Engineering a Quantum Many-body Hamiltonian with Trapped Ions

While fault-tolerant quantum computation might still be years away, analog quantum simulators offer a way to leverage current quantum technologies to study classically intractable quantum systems. Cutting edge quantum simulators such as those utilizing ultracold atoms are beginning to study physics which surpass what is classically tractable. As the system sizes of these quantum simulators increase, there are also concurrent gains in the complexity and types of Hamiltonians which can be simulated. In this work, I describe advances toward the realization of an adaptable, tunable quantum simulator capable of surpassing classical computation. We simulate long-ranged Ising and XY spin models which can have global arbitrary transverse and longitudinal fields in addition to individual transverse fields using a linear chain of up to 24 Yb+ 171 ions confined in a linear rf Paul trap. Each qubit is encoded in the ground state hyperfine levels of an ion. Spin-spin interactions are engineered by the application of spin-dependent forces from laser fields, coupling spin to motion. Each spin can be read independently using state-dependent fluorescence. The results here add yet more tools to an ever growing quantum simulation toolbox. One of many challenges has been the coherent manipulation of individual qubits. By using a surprisingly large fourth-order Stark shifts in a clock-state qubit, we demonstrate an ability to individually manipulate spins and apply independent Hamiltonian terms, greatly increasing the range of quantum simulations which can be implemented. As quantum systems grow beyond the capability of classical numerics, a constant question is how to verify a quantum simulation. Here, I present measurements which may provide useful metrics for large system sizes and demonstrate them in a system of up to 24 ions during a classically intractable simulation. The observed values are consistent with extremely large entangled states, as much as ~95% of the system entangled. Finally, we use many of these techniques in order to generate a spin Hamiltonian which fails to thermalize during experimental time scales due to a meta-stable state which is often called prethermal. The observed prethermal state is a new form of prethermalization which arises due to long-range interactions and open boundary conditions, even in the thermodynamic limit. This prethermalization is observed in a system of up to 22 spins. We expect that system sizes can be extended up to 30 spins with only minor upgrades to the current apparatus. These results emphasize that as the technology improves, the techniques and tools developed here can potentially be used to perform simulations which will surpass the capability of even the most sophisticated classical techniques, enabling the study of a whole new regime of quantum many-body physics.

The export performance of the 2004 EU enlargement economies since the 1990s : a constant market share analysis

This study focuses the export performance of the 2004 EU enlargement economies between 1990 and 2013. The long time span analysed allows to capture different stages in the relationship of these new members with the EU before and after accession. The study is based on the Constant Market Share methodology of decomposing an ex-post country’s export performance into different effects. Two different Constant Market Share Analysis (CMSA) were selected in order to disentangle, for the exports of the new members to the EU15, (i) the growth rate of exports and (ii) the growth rate of exports relatively to the world. Both approaches are applied to manufactured products first without disaggregating results by sectors and then grouping all products into two different classification of sectors: one considering the technological intensity of manufactured exports and another evaluating the specialization factors of the products exported. Results provide information not only on the ten economies’ export performance as a group but also individually considered and on the importance of each EU15 destination market to the export performance of these countries.

Exploration of Ground Penetrating Radar and Time Domain Reflectometry Methods for the Determination of Pavement Dielectric Constant

