Numerische und analytische Untersuchungen stark korrelierter fermionischer Mehrbandsysteme

In dieser Arbeit werden vier unterschiedliche, stark korrelierte, fermionische Mehrbandsysteme untersucht. Es handelt sich dabei um ein Mehrstörstellen-Anderson-Modell, zwei Hubbard-Modelle sowie ein Mehrbandsystem, wie es sich aus einer ab initio-Beschreibung für ein korreliertes Halbmetall ergibt.rnrnDie Betrachtung des Mehrstörstellen-Anderson-Modells konzentriert sich auf die Untersuchung des Einflusses der Austauschwechselwirkung und der nicht-lokalen Korrelationen zwischen zwei Störstellen in einem einfach-kubischen Gitter. Das zentrale Resultat ist die Abstandsabhängigkeit der Korrelationen der Störstellenelektronen, welche stark von der Gitterdimension und der relativen Position der Störstellen abhängen. Bemerkenswert ist hier die lange Reichweite der Korrelationen in der Diagonalrichtung des Gitters. Außerdem ergibt sich, dass eine antiferromagnetische Austauschwechselwirkung ein Singulett zwischen den Störstellenelektronen gegenüber den Kondo-Singuletts der einzelnen Störstellen favorisiert und so den Kondo-Effekt der einzelnen Störstellen behindert.rnrnEin Zweiband-Hubbard-Modell, das Jz-Modell, wird im Hinblick auf seine Mott-Phasen in Abhängigkeit von Dotierung und Kristallfeldaufspaltung auf dem Bethe-Gitter untersucht. Die Entartung der Bänder ist durch eine unterschiedliche Bandbreite aufgehoben. Wichtigstes Ergebnis sind die Phasendiagramme in Bezug auf Wechselwirkung, Gesamtfüllung und Kristallfeldparameter. Im Vergleich zu Einbandmodellen kommen im Jz-Modell sogenannte orbital-selektive Mott-Phasen hinzu, die, abhängig von Wechselwirkung, Gesamtfüllung und Kristallfeldparameter, einerseits metallischen und andererseits isolierenden Charakter haben. Ein neuer Aspekt ergibt sich durch den Kristallfeldparameter, der die ionischen Einteilchenniveaus relativ zueinander verschiebt, und für bestimmte Werte eine orbital-selektive Mott-Phase des breiten Bands ermöglicht. Im Vergleich mit analytischen Näherungslösungen und Einbandmodellen lassen sich generische Vielteilchen- und Korrelationseffekte von typischen Mehrband- und Einteilcheneffekten differenzieren.rnrnDas zweite untersuchte Hubbard-Modell beschreibt eine magneto-optische Falle mit einer endlichen Anzahl Gitterplätze, in welcher fermionische Atome platziert sind. Es wird eine z-antiferromagnetische Phase unter Berücksichtigung nicht-lokaler Vielteilchenkorrelationen erhalten, und dabei werden bekannte Ergebnisse einer effektiven Einteilchenbeschreibung verbessert.rnrnDas korrelierte Halbmetall wird im Rahmen einer Mehrbandrechnung im Hinblick auf Korrelationseffekte untersucht. Ausgangspunkt ist eine ab initio-Beschreibung durch die Dichtefunktionaltheorie (DFT), welche dann durch die Hinzunahme lokaler Korrelationen ergänzt wird. Die Vielteilcheneffekte werden an Hand einer einfachen Wechselwirkungsnäherung verdeutlicht, und für ein Wechselwirkungsmodell in sphärischer Symmetrie präzisiert. Es ergibt sich nur eine schwache Quasiteilchenrenormierung. Besonders für röntgenspektroskopische Experimente wird eine gute Übereinstimmung erzielt.rnrnDie numerischen Ergebnisse für das Jz-Modell basieren auf Quanten-Monte-Carlo-Simulationen im Rahmen der dynamischen Molekularfeldtheorie (DMFT). Für alle anderen Systeme wird ein Mehrband-Algorithmus entwickelt und implementiert, welcher explizit nicht-diagonale Mehrbandprozesse berücksichtigt.rnrn

