As more emphasis is put on biodiversity conservation, how best to select a system of protected areas for wildlife conservation is an issue of great importance. There is a rich economics literature on the reserve site selection problem. However, most economic studies assume the independence of risks that affect wildlife species, leaving the issue of spatially correlated risk largely unexplored. This study contributes to the literature in twoaspects. First, this study incorporates spatially correlated risk, into a reserve site selection model. And second, this study incorporates heterogeneous spatial risk, in the context of land development risk in Virginia, both with and without a budget constraint. To evaluate the significance of spatially correlated risk in conservation design, I apply the reserve site selection model to a Virginia landscape. In a basic setting, a hazard is introduced which is allowed to spread to adjacent land parcels, where I investigate the impact of spatially correlated risk at three spatial scales: one-county, four-county, and state-level. Optimal reserve designs are characterized by similar spatial patterns indicating that spatially correlated risk plays an important role in the selection of parcels for reserve. Specifically, as spatially correlated risk increases, I find that, in general, reserve connectivity decreases. I also examine a setting with heterogeneous risk and observe similar patterns in the optimal reserve design. I find that the reserve becomes more dispersed in higher risk areas primarily. Finally, I explore the tradeoffs between species protection and budget constraints in the presence of heterogeneous spatial risk. All comparative statics indicate that spatial correlated risk plays an important role in conservation reserve design. / Master of Science

Yes / Thermal desolvation of poly(N‐isopropylacrylamide) (PNIPAM) in the presence of a low concentration of gold nanoparticles incorporates the nanoparticles resulting in suspended aggregates. By covalently incorporating <1% acenaphthylene into the polymerization feed this copolymer is enabled to be used as a model to study the segmental mobility of the PNIPAM backbone in response to gold nanoparticles both below and above the desolvation temperature, showing that there is a physical conformational rearrangement of the soluble polymer at ultralow nanoparticle loadings, indicating low affinity interactions with the nanoparticles. Thermal desolvation is capable of extracting >99.9% of the nanoparticles from their solutions and hence demonstrates that poly(N‐isopropylacrylamide) can act as an excellent scrubbing system to remove metallic nanomaterial pollutants from solution. / Science Foundation Ireland's ETS. Grant Number: 11/W.I/12085; MRC. Grant Number: MR/N501888/2

Nesta tese são propostas duas distribuições discretas: COM-Poisson correlacionada (CPC) e COM-Poisson generalizada parcialmente correlacionada (CPGPC). Também foram propostos modelos de regressão para a distribuição Poisson generalizada parcialmente correlacionada (PGPC) (proposto por Luceño (1995)). Calculamos a função massa de probabilidade (fmp) para todas as distribuições com duas parametrizações. As distribuições foram construídas usando a mesma expansão feita por (Luceño, 1995) na construção da distribuição Poisson generalizada parcialmente correlacionada. A distribuição CPC(l;f;r) é a mesma expansão da distribuição COM-Poisson zero inflacionada ZICMP(m;f;r). Para a distribuição CPGPC(l;f;r;L;K) foi determinada a função característica, função geradora de probabilidade, momentos e a estimação pelo método de máxima verossimilhança para as duas parametrizações. Fizemos a fmp, quantil e gerador de números aleatórios das distribuições citadas no programa R. / In this thesis two discrete distributions are proposed: Correlated COM-Poisson (CPC) and Generalized partially correlated COM-Poisson (CPGPC). We have also proposed regression models for the Generalized partially correlated Poisson distribution (PGPC) (proposed by Luceño (1995)). We calculated the probability mass function for all distributions with two parametrizations. The distributions were constructed using the same expansion made by Luceño (1995) in the construction of the correlated generalized Poisson distribution. The CPC(l;f;r) Correlated COM-Poisson distribution is the same expansion of the zero-inflated COM-Poisson distribution ZICMP(m;f;r). For the CPGPC(l;f;r;L;K) Generalized partially correlated COM-Poisson distribution, the characteristic function, probability-generating function, moments, and the maximum likelihood estimation for the two parametrizations were determined. We performed the probability mass function, quantile and random number generator of the distributions quoted in program R.

