Analytical and numerical studies of disordered spin-1 Heisenberg chains with aperiodic couplings

We investigate the low-temperature properties of the one-dimensional spin-1 Heisenberg model with geometric fluctuations induced by aperiodic but deterministic coupling distributions, involving two parameters. We focus on two aperiodic sequences, the Fibonacci sequence and the 6-3 sequence. Our goal is to understand how these geometric fluctuations modify the physics of the (gapped) Haldane phase, which corresponds to the ground state of the uniform spin-1 chain. We make use of different adaptations of the strong-disorder renormalization-group (SDRG) scheme of Ma, Dasgupta and Hu, widely employed in the study of random spin chains, supplemented by quantum Monte Carlo and density-matrix renormalization-group numerical calculations, to study the nature of the ground state as the coupling modulation is increased. We find no phase transition for the Fibonacci chain, while we show that the 6-3 chain exhibits a phase transition to a gapless, aperiodicity-dominated phase similar to the one found for the aperiodic spin-1/2 XXZ chain. Contrary to what is verified for random spin-1 chains, we show that different adaptations of the SDRG scheme may lead to different qualitative conclusions about the nature of the ground state in the presence of aperiodic coupling modulations.Comment: Accepted for publication in Physical Review

Os estudos sobre o Ciclo Confederativo e a História da Integração latino-americana no século XIX

Os esforços de integração das nações latino-americanas ocorreram imediatamente após os processos de independência das colônias da América e ficaram conhecidos como Ciclo Confederativo Latino-americano. Fortemente influenciado pelas anfictionias europeias, o ciclo reuniu as nações recém emancipadas pela primeira vez no Congresso do Panamá, em 1826. Apesar das intenções integracionistas, malogrou precocemente diante de inúmeros conflitos entre os países, da resistência de grupos locais, das pressões dos Estados Unidos, entre outros fatores. Os objetivos deste trabalho são conhecer os principais aspectos e elementos que configuram o Ciclo Confederativo e analisar os estudos sobre o tema da integração latino-americana a partir da perspectiva singular do historiador mexicano, Gérman Adolfo de la Reza

Mathematical Modeling of Flowback Water Treatment Using Reverse Osmosis and Nanofiltration Technologies

The main objective of this study is to assess, through mathematical modeling, the potential use and feasibility of deploying nanofiltration and reverse osmosis technologies in the treatment of flowback water. Field data of flowback water flow rates and chemical composition were used in the models in order to provide an accurate assessment of each technology. Operating conditions based on the current commercial reverse osmosis and nanofiltration membranes for water treatment were also considered. Mathematical models for the reverse osmosis and nanofiltration processes were developed to assess the performance of these processes in the treatment of flowback water produced during the hydraulic fracturing for natural gas production from shale plays. The models, based on the mass balance and thermodynamics, were verified and implemented in Matlab version R2015. The models were used to perform a sensitivity analysis for the two processes in order to determine the effect of the operating variables on the membrane performance in terms of solute concentration and filtration time. For the reverse osmosis, it was found that pressure drop, inlet flow rate and membrane area were the major parameters governing the process. For nanofiltration, on the other hand, pressure drop, reflection coefficient and membrane area were the most important parameters affecting the process performance. The models were also used to assess and compare the performance of four different commercial reverse osmosis and three nanofiltration membranes using actual field data, such as inlet flowrate and flowback water composition. The predictions of the two models showed that the reverse osmosis was significantly superior to the nanofiltration membranes in the removal of Na+ and Ca2+. Nanofiltration membranes, however, exhibited higher removal efficiencies for Cl- than that of the reverse osmosis membranes. This behavior was attributed primarily to the nature of both processes; since the reverse osmosis is mainly driven by the chemical potential of chlorine, whereas, the nanofiltration is controlled by the molecule size

City of Casa Grande special election: 2005 mail ballot election water franchise election

3 pages

Dimer models on planar lattice. Transfer matrix and soutions by fermion representation