Superfluid and antiferromagnetic phases in ultracold fermionic quantum gases

In this thesis several models are treated, which are relevant for ultracold fermionic quantum gases loaded onto optical lattices. In particular, imbalanced superfluid Fermi mixtures, which are considered as the best way to realize Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states experimentally, and antiferromagnetic states, whose experimental realization is one of the next major goals, are examined analytically and numerically with the use of appropriate versions of the Hubbard model.rnrnThe usual Bardeen-Cooper-Schrieffer (BCS) superconductor is known to break down in a magnetic field with a strength exceeding the size of the superfluid gap. A spatially inhomogeneous spin-imbalanced superconductor with a complex order parameter known as FFLO-state is predicted to occur in translationally invariant systems. Since in ultracold quantum gases the experimental setups have a limited size and a trapping potential, we analyze the realistic situation of a non-translationally invariant finite sized Hubbard model for this purpose. We first argue analytically, why the order parameter should be real in a system with continuous coordinates, and map our statements onto the Hubbard model with discrete coordinates defined on a lattice. The relevant Hubbard model is then treated numerically within mean field theory. We show that the numerical results agree with our analytically derived statements and we simulate various experimentally relevant systems in this thesis.rnrnAnalogous calculations are presented for the situation at repulsive interaction strength where the N'eel state is expected to be realized experimentally in the near future. We map our analytical results obtained for the attractive model onto corresponding results for the repulsive model. We obtain a spatially invariant unit vector defining the direction of the order parameter as a consequence of the trapping potential, which is affirmed by our mean field numerical results for the repulsive case. Furthermore, we observe domain wall formation, antiferromagnetically induced density shifts, and we show the relevant role of spin-imbalance for antiferromagnetic states.rnrnSince the first step for understanding the physics of the examined models was the application of a mean field approximation, we analyze the effect of including the second order terms of the weak coupling perturbation expansion for the repulsive model. We show that our results survive the influence of quantum fluctuations and show that the renormalization factors for order parameters and critical temperatures lead to a weaker influence of the fluctuations on the results in finite sized systems than on the results in the thermodynamical limit. Furthermore, in the context of second order theory we address the question whether results obtained in the dynamical mean field theory (DMFT), which is meanwhile a frequently used method for describing trapped systems, survive the effect of the non-local Feynman diagrams neglected in DMFT.

Master Equation: Biological Applications and Thermodynamic Description

It is well known that many realistic mathematical models of biological systems, such as cell growth, cellular development and differentiation, gene expression, gene regulatory networks, enzyme cascades, synaptic plasticity, aging and population growth need to include stochasticity. These systems are not isolated, but rather subject to intrinsic and extrinsic fluctuations, which leads to a quasi equilibrium state (homeostasis). The natural framework is provided by Markov processes and the Master equation (ME) describes the temporal evolution of the probability of each state, specified by the number of units of each species. The ME is a relevant tool for modeling realistic biological systems and allow also to explore the behavior of open systems. These systems may exhibit not only the classical thermodynamic equilibrium states but also the nonequilibrium steady states (NESS). This thesis deals with biological problems that can be treat with the Master equation and also with its thermodynamic consequences. It is organized into six chapters with four new scientific works, which are grouped in two parts: (1) Biological applications of the Master equation: deals with the stochastic properties of a toggle switch, involving a protein compound and a miRNA cluster, known to control the eukaryotic cell cycle and possibly involved in oncogenesis and with the propose of a one parameter family of master equations for the evolution of a population having the logistic equation as mean field limit. (2) Nonequilibrium thermodynamics in terms of the Master equation: where we study the dynamical role of chemical fluxes that characterize the NESS of a chemical network and we propose a one parameter parametrization of BCM learning, that was originally proposed to describe plasticity processes, to study the differences between systems in DB and NESS.

