Characteristic functions on the boundary of a planar domain need not be traces of least gradient functions

Given a smooth bounded planar domain, we construct a compact set on the boundary s.t. its characteristic function is not the trace of a least gradient function. This generalize the construction of Spradlin and Tamasan [ST14] on the disc

Non-trivial linear bounds for a random walk driven by a simple symmetric exclusion process

Non-trivial linear bounds are obtained for the displacement of a random walk in a dynamic random environment given by a one-dimensional simple symmetric exclusion process in equilibrium. The proof uses an adaptation of multiscale renormalization methods of Kesten and Sidoravicius.Comment: 20 pages, 3 figure

Introduction to Gauge Theory of Gravitation

The fundamental interactions of nature, the electroweak and the quantum chromodynamics, are described in the Standard Model by the Gauge Theory under internal symmetries that maintain the invariance of the functional action. The fundamental interaction of gravitation is very well described by Einstein's General Relativity in a Riemannian spacetime metric, but General Relativity has been over time a gravitational field theory apart from the Standard Model. The theory of Gauge allows under symmetries of the group of Poincar\'e to impose invariances in the functional of the action of the spinor field that result in the gravitational interaction with the fermions. In this approach the gravitational field, besides being described by the equation similar to General Relativity, also brings a spin-gravitational interaction in a Riemann-Cartan spacetime.Comment: 23 page

Higher order self-dual models for spin-3 particles in D=2+1D=2+1

In $D=2+1$ dimensions, elementary particles of a given helicity can be described by local Lagrangians (parity singlets). By means of a "soldering" procedure two opposite helicities can be joined together and give rise to massive spin-$s$ particles carrying both helicities $\pm s$ (parity doublets), such Lagrangians can also be used in $D=3+1$ to describe massive spin-$s$ particles. From this point of view the parity singlets (self-dual models) in $D=2+1$ are the building blocks of real massive elementary particles in $D=3+1$. In the three cases $s=1,\, 3/2,\, 2$ there are $2s$ self-dual models of order $1,2, \cdots, 2s$ in derivatives. In the spin-3 case the 5th order model is missing in the literature. Here we deduce a 5th order spin-3 self-dual model and fill up this gap. It is shown to be ghost free by means of a master action which relates it with the top model of 6th order. We believe that our approach can be generalized to arbitrary integer spin-$s$ in order to obtain the models of order $2s$ and $2s-1$. We also comment on the difficulties in relating the 5th order model with their lower order duals

Nanocrystalline cathodes for PC-SOFCs

Ceramic proton conductors are of great interest for the development of solid oxide fuel cells (PC-SOFC) operating at relatively low temperatures between 400 and 700 ºC. Perovskites based on BaCeO3-δ exhibit the highest proton conductivity among this class of materials, however, they are susceptible to hydra-tion and carbonation in presence of water vapor and CO2 [1]. In contrast, the chemical stability of BaZrO3-based protonic conductors is better, but they require sintering temperatures as high as 1700 ºC and usually suffer from high intrinsic grain boundary resistance, limiting the final performance. Partial substitution of Zr for Ce in Ba(Ce0.9-xZrx)Y0.2O3-δ allows obtaining electrolytes with both high proton conductivity and good chemical stability. The performance of a PC-SOFC at low tempe-ratures depends significantly on the ohmic resis-tance of the electrolyte, although it can be lowered by reducing the electrolyte thickness. Another im-portant limiting factor is the increase of the cathode polarization resistance due to the thermally activated nature of the oxygen reduction reaction. For this reason, it is essential to obtain high efficiency cathodes operating at reduced temperatures. In this work, BaCe0.6Zr0.2Y0.2O3-δ (BCZY) powders were prepared by freeze-drying precursor method. These powders were mixed with a Zn-containing solution as sintering additive in order to obtain dense pellets with submicrometric grain size at only 1200 ºC. After that, La0.6Sr0.4Co0.8Fe0.2O3 nanocrystalline electrodes were deposited symmet-rically onto dense pellets BCZY by conventional spray-pyrolysis [3]. The structure, microstructure and electrochemical properties of these electrodes have been examined by XRD, FE-SEM and im-pedance spectroscopy. The stability of these elec-trodes at intermediate temperatures was evaluated as a function of time. These nanocrystalline cathodes exhibit a sub-stantial improvement of the electrode polarization resistance with respect to the same materials pre-pared by screen-printing method at high sintering temperatures, e.g. 0.7 and 3.2 cm2 at 600ºC for LSCF cathodes prepared by spray-pyrolysis and screen-printing method respectively (Fig. 1). An anode supported cell with composition LSCF/BCZY/NiO-BCZY was also prepared to test the electrochemical performance.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech