practical self-understanding at the heart of grief. I argue that this breakdown cannot be sufficiently understood as a breakdown of formerly shared practices and habitual patterns of navigating lived-in space that leaves the bereaved individual at a loss as to how to go on. Examining the experience of losing a loved person and a loved person-to-be, I instead propose that this breakdown should be understood primarily in relation to a distinctive kind of futurity operative in disorientation, irrespective of the extent to which there is a breakdown of formerly shared practices and habitual patterns of navigating lived-in space. Drawing on the resources afforded by Heidegger’s phenomenology, I argue that it is a core characteristic of the experience of disorientation in grief that the grieving person can no longer meaningfully press ahead into a specific futural self. This view comes with certain advantages over existing accounts of the temporality of grief for making sense of the disorientated relationship to futurity, which the appeal to Heideggerian resources makes possible.</jats:p

Possibility of Hermeneutic Conversation and Ethics

In this paper, I aim to defend Gadamer’s philosophical hermeneutics against what I call the radical hermeneutic critique, specifically the critique developed in Robert Bernasconi’s article “’You Don’t Know What I’m Talking About’: Alterity and the Hermeneutic Ideal” (1995). Key to this critique is the claim that Gadamer’s account does not rise to the ethical task of embracing the alterity of the Other, but instead reduces it to a projection of one’s self. The implication is therefore that Gadamer’s philosophical hermeneutics has to be rejected on ethical grounds, as it does not appreciate but assimilates the alterity of the Other. In contrast to this radical hermeneutic critique, I argue that Gadamer’s philosophical hermeneutics can accommodate an Other that is not assimilated but appreciated, on the condition that the unique status of a dialogue with the Other as a person is no longer neglected, as Gadamer does, but instead truly distinguished from a dialogue with the Other as a text

Kiri Karl Morgensternile, Erlangen

http://tartu.ester.ee/record=b1777011~S1*es

Assessment of Extraterrestrial Tracers Ir, Pt and ³He in Polar Ice Cores

This thesis focuses on the investigation of extraterrestrial tracers Ir, Pt and 3He in polar ice cores. These tracers may be used to identify characteristics of interplanetary dust particles, and to quantify the flux of extraterrestrial material during impact events, certain volcanic eruptions, and stable background periods. In the first chapter I present novel Ir and Pt concentration records in ice cores from Summit Greenland, spanning the Tambora eruption of 1815 and the Tunguska impact event of 1908. A significant Pt signal is observed within a year of the Tambora eruption, but no observed signal is associated with the Tunguska event. Also presented here is a direct comparison between two established chemical digestion procedures, to assess what portions of the Ir and Pt signal are captured by each. An average Ir concentration of ~0.4 fg/g and average Pt concentration of ~15.7 fg/g are recorded, suggesting a total flux of interplanetary dust particles between 43.5 – 217 metric tons/day on Earth. In the second chapter, I present ³He concentrations in very large ice samples (3+ kg) from Taylor Glacier, Antarctica, and report an average concentration among 7 samples of 5.32 x 10⁻¹⁷ ccSTP/g, with an average ³He/⁴He ratio of 98.77 RA (SD: 34.4 RA), where RA is the atmospheric ³He/⁴He ratio comparable to stratospheric IDPs. Size fraction experiments and magnetic separation experiments were also performed on ³He- bearing particles in ice samples, and several bulk ice samples recorded ³He/⁴He ratios over 200 RA

Kiri Karl Morgensternile, Erlangen

http://tartu.ester.ee/record=b1809777~S1*es

Apatite-type SrPr4(SiO4)3O

Single crystals of the title compound, strontium tetra­praseo­dymium tris­(silicate) oxide, SrPr4(SiO4)3O, have been grown by the self-flux method using SrCl2. The structure is isotypic with the apatite supergroup family having the generic formula IX M12 VII M23(IV TO4)3 X, where M = alkaline earth and rare earth metals, T = Si and X = O. The M1 site (3.. symmetry) is occupied by Pr and Sr atoms with almost even proportions and is surrounded by nine O atoms forming a tricapped trigonal prism. The M2 site (m.. symmetry) is almost exclusively occupied by Pr and surrounded by seven O atoms, forming a distorted penta­gonal bipyramid. The Si atom (m.. symmetry) is surrounded by two O (m.. symmetry) and two O atoms in general positions, forming an isolated SiO4 tetra­hedron. Another O atom at the inversion centre (.. symmetry) is surrounded by three M2 sites, forming an equilateral triangle perpendicular to the c axis

Transmembrane domain length of viral K+ channels is a signal for mitochondria targeting

K+ channels operate in the plasma membrane and in membranes of organelles including mitochondria. The mechanisms and topogenic information for their differential synthesis and targeting is unknown. This article describes 2 similar viral K+ channels that are differentially sorted; one protein (Kesv) is imported by the Tom complex into the mitochondria, the other (Kcv) to the plasma membrane. By creating chimeras we discovered that mitochondrial sorting of Kesv depends on a hierarchical combination of N- and C-terminal signals. Crucial is the length of the second transmembrane domain; extending its C terminus by \u3e2 hydrophobic amino acids redirects Kesv from the mitochondrial to the plasma membrane. Activity of Kesv in the plasma membrane is detected electrically or by yeast rescue assays only after this shift in sorting. Hence only minor structural alterations in a transmembrane domain are sufficient to switch sorting of a K+ channel between the plasma membrane and mitochondria