A mesoscopic simulation method for electrolyte solutions

This thesis deals with the development of a novel simulation technique for macromolecules in electrolyte solutions, with the aim of a performance improvement over current molecular-dynamics based simulation methods. In solutions containing charged macromolecules and salt ions, it is the complex interplay of electrostatic interactions and hydrodynamics that determines the equilibrium and non-equilibrium behavior. However, the treatment of the solvent and dissolved ions makes up the major part of the computational effort. Thus an efficient modeling of both components is essential for the performance of a method. With the novel method we approach the solvent in a coarse-grained fashion and replace the explicit-ion description by a dynamic mean-field treatment. Hence we combine particle- and field-based descriptions in a hybrid method and thereby effectively solve the electrokinetic equations. The developed algorithm is tested extensively in terms of accuracy and performance, and suitable parameter sets are determined. As a first application we study charged polymer solutions (polyelectrolytes) in shear flow with focus on their viscoelastic properties. Here we also include semidilute solutions, which are computationally demanding. Secondly we study the electro-osmotic flow on superhydrophobic surfaces, where we perform a detailed comparison to theoretical predictions.

Exact quantum Monte Carlo methods for correlated electron systems

Thema dieser Arbeit ist die Entwicklung und Kombination verschiedener numerischer Methoden, sowie deren Anwendung auf Probleme stark korrelierter Elektronensysteme. Solche Materialien zeigen viele interessante physikalische Eigenschaften, wie z.B. Supraleitung und magnetische Ordnung und spielen eine bedeutende Rolle in technischen Anwendungen. Es werden zwei verschiedene Modelle behandelt: das Hubbard-Modell und das Kondo-Gitter-Modell (KLM). In den letzten Jahrzehnten konnten bereits viele Erkenntnisse durch die numerische Lösung dieser Modelle gewonnen werden. Dennoch bleibt der physikalische Ursprung vieler Effekte verborgen. Grund dafür ist die Beschränkung aktueller Methoden auf bestimmte Parameterbereiche. Eine der stärksten Einschränkungen ist das Fehlen effizienter Algorithmen für tiefe Temperaturen.rnrnBasierend auf dem Blankenbecler-Scalapino-Sugar Quanten-Monte-Carlo (BSS-QMC) Algorithmus präsentieren wir eine numerisch exakte Methode, die das Hubbard-Modell und das KLM effizient bei sehr tiefen Temperaturen löst. Diese Methode wird auf den Mott-Übergang im zweidimensionalen Hubbard-Modell angewendet. Im Gegensatz zu früheren Studien können wir einen Mott-Übergang bei endlichen Temperaturen und endlichen Wechselwirkungen klar ausschließen.rnrnAuf der Basis dieses exakten BSS-QMC Algorithmus, haben wir einen Störstellenlöser für die dynamische Molekularfeld Theorie (DMFT) sowie ihre Cluster Erweiterungen (CDMFT) entwickelt. Die DMFT ist die vorherrschende Theorie stark korrelierter Systeme, bei denen übliche Bandstrukturrechnungen versagen. Eine Hauptlimitation ist dabei die Verfügbarkeit effizienter Störstellenlöser für das intrinsische Quantenproblem. Der in dieser Arbeit entwickelte Algorithmus hat das gleiche überlegene Skalierungsverhalten mit der inversen Temperatur wie BSS-QMC. Wir untersuchen den Mott-Übergang im Rahmen der DMFT und analysieren den Einfluss von systematischen Fehlern auf diesen Übergang.rnrnEin weiteres prominentes Thema ist die Vernachlässigung von nicht-lokalen Wechselwirkungen in der DMFT. Hierzu kombinieren wir direkte BSS-QMC Gitterrechnungen mit CDMFT für das halb gefüllte zweidimensionale anisotrope Hubbard Modell, das dotierte Hubbard Modell und das KLM. Die Ergebnisse für die verschiedenen Modelle unterscheiden sich stark: während nicht-lokale Korrelationen eine wichtige Rolle im zweidimensionalen (anisotropen) Modell spielen, ist in der paramagnetischen Phase die Impulsabhängigkeit der Selbstenergie für stark dotierte Systeme und für das KLM deutlich schwächer. Eine bemerkenswerte Erkenntnis ist, dass die Selbstenergie sich durch die nicht-wechselwirkende Dispersion parametrisieren lässt. Die spezielle Struktur der Selbstenergie im Impulsraum kann sehr nützlich für die Klassifizierung von elektronischen Korrelationseffekten sein und öffnet den Weg für die Entwicklung neuer Schemata über die Grenzen der DMFT hinaus.