Traditionally, densities of newly built roadways are checked by direct sampling (cores) or by nuclear density gauge measurements. For roadway engineers, density of asphalt pavement surfaces is essential to determine pavement quality. Unfortunately, field measurements of density by direct sampling or by nuclear measurement are slow processes. Therefore, I have explored the use of rapidly-deployed ground penetrating radar (GPR) as an alternative means of determining pavement quality. The dielectric constant of pavement surface may be a substructure parameter that correlates with pavement density, and can be used as a proxy when density of asphalt is not known from nuclear or destructive methods. The dielectric constant of the asphalt can be determined using ground penetrating radar (GPR). In order to use GPR for evaluation of road surface quality, the relationship between dielectric constants of asphalt and their densities must be established. Field measurements of GPR were taken at four highway sites in Houghton and Keweenaw Counties, Michigan, where density values were also obtained using nuclear methods in the field. Laboratory studies involved asphalt samples taken from the field sites and samples created in the laboratory. These were tested in various ways, including, density, thickness, and time domain reflectometry (TDR). In the field, GPR data was acquired using a 1000 MHz air-launched unit and a ground-coupled unit at 200 and 500 MHz. The equipment used was owned and operated by the Michigan Department of Transportation (MDOT) and available for this study for a total of four days during summer 2005 and spring 2006. The analysis of the reflected waveforms included “routine” processing for velocity using commercial software and direct evaluation of reflection coefficients to determine a dielectric constant. The dielectric constants computed from velocities do not agree well with those obtained from reflection coefficients. Perhaps due to the limited range of asphalt types studied, no correlation between density and dielectric constant was evident. Laboratory measurements were taken with samples removed from the field and samples created for this study. Samples from the field were studied using TDR, in order to obtain dielectric constant directly, and these correlated well with the estimates made from reflection coefficients. Samples created in the laboratory were measured using 1000 MHz air-launched GPR, and 400 MHz ground-coupled GPR, each under both wet and dry conditions. On the basis of these observations, I conclude that dielectric constant of asphalt can be reliably measured from waveform amplitude analysis of GJPR data, based on the consistent agreement with that obtained in the laboratory using TDR. Because of the uniformity of asphalts studied here, any correlation between dielectric constant and density is not yet apparent.

A SURVEY OF DISTANCE MAGIC GRAPHS

In this report, we survey results on distance magic graphs and some closely related graphs. A distance magic labeling of a graph G with magic constant k is a bijection l from the vertex set to {1, 2, . . . , n}, such that for every vertex x Σ l(y) = k,y∈NG(x) where NG(x) is the set of vertices of G adjacent to x. If the graph G has a distance magic labeling we say that G is a distance magic graph. In Chapter 1, we explore the background of distance magic graphs by introducing examples of magic squares, magic graphs, and distance magic graphs. In Chapter 2, we begin by examining some basic results on distance magic graphs. We next look at results on different graph structures including regular graphs, multipartite graphs, graph products, join graphs, and splitting graphs. We conclude with other perspectives on distance magic graphs including embedding theorems, the matrix representation of distance magic graphs, lifted magic rectangles, and distance magic constants. In Chapter 3, we study graph labelings that retain the same labels as distance magic labelings, but alter the definition in some other way. These labelings include balanced distance magic labelings, closed distance magic labelings, D-distance magic labelings, and distance antimagic labelings. In Chapter 4, we examine results on neighborhood magic labelings, group distance magic labelings, and group distance antimagic labelings. These graph labelings change the label set, but are otherwise similar to distance magic graphs. In Chapter 5, we examine some applications of distance magic and distance antimagic labeling to the fair scheduling of tournaments. In Chapter 6, we conclude with some open problems.

Splitting of a prevalent Mycobacterium bovis spoligotype by variable-number tandem-repeat typing reveals high heterogeneity in an evolving clonal group

Mycobacterium bovis populations in countries with persistent bovine tuberculosis usually show a prevalent spoligotype with a wide geographical distribution. This study applied mycobacterial interspersed repetitive-unit-variable-number tandem-repeat (MIRU-VNTR) typing to a random panel of 115 M. bovis isolates that are representative of the most frequent spoligotype in the Iberian Peninsula, SB0121. VNTR typing targeted nine loci: ETR-A (alias VNTR2165), ETR-B (VNTR2461), ETR-D (MIRU4, VNTR580), ETR-E (MIRU31, VNTR3192), MIRU26 (VNTR2996), QUB11a (VNTR2163a), QUB11b (VNTR2163b), QUB26 (VNTR4052), and QUB3232 (VNTR3232). We found a high degree of diversity among the studied isolates (discriminatory index [D] = 0.9856), which were split into 65 different MIRU-VNTR types. An alternative short-format MIRU-VNTR typing targeting only the four loci with the highest variability values was found to offer an equivalent discriminatory index. Minimum spanning trees using the MIRU-VNTR data showed the hypothetical evolution of an apparent clonal group. MIRU-VNTR analysis was also applied to the isolates of 176 animals from 15 farms infected by M. bovis SB0121; in 10 farms, the analysis revealed the coexistence of two to five different MIRU types differing in one to six loci, which highlights the frequency of undetected heterogeneity.

