The repulsive delta-function interaction model in one dimension is reviewed for spinless particles and for spin-1/2 fermions. The problem of solving the differential equation related to the Schrödinger equation is reduced by the Bethe ansatz to a system of algebraic equations. The delta-function interaction is shown to have no effect on spinless fermions which therefore behave like free fermions, in agreement with Pauli's exclusion principle. The ground-state problem of spinless bosons is reduced to an inhomogeneous Fredholm equation of the second kind. In the limit of impenetrable interactions, the spinless bosons are shown to have the energy spectrum of free fermions. The model for spin-1/2 fermions is reduced by the Bethe ansatz to an eigenvalue problem of matrices of the same sizes as the irreducible representations R of the permutation group of N elements. For some R's this eigenvalue problem itself is solved by a generalized Bethe ansatz. The ground-state problem of spin-1/2 fermions is reduced to a generalized Fredholm equation.

Diese Dissertation beschäftigt sich mit theoretischen Untersuchung der elektronischen und magnetischen Eigenschaften von 4f-Systemen mit Filmgeometrie. Die vorgestellte Theorie basiert auf dem s-f-Modell, welches durch einen intra-atomaren Austausch zwischen einem System lokaler magnetischer Momente und den Leitungselektronen charakterisiert ist. Das Modell wird für den Fall des leeren Leitungsbandes untersucht. Der untersuchte Spezialfall ist anwendbar auf die Klasse der ferromagnetischen Halbleiter mit den Europiumchalkogeniden EuO und EuS als Prototypen solcher Substanzen. Für den Grenzfall ferromagnetischer Sättigung des Systems lokaler magnetischer Momente existiert eine exakte Lösung für das Problem. Für endliche Temperaturen wird eine Methode vorgestellt, die auf einer momentenerhaltenden Entkopplungsprozedur für passend definierte Green-Funktionen basiert. Die Theorie für endliche Temperaturen leitet sich dabei übergangslos aus dem exakt lösbaren Grenzfall ab. Mit Hilfe der vorgestellten Theorie wird das temperaturabhängige Quasiteilchenspektrum eines ferromagnetischen Modellfilmes berechnet. Die Rechnungen zeigen ein deutliches korrelationsinduziertes Aufspalten der Spektren, das in der Existenz eines neuen Quasiteilchens, des magnetischen Polarons, resultiert. Der zweite Teil der Dissertation beschäftigt sich mit der Berechnung der elektronischen und magnetischen Eigenschaften eines realen ferromagnetischen Halbleiterfilms. Um den vielfachen Leitungsbändern eines realen Systems Rechnung tragen zu können, wird das ursprüngliche s-f-Modell zu einem Mehrbandmodell erweitert. Das so erweiterte s-f-Modell wird dazu benutzt, die temperaturabhängige Bandstruktur von Volumen-EuO und von EuO(100)-Filmen zu berechnen. Die T=0-Bandstrukturen, die als Input für die Modellrechnungen dienen, werden hierbei mittels einer TB-LMTO-ASA-Bandstrukturrechnung berechnet. Die spezielle Struktur der Lösung des s-f-Modells für den exakt lösbaren Grenzfall von T=0 verhindert dabei das Auftreten von Doppelzählungen relevanter Wechselwirkungen bei der Kombination von ab-initio-Rechnungen und s-f-Modellrechnungen. Die erhaltenen temperaturabhängigen Bandstrukturen geben wertvolle Einblicke in das Wechselspiel zwischen elektronischen und magnetischen Eigenschaften in EuO-Systemen und gestatten es, verifizierbare Vorhersagen für künftige Experimente zu machen. Insbesondere wird die Existenz eines EuO(100)-Oberflächenzustandes vorhergesagt, der das Auftreten eines Oberflächen-Metall-Isolator-Übergangs induzieren kann. / This dissertation is concerned with the theoretical investigation of the electronic and magnetic properties of 4f systems with film geometry. The presented theory is based on the s-f model which features an intra-atomic exchange between a system of localized magnetic moments and the conduction electrons. The model is investigated for the special case of zero band occupation of the conduction bands which is applicable to the situation in ferromagnetic semiconductors such as the europium chalcogenides EuO and EuS. For the special case of ferromagnetic saturation of the local-moment system the problem is exactly solvable. For finite temperatures, the presented approach is based on a moment-conserving decoupling approximation for suitably defined Green functions and evolves continuously from the exact limiting case. The theory is used to calculate the temperature-dependent quasiparticle spectrum of a ferromagnetic model film. Within these calculations, one finds a marked correlation-induced splitting of the spectra resulting in the existence of a new quasiparticle, the magnetic polaron. The second part of the thesis is devoted to the calculation of the electronic and magnetic properties of a real ferromagnetic semiconductor film. The original s-f model is extended to a multi-band s-f model to account for the multiple conduction bands in a real system. Based on the resulting model, the temperature-dependent band structures of bulk EuO and EuO(100) films are calculated. Here, the T=0 band structures of the systems, which have to be taken as input for the model calculations, are calculated using the TB-LMTO-ASA band-structure technique. Due to the special form of the solution of the s-f model for the exactly solvable limiting case of T=0 the employed approach for combining the first-principles calculations with the model calculations prevents the problem of double counting of relevant interactions. The calculated temperature-dependent band structures yield a valuable insight into the temperature-dependent interplay between the magnetic and electronic properties in the EuO systems and allow to make verifiable predictions for future experiments. In particular, the existence of a EuO(100) surface state has been predicted and been shown to possibly induce a surface insulator-metal transition.