Interplay Between Finite Resources and a Local Defect in an Asymmetric Simple Exclusion Process

When particle flux is regulated by multiple factors such as particle supply and varying transport rate, it is important to identify the respective dominant regimes. We extend the well-studied totally asymmetric simple exclusion model to investigate the interplay between a controlled entrance and a local defect site. The model mimics cellular transport phenomena where there is typically a finite particle pool and nonuniform moving rates due to biochemical kinetics. Our simulations reveal regions where, despite an increasing particle supply, the current remains constant while particles redistribute in the system. Exploiting a domain wall approach with mean-field approximation, we provide a theoretical ground for our findings. The results in steady-state current and density profiles provide quantitative insights into the regulation of the transcription and translation process in bacterial protein synthesis.

Bulk Metallic Glasses Deform via Slip Avalanches

For the first time in metallic glasses, we extract both the exponents and scaling functions that describe the nature, statistics, and dynamics of slip events during slow deformation, according to a simple mean field model. We model the slips as avalanches of rearrangements of atoms in coupled shear transformation zones (STZs). Using high temporal resolution measurements, we find the predicted, different statistics and dynamics for small and large slips thereby excluding self-organized criticality. The agreement between model and data across numerous independent measures provides evidence for slip avalanches of STZs as the elementary mechanism of inhomogeneous deformation in metallic glasses.

Structure-activity relationships from in vitro efficacies of the thiazolide series against the intracellular apicomplexan protozoan Neospora caninum

Nitazoxanide (2-acetolyloxy-N-(5-nitro 2-thiazolyl) benzamide; NTZ) represents the parent compound of a novel class of broad-spectrum anti-parasitic compounds named thiazolides. NTZ is active against a wide variety of intestinal and tissue-dwelling helminths, protozoa, enteric bacteria and a number of viruses infecting animals and humans. While potent, this poses a problem in practice, since this obvious non-selectivity can lead to undesired side effects in both humans and animals. In this study, we used real time PCR to determine the in vitro activities of 29 different thiazolides (NTZ-derivatives), which carry distinct modifications on both the thiazole- and the benzene moieties, against the tachyzoite stage of the intracellular protozoan Neospora caninum. The goal was to identify a highly active compound lacking the undesirable nitro group, which would have a more specific applicability, such as in food animals. By applying self-organizing molecular field analysis (SOMFA), these data were used to develop a predictive model for future drug design. SOMFA performs self-alignment of the molecules, and takes into account the steric and electrostatic properties, in order to determine 3D-quantitative structure activity relationship models. The best model was obtained by overlay of the thiazole moieties. Plotting of predicted versus experimentally determined activity produced an r2 value of 0.8052 and cross-validation using the "leave one out" methodology resulted in a q2 value of 0.7987. A master grid map showed that large steric groups at the R2 position, the nitrogen of the amide bond and position Y could greatly reduce activity, and the presence of large steric groups placed at positions X, R4 and surrounding the oxygen atom of the amide bond, may increase the activity of thiazolides against Neospora caninum tachyzoites. The model obtained here will be an important predictive tool for future development of this important class of drugs.