Design principles for maximizing photovoltage in metal-oxide-protected water-splitting photoanodes

Metal oxide protection layers for photoanodes may enable the development of large-scale solar fuel and solar chemical synthesis, but the poor photovoltages often reported so far will severely limit their performance. Here we report a novel observation of photovoltage loss associated with a charge extraction barrier imposed by the protection layer, and, by eliminating it, achieve photovoltages as high as 630mV, the maximum reported so far for water-splitting silicon photoanodes. The loss mechanism is systematically probed in metal-insulator-semiconductor Schottky junction cells compared to buried junction p(+) n cells, revealing the need to maintain a characteristic hole density at the semiconductor/insulator interface. A leaky-capacitor model related to the dielectric properties of the protective oxide explains this loss, achieving excellent agreement with the data. From these findings, we formulate design principles for simultaneous optimization of built-in field, interface quality, and hole extraction to maximize the photovoltage of oxide-protected water-splitting anodes.

Engineering interfacial silicon dioxide for improved metal-insulator-semiconductor silicon photoanode water splitting performance

Silicon photoanodes protected by atomic layer deposited (ALD) TiO2 show promise as components of water splitting devices that may enable the large-scale production of solar fuels and chemicals. Minimizing the resistance of the oxide corrosion protection layer is essential for fabricating efficient devices with good fill factor. Recent literature reports have shown that the interfacial SiO2 layer, interposed between the protective ALD-TiO2 and the Si anode, acts as a tunnel oxide that limits hole conduction from the photoabsorbing substrate to the surface oxygen evolution catalyst. Herein, we report a significant reduction of bilayer resistance, achieved by forming stable, ultrathin (<1.3 nm) SiO2 layers, allowing fabrication of water splitting photoanodes with hole conductances near the maximum achievable with the given catalyst and Si substrate. Three methods for controlling the SiO2 interlayer thickness on the Si(100) surface for ALD-TiO2 protected anodes were employed: (1) TiO2 deposition directly on an HF-etched Si(100) surface, (2) TiO2 deposition after SiO2 atomic layer deposition on an HF-etched Si(100) surface, and (3) oxygen scavenging, post-TiO2 deposition to decompose the SiO2 layer using a Ti overlayer. Each of these methods provides a progressively superior means of reliably thinning the interfacial SiO2 layer, enabling the fabrication of efficient and stable water oxidation silicon anodes.

Locating the maximum power point for thermoelectric generators for constant heat operation

Thermoelectric generators (TEGs) are solid-state devices that can be used for the direct conversion between heat and electricity. These devices are an attractive option for generating clean energy from heat. There are two modes of operation for TEGs; constant heat and constant temperature. It is a well-known fact that for constant temperature operation, TEGs have a maximum power point lying at half the open circuit voltage of the TEG, for a particular temperature. This work aimed to investigate the position of the maximum power point for Bismuth Telluride TEGs working under constant heat conditions i.e. the heat supply to the TEG is fixed however the temperature across the TEG can vary depending upon its operating conditions. It was found that for constant heat operation, the maximum power point for a TEG is greater than half the open circuit voltage of the TEG.

One-dimensional Model for Fluids of Third-grade in Tubes with Constant Radius

Our goal in this paper is to extend previous results obtained for Newtonian and secondgrade fluids to third-grade fluids in the case of an axisymmetric, straight, rigid and impermeable tube with constant cross-section using a one-dimensional hierarchical model based on the Cosserat theory related to fluid dynamics. In this way we can reduce the full threedimensional system of equations for the axisymmetric unsteady motion of a non-Newtonian incompressible third-grade fluid to a system of equations depending on time and on a single spatial variable. Some numerical simulations for the volume flow rate and the the wall shear stress are presented.

Competitividade e parcelas de mercado: um estudo do modelo Constant Market Share para as exportações do melão brasileiro.

