Some z_n-1 terraces from z_n power-sequences, n being an odd prime power

A terrace for Zm is a particular type of sequence formed from the m elements of Zm. For m odd, many procedures are available for constructing power-sequence terraces for Zm; each terrace of this sort may be partitioned into segments, of which one contains merely the zero element of Zm, whereas every other segment is either a sequence of successive powers of an element of Zm or such a sequence multiplied throughout by a constant. We now refine this idea to show that, for m=n−1, where n is an odd prime power, there are many ways in which power-sequences in Zn can be used to arrange the elements of Zn \ {0} in a sequence of distinct entries i, 1 ≤ i ≤ m, usually in two or more segments, which becomes a terrace for Zm when interpreted modulo m instead of modulo n. Our constructions provide terraces for Zn-1 for all prime powers n satisfying 0 < n < 300 except for n = 125, 127 and 257

The Gordon game

In 1992, about 30 years after Gordon introduced group sequencings to construct row-complete Latin squares, John Isbell introduced the idea of competitive sequencing, the Gordon Game. Isbell investigated the Gordon Game and found solutions for groups of small order. The purpose of this thesis is to analyze the Gordon Game and develop a brute force method of determining solutions to the game for all groups of order 12 (up to isomorphism) as well as for abelian groups of order less than 20. The method used will be a depth first search program written in MATLAB. Consequently, group representation using matrices will be studied within the thesis --Document

Thermodynamics and Kinetics of Defects at Surfaces

Fundamental understanding of the various electronic and structural properties at surfaces is a prerequisite for improved control of nanometer-scale patterning of surfaces for potential technological applications. In this dissertation, we have used multi-scale theoretical approaches to investigate the thermodynamic and kinetic properties of a few elemental types of surface defects. The multi-scale approaches range from first-principles calculations within density functional theory to empirical embedded atom method (EAM) to statistical analysis to kinetic Monte Carlo simulations. In studying the thermodynamic properties of intrinsic line defects on a vicinal TaC(910) surface, our Monte Carlo simulations in comparison with scanning tuning microscope (STM) images have established the existence of long-range attractive interaction between the steps. For extrinsic point defects underneath a GaAs surface, we have established through our theoretical analysis in comparison with STM observations that many-body effects in a system with purely repulsive interactions can give rise to an effective attractive interaction between the dopants at high dopant densities. In the study of the morphological evolution of monatomiclayer- high islands grown on metal surfaces, we have carried out Kinetic Monte Carlo simulations to demonstrate the importance of the island corner barriers. Our study has shown that if the island corner barrier effect is operational in preventing adatoms v located at an island edge to reach a neighboring edge defining the island corner, the islands thus formed must be non-compact, and develop fractal or dendritic shapes. Based on our EAM calculations of the diffusion barriers for various atomic processes and rate equation analysis, we have explained why fractal islands have rarely been observed on metal fcc(100) surfaces. For ideal surfaces, we have investigated the various driving forces for lattice relaxation based on first-principles calculations, and have proposed a new approach that has the promise to predict the direction of relaxation of the atoms in the surface layer strictly based on bulk properties of the given system. Finally, our fist-principles based interpretation of STM images within the framework of the Tersoff-Hamann theory has resulted in good agreement with STM experiments in revealing the anisotropy of electron density corrugations on several open metallic surfaces

Atomic Scale Modeling of Fundamental Characteristics of Metal Anodes and Solid Electrolytes: Overpotentials, Elastic Properties, and Grain Boundary Transport

