Integral form of Yang-Mills equations and its gauge invariant conserved charges

Despite the fact that the integral form of the equations of classical electrodynamics is well known, the same is not true for non-Abelian gauge theories. The aim of the present paper is threefold. First, we present the integral form of the classical Yang-Mills equations in the presence of sources and then use it to solve the long-standing problem of constructing conserved charges, for any field configuration, which are invariant under general gauge transformations and not only under transformations that go to a constant at spatial infinity. The construction is based on concepts in loop spaces and on a generalization of the non-Abelian Stokes theorem for two-form connections. The third goal of the paper is to present the integral form of the self-dual Yang-Mills equations and calculate the conserved charges associated with them. The charges are explicitly evaluated for the cases of monopoles, dyons, instantons and merons, and we show that in many cases those charges must be quantized. Our results are important in the understanding of global properties of non-Abelian gauge theories.

NATURAL REGENERATION IN ABANDONED FIELDS FOLLOWING INTENSIVE AGRICULTURAL LAND USE IN AN ATLANTIC FOREST ISLAND, BRAZIL

The time required to regrowth a forest in degraded areas depends on how the forest is removed and on the type of land use following removal. Natural regeneration was studied in abandoned old fields after intensive agricultural land use in areas originally covered by Brazilian Atlantic Forests of the Anchieta Island, Brazil in order to understand how plant communities reassemble following human disturbances as well as to determine suitable strategies of forest restoration. The fields were classified into three vegetation types according to the dominant plant species in: 1) Miconia albicans (Sw.) Triana (Melastomataceae) fields, 2) Dicranopteris flexuosa (Schrader) Underw. (Gleicheniaceae) thickets, and 3) Gleichenella pectinata (Willd.) Ching. (Gleicheniaceae) thickets. Both composition and structure of natural regeneration were compared among the three dominant vegetation types by establishing randomly three plots of 1 x 3 m in five sites of the island. A gradient in composition and abundance of species in natural regeneration could be observed along vegetation types from Dicranopteris fern thickets to Miconia fields. The gradient did not accurately follow the pattern of spatial distribution of the three dominant vegetation types in the island regarding their proximity of the remnant forests. A complex association of biotic and abiotic factors seems to be affecting the seedling recruitment and establishment in the study plots. The lowest plant regeneration found in Dicranopteris and Gleichenella thickets suggests that the ferns inhibit the recruitment of woody and herbaceous species. Otherwise, we could not distinguish different patterns of tree regeneration among the three vegetation types. Our results showed that forest recovery following severe anthropogenic disturbances is not direct, predictable or even achievable on its own. Appropriated actions and methods such as fern removal, planting ground covers, and enrichment planting with tree species were suggested in order to restore the natural forest regeneration process in the abandoned old fields.

Effect of external fields in Axelrod's model of social dynamics

The study of the effects of spatially uniform fields on the steady-state properties of Axelrod's model has yielded plenty of counterintuitive results. Here, we reexamine the impact of this type of field for a selection of parameters such that the field-free steady state of the model is heterogeneous or multicultural. Analyses of both one- and two-dimensional versions of Axelrod's model indicate that the steady state remains heterogeneous regardless of the value of the field strength. Turning on the field leads to a discontinuous decrease on the number of cultural domains, which we argue is due to the instability of zero-field heterogeneous absorbing configurations. We find, however, that spatially nonuniform fields that implement a consensus rule among the neighborhood of the agents enforce homogenization. Although the overall effects of the fields are essentially the same irrespective of the dimensionality of the model, we argue that the dimensionality has a significant impact on the stability of the field-free homogeneous steady state.

Polynomial and Poisson dependence in free Poisson algebras and free Poisson fields

We prove that any two Poisson dependent elements in a free Poisson algebra and a free Poisson field of characteristic zero are algebraically dependent, thus answering positively a question from Makar-Limanov and Umirbaev (2007) [8]. We apply this result to give a new proof of the tameness of automorphisms for free Poisson algebras of rank two (see Makar-Limanov and Umirbaev (2011) [9], Makar-Limanov et al. (2009) [10]). (C) 2011 Elsevier Inc. All rights reserved.

Natural regeneration in abandoned fields following intensive agricultural land use in an Atlantic Forest Island, Brazil

The time required to regrowth a forest in degraded areas depends on how the forest is removed and on the type of land use following removal. Natural regeneration was studied in abandoned old fields after intensive agricultural land use in areas originally covered by Brazilian Atlantic Forests of the Anchieta Island, Brazil in order to understand how plant communities reassemble following human disturbances as well as to determine suitable strategies of forest restoration. The fields were classified into three vegetation types according to the dominant plant species in: 1) Miconia albicans (Sw.) Triana (Melastomataceae) fields, 2) Dicranopteris flexuosa (Schrader) Underw. (Gleicheniaceae) thickets, and 3) Gleichenella pectinata (Willd.) Ching. (Gleicheniaceae) thickets. Both composition and structure of natural regeneration were compared among the three dominant vegetation types by establishing randomly three plots of 1 x 3 m in five sites of the island. A gradient in composition and abundance of species in natural regeneration could be observed along vegetation types from Dicranopteris fern thickets to Miconia fields. The gradient did not accurately follow the pattern of spatial distribution of the three dominant vegetation types in the island regarding their proximity of the remnant forests. A complex association of biotic and abiotic factors seems to be affecting the seedling recruitment and establishment in the study plots. The lowest plant regeneration found in Dicranopteris and Gleichenella thickets suggests that the ferns inhibit the recruitment of woody and herbaceous species. Otherwise, we could not distinguish different patterns of tree regeneration among the three vegetation types. Our results showed that forest recovery following severe anthropogenic disturbances is not direct, predictable or even achievable on its own. Appropriated actions and methods such as fern removal, planting ground covers, and enrichment planting with tree species were suggested in order to restore the natural forest regeneration process in the abandoned old fields.