Depuis les premiers ordinateurs on est en quête de machines plus rapides, plus puissantes, plus performantes. Après avoir épuisé le filon de l’augmentation de la fréquence, les constructeurs se sont tournés vers les multi-cœurs. Le modèle de calcul actuel repose sur les threads de l'OS qu’on exploite à travers différents langages à constructions parallèles. Cependant, la programmation multithread reste un art délicat car le calcul parallèle découpé en threads souffre d’un grand défaut : il est non déterministe.Pourtant, on peut faire du calcul parallèle déterministe, à condition de remplacer le modèle des threads par un modèle s’appuyant sur l’ordre partiel des dépendances. Dans cette thèse, nous proposons un modèle alternatif d’architecture qui exploite le parallélisme d’instructions (ILP) présent dans les programmes. Nous proposons de nombreuses techniques pour s’affranchir de la plupart des dépendances architecturales et obtenir ainsi un ILP qui croît avec la taille de l’exécution. L’ILP qu’on atteint de cette façon est suffisant pour permettre d’alimenter plusieurs milliers de cœurs. Les dépendances architecturales sérialisantes ayant été supprimées, l’ILP peut être bien mieux exploité que dans les architectures actuelles. Un code VHDL au niveau RTL de l’architecture a été développé pour en mesurer les avantages. Les résultats de synthèse d’un processeur allant de 2 à 64 cœurs montrent que la vitesse du matériel que nous proposons reste constante et que sa surface varie linéairement avec le nombre de cœurs. Cela prouve que le modèle d’interconnexion proposé est extensible. / The pursuit for faster and more powerful machines started from the first computers. After exhausting the increase of the frequency, the manufacturers have turned to another solution and started to introduce multiples cores on a chip. The computational model is today based on the OS threads exploited through different languages offering parallel constructions. However, parallel programming remains an art because the thread management by the operating system is not deterministic.Nonetheless, it is possible to compute in a parallel deterministic way if we replace the thread model by a model built on the partial order of dependencies. In this thesis, we present an alternative architectural model exploiting the Instruction Level Parallelism (ILP) naturally present in applications. We propose many techniques to remove most of the architectural dependencies which leads to an ILP increasing with the execution length. The ILP which is reached this way is enough to allow feeding thousands of cores. Eliminating the architecutral dependencies serializing the run allows to exploit the ILP better than in actual microarchitectures. A VHDL code at the RTL level has been implemented to mesure the benefits of our design. The results of the synthesis of a processeur ranging from 2 to 64 cores are reported. They show that the speed of the proposed material keeps constant and the surface grows linearly with the number of cores : our interconnect solution is scalable.

We consider systems of polynomial equations and inequalities to be solved in integers. By applying the circle method, when the number of variables is large and the system is geometrically well-behaved we give an asymptotic estimate for the number of solutions of bounded size. In the case of R homogeneous equations having the same degree d, a classic theorem of Birch provides such an estimate provided the number of variables is R(R+1)(d-1)2^d-1+R or greater and the system is nonsingular. In many cases this conclusion has been improved, but except in the case of diagonal equations the number of variables needed has always grown quadratically in R. We give a result requiring only d2^dR+R variables, obtaining linear growth in R. When d = 2 or 3 we require only that the system be nonsingular; when d<4 we require that the coefficients of the equations belong to a certain explicit Zariski open set. These conditions are satisfied for typical systems of equations, and can in principle be checked algorithmically for any particular system. We also give an asymptotic estimate for the number of solutions to R polynomial inequalities of degree d with real coefficients, in the same number of variables and satisfying the same geometric conditions as in our work on equations. Previously one needed the number of variables to grow super-exponentially in the degree d in order to show that a nontrivial solution exists.