Phase diagram with an enhanced spin-glass region of the mixed Ising–XY magnet LiHo{x}Er{1-x}F{4}

We present the experimental phase diagram of LiHoxEr1-xF4, a dilution series of dipolar-coupled model magnets. The phase diagram was determined using a combination of ac susceptibility and neutron scattering. Three unique phases in addition to the Ising ferromagnet LiHoF4 and the XY antiferromagnet LiErF4 have been identified. Below x = 0.86, an embedded spin-glass phase is observed, where a spin glass exists within the ferromagnetic structure. Below x = 0.57, an Ising spin glass is observed consisting of frozen needlelike clusters. For x ∼ 0.3–0.1, an antiferromagnetically coupled spin glass occurs. A reduction of TC(x) for the ferromagnet is observed which disobeys the mean-field predictions that worked for LiHoxY1-xF4.

Nonequilibrium hysteresis and spin relaxation in the mixed-anisotropy dipolar-coupled spin-glass LiHo0.5Er0.5F4

We present a study of the model spin-glass LiHo0.5Er0.5F4 using simultaneous ac susceptibility, magnetization, and magnetocaloric effect measurements along with small angle neutron scattering (SANS) at sub-Kelvin temperatures. All measured bulk quantities reveal hysteretic behavior when the field is applied along the crystallographic c axis. Furthermore, avalanchelike relaxation is observed in a static field after ramping from the zero-field-cooled state up to 200–300 Oe. SANS measurements are employed to track the microscopic spin reconfiguration throughout both the hysteresis loop and the related relaxation. Comparing the SANS data to inhomogeneous mean-field calculations performed on a box of one million unit cells provides a real-space picture of the spin configuration. We discover that the avalanche is being driven by released Zeeman energy, which heats the sample and creates positive feedback, continuing the avalanche. The combination of SANS and mean-field simulations reveal that the conventional distribution of cluster sizes is replaced by one with a depletion of intermediate cluster sizes for much of the hysteresis loop.

Temporally Coherent Disparity Maps Using CRFs with Fast 4D Filtering

State of the art methods for disparity estimation achieve good results for single stereo frames, but temporal coherence in stereo videos is often neglected. In this paper we present a method to compute temporally coherent disparity maps. We define an energy over whole stereo sequences and optimize their Conditional Random Field (CRF) distributions using mean-field approximation. We introduce novel terms for smoothness and consistency between the left and right views, and perform CRF optimization by fast, iterative spatio-temporal filtering with linear complexity in the total number of pixels. Our results rank among the state of the art while having significantly less flickering artifacts in stereo sequences.

The Effects of Credit Risk on Dynamic Portfolio Management: A New Computational Approach

The study investigates the role of credit risk in a continuous time stochastic asset allocation model, since the traditional dynamic framework does not provide credit risk flexibility. The general model of the study extends the traditional dynamic efficiency framework by explicitly deriving the optimal value function for the infinite horizon stochastic control problem via a weighted volatility measure of market and credit risk. The model's optimal strategy was then compared to that obtained from a benchmark Markowitz-type dynamic optimization framework to determine which specification adequately reflects the optimal terminal investment returns and strategy under credit and market risks. The paper shows that an investor's optimal terminal return is lower than typically indicated under the traditional mean-variance framework during periods of elevated credit risk. Hence I conclude that, while the traditional dynamic mean-variance approach may indicate the ideal, in the presence of credit-risk it does not accurately reflect the observed optimal returns, terminal wealth and portfolio selection strategies.

Conservación de zapallos (Cucurbita pepo L.) var. Frontera : cultivo orgánico y tradicional

