Hierarchical spherical model from a geometric point of view

A continuous version of the hierarchical spherical model at dimension d=4 is investigated. Two limit distributions of the block spin variable X(gamma), normalized with exponents gamma = d + 2 and gamma=d at and above the critical temperature, are established. These results are proven by solving certain evolution equations corresponding to the renormalization group (RG) transformation of the O(N) hierarchical spin model of block size L(d) in the limit L down arrow 1 and N ->infinity. Starting far away from the stationary Gaussian fixed point the trajectories of these dynamical system pass through two different regimes with distinguishable crossover behavior. An interpretation of this trajectories is given by the geometric theory of functions which describe precisely the motion of the Lee-Yang zeroes. The large-N limit of RG transformation with L(d) fixed equal to 2, at the criticality, has recently been investigated in both weak and strong (coupling) regimes by Watanabe (J. Stat. Phys. 115:1669-1713, 2004) . Although our analysis deals only with N = infinity case, it complements various aspects of that work.

Supersymmetric extension of the quantum spherical model

In this work, we present a supersymmetric extension of the quantum spherical model, both in components and also in the superspace formalisms. We find the solution for short- and long-range interactions through the imaginary time formalism path integral approach. The existence of critical points (classical and quantum) is analyzed and the corresponding critical dimensions are determined.

Quantum spherical model with competing interactions

We analyse the phase diagram of a quantum mean spherical model in terms of the temperature T, a quantum parameter g, and the ratio p = -J(2)/J(1) where J(1) > 0 refers to ferromagnetic interactions between first-neighbour sites along the d directions of a hypercubic lattice, and J(2) < 0 is associated with competing anti ferromagnetic interactions between second neighbours along m <= d directions. We regain a number of known results for the classical version of this model, including the topology of the critical line in the g = 0 space, with a Lifshitz point at p = 1/4, for d > 2, and closed-form expressions for the decay of the pair correlations in one dimension. In the T = 0 phase diagram, there is a critical border, g(c) = g(c) (p) for d >= 2, with a singularity at the Lifshitz point if d < (m + 4)/2. We also establish upper and lower critical dimensions, and analyse the quantum critical behavior in the neighborhood of p = 1/4. 2012 (C) Elsevier B.V. All rights reserved.

Irreversible spherical model and its stationary entropy production rate

The nonequilibrium stationary state of an irreversible spherical model is investigated on hypercubic lattices. The model is defined by Langevin equations similar to the reversible case, but with asymmetric transition rates. In spite of being irreversible, we have succeeded in finding an explicit form for the stationary probability distribution, which turns out to be of the Boltzmann-Gibbs type. This enables one to evaluate the exact form of the entropy production rate at the stationary state, which is non-zero if the dynamical rules of the transition rates are asymmetric.

Stochastic quantization of the spherical model and supersymmetry.

In this work, we reported some results about the stochastic quantization of the spherical model. We started by reviewing some basic aspects of this method with emphasis in the connection between the Langevin equation and the supersymmetric quantum mechanics, aiming at the application of the corresponding connection to the spherical model. An intuitive idea is that when applied to the spherical model this gives rise to a supersymmetric version that is identified with one studied in Phys. Rev. E 85, 061109, (2012). Before investigating in detail this aspect, we studied the stochastic quantization of the mean spherical model that is simpler to implement than the one with the strict constraint. We also highlight some points concerning more traditional methods discussed in the literature like canonical and path integral quantization. To produce a supersymmetric version, grounded in the Nicolai map, we investigated the stochastic quantization of the strict spherical model. We showed in fact that the result of this process is an off-shell supersymmetric extension of the quantum spherical model (with the precise supersymmetric constraint structure). That analysis establishes a connection between the classical model and its supersymmetric quantum counterpart. The supersymmetric version in this way constructed is a more natural one and gives further support and motivations to investigate similar connections in other models of the literature.

A theory of strong and weak scintillations with applications to astrophysics

The propagation of waves in an extended, irregular medium is studied under the "quasi-optics" and the "Markov random process" approximations. Under these assumptions, a Fokker-Planck equation satisfied by the characteristic functional of the random wave field is derived. A complete set of the moment equations with different transverse coordinates and different wavenumbers is then obtained from the characteristic functional. The derivation does not require Gaussian statistics of the random medium and the result can be applied to the time-dependent problem. We then solve the moment equations for the phase correlation function, angular broadening, temporal pulse smearing, intensity correlation function, and the probability distribution of the random waves. The necessary and sufficient conditions for strong scintillation are also given.

