Energy-level statistics of interacting trapped bosons

It is a well-established fact that statistical properties of energy-level spectra are the most efficient tool to characterize nonintegrable quantum systems. The statistical behavior of different systems such as complex atoms, atomic nuclei, two-dimensional Hamiltonians, quantum billiards, and noninteracting many bosons has been studied. The study of statistical properties and spectral fluctuations in interacting many-boson systems has developed interest in this direction. We are especially interested in weakly interacting trapped bosons in the context of Bose-Einstein condensation (BEC) as the energy spectrum shows a transition from a collective nature to a single-particle nature with an increase in the number of levels. However this has received less attention as it is believed that the system may exhibit Poisson-like fluctuations due to the existence of an external harmonic trap. Here we compute numerically the energy levels of the zero-temperature many-boson systems which are weakly interacting through the van der Waals potential and are confined in the three-dimensional harmonic potential. We study the nearest-neighbor spacing distribution and the spectral rigidity by unfolding the spectrum. It is found that an increase in the number of energy levels for repulsive BEC induces a transition from a Wigner-like form displaying level repulsion to the Poisson distribution for P(s). It does not follow the Gaussian orthogonal ensemble prediction. For repulsive interaction, the lower levels are correlated and manifest level-repulsion. For intermediate levels P(s) shows mixed statistics, which clearly signifies the existence of two energy scales: external trap and interatomic interaction, whereas for very high levels the trapping potential dominates, generating a Poisson distribution. Comparison with mean-field results for lower levels are also presented. For attractive BEC near the critical point we observe the Shnirelman-like peak near s = 0, which signifies the presence of a large number of quasidegenerate states.

Simulação tridimensional adaptativa da separação das fases de uma mistura bifásica usando a equação de Cahn-Hilliard

Simulamos a separação dos componentes de uma mistura bifásica com a equação de Cahn-Hilliard. Esta equação contém intrincados termos não lineares e derivadas de alta ordem. Além disso, a delgada região de transição entre os componentes da mistura requer muita resolução. Assim, determinar a solução numérica da equação de Cahn-Hilliard não é uma tarefa fácil, principalmente em três dimensões. Conseguimos a resolução exigida no tempo usando uma discretização semi-implícita de segunda ordem. No espaço, obtemos a precisão requerida utilizando malhas refinadas localmente com a estratégia AMR. Essas malhas se adaptam dinamicamente para recobrir a região de transição. O sistema linear proveniente da discretização é solucionado por intermédio de técnicas multinível-multigrid.

A stochastic spatially structured epidemic model with diffusive processes

We developed a stochastic lattice model to describe the vector-borne disease (like yellow fever or dengue). The model is spatially structured and its dynamical rules take into account the diffusion of vectors. We consider a bipartite lattice, forming a sub-lattice of human and another occupied by mosquitoes. At each site of lattice we associate a stochastic variable that describes the occupation and the health state of a single individual (mosquito or human). The process of disease transmission in the human population follows a similar dynamic of the Susceptible-Infected-Recovered model (SIR), while the disease transmission in the mosquito population has an analogous dynamic of the Susceptible-Infected-Susceptible model (SIS) with mosquitos diffusion. The occurrence of an epidemic is directly related to the conditional probability of occurrence of infected mosquitoes (human) in the presence of susceptible human (mosquitoes) on neighborhood. The probability of diffusion of mosquitoes can facilitate the formation of pairs Susceptible-Infected enabling an increase in the size of the epidemic. Using an asynchronous dynamic update, we study the disease transmission in a population initially formed by susceptible individuals due to the introduction of a single mosquito (human) infected. We find that this model exhibits a continuous phase transition related to the existence or non-existence of an epidemic. By means of mean field approximations and Monte Carlo simulations we investigate the epidemic threshold and the phase diagram in terms of the diffusion probability and the infection probability.

Pair approximation for a model of vertical and horizontal transmission of parasites.

We apply Stochastic Dynamics method for a differential equations model, proposed by Marc Lipsitch and collaborators (Proc. R. Soc. Lond. B 260, 321, 1995), for which the transmission dynamics of parasites occurs from a parent to its offspring (vertical transmission), and by contact with infected host (horizontal transmission). Herpes, Hepatitis and AIDS are examples of diseases for which both horizontal and vertical transmission occur simultaneously during the virus spreading. Understanding the role of each type of transmission in the infection prevalence on a susceptible host population may provide some information about the factors that contribute for the eradication and/or control of those diseases. We present a pair mean-field approximation obtained from the master equation of the model. The pair approximation is formed by the differential equations of the susceptible and infected population densities and the differential equations of pairs that contribute to the former ones. In terms of the model parameters, we obtain the conditions that lead to the disease eradication, and set up the phase diagram based on the local stability analysis of fixed points. We also perform Monte Carlo simulations of the model on complete graphs and Erdös-Rényi graphs in order to investigate the influence of population size and neighborhood on the previous mean-field results; by this way, we also expect to evaluate the contribution of vertical and horizontal transmission on the elimination of parasite. Pair Approximation for a Model of Vertical and Horizontal Transmission of Parasites.