Terceiro maior produtor de frutas frescas do mundo, o Brasil se destaca no mercado agrícola por apresentar um clima tropical favorável à produção de diversas frutas. O melão e a manga são exemplos de frutas frescas que apresentam grandes índices de exportação. Os estados do Ceará e do Rio Grande do Norte são responsáveis pela maior parte da produção do melão brasileiro, já o mercado da União Europeia, é responsável quase que pela totalidade da importação do melão brasileiro. O objetivo desta pesquisa é analisar a competitividade e as parcelas de mercado do melão brasileiro no mercado mundial, no período de 2003 a 2011, tomando como base o modelo Constant Market Share. Os resultados mostram a diferença de direção dos subperíodos analisados. No primeiro subperíodo, têm-se o crescimento da exportação ocasionado pelo crescimento do comércio mundial e pelo fator competitividade, diferente do segundo período em que há uma queda principalmente na competitividade ocasionando o declínio na exportação da fruta produzida no Brasil

Nanocarbon-Supported Electrocatalysts for the Alkaline Water Splitting and Fuel Cells

Electrocatalysts play a significant role in the processes of electrochemical energy conversion. This thesis focuses on the preparation of carbon-supported nanomaterials and their application as electrocatalysts for alkaline water electrocatalysis and fuel cell. A general synthetic route was developed, i.e., species intercalate into carbon layers of graphite forming graphite intercalation compound, followed by dispersion producing graphenide solution, which then as reduction agent reacts with different metal sources generating the final materials. The first metal precursor used was non-noble metal iron salt, which generated iron (oxide) nanoparticles finely dispersed on carbon layers in the final composite materials. Meanwhile, graphite starting materials differing in carbon layer size were utilized, which would diversify corresponding graphenide solutions, and further produce various nanomaterials. The characterization results showed that iron (oxide) nanoparticles varying in size were obtained, and the size was determined by the starting graphite material. It was found that they were electrocatalytically active for oxygen reactions. In particular, the one with small iron (oxide) nanoparticles showed excellent electrocatalytic activity for both oxygen reduction reaction (ORR) and oxygen evolution reaction (OER). Afterwards, the metal precursor was tuned from non-noble metal salt to noble metal salt. It was confirmed that carbon-supported Rh, Pt, and RhPt (oxide) nanoparticle composite materials were also successfully obtained from the reaction between graphenide solution and corresponding noble metal precursor. The electrochemical measurements showed that the prepared noble metal-based nanomaterials were quite effective for hydrogen evolution reaction (HER) electrocatalysis, and the Rh sample could also display excellent electrocatalytic property towards OER. Moreover, by this synthetic approach carbon-supported noble metal Pt and non-noble metal nickel (Ni) composite material was also prepared. Therefore, the utilization efficiency of noble metal could be improved. The prepared NiPt sample displayed a property close to benchmark HER electrocatalyst.

Spectral Splitting of Purely Magnetic Schrödinger Operator in 2-d

La tesi ripercorre i procedimenti utilizzati per il calcolo dell'asintotica dello splitting dell'operatore puramente magnetico di Schrödinger nel limite semiclassico (con campo magnetico costante) in un dominio aperto limitato e semplicemente connesso il cui bordo ha simmetria assiale ed esattamente due punti di curvatura massima non degeneri. Il punto di partenza è trovare stime a priori sulle sue autofunzioni, che permettono di dire che sono localizzate esponenzialmente vicino al bordo del dominio in oggetto, grazie a queste stime di riesce a modificare l'operatore in maniera tale che l'asintotica dello splitting rimanga equivalente. Si passa in seguito a coordinate tubulari, quindi si rettifica il borso del dominio, andando però a complicare il potenziale magnetico. Si ottengono nuove stime a priori per le autofunzioni. A questo punto si considera lo stesso operatore differenziale ma su un dominio modificato, in cui viene eliminato uno dei punti di curvatura massima. Per tale operatore si ha uno sviluppo asintotico delle autofunzioni (anche dette soluzioni WKB). Si utilizzano poi strumenti di calcolo pseudo-differenziale per studiare l'operatore nel nuovo dominio, ne si localizza la fase per renderlo limitato ed ottenere così una parametrice (anch'essa limitata) avente un simbolo esplicito. Se ne deducono stime di tipo ellittico che possono essere portate all'operatore senza la fase localizzata aggiungendo dei termini di errore. Grazie queste stime si riesce ad approssimare lo splitting (controllando sempre l'errore) che volevamo calcolare (quello dell'operatore sul dominio con due punti di curvatura massima) tramite le autofunzioni dell'operatore sul dominio con un solo punto di curvatura massima, e per queste autofunzioni abbiamo lo sviluppo asintotico (WKB). Considerando l'ordine principale di questi sviluppi si riesce a calcolare esplicitamente il termine dominante dello splitting, ottenendone così l'asintotica nel limite semiclassico.