We also consider the problem of diffraction of waves by a random, phase-changing screen. The intensity correlation function is solved in the whole Fresnel diffraction region and the temporal pulse broadening function is derived rigorously from the wave equation.

The method of smooth perturbations is applied to interplanetary scintillations. We formulate and calculate the effects of the solar-wind velocity fluctuations on the observed intensity power spectrum and on the ratio of the observed "pattern" velocity and the true velocity of the solar wind in the three-dimensional spherical model. The r.m.s. solar-wind velocity fluctuations are found to be ~200 km/sec in the region about 20 solar radii from the Sun.

We then interpret the observed interstellar scintillation data using the theories derived under the Markov approximation, which are also valid for the strong scintillation. We find that the Kolmogorov power-law spectrum with an outer scale of 10 to 100 pc fits the scintillation data and that the ambient averaged electron density in the interstellar medium is about 0.025 cm^-3. It is also found that there exists a region of strong electron density fluctuation with thickness ~10 pc and mean electron density ~7 cm^-3 between the PSR 0833-45 pulsar and the earth.

Superluminal radio source PKS 0420-014

The very long baseline interferometry result of a superluminal radio source PKS 0420-014 at 5 GHz with Shanghai (China), Urumqi (China), Note (Italy), and HartRAO (South Africa) telescopes is presented. Proper motions of the relativistic jet components in the source are calculated. Based on the Self-Compton emission in a uniform spherical model, the beaming parameters of the source are estimated. The results show that PKS 0420-014 has a high Doppler factor of 9.3, a Lorentz factor of 6.5, and a small angle of 5.5 degrees to the line of sight.

Polarization spectral synthesis for Type Ia supernova explosion models

We present a Monte Carlo radiative transfer technique for calculating synthetic spectropolarimetry for multidimensional supernova explosion models. The approach utilizes 'virtual-packets' that are generated during the propagation of the Monte Carlo quanta and used to compute synthetic observables for specific observer orientations. Compared to extracting synthetic observables by direct binning of emergent Monte Carlo quanta, this virtual-packet approach leads to a substantial reduction in the Monte Carlo noise. This is not only vital for calculating synthetic spectropolarimetry (since the degree of polarization is typically very small) but also useful for calculations of light curves and spectra. We first validate our approach via application of an idealized test code to simple geometries. We then describe its implementation in the Monte Carlo radiative transfer code ARTIS and present test calculations for simple models for Type Ia supernovae. Specifically, we use the well-known one-dimensional W7 model to verify that our scheme can accurately recover zero polarization from a spherical model, and to demonstrate the reduction in Monte Carlo noise compared to a simple packet-binning approach. To investigate the impact of aspherical ejecta on the polarization spectra, we then use ARTIS to calculate synthetic observables for prolate and oblate ellipsoidal models with Type Ia supernova compositions.

Spatial analysis of the distribution of Spodoptera frugiperda (J.E. Smith) (Lepidoptera: Noctuidae) and losses in maize crop productivity using geostatistics

A lagarta-do-cartucho, Spodoptera frugiperda (J.E. Smith), é uma das principais pragas do milho nas Américas. O estudo de sua distribuição espacial é fundamental para a utilização de estratégias de controle, otimização de técnicas de amostragens, determinação de danos econômicos e incorporação de um programa de agricultura de precisão. em uma área cultivada com milho foram realizadas amostragens com intervalo semanal, correspondendo ao estádio vegetativo que compreende desde a germinação até o pendoamento. Foram amostradas 10 plantas ao acaso por parcela, no total de 2000 plantas em cada amostragem. A produtividade foi obtida através da colheita de todas as parcelas que eram pesadas separadamente no campo e em cada parcela foram coletadas 15 espigas aleatoriamente para estimar o comprimento e o diâmetro médio. As análises espaciais, utilizando geoestatística, mostraram que o modelo esférico apresentou o melhor ajuste às lagartas pequenas. À medida que as lagartas foram se desenvolvendo sua distribuição foi tornando aleatória, representada por um modelo ajustado por uma reta, não tendo sido detectado nenhum tipo de dependência espacial nos pontos de amostragem. A produtividade e o diâmetro e comprimento da espiga foram descritos por modelos esféricos, indicando uma variabilidade espacial nos parâmetros de produtividade na área cultivada. A geoestatística mostrou-se promissora para a aplicação de métodos precisos no controle integrado de pragas.