Use of recent geoid models to estimate mean dynamic topography and geostrophic currents in South Atlantic and Brazil Malvinas confluence

The use of geoid models to estimate the Mean Dynamic Topography was stimulated with the launching of the GRACE satellite system, since its models present unprecedented precision and space-time resolution. In the present study, besides the DNSC08 mean sea level model, the following geoid models were used with the objective of computing the MDTs: EGM96, EIGEN-5C and EGM2008. In the method adopted, geostrophic currents for the South Atlantic were computed based on the MDTs. In this study it was found that the degree and order of the geoid models affect the determination of TDM and currents directly. The presence of noise in the MDT requires the use of efficient filtering techniques, such as the filter based on Singular Spectrum Analysis, which presents significant advantages in relation to conventional filters. Geostrophic currents resulting from geoid models were compared with the HYCOM hydrodynamic numerical model. In conclusion, results show that MDTs and respective geostrophic currents calculated with EIGEN-5C and EGM2008 models are similar to the results of the numerical model, especially regarding the main large scale features such as boundary currents and the retroflection at the Brazil-Malvinas Confluence.

Scalar field description for parametric models of dark energy

We investigate theoretical and observational aspects of a time-dependent parameterization for the dark energy equation of state w(z), which is a well behaved function of the redshift z over the entire cosmological evolution, i.e., z is an element of [-1, infinity). By using a theoretical algorithm of constructing the quintes-sence potential directly from the w(z) function, we derive and discuss the general features of the resulting potential for the cases in which dark energy is separately conserved and when it is coupled to dark matter. Since the parameterization here discussed allows us to divide the parametric plane in defined regions associated to distinct classes of dark energy models, we use some of the most recent observations from type Ia supernovae, baryon acoustic oscillation peak and Cosmic Microwave Background shift parameter to check which class is observationally preferred. We show that the largest portion of the confidence contours lies into the region corresponding to a possible crossing of the so-called phantom divide line at some point of the cosmic evolution.

Holographic field theory models of dark energy in interaction with dark matter

We discuss two Lagrangian interacting dark energy models in the context of the holographic principle. The potentials of the interacting fields are constructed. The models are compared with CMB distance information, baryonic acoustic oscillations, lookback time and the Constitution supernovae sample. For both models, the results are consistent with a nonvanishing interaction in the dark sector of the Universe and the sign of coupling is consistent with dark energy decaying into dark matter, alleviating the coincidence problem-with more than 3 standard deviations of confidence for one of them. However, this is because the noninteracting holographic dark energy model is a bad fit to the combination of data sets used in this work as compared to the cosmological constant with cold dark matter model, so that one needs to introduce the interaction in order to improve this model.

Validation of models for predicting milk urea nitrogen concentrations, estimating dry matter intake by the NRC (2001)

The objective of this study was to validate three different models for predicting milk urea nitrogen using field conditions, attempting to evaluate the nutritional adequacy diets for dairy cows and prediction of nitrogen excreted to the environment. Observations (4,749) from 855 cows were used. Milk yield, body weight (BW), days in milk and parity were recorded on the milk sampling days. Milk was sampled monthly, for analysis of milk urea nitrogen (MUN), fat, protein, lactose and total solids concentration and somatic cells count. Individual dry matter intake was estimated using the NRC (2001). The three models studied were derived from a first one to predict urinary nitrogen (UN). Model 1 was MUN = UN/12.54, model 2 was MUN = UN/17.6 and model 3 was MUN = UN/(0.0259 × BW), adjusted by body weight effect. To evaluate models, they were tested for accuracy, precision and robustness. Despite being more accurate (mean bias = 0.94 mg/dL), model 2 was less precise (residual error = 4.50 mg/dL) than model 3 (mean bias = 1.41 and residual error = 4.11 mg/dL), while model 1 was the least accurate (mean bias = 6.94 mg/dL) and the least precise (residual error = 5.40 mg/dL). They were not robust, because they were influenced by almost all the variables studied. The three models for predicting milk urea nitrogen were different with respect to accuracy, precision and robustness.

Use of recent geoid models to estimate mean dynamic topography and geostrophic currents in South Atlantic and Brazil Malvinas confluence

The use of geoid models to estimate the Mean Dynamic Topography was stimulated with the launching of the GRACE satellite system, since its models present unprecedented precision and space-time resolution. In the present study, besides the DNSC08 mean sea level model, the following geoid models were used with the objective of computing the MDTs: EGM96, EIGEN-5C and EGM2008. In the method adopted, geostrophic currents for the South Atlantic were computed based on the MDTs. In this study it was found that the degree and order of the geoid models affect the determination of TDM and currents directly. The presence of noise in the MDT requires the use of efficient filtering techniques, such as the filter based on Singular Spectrum Analysis, which presents significant advantages in relation to conventional filters. Geostrophic currents resulting from geoid models were compared with the HYCOM hydrodynamic numerical model. In conclusion, results show that MDTs and respective geostrophic currents calculated with EIGEN-5C and EGM2008 models are similar to the results of the numerical model, especially regarding the main large scale features such as boundary currents and the retroflection at the Brazil-Malvinas Confluence.