Neste trabalho exploramos o emaranhamento em sistemas de muitos férmions. Para o estudo de sistemas inomogêneos, propusemos uma aproximação de densidade local (LDA) para a entropia de emaranhamento de um único sítio com o restante do sistema e uma LDA para o emaranhamento entre blocos de sítios. Analisamos as contribuições universal e não-universal do emaranhamento entre blocos e obtivemos uma expressão para o termo não-universal. Usando o modelo de Hubbard unidimensional, investigamos o emaranhamento em nanoestruturas eletrônicas, quantificando o emaranhamento de um único sítio com relação ao restante da cadeia via entropia de emaranhamento. Para o modelo de Hubbard homogêneo estudamos o comportamento do emaranhamento em função da densidade, da magnetização, da interação eletrônica e de campos magnéticos externos. Encontramos que o emaranhamento é sensível às fases metálica, isolante e supercondutora. Observamos um platô de emaranhamento na região do gap de spin e verificamos que susceptibilidade magnética e emaranhamento estão intrinsecamente relacionados. Obtendo as energias e densidades do modelo de Hubbard inomogêneo através da Teoria do Funcional da Densidade e usando nossa proposta LDA para a entropia de emaranhamento, exploramos o comportamento do emaranhamento na presença de diversas inomogeneidades: superredes, impurezas e confinamento harmônico. Verificamos que o emaranhamento sempre diminui com a inomogeneidade, embora os efeitos de cada inomogeneidade sejam completamente diferentes. Encontramos uma relação entre energias de troca e correlação, de Hartree e cinética, capaz de prever quantitativamente o emaranhamento em função de qualquer das inomogeneidades. / In this work we investigated entanglement in many-fermions systems. To explore inhomogeneous systems we proposed a local density approximation (LDA) for the single-site entanglement entropy. We analysed the universal and nonuniversal contributions to block-block entanglement and obtained an expression for the nonuniversal term. We employ a description in terms of the one-dimensional Hubbard model to investigate the entanglement in electronic nanostructures and to quantify the single-site entanglement with respect to the rest of the chain by means of the entanglement entropy. For the homogeneous Hubbard model we studied the entanglement behavior as a function of density, magnetization, electronic interaction and external magnetic fields. We found that the entanglement is sensitive to the metallic, insulating and superconducting phases. We observed an entanglement plateau in the region of the spin gap and verified that magnetic susceptibility and entanglement are intrinsically related. Energies and densities of the inhomogeneous Hubbard model, obtained from Density Functional Theory, combined with our proposal of an LDA for the entanglement entropy, were used to explore the behavior of the entanglement entropy in the presence of several inhomogeneities: superlattices, impurities and harmonic confinement. We verified that entanglement always decreases with the inhomogeneity, although the effect of each inhomogeneity is completely different. For the same model we found a relation of exchange-correlation, Hartree and kinetic energies, able to predict quantitatively the entanglement as a function of any inhomogeneity.

Neste trabalho exploramos o emaranhamento em sistemas de muitos férmions. Para o estudo de sistemas inomogêneos, propusemos uma aproximação de densidade local (LDA) para a entropia de emaranhamento de um único sítio com o restante do sistema e uma LDA para o emaranhamento entre blocos de sítios. Analisamos as contribuições universal e não-universal do emaranhamento entre blocos e obtivemos uma expressão para o termo não-universal. Usando o modelo de Hubbard unidimensional, investigamos o emaranhamento em nanoestruturas eletrônicas, quantificando o emaranhamento de um único sítio com relação ao restante da cadeia via entropia de emaranhamento. Para o modelo de Hubbard homogêneo estudamos o comportamento do emaranhamento em função da densidade, da magnetização, da interação eletrônica e de campos magnéticos externos. Encontramos que o emaranhamento é sensível às fases metálica, isolante e supercondutora. Observamos um platô de emaranhamento na região do gap de spin e verificamos que susceptibilidade magnética e emaranhamento estão intrinsecamente relacionados. Obtendo as energias e densidades do modelo de Hubbard inomogêneo através da Teoria do Funcional da Densidade e usando nossa proposta LDA para a entropia de emaranhamento, exploramos o comportamento do emaranhamento na presença de diversas inomogeneidades: superredes, impurezas e confinamento harmônico. Verificamos que o emaranhamento sempre diminui com a inomogeneidade, embora os efeitos de cada inomogeneidade sejam completamente diferentes. Encontramos uma relação entre energias de troca e correlação, de Hartree e cinética, capaz de prever quantitativamente o emaranhamento em função de qualquer das inomogeneidades. / In this work we investigated entanglement in many-fermions systems. To explore inhomogeneous systems we proposed a local density approximation (LDA) for the single-site entanglement entropy. We analysed the universal and nonuniversal contributions to block-block entanglement and obtained an expression for the nonuniversal term. We employ a description in terms of the one-dimensional Hubbard model to investigate the entanglement in electronic nanostructures and to quantify the single-site entanglement with respect to the rest of the chain by means of the entanglement entropy. For the homogeneous Hubbard model we studied the entanglement behavior as a function of density, magnetization, electronic interaction and external magnetic fields. We found that the entanglement is sensitive to the metallic, insulating and superconducting phases. We observed an entanglement plateau in the region of the spin gap and verified that magnetic susceptibility and entanglement are intrinsically related. Energies and densities of the inhomogeneous Hubbard model, obtained from Density Functional Theory, combined with our proposal of an LDA for the entanglement entropy, were used to explore the behavior of the entanglement entropy in the presence of several inhomogeneities: superlattices, impurities and harmonic confinement. We verified that entanglement always decreases with the inhomogeneity, although the effect of each inhomogeneity is completely different. For the same model we found a relation of exchange-correlation, Hartree and kinetic energies, able to predict quantitatively the entanglement as a function of any inhomogeneity.