A rechargeable battery with a metallic anode offers the possibility of significant energy density improvement. However, mass commercialization has been hampered by a number of issues, including safety concerns posed by the formation and growth of dendrites during cycling. Use of the solid electrolyte Li7La3Zr2O12 (LLZO) can potentially address these concerns, and is promising in conjunction with Li metal due to its favorable combination of high conductivity and chemical stability. The present work characterizes several important properties of metallic anodes and LLZO at the atomic scale using Density Functional Theory (DFT) and molecular dynamics (MD) simulations. First, thermodynamic deposition/dissolution efficiencies and nucleation rates for seven metals were assessed. Thermodynamic overpotentials were evaluated via DFT at terraces and steps on several low-energy surfaces. In general, overpotentials were observed to be smallest for plating/stripping at steps, and largest at terraces. Differences in coordination numbers between a surface and a bulk atom were found to correlate with overpotential magnitude. Due to their low bulk coordination, body-centered alkali metals were predicted to be thermodynamically efficient for plating/stripping. In contrast, metals with larger bulk coordination, such as Al, Zn, and alkaline earths, exhibited higher thermodynamic overpotentials. The rate of steady-state nucleation during electrodeposition was estimated using a classical nucleation model informed by DFT calculations. Nucleation rates were predicted to be several orders of magnitude larger on alkali metal surfaces than on other metals. This multi-scale model highlighted the sensitivity of nucleation behavior on the morphology and composition of the electrode surface. Next, DFT calculations were employed to assess the elastic properties of eight anode materials. These were predicted as a function of temperature within the quasi-harmonic approximation. Anisotropy was assessed by resolving the moduli as a function of crystallographic direction. The alkali metals were predicted to have the smallest elastic moduli overall, which decreased with increasing atomic number. Al and Mg were predicted to exhibit highly isotropic elastic properties, while the alkali metals were highly anisotropic. In cubic systems, crystallographic directions exhibiting extrema in the elastic properties were diametrically opposed: under axial loading, the stiffest (most compliant) orientation was (), while in shear () was the stiffest (most compliant). The maximum anisotropic shear modulus of some metals was observed to be more than twice as large as their respective polycrystalline values. Finally, to better understand the impact of grain boundaries (GB's) on LLZO's performance as a solid electrolyte, the structure of a wide range of tilt and twist axis GB's, including amorphous GB's, were predicted via classical MD and Monte Carlo simulations. Their energetics, composition, and Li transport properties were assessed. Little to no change was observed in the concentration of the four constituent elements across GB's, with the exception of amorphous Σ9(221)/[10], which showed a significant decrease in all four. Trajectories indicated disrupted diffusion pathways. Diffusivity showed greater sensitivity to temperature within crystalline GB's than in amorphous GB's. At the GB, Li diffusivity was consistently reduced compared to the bulk, while activation energy (∆Ea) was comparable or higher. Interestingly, diffusivity and ∆Ea both decreased with increasing grain boundary energy. A relationship between the pre-exponential factor (D0) and ∆Ea was observed, which suggested significant variation of D0 within the grain boundaries examined. Diffusivity at the GB's demonstrated anisotropy, with diffusion slower parallel to the GB plane, and faster normal to the GB plane.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/163115/1/nagyky_1.pd

Investigating Ancient Man-Made Terraces of Petra–Jordan

Künstliche Terrassen sind künstlich konstruierte Trockenmauern, die Hänge in Ebenen unterteilen. Petra im Süden Jordaniens gehört zu einer trockenen Klimazone, die sich durch unwegsames Gelände und eine mit Terrassen durchsetzte Landschaft auszeichnet. Die vorliegenden Ergebnisse wurden vom Autor im Rahmen einer multidisziplinären Studie gesammelt, die aus Vermessungen, Erkundungsgrabungen, geophysikalischen Prospektionen, Untersuchungen der Bodentextur sowie chemischen Analysen, optisch stimulierender Lumineszenzdatierung (OSL), Radiokohlenstoffdatierung (14C), Phytolithanalysen und geografischen Analysen zur Untersuchung der Terrassen in einem Gebiet von etwa 391 km2 bestand. Die vorliegende Studie zeigt, dass die künstlichen Terrassen in Trockengebieten für eine Vielzahl von Funktionen konzipiert und genutzt wurden. Die Terrassen dienten somit der Rückhaltung, Sammlung und Verteilung von Boden und Wasser und verhinderten, dass Wasser unkontrolliert abfließt und Erde weggespült wird. Das trockene Klima, das raue Gelände und die für dieses Gebiet charakteristischen Überschwemmungen machten diese Eingriffe in die Natur notwendig. Neben diesen beiden Hauptaufgaben konnten die Terrassen der Nabatäer noch andere Funktionen erfüllen. Neben der landwirtschaftlichen Nutzung der Terrassen nutzten die Nabatäer sie auch zum Schutz ihrer Infrastruktur wie Straßen und hydrologische Einrichtungen. Ein Aspekt, der in der Forschung noch nicht diskutiert wurde. All dies deutet darauf hin, dass die Nabatäer die Gegend sehr gut kannten und gezielt den Bau einer bestimmten Art von Terrasse nutzten. Basierend auf verschiedenen Datierungstechniken begann der Bau der Terrassen in Petra um 350-320 v. Chr. Drei zeitliche Höhepunkte in der Bauausweitung lassen sich unterscheiden: um das 1. Jahrhundert n. Chr., um das 6. bis 7. Jahrhundert n. Chr. und um das 12. Jahrhundert n. Chr.Man-made terraces are often-overlooked feature in the landscapes of southern Jordan, especially around Petra. These features are artificial constructions dry walls that create flat surfaces on slopes (Spencer, J. and Hale, G. 1961: 3; Treacy, J. and Denevan, W. 1994: 93; Kvapil, L. 2013: 6612). These terraces are usually attributed to have agricultural functions, which is only partially true. This study shows that terraces constructed in arid areas have been designed and used for a wide set of functions that go beyond their agrarian aspects. Petra, located in the south of Jordan, falls within an arid climatic zone, is of rough terrain, and has a landscape dotted with terraces. A multidisciplinary study was conducted by the author which included survey, sounding excavations, geophysical prospecting, soil texture and chemical analysis, Optical Stimulating Luminescence (OSL), radiocarbon dating (14C), phytolith analysis and spatial analysis for studying the terraces. Two major functions were assigned to the constructed terraces: hydrological (water) and pedogenic (soil). Applied to prevent, retain, collect and distribute soil and water. Nabataeans managed to apply terraces to a wide range of fields such as: agriculture, infrastructure such as roads and hydrological installations, an aspect never discussed before. The study concluded, based on OSL, pottery sherds and 14C dates, terrace construction in Petra started around 350-320 B.C.E. at the upper catchment areas, probably for flood water mitigation. Three peaks in the construction expansion can be grouped: around the 1st century A.D, around 6th -7th century and around 12th century, which correspond to more humid climatic conditions and stability in the political situation