A rating design is a pre-specified plan for collecting ratings. The best design for a rater-mediated assessment both psychometrically and from the perspective of fairness is a fully-crossed design in which all objects are rated by all raters. An incomplete rating design is one in which all objects are not rated by all raters, instead each object is rated by an assigned subset of raters usually to reduce the time and/or cost of the assessment. Human raters have varying propensities to rate severely or leniently. One method of compensating for rater severity is the many-facets Rasch model (MFRM). However, unless the incomplete rating design used to gather the ratings is appropriately linked, the results of the MFRM analysis may not be on the same scale and therefore may not be fairly compared. Given non-trivial numbers of raters and/or objects to rate, there are numerous possible incomplete designs with various levels of linkage. The literature provides little guidance on the extent to which differently linked rating designs might affect the results of a MFRM analysis. Eighty different subsets of data were extracted from a pre-existing fully-crossed rating data set originally gathered from 24 essays rated by eight raters. These subsets represented 20 different incomplete rating designs and four specific assignments of raters to essays. The subsets of rating data were analyzed in Facets software to investigate the effects of incomplete rating designs on the MFRM results. The design attributes related to linkage that were varied in the incomplete designs include (a) rater coverage: the number of raters-per-essay, (b) repetition-size: the number of essays rated in one repetition of the sub-design pattern, (c) design structure: the linking network structure of the incomplete design, and (d) rater order: the specific assignments of raters to essays. A number of plots and graphs were used to visualize the incomplete designs and the rating results. Several measures including the observed and fair averages for raters and essays from the 80 MFRM analyses were compared against the fair averages for the fully-crossed design. Results varied widely depending on different combinations of design attributes and rater orders. Rater coverage had the overall largest effect, with rater order producing larger ranges of values for sparser designs. Many of the observed averages for raters and essays more closely approximated the results from the fully-crossed design than did the adjusted fair-averages, particularly for the more sparsely linked designs. The stability of relative standing measures was unexpectedly low.

No description available.

This thesis is focused on two topics: (i) synthesis and characterization of bilayer graphene and pyrolytic carbon by atmospheric pressure chemical vapor deposition, and (ii) application of graphene in the fabrication of a buckyball memory device. Monolayer and bilayer graphene are semi-metal with zero bandgap. One can induce a bandgap in bilayer graphene by applying a gate voltage in the stacking direction. Thus, bandgap and Fermi level in bilayer graphene can be controlled simultaneously with a double-gate device, making it a useful material for future semiconducting applications. Controlled synthesis of bilayer graphene would be the first step to fabricate bilayer graphene based devices. In this context, we report a uniform and low-defect synthesis of bilayer graphene on evaporated nickel films. Ultra-fast cooling is employed to control the number of layers and sample uniformity. The process is self-limiting, which leads to bilayer graphene synthesis over a wide range of growth-time and precursor flow-rate. Pryolytic carbon is another important carbon nanomaterial, due to its diverse applications in electronic and biomedicalengineering. We employ chemical vapor deposition with ultra-fast cooling technique to synthesize pyrolytic carbon. Furthermore, we elucidate a method to calculate the in-plane crystal size by using Raman spectroscopy. Finally, the use of bilayer graphene in a write-once read-many memory device has been demonstrated. The device showed irreversible switching from low-resistance to high-resistance state, with hysteresis in the transport characteristics. The control sample showed random switching and hysteresis due to electromigration of metal atoms into the active material of the device. We attribute the reliability and performance of the reported device to the ultra-smooth graphene contacts, which additionally inhibits electromigration from the underlying metallic film. Moreover, the memory device showed excellent endurance and retention characteristics.

Many-body perturbation theory and coupled-cluster theory, combined with carefully constructed basis sets, can be used to accurately compute the properties of small molecules. We applied a series of methods and basis sets aimed at reaching the ab initio limit to determine the barrier to planarity for ethylene cation. For potential energy surfaces corresponding to bond dissociation, a single Slater determinant is no longer an appropriate reference, and the single-reference hierarchy breaks down. We computed full configuration interaction benchmark data for calibrating new and existing quantum chemical methods for the accurate description of potential energy surfaces. We used the data to calibrate single-reference configuration interaction, perturbation theory, and coupled-cluster theory and multi-reference configuration interaction and perturbation theory, using various types of molecular orbitals, for breaking single and multiple bonds on ground-state and excited-state surfaces. We developed a determinant-based method which generalizes the formulation of many-body wave functions and energy expectation values. We used the method to calibrate single-reference and multi-reference configuration interaction and coupled-cluster theories, using different types of molecular orbitals, for the symmetric dissociation of water. We extended the determinant-based method to work with general configuration lists, enabling us to study, for the first time, arbitrarily truncated coupled-cluster wave functions. We used this new capability to study the importance of configurations in configuration interaction and coupled-cluster wave functions at different regions of a potential energy surface.

In our study Fq denotes the finite field with q elements. It is interesting to construct curves of given genus over Fq with many Fq -rational points. Drinfeld modular curves can be used to construct that kind of curves over Fq . In this study we will use reductions of the Drinfeld modular curves X_{0} (n) to obtain curves over finite fields with many rational points. The main idea is to divide the Drinfeld modular curves by an Atkin-Lehner involution which has many fixed points to obtain a quotient with a better #{rational points} /genus ratio. If we divide the Drinfeld modular curve X_{0} (n) by an involution W, then the number of rational points of the quotient curve WX_{0} (n) is not less than half of the original number. On the other hand, if this involution has many fixed points, then by the Hurwitz-Genus formula the genus of the curve WX_{0} (n) is much less than half of the g (X_{0}(n)).

In continuation of a successful series of events, the 4th Many-core Applications Research Community (MARC) symposium took place at the HPI in Potsdam on December 8th and 9th 2011. Over 60 researchers from different fields presented their work on many-core hardware architectures, their programming models, and the resulting research questions for the upcoming generation of heterogeneous parallel systems.