Resolvemos o modelo de d´meros em duas redes planas diferentes, a rede 4-8 e a rede hexagonal (favo de mel). Na rede 4-8 ocorre uma transição do tipo Ising (bidimensional); na rede hexagonal há uma transição conhecida como 3/2. Após a definição do modelo mostramos que o cálculo da função de partição pode ser formulado em termos do traço de uma matriz de transferência escrita numa representação de matrizes de Pauli. Usando a transformação de Jordan-Wigner, os operadores de Pauli são transformados em operadores de criação e aniquilação de férmions, e a matriz de transferência pode ser diagonalizada pela redução a um problema de férmions livres. Comparamos as soluções do modelo de dímeros na rede 4-8 e do modelo de Ising bidimensional; em particular, comparamos o comportamento do calor específico e analisamos o espectro da matriz de transferência. Verificamos que as nossas soluções concordam com resultados obtidos pelas técnicas combinatórias. Utilizamos a formulação da matriz de transferência para construir uma versão de tempo contínuo dos modelos de dímeros nas redes quadrada, 4-8 e hexagonal. Ao contrário do modelo de Ising, no caso dos dímeros essa aproximação de tempo contínuo altera a natureza do comportamento crítico.We solve the dimer model on two different planar lattices, the 4-8 lattice and the honeycomb lattice. In the dimer model on the 4-8 lattice there is a phase transition of the (two-dimensional) Ising type; on the honeycomb lattice there is a phase transition known as 3/2. After defining the model we show that the calculation of the partition function can be formulated as the trace of a transfer matrix that is written in terms of Pauli matrices. Using the Jordan-Wigner transformation, the Pauli matrices give rise to fermion creation and annihilation operators, and the problem is reduced to the diagonalization of a system of free fermions. We compare the solutions of the dimer model on the 4-8 lattice and of the two-dimensional Ising model; in particular, we compare the behavior of the specific heat and we analyze the spectrum of the transfer matrix. These solutions agree with well-known results from combinatorial techniques. We then use the transfer matrix approach to obtain a continuum time formulation for the dimer models on the square, 4-8 an d honeycomb lattices. In contrast to the Ising case, for the dimer models this approximation changes the nature of critical behavior

Analytical and numerical studies of disordered spin-1 Heisenberg chains with aperiodic couplings.

Investigamos as propriedades de baixa temperatura do modelo de Heisenberg unidimensional de spin 1 desordenado, com flutuações geométricas nos acoplamentos induzidas por sequências aperiódicas e determinísticas. Escolhemos duas sequências com propriedades distintas, a sequência de Fibonacci e a sequência 6-3. Nosso objetivo é entender como essas flutuações geométricas modificam a física da fase de Haldane, que corresponde ao estado fundamental da cadeia de spin 1 uniforme. Introduzimos deferentes adaptações do grupo de renormalização de desordem forte (SDRG) de Ma, Dasgupta e Hu, que tem sido amplamente usado no estudo de cadeias de spin aleatórias. Usamos ainda simulações numéricas de Monte Carlo quântico e do grupo de renormalização da matriz densidade para confirmar as previsões do SDRG, assim como estudar as propriedades do estado fundamental, conforme a modulação se torna mais forte. Não encontramos uma transição de fase para a cadeia modulada pela sequência de Fibonacci, enquanto para a cadeia modulada pela sequência 6-3 encontramos uma transição para uma fase sem gap, dominada pela aperiodicidade, similar àquela encontrada na cadeia XXZ de spin 1/2. Mostramos que abordagens que preveem o mesmo comportamento qualitativo na cadeia aleatória de spin 1 podem levar a previsões qualitativamente incompatíveis na cadeia aperiódica.We investigate the low-temperature properties of the one-dimensional spin-1 Heisenberg model with geometric fluctuations induced by aperiodic but deterministic coupling distributions, involving two parameters. We focus on two aperiodic sequences, the Fibonacci sequence and the 6-3 sequence. Our goal is to understand how these geometric fluctuations modify the physics of the (gapped) Haldane phase, which corresponds to the ground state of the uniform spin-1 chain. We utilize different adaptations of the strong-disorder renormalization-group (SDRG) scheme of Ma, Dasgupta and Hu, widely employed in the study of random spin chains, supplemented by quantum Monte Carlo and density-matrix renormalization-group numerical calculations, to study the nature of the ground state as the coupling modulation is increased. We find no phase transition for the Fibonacci chain, while we show that the 6-3 chain exhibits a phase transition to a gapless, aperiodicity-dominated phase similar to that found for the aperiodic spin-1/2 XXZ chain. We show that approaches providing the same qualitative behaviour in the random spin-1 chain may lead to qualitatively incompatible predictions in aperiodic chain