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.

Functional coupling of sensorimotor and associative areas during a catching ball task: a qEEG coherence study

Abstract Background Catching an object is a complex movement that involves not only programming but also effective motor coordination. Such behavior is related to the activation and recruitment of cortical regions that participates in the sensorimotor integration process. This study aimed to elucidate the cortical mechanisms involved in anticipatory actions when performing a task of catching an object in free fall. Methods Quantitative electroencephalography (qEEG) was recorded using a 20-channel EEG system in 20 healthy right-handed participants performed the catching ball task. We used the EEG coherence analysis to investigate subdivisions of alpha (8-12 Hz) and beta (12-30 Hz) bands, which are related to cognitive processing and sensory-motor integration. Results Notwithstanding, we found the main effects for the factor block; for alpha-1, coherence decreased from the first to sixth block, and the opposite effect occurred for alpha-2 and beta-2, with coherence increasing along the blocks. Conclusion It was concluded that to perform successfully our task, which involved anticipatory processes (i.e. feedback mechanisms), subjects exhibited a great involvement of sensory-motor and associative areas, possibly due to organization of information to process visuospatial parameters and further catch the falling object.

On Ti-18Si-6B and Ti-7.5Si-22.5B powder alloys prepared by high-energy ball milling and sintering

Recently, a new ternary phase was discovered in the Ti-Si-B system, located near the Ti6Si2B composition. The present study concerns the preparation of titanium alloys that contain such phase mixed with α-titanium and other intermetallic phases. High-purity powders were initially processed in a planetary ball-mill under argon atmosphere with Ti-18Si-6B and Ti-7.5Si-22.5B at. (%) initial compositions. Variation of parameters such as rotary speed, time, and ball diameters were adopted. The as-milled powders were pressureless sintered and hot pressed. Both the as-milled and sintered materials were characterized by X-ray diffraction, scanning electron microscopy and energy-dispersive spectrometry. Sintered samples have presented equilibrium structures formed mainly by the α-Ti+Ti6Si2B+Ti5Si3+TiB phases. Silicon and boron peaks disappear throughout the milling processes, as observed in the powder diffraction data. Furthermore, an iron contamination of up to 10 at. (%) is measured by X-ray spectroscopy analysis on some regions of the sintered samples. Density, hardness and tribological results for these two compositions are also presented here.