Reliable estimation of dense optical flow fields with large displacements

[EN] In this paper we show that a classic optical flow technique by Nagel and Enkelmann can be regarded as an early anisotropic diffusion method with a diffusion tensor. We introduce three improvements into the model formulation that avoid inconsistencies caused by centering the brightness term and the smoothness term in different images use a linear scale-space focusing strategy from coarse to fine scales for avoiding convergence to physically irrelevant local minima, and create an energy functional that is invariant under linear brightness changes.  Applying a gradient descent method to the resulting energy functional leads to a system of diffusion-reaction equations. We prove that this system has a unique solution under realistic assumptions on the initial data, and we present an efficient linear implicit numerical scheme in detail. Our method creates flow fields with 100% density over the entire image domain, it is robust under a large range of parameter variations, and it can recover displacement fields that are far beyond the typical one-pixel limits which are characteristic for many differential methods for determining optical flow. We show that it performs better than the classic optical flow methods with 100%  density that are evaluated by Barron et al. (1994). Our software is available from the Internet.

Wordline approach to higher spin fields

The main object of this thesis is the analysis and the quantization of spinning particle models which employ extended ”one dimensional supergravity” on the worldline, and their relation to the theory of higher spin fields (HS). In the first part of this work we have described the classical theory of massless spinning particles with an SO(N) extended supergravity multiplet on the worldline, in flat and more generally in maximally symmetric backgrounds. These (non)linear sigma models describe, upon quantization, the dynamics of particles with spin N/2. Then we have analyzed carefully the quantization of spinning particles with SO(N) extended supergravity on the worldline, for every N and in every dimension D. The physical sector of the Hilbert space reveals an interesting geometrical structure: the generalized higher spin curvature (HSC). We have shown, in particular, that these models of spinning particles describe a subclass of HS fields whose equations of motions are conformally invariant at the free level; in D = 4 this subclass describes all massless representations of the Poincar´e group. In the third part of this work we have considered the one-loop quantization of SO(N) spinning particle models by studying the corresponding partition function on the circle. After the gauge fixing of the supergravity multiplet, the partition function reduces to an integral over the corresponding moduli space which have been computed by using orthogonal polynomial techniques. Finally we have extend our canonical analysis, described previously for flat space, to maximally symmetric target spaces (i.e. (A)dS background). The quantization of these models produce (A)dS HSC as the physical states of the Hilbert space; we have used an iterative procedure and Pochhammer functions to solve the differential Bianchi identity in maximally symmetric spaces. Motivated by the correspondence between SO(N) spinning particle models and HS gauge theory, and by the notorious difficulty one finds in constructing an interacting theory for fields with spin greater than two, we have used these one dimensional supergravity models to study and extract informations on HS. In the last part of this work we have constructed spinning particle models with sp(2) R symmetry, coupled to Hyper K¨ahler and Quaternionic-K¨ahler (QK) backgrounds.

Probabilistic approaches in civil engineering: generation of random fields and structural identification with genetic algorithms

The inherent stochastic character of most of the physical quantities involved in engineering models has led to an always increasing interest for probabilistic analysis. Many approaches to stochastic analysis have been proposed. However, it is widely acknowledged that the only universal method available to solve accurately any kind of stochastic mechanics problem is Monte Carlo Simulation. One of the key parts in the implementation of this technique is the accurate and efficient generation of samples of the random processes and fields involved in the problem at hand. In the present thesis an original method for the simulation of homogeneous, multi-dimensional, multi-variate, non-Gaussian random fields is proposed. The algorithm has proved to be very accurate in matching both the target spectrum and the marginal probability. The computational efficiency and robustness are very good too, even when dealing with strongly non-Gaussian distributions. What is more, the resulting samples posses all the relevant, welldefined and desired properties of “translation fields”, including crossing rates and distributions of extremes. The topic of the second part of the thesis lies in the field of non-destructive parametric structural identification. Its objective is to evaluate the mechanical characteristics of constituent bars in existing truss structures, using static loads and strain measurements. In the cases of missing data and of damages that interest only a small portion of the bar, Genetic Algorithm have proved to be an effective tool to solve the problem.

Influence of electric fields over the nucleation ratio of the lithium-potassium sulfate and its pedagogical value

[EN]This paper presents our research about nucleation and its dependency with external conditions, as well as the internal characteristics of the solution itself. Among the research lines of our group, we has been studying the influence of electric fields over two different but related compounds: Lithium-Potassium Sulfate and Lithium-Amonium Sulfate, which both of them show a variation on the nucleation ratio when an electric field is applied during the crystal growth. Moreover, in this paper will be explained a laboratory protocol to teach universitary Science students the nucleation process itself and how it depends on external applied conditions, e.g. electric fields.

Three-dimensional simulation of wind fields and air pollution over complex terrain

[EN]In this talk we introduce a new methodology for wind field simulation or forecasting over complex terrain. The idea is to use wind measurements or predictions of the HARMONIE mesoscale model as the input data for an adaptive finite element mass consistent wind model [1,2]. The method has been recently implemented in the freely-available Wind3D code [3]. A description of the HARMONIE Non-Hydrostatic Dynamics can be found in [4]. The results of HARMONIE (obtained with a maximum resolution about 1 Km) are refined by the finite element model in a local scale (about a few meters). An interface between both models is implemented such that the initial wind field approximation is obtained by a suitable interpolation of the HARMONIE results…