arXiv subjects

M. Vilches

Publications and source records attributed to M. Vilches.

4 recordsLinked to original sources

arXiv2014

A curvature form for pseudoconnections

We obtain the curvature form $F^\nabla=P\circ d^\nabla\circ\nabla-d^\nabla\circ P\circ\nabla+d^\nabla\circ\nabla\circ P$ for a vector bundle pseudoconnection $\nabla$, where $d^\nabla$ is the exterior derivative associated to $\nabla$. We use $F^\nabla$ to obtain the curvature of $\nabla$. We also prove that $F^\nabla=0$ is a necessary (but not sufficient) condition for $d^\nabla$ to be a chain complex. Instead we prove that $F^\nabla=0$ and $d^\nabla\circ d^\nabla\circ\nabla=0$ are necessary and sufficient conditions for $d^\nabla$ to be a {\em chain $2$-complex}, i.e., $d^\nabla\circ d^\nabla\circ d^\nabla=0$.

math.DG↗

arXiv2012

2-Riemannian manifolds

A {\em 2-Riemannian manifold} is a differentiable manifold exhibiting a 2-inner product on each tangent space. We first study lower dimensional 2-Riemannian manifolds by giving necessary and sufficient conditions for flatness. Afterward we associate to each 2-Riemannian manifold a unique torsion free compatible pseudoconnection. Using it we define a curvature for 2-Riemannian manifolds and study its properties. We also prove that 2-Riemannian pseudoconnections do not have Koszul derivatives. Moreover, we define stationary vector field with respect to a 2-Riemannian metric and prove that the stationary vector fields in $\mathbb{R}^2$ with respect to the 2-Riemannian metric induced by the Euclidean product are the divergence free ones.

math.DG↗

arXiv2006

Monte Carlo simulation of the electron transport through thin slabs: A comparative study of PENELOPE, GEANT3, GEANT4, EGSnrc and MCNPX

The Monte Carlo simulation of the electron transport through thin slabs is studied with five general purpose codes: PENELOPE, GEANT3, GEANT4, EGSnrc and MCNPX. The different material foils analyzed in the old experiments of Kulchitsky and Latyshev [Phys. Rev. 61 (1942) 254-266] and Hanson et al. [Phys. Rev. 84 (1951) 634-637] are used to perform the comparison between the Monte Carlo codes. Non-negligible differences are observed in the angular distributions of the transmitted electrons obtained with the some of the codes. The experimental data are reasonably well described by EGSnrc, PENELOPE (v. 2005) and GEANT4. A general good agreement is found for EGSnrc and GEANT4 in all the cases analyzed.

physics.med-ph↗

arXiv1999

A Method to Determine the In-Air Spatial Spread of Clinical Electron Beams

We propose and analyze in detail a method to measure the in-air spatial spread parameter of clinical electron beams. Measurements are performed at the center of the beam and below the adjustable collimators sited in asymmetrical configuration in order to avoid the distortions due to the presence of the applicator. The main advantage of our procedure lies in the fact that the dose profiles are fitted by means of a function which includes, additionally to the Gaussian step usually considered, a background which takes care of the dose produced by different mechanisms that the Gaussian model does not account for. As a result, the spatial spread is obtained directly from the fitting procedure and the accuracy permits a good determination of the angular spread. The way the analysis is done is alternative to that followed by the usual methods based on the evaluation of the penumbra width. Besides, the spatial spread found shows the quadratic-cubic dependence with the distance to the source predicted by the Fermi-Eyges theory. However, the corresponding values obtained for the scattering power are differing from those quoted by ICRU nr. 35 by a factor ~2 or larger, what requires of a more detailed investigation.

physics.med-ph↗