No description available.

Studies on strongly correlated electron systems over decades have allowed physicists to discover unusual properties such as spin density waves, ferromagnetic and antiferromagnetic states with unusual ordering of spins and orbitals, and Mott insulating states, to name a few. In this thesis, the focus will be on the specific heat property of these materials exhibiting novel electronic ground states in the presence and absence of a field. The purpose of these measurements is to characterize the phase transitions into these states and the low energy excitations in these states. From measurements at the phase transitions, one can learn about the amount of order involved [i.e. entropy: ΔS = ∫Δc p/T dT], while measurements at low temperatures illuminate the excitation spectrum. In order to study the thermodynamic properties of the materials at their phase transitions, a high sensitive technique, ac-calorimetry was used. The ac-calorimeter, workhorse of our low dimensional materials lab, is based on modulating the power that heats the sample and measuring the temperature oscillations of the sample around its mean value. The in-house ac-calorimetry set up in our lab has the capability to produce a quasi-continuous readout of heat capacity as a function of temperature. A variety of single crystals were investigated using this technique and a few among them are discussed in my thesis. Since many of the crystals that are studied by our group are magnetically active, it becomes useful for us to also study them in the presence of a moderate to high magnetic field. This motivated me to design, develop, and build a heat capacity probe that would enable us to study the crystals in the presence of non-zero magnetic fields and at low temperatures. The probe helped us not only to revisit some of the studied materials and to draw firm conclusions on the previous results but also is vital in exploring the untouched territory of novel materials at high magnetic fields (~ 14 T).

In the first part of this work, we describe a theory of the ground states and charge gaps in the fractional quantum Hall states of graphene. The theory relies on knowledge of these properties for filling fractions smaller than one. Then, by the application of two mapping rules, one is able to obtain these properties for fractional quantum Hall states at arbitrary fillings, by conceiving the quantum Hall ferromagnets as vacua on which correlated electrons or correlated holes are added. The predicted charge gaps and phase transitions between different fractional quantum Hall states are in good agreement with recent experiments. In the second part, we investigate the low energy theory for the neutral Landau level of bilayer graphene. We closely analyze the way different terms in the Hamiltonian transform under the action of particle-hole conjugation symmetries, and identify several terms that are relevant in explaining the lack of such symmetry in experiments. Combining an accurate parametrization of the electronic structure of bilayer graphene with a systematic account of the impact of screening we are able to explain the absence of particle-hole symmetry reported in recent experiments. We also study the energetics of fractional quantum Hall states with coherence between n=0 and n=1 cyclotron quantum numbers, and obtain a general formula to map the two-point correlation function from their well-known counterparts made from only n=0 quantum numbers. Bilayer graphene has the potential for realizing these states which have no analogue in other two-dimensional electron systems such as Gallium Arsenide. We apply this formula to describe the properties of the n=0/n=1 coherent Laughlin state which displays nematic correlations. / text

No description available.

Ultracold atoms in optical lattices can be used to model condensed matter systems. They provide a clean, tuneable system which can be engineered to reach parameter regimes that are not accessible in condensed matter systems. Furthermore, they provide different techniques for probing the properties of these systems. This thesis presents an experimental and theoretical study of ultracold atoms in optical lattices for quantum simulation of two-dimensional systems.The first part of this thesis describes an experiment with a Bose-Einstein condensate of 87Rb loaded into a two-dimensional optical lattice. The beams that generate the optical lattice are controlled by acousto-optic deflection to provide a flexible optical lattice potential. The use of a dynamic ‘accordion’ lattice with ultracold atoms, where the spacing of the lattice is increased in both directions from 2.2 to 5.5 μm, is described. This technique allows an experiment such as quantum simulations to be performed with a lattice spacing smaller than the resolution limit of the imaging system, while allowing imaging of the atoms at individual lattice sites by subsequent expansion of the optical lattice. The optical lattice can also be rotated, generating an artificial magnetic field. Previous experiments with the rotating optical lattice are summarised, and steps to reaching the strongly correlated regime are discussed. The second part of this thesis details numerical techniques that can be used to describe strongly correlated two-dimensional systems. These systems are challenging to simulate numerically, as the exponential growth in the size of the Hilbert space with the number of particles means that they can only be solved exactly for very small systems. Recently proposed correlator product states [Phys. Rev. B 80, 245116 (2009)] provide a numerically efficient description which can be used to simulate large two-dimensional systems. In this thesis we apply this method to the two-dimensional quantum Ising model, and the Bose-Hubbard model subject to an artificial magnetic field in the regime where fractional quantum Hall states are predicted to occur.