Pion structure in the instanton liquid model

The covariant quark model of the pion based on the effective nonlocal quark-hadron Lagrangian involving nonlocality induced by instanton fluctuations of the QCD vacuum is reviewed. Explicit gauge invariant formalism allows us to construct the conserved vector and axial currents and to demonstrate their consistency with the Ward-Takahashi identities and low-energy theorems. The spontaneous breaking of chiral symmetry results in the dynamic quark mass and the vertex of the quark-pion interaction, both momentum-dependent. The parameters of the instanton vacuum, the average size of the instantons, and the effective quark mass are expressed in terms of the vacuum expectation values of the lowest dimension quark-gluon operators and low-energy pion observables. The transition pion form factor for the processes gamma*gamma --> pi (0) and gamma*gamma* --> pi (0) is analyzed in detail. The kinematic dependence of the transition form factor at high momentum transfers allows one to determine the relationship between the light-cone amplitude of the quark distribution in the pion and the quark-pion vertex function. Its dynamic dependence implies that the transition form factor gamma*gamma --> pi (0) at high momentum transfers is acutely sensitive to the size of the nonlocality of nonperturbative fluctuations in the QCD vacuum. In the leading twist, the distribution amplitude and the distribution function of the valence quarks in the pion are calculated at a low normalization point of the order of the inverse average instanton size rho (-1)(c). The QCD results are evolved to higher momentum transfers and are in reasonable agreement with available experimental data on the pion structure.

Composition and electronic structure of Zn7-xMxSb2O12 (M = Ni and Co) spinel compounds

The relation between the composition and electronic structure of the perfectly inverse spinel compound Zn7-xMxSb2O12 (M = Ni and Co) has been studied by powder X-ray diffraction and X-ray photoelectron spectroscopy. Changes in the site occupancy are associated with shifts in the core levels as observed in the core level spectral analyses. The configuration of the density of states in the valence band due to the Co and Ni states can be observed in the valence band spectra. (C) 2004 Elsevier B.V. All rights reserved.

Pion structure function within the instanton model

The leading-twist valence-quark distribution function in the pion is obtained at a low normalization scale of an order of the inverse average size of an instanton pc. The momentum dependent quark mass and the quark-pion vertex are constructed in the framework of the instanton liquid model, using a gauge invariant approach. The parameters of instanton vacuum, the effective instanton radius and quark mass, are related to the vacuum expectation values of the lowest dimension quark-gluon operators and to the pion low energy observables. An analytic expression for the quark distribution function in the pion for a general vertex function is derived. The results are QCD evolved to higher momentum-transfer values, and reasonable agreement with phenomenological analyses of the data on parton distributions for the pion is found. ©2000 The American Physical Society.

Spatial variability structure of soil CO2 emission and soil attributes in a sugarcane area

Soil CO2 emission (F-CO2) is influenced by chemical, physical and biological factors that affect the production of CO2 in the soil and its transport to the atmosphere. F-CO2 varies in time and space depending on environmental conditions, including the management of the agricultural area. The aim of this study was to investigate the spatial variability structure of F-CO2 and soil attributes in a mechanically harvested sugarcane area (green harvest) using fractal dimension (D-F) derived from isotropic variograms at different scales (fractograms). F-CO2 showed an overall average of 1.51 mu mol CO2 m(-2) s(-1) and correlated significantly (P < 0.05) with soil physical attributes, such as soil bulk density, air-filled pore space, macroporosity and microporosity. Topologically significant DF values were obtained from the characterization of F-CO2 at medium and large scales (above 20 m), with values of 2.92 and 2.90, respectively. The variations in D-F with scales indicate that the spatial variability structure of F-CO2 was similar to that observed for soil temperature and total pore volume and was the inverse of that observed for other soil attributes, such as soil moisture, soil bulk density, microporosity, air-filled pore space, silt and clay content, pH, available phosphorus and the sum of bases. Thus, the spatial variability structure of F-CO2 presented a significant relationship with the spatial variability structure for most soil attributes, indicating the possibility of using fractograms as a tool to better describe the spatial dependence of variables along the scale. (C) 2014 Elsevier B.V. All rights reserved.