Modelagem da variação horária da temperatura do ar em Petrolina, PE, e Botucatu, SP

The air temperature is a climatic element of interest for several agricultural related studies. Hence, daily air temperature from two locations in Brazil (Botucatu and Petrolina, with different climate classification), hourly recorded from January 2004 to December 2005, were analysed to verify if 24 h long air temperature variation can be predicted with 6 h interval records. Three data set were selected, with different first time record of air temperature, and analyses performed using geoestatistics to confirm the temporal dependency of records. Then, ordinary krigging was used to model air temperature variation within 1 h interval, and spherical model presented the best approach, with range of 11.6 h for Botucatu and 12.7 for Petrolina. For both locations, the time of air temperature recording was the most importnat factor on accuracy of estimation of air temperature variation. Records at 2, 8, 14 and 20 h and at 4, 10, 16 and 22 h presented the best approaches, but for records at 9, 15 and 21 h, the approach was worst.

Variabilidade espacial da resistência do solo à penetração e do teor de água em sistema de plantio direto na cultura da soja

A harmful and limiting factor regarding culture productivity is soil compaction, a parameter that can be quantified by the resistance of the soil to penetration and highly influenced by water content. These variables present spatial and temporary variability, characteristics which can be determined by the geostatistical technique. In the light of the above, the present work had as its objective the study of spatial variability of soil resistance to penetration (RP) and water content in the soil (U) in soy culture. The RP values at depths of 0,00-0,10; 0,11-0,20 and 0,21-0,30 m varied from 2,9 to 4,28 MPa and are considered harmful to the root development of legumes, although they have not influenced soy productivity which was 3887 kg ha(-1). The medium water content of the soil was between 0,210 and 0,213 kg kg(-1) for the three depths studied. The resistance of the soil to penetration, expressed through semivariograms, presented spatial dependence at all depths, being adjusted to the spherical model at depths of 0,00-0,10m and exponential at depths of 0,110,20 and 0,21-0,30 m. The spatial variability for all studied layers presented a range of about 20m. The water content in the soil did not present spatial dependence for the depths, presenting randomized distribution.

Calculo de reserva de uma jazida de carvao por metodologia geoestatistica

A coal deposit was studied at Sapopema (PR) in the upper part of the Tubarao Group. The eliptical deposit is made up by a single layer of 1.2 m mean thickness and lies at a depth of 380 to 700 m. The semi-variogram, using the spherical model, revealed a range of 1.5 km and no nugget effect. Area kriging estimation for a grid of 0.5 × 0.5 km showed a value of 50.121.750 ton, very close to the real reserve one. -from English summary

Dinâmica populacional de mosca-negra-dos-citros (Aleurocanthus woglumi Ashby, 1915) em pomares de citros em sistema agroflorestal e monocultura

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Spatial distribution of Yellow Sigatoka Leaf Spot correlated with soil fertility and plant nutrition

This study analyzed the spatial distribution of Yellow Sigatoka Leaf Spot relative to soil fertility and plant nutritional status using geostatistics. The experimental area comprised 1.2 ha, where 27 points were georeferenced and spaced on a regular grid 18 × 18 m. The severity of Yellow Sigatoka, soil fertility and plant nutritional status were evaluated at each point. The spherical model was adjusted for all variables using restricted maximum likelihood. Kriging maps showed the highest infection rate of Sigatoka occurred in high areas of the field which had the highest concentration of sand, while the lowest disease was found in lower areas with lower silt, organic matter, total exchangeable bases, effective cation exchange capacity, base saturation, Ca and Mg in soil, and foliar sulfur (S). These results may help farmers manage Yellow Sigatoka disease more effectively, with balanced fertilization and reduced fungicide application. This practice minimizes the environmental impact and cost of production while contributing to production sustainability.

Variabilidade espacial dos atributos químicos do solo sob pastagem irrigada e de sequeiro: impactos na produtividade e qualidade do capim tifton 85

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)