Objetivos: Determinar el período de conservación de zapallo orgánico respecto del tradicional, en dos condiciones de almacenamiento. Materiales y métodos: Zapallos variedad Frontera se limpiaron en seco y se pesaron individualmente para controlar pérdida de peso; se consignaron características externas. Para determinar deshidratación se midió humedad en la pulpa (estufa 105 °C). Para conservación, acondicionamiento en cajones de madera con viruta, en galpón (temperatura y humedad ambiente) y antecámara (15- 20 °C y 70-85 % HR). Duración 187 días. Comparación sensorial, al inicio y al final de la conservación, considerando: color, olor, sabor, retrogusto, jugosidad, textura y calidad general. Se utilizó planilla con escala mixta estructurada de 9 puntos y participaron jueces semientrenados (n = 10). Evaluación de datos por análisis de varianza = 0.05. Conclusiones: En las condiciones del ensayo, el período de conservación no debe ser superior a los 105 días por aparición de podredumbre. Por deshidratación superior al 60 %, debe ser inferior a 68 días para antecámara, 105 días para orgánicos de galpón y 105-126 días para tradicionales de galpón. Las características sensoriales iniciales de los zapallos orgánicos fueron mejores; al final se destacaron los tradicionales en galpón, luego los orgánicos en galpón y los conservados en antecámara presentaron características inferiores.

Preliminary results and documentation of sediment cores CRP2 and CRP-2A from the Ross Sea off Cape Roberts, Antarctica