STEPS ON VICINAL SURFACES: DENSITY-FUNCTIONAL THEORY CALCULATIONS AND TRANSCENDING MINIMAL STATISTICAL-MECHANICAL MODELS

Using both density-functional theory calculations and Monte Carlo simulations, we compute various key parameters that are used to model steps on vicinal surfaces. In the first part, we discuss the importance of multi-site interactions (trios and quartos) in the lattice-gas characterization of adatom interactions. Using density-functional theory calculations, we show that multi-site interactions with substantial contributions from direct interactions are sensitive to adatom relaxations. Such sensitivity to adatom relaxations complicates the lattice-gas approach to modeling overlayer systems. Our results show that a careful consideration of relaxation effects is required to make connections with experiments. In the second part, we use both density-functional theory calculations and kinetic Monte Carlo simulations to identify the impurity atom responsible for growth instabilities on Cu vicinals. In addition to that, we also show that a small quantity of codeposited impurities significantly alters the growth behavior. Our results indicate that growth morphologies could be controlled through the codeposition of an appropriate impurity. Hence, impurities could play a crucial role in nanostructuring of surfaces. Step configurations have fruitfully been related to the worldlines of spinless fermions in one dimension. However, in addition to the realistic no-crossing condition, the fermion picture imposes a more restrictive non-touching condition. in the third part of this thesis, we use Metropolis Monte Carlo method to study the effects of loosening this non-touching condition on the resulting TWDs. Our results show that allowing step touching leads to an effective attraction in the step-step interaction strength measurements. We show that this effective attraction can be incorporated into the fermion picture as a finite-size effect

The hydrology of prehistoric farming systems in a central Arizona ecotone

The prehistoric land use and water management in the semi-arid Southwest was examined. Remote sensing data, geology, hydrology and biology are discussed along with an evaluation of remote sensing contributions, recommendations for applications, and proposed future remote sensing studies

Bronze age landscape degradation in the Northern Argolid: a micromorphological investigation of anthropogenic erosion in the environs of Mycenae, Greece

In this dissertation, I examine the relationship between environmental conditions and human activity in the landscape of the Argive Plain of Greece after the collapse of the Bronze Age palatial system (1200–750 B.C.). I use evidence from four locales: the Petsas House and the Lower Town at Mycenae, to the immediate northwest and southwest of the citadel respectively; the settlement at Chania, three kilometers downstream; and the Northwest Town of Tiryns, in the lower reaches of the plain. I apply micromorphological analysis (the microscopic analysis of soils and sediments) integrated with analysis of grain-size and soil chemistry (assessed by X-Ray Fluorescence and Fourier Transform Infrared) in order to place depositional events within the context of settlement change at the end of the Bronze Age. The climate had been drying during the Late Bronze. An earthquake ca. 1200 B.C. is concurrent with the beginning of the final period of occupation on the edge of the plain around Mycenae. Some accumulation of sandy muds, destabilized sediments from the largely abandoned citadel, is observed at Petsas House as well as in the Lower Town where, additionally, remains were buried by two deposits of red muddy gravels from uncultivated mountain slopes. The gravels are separated by a brief period of stability (less than a century) marked by a weak soil formation, and reached final equilibrium in the Early to Middle Geometric period (900–760 B.C.). At the same time, three kilometers downstream, similar red muddy gravels resulted in the interruption of activity at the settlement of Chania. Meanwhile, at Tiryns, 30 cm of sandy muds, also destabilized by drier conditions, were deposited over decaying mudbrick, implying that the site was already abandoned before sedimentation occurred. The burial of both Mycenae and Tiryns demonstrates the instability in the Argive landscape and the complications of relating these changes to settlement. In the environs of Mycenae, the sudden deposition of muddy gravels certainly brought about the abandonment at Chania, and possibly also in the Lower Town; while at Tiryns abandonment preceded accumulation. This study demonstrates how intensive geoarchaeological study must be a component in properly situating sites in their particular landscapes