Secondary nontwist phenomena in area-preserving maps

Phenomena as reconnection scenarios, periodic-orbit collisions, and primary shearless tori have been recognized as features of nontwist maps. Recently, these phenomena and secondary shearless tori were analytically predicted for generic maps in the neighborhood of the tripling bifurcation of an elliptic fixed point. In this paper, we apply a numerical procedure to find internal rotation number profiles that highlight the creation of periodic orbits within islands of stability by a saddle-center bifurcation that emerges out a secondary shearless torus. In addition to the analytical predictions, our numerical procedure applied to the twist and nontwist standard maps reveals that the atypical secondary shearless torus occurs not only near a tripling bifurcation of the fixed point but also near a quadrupling bifurcation. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4750040]

Divertor map with freedom of geometry and safety factor profile

An explicit, area-preserving and integrable magnetic field line map for a single-null divertor tokamak is obtained using a trajectory integration method to represent equilibrium magnetic surfaces. The magnetic surfaces obtained from the map are capable of fitting different geometries with freely specified position of the X-point, by varying free model parameters. The safety factor profile of the map is independent of the geometric parameters and can also be chosen arbitrarily. The divertor integrable map is composed of a nonintegrable map that simulates the effect of external symmetry-breaking resonances, so as to generate a chaotic region near the separatrix passing through the X-point. The composed field line map is used to analyze escape patterns (the connection length distribution and magnetic footprints on the divertor plate) for two equilibrium configurations with different magnetic shear profiles at the plasma edge.

Scaling invariance for the escape of particles from a periodically corrugated waveguide

The escape dynamics of a classical light ray inside a corrugated waveguide is characterised by the use of scaling arguments. The model is described via a two-dimensional nonlinear and area preserving mapping. The phase space of the mapping contains a set of periodic islands surrounded by a large chaotic sea that is confined by a set of invariant tori. When a hole is introduced in the chaotic sea, letting the ray escape, the histogram of frequency of the number of escaping particles exhibits rapid growth, reaching a maximum value at n(p) and later decaying asymptotically to zero. The behaviour of the histogram of escape frequency is characterised using scaling arguments. The scaling formalism is widely applicable to critical phenomena and useful in characterisation of phase transitions, including transitions from limited to unlimited energy growth in two-dimensional time varying billiard problems. (C) 2011 Elsevier B.V. All rights reserved.

COMPARISON MEASURES OF MAPS GENERATED BY GEOSTATISTICAL METHODS

This study uses several measures derived from the error matrix for comparing two thematic maps generated with the same sample set. The reference map was generated with all the sample elements and the map set as the model was generated without the two points detected as influential by the analysis of local influence diagnostics. The data analyzed refer to the wheat productivity in an agricultural area of 13.55 ha considering a sampling grid of 50 x 50 m comprising 50 georeferenced sample elements. The comparison measures derived from the error matrix indicated that despite some similarity on the maps, they are different. The difference between the estimated production by the reference map and the actual production was of 350 kilograms. The same difference calculated with the mode map was of 50 kilograms, indicating that the study of influential points is of fundamental importance to obtain a more reliable estimative and use of measures obtained from the error matrix is a good option to make comparisons between thematic maps.

Comparison measures of maps generated by geostatistical methods

This study uses several measures derived from the error matrix for comparing two thematic maps generated with the same sample set. The reference map was generated with all the sample elements and the map set as the model was generated without the two points detected as influential by the analysis of local influence diagnostics. The data analyzed refer to the wheat productivity in an agricultural area of 13.55 ha considering a sampling grid of 50 x 50 m comprising 50 georeferenced sample elements. The comparison measures derived from the error matrix indicated that despite some similarity on the maps, they are different. The difference between the estimated production by the reference map and the actual production was of 350 kilograms. The same difference calculated with the mode map was of 50 kilograms, indicating that the study of influential points is of fundamental importance to obtain a more reliable estimative and use of measures obtained from the error matrix is a good option to make comparisons between thematic maps.

Spatial variability of soil fertility and its relationship with seed physiological potential in a soybean production area

The correlation of soil fertility x seed physiological potential is very important in the area of seed technology but results published with that theme are contradictory. For this reason, this study to evaluate the correlations between soil chemical properties and physiological potential of soybean seeds. On georeferenced points, both soil and seeds were sampled for analysis of soil fertility and seed physiological potential. Data were assessed by the following analyses: descriptive statistics; Pearson's linear correlation; and geostatistics. The adjusted parameters of the semivariograms were used to produce maps of spatial distribution for each variable. Organic matter content, Mn and Cu showed significant effects on seed germination. Most variables studied presented moderate to high spatial dependence. Germination and accelerated aging of seeds, and P, Ca, Mg, Mn, Cu and Zn showed a better fit to spherical semivariogram: organic matter, pH and K had a better fit to Gaussian model; and V% and Fe showed a better fit to the linear model. The values for range of spatial dependence varied from 89.9 m for P until 651.4 m for Fe. These values should be considered when new samples are collected for assessing soil fertility in this production area.

Vegetation mapping in an area of Ombrophilous Dense Forest at Parque Estadual da Serra do Mar, São Paulo State, Brazil, and floristic composition of the tree component of some physiognomies*

This study aimed to map phytophysiognomies of an area of Ombrophilous Dense Forest at Parque Estadual da Serra do Mar and characterize their floristic composition. Photointerpretation of aerial photographs in scale of 1:35,000 was realized in association with field work. Thirteen physiognomies were mapped and they were classified as Montane Ombrophilous Dense Forest, Alluvial Ombrophilous Dense Forest or Secondary System. Three physiognomies identified at Casa de Pedra streamlet's basin were studied with more details. Riparian forest (RF), valley forest (VF), and hill forest (HF) presented some floristic distinction, as confirmed by Detrended Correspondence Analysis (DCA) and Indicator Species Analysis (ISA) conducted here. Anthropic or natural disturbances and heterogeneity of environmental conditions may be the causes of physiognomic variation in the vegetation of the region. The results presented here may be useful to decisions related to management and conservation of Núcleo Santa Virgínia forests, in general.