The site for CRP-2, 14 km east of Cape Roberts (77.006°S; 163.719°E), was selected to overlap the early Miocene strata cored in nearby CRP-1, and to sample deeper into the east-dipping strata near the western margin ofe he Victoria Land Basin to investigate Palaeogene climatic and tectonic history. CRP-2 was cored from 5 to 57 mbsf (metres below the sea floor) (core recovery 91 %), with a deviation resulting in CRP-2A being cored at the same site. CRP-2A reached down to 624mbsf (recovery 95%), and to strata with an age of c. 33-35 Ma. Drilling took place from 16 October to 25 November 1998, on 2.0-2.2 m of sea ice and through 178 m of water. Core fractures and other physical properties, such as sonic velocity, density and magnetic susceptibility, were measured throughout the core. Down-hole logs for these and other properties were run from 63 to 167 mbsf and subsequently from 200 to 623 mbsf, although density and velocity data could be obtained only to 440 mbsf because of hole collapse. Sonic velocity averages c. 2.0 km S-1 for the upper part of the hole, but there is an sharp increase to c. 3.0 km s-1 and also a slight angular unconformity, at 306 mbsf, corresponding most likely to the early/late Oligocene boundary (c. 28-30 Ma). Velocity then increases irregularly to around 3.6 km s-1 at the bottom of the hole, which is estimated to lie 120 m above the V4/V5 boundary. The higher velocities below 306 mbsf probably reflect more extensive carbonate and common pyrite cementation, in patches, nodules, bedding-parallel masses and as vein infills. Dip of the strata also increases down-hole from 3° in the upper 300 in to over 10° at the bottom. Temperature gradient is 21° k-1. Over 2 000 fractures were logged through the hole. Borehole televiewer imagery was obtained for the interval from 200 to 440 mbsf to orient the fractures for stress field analysis. Lithostratigraphical descriptions on a scale of 1:20 are presented for the full length of the core, along with core box images, as a 200 page supplement to this issue. The hole initially passed through a layer of muddy gravel to 5.5 mbsf (Lithological Sub-Unit or LSU 1.1), and then into a Quaternary diatom-bearing clast-rich diamicton to 21 mbsf (LSU 2. l), with an interval of alternating compact diamicton and loose sand, and containing a rich Pliocene foraminiferal fauna, to 27 mbsf (LSU 2.2). The unit beneath this (LSU 3.1) has similar physical properties (sonic velocity, porosity, magnetic susceptibility) and includes diamictites of similar character to those of LSU 2.1 and 2.2, but an early Miocene (c. 19 Ma) diatom assemblage at 28 mbsf (top of LSU 3.1) shows that this sub-unit is part of the older section. The strata beneath 27 mbsf, primary target for the project, extend from early Miocene to perhaps latest Eocene age, and are largely cyclic glacimarine nearshore to offshore sediments. They are described as 41 lithological sub-units and interpreted in terms of 12 recurrent lithofacies. These are 1) mudstone, 2) inter-stratified mudstone and sandstone, 3) muddy very fine to coarse sandstone, 4) well-sorted stratified fine sandstone, 5) moderately to well-sorted, medium-grained sandstone, 6) stratified diamictite, 7) massive diamictite, 8) rhythmically inter-stratified sandstone and mudstone, 9) clast-supported conglomerate, 10) matrix-supported conglomerate, 11) mudstone breccia and 12) volcaniclastic sediment. Sequence stratigraphical analysis has identified 22 unconformity-bounded depositional sequences in pre- Pliocene strata. They typically comprise a four-part architecture involving, in ascending order, 1) a sharp-based coarse-grained unit (Facies 6,7,9 or 10), 2) a fining-upward succession of sandstones (Facies 3 and 4), 3) a mudstone interval (Facies l), in some cases coarsening upward to muddy sandstones (Facies 3), and 4) a sharp-based sandstone dominated succession (mainly Facies 4). The cyclicity recorded by the strata is interpreted in terms of a glacier ice margin retreating and advancing from land to the west, and of rises and falls in sea level. Analysis of sequence periodicity awaits afirmer chronology. However, apreliminary spectral analysis of magnetic susceptibility for a deepwater mudstone within one of the sequences (from 339 to 347 mbsf) reveals ratios between hierarchical levels that are similar to those of the three Milankovitch orbital forcing periodicities. The strata contain a wide range of fossils, the most abundant being marine diatoms. These commonly form up to 5% of the sediment, though in places the core is barren (notably between 300 and 412 mbsf). Fifty samples out of 250 reviewed were studied in detail. The assemblages define ten biostratigraphical zones, some of them based on local or as yet undescribed forms. The assemblages are neritic, and largely planktonic, suggesting that the sea floor was mostly below the photic zone throughout deposition of the corcd sequence. Calcareous nannofossils, representing incursions of ocean surface waters, are much less common (72 out of 183 samples examined) and restricted to mudstone intervals a few tens of metres thick, but are important for dating. Foraminifera are also sparse (73 out of 135 samples) and represented only by calcareous benthic species. Changing assemblages indicate a shift from inshore environments in the early Oligocenc to outer shelf in the late Oligocenc, returning to inshore in the early Miocene. Marine palynomorplis yielded large numbers of well-preserved forms from most of the 116 samples examined. The new in situ assemblagc found last year in CRP-1 is extended down into the late Oligocene and a further new assemblage is found in the early Oligoccnc. Many taxa are new, and cannot us yet contribute to an improved understanding of chronology or ecology. Marine invertebrate macrofossils, mostly molluscs and serpulid tubes, are scattered throughout the core. Preservation is good in mudstones but poor in other lithologies. Climate on land is reflected in the content of terrestrial palynomorphs, which are extremely scarce down to c. 300 mbsf. Some forms are reworked, and others represent a low growing sparse tundra with at least one species of Nothofagus. Beneath this level, a significantly greater diversity and abundance suggests a milder climate and a low diversity woody vegetation in the early Oligocene, but still far short of the richness found in known Eocene strata of the region. Sedimentary facies in the oldest strata also suggest a milder climate in the oldest strata cored, with indications of substantial glacial melt-water discharges, but are typical of a coldcr climate in late Oligocene and early Miocene times. Clast analyses from diamictites reveal weak to random fabrics, suggesting either lack of ice-contact deposition or post-depositional modification, but periods when ice grounded at the drill site are inferred from thin zones of in-situ brecciated rock and soft-sediment folding. These are more common above c. 300 mbsf, perhaps reflecting more extensive glacial advances during deposition of those strata. Erosion of the adjacent Transantarctic Mountains through Jurassic basalt and dolerite-intruded Beacon strata into basement rocks beneath is recorded by petrographical studies of clast and sand grain assemblages. Core below 310 mbsf contains a dominance of fine-grained Jurassic dolerite and basalt fragments along with Beacon-derived coal debris and rounded quartz grains, whereas the strata above this level have a much higher proportion of basement derived granitoids, implying that the large areas of the adjacent mountains had been eroded to basement by the end of the early Oligocene. There is little indication of rift-related volcanism below 310 mbsf. Above this, however, basaltic and trachytic tephras are common, especially from 280 to 200 mbsf, from 150 to 46 mbsf, and in Pliocene LSU 2.2 from 21 to 27 mbsf. The largest volcanic eruptions generated layers of coarse (up to 1 cm) trachytic pumice lapilli between 97 and 114 mbsf. The thickest of these (1.2 m at 112 mbsf) may have produced an eruptive column extending tens of km into the stratosphere. A source within a few tens of km of the drill site is considered most likely. Present age estimates for the pre-Pliocene sequence are based mainly on biostratigraphy (using mainly marine diatoms and to a lesser extent calcareous nannofossils), with the age of the tephra from 112 to 114 mbsf (21.44k0.05 Ma from 84 crystals by Ar-Ar) as a key reference point. Although there are varied and well-preserved microfossil assemblages through most of the sequence (notably of diatoms and marine palynomorphs), they comprise largely taxa either known only locally or as yet undescribed. In addition, sequence stratigraphical analysis and features in the core itself indicate numerous disconformities. The present estimate from diatom assemblages is that the interval from 27 to 130 mbsf is early Miocene in age (c. 19 to 23.5 Ma), consistent with the Ar-Ar age from 112 to 114 mbsf. Diatom assemblages also indicate that the late Oligocene epoch extends from c. 130 to 307 mbsf, which is supported by late Oligocene nannofossils from 130 to 185 mbsf. Strata from 307 to 412 mbsf have no age-diagnostic assemblages, but below this early Oligocene diatoms and nannofossils have been recovered. A nannoflora at the bottom of the hole is consistent with an earliest Oligocene or latest Eocene age. Magnetostratigraphical studies based on about 1000 samples, 700 of which have so far undergone demagnetisation treatment, have provided a polarity stratigraphy of 12 pre-Pliocene magnetozones. Samples above 270 mbsf are of consistently high quality. Below this, magnetic behaviour is more variable. A preliminary age-depth plot using the Magnetic Polarity Time Scale (MPTS) and constrained by biostratigraphical data suggests that episodes of relatively rapid sedimentation took place at CRP-2 during Oligocene times (c. 100 m/My), but that more than half of the record was lost in a few major and many minor disconformities. Age estimates from Sr isotopes in shell debris and further tephra dating are expected to lead to a better comparison with the MPTS. CRP-2/2A has recorded a history of subsidence of the Victoria Land Basin margin that is similar to that found in CIROS-170 km to the south, reflecting stability in both basin and the adjacent mountains in late Cenozoic times, but with slow net accumulation in the middle Cenozoic. The climatic indicators from both drill holes show a similar correspondence, indicating polar conditions for the Quaternary but with sub-polar conditions in the early Miocene-late Oligocene and indications of warmer conditions still in the early Oligocene. Correlation between the CRP-2A core and seismic records shows that seismic units V3 and V4, both widespread in the Victoria Land Basin, represent a period of fluctuating ice margins and glacimarine sedimentation. The next drill hole, CRP-3, is expected to core deep into V5 and extend this record of climate and tectonics still further back in time.

Phase transitions in number theory: from the birthday problem to Sidon sets

In this work, we show how number theoretical problems can be fruitfully approached with the tools of statistical physics. We focus on g-Sidon sets, which describe sequences of integers whose pairwise sums are different, and propose a random decision problem which addresses the probability of a random set of k integers to be g-Sidon. First, we provide numerical evidence showing that there is a crossover between satisfiable and unsatisfiable phases which converts to an abrupt phase transition in a properly defined thermodynamic limit. Initially assuming independence, we then develop a mean-field theory for the g-Sidon decision problem. We further improve the mean-field theory, which is only qualitatively correct, by incorporating deviations from independence, yielding results in good quantitative agreement with the numerics for both finite systems and in the thermodynamic limit. Connections between the generalized birthday problem in probability theory, the number theory of Sidon sets and the properties of q-Potts models in condensed matter physics are briefly discussed