A fully-discrete Semi-Lagrangian scheme for a first order mean field game problem

In this work we propose a fully-discrete Semi-Lagrangian scheme for a {\it first order mean field game system}. We prove that the resulting discretization admits at least one solution and, in the scalar case, we prove a convergence result for the scheme. Numerical simulations and examples are also discussed.Comment: 28 pages,16 figure

High harmonic generation in crystals using Maximally Localized Wannier functions

In this work, the nonlinear optical response, and in particular, the high harmonic generation of semiconductors is addressed by using the Wannier gauge. One of the main problems in the time evolution of the Semiconductor Bloch equations resides in the fact that the dipole couplings between different bands can diverge and have a random phase along the reciprocal space and this leads to numerical instability. To address this problem, we propose the use of the Maximally Localized Wannier functions that provide a framework to map ab-initio calculations to an effective tight-binding Hamiltonian with great accuracy. We show that working in the Wannier gauge, the basis set in which the Bloch functions are constructed directly from the Wannier functions, the dipole couplings become smooth along the reciprocal space thus avoiding the problem of random phases. High harmonic generation spectrum is computed for a 2D monolayer of hBN as a numerical demonstration

Effects of quantum deformation on the spin-1/2 Aharonov-Bohm problem

In this letter we study the Aharonov-Bohm problem for a spin-1/2 particle in the quantum deformed framework generated by the $\kappa$-Poincar\'{e}-Hopf algebra. We consider the nonrelativistic limit of the $\kappa$-deformed Dirac equation and use the spin-dependent term to impose an upper bound on the magnitude of the deformation parameter $\varepsilon$. By using the self-adjoint extension approach, we examine the scattering and bound state scenarios. After obtaining the scattering phase shift and the $S$-matrix, the bound states energies are obtained by analyzing the pole structure of the latter. Using a recently developed general regularization prescription [Phys. Rev. D. \textbf{85}, 041701(R) (2012)], the self-adjoint extension parameter is determined in terms of the physics of the problem. For last, we analyze the problem of helicity conservation.Comment: 12 pages, no figures, submitted for publicatio

Remarks on the Aharonov-Casher dynamics in a CPT-odd Lorentz-violating background

The Aharonov-Casher problem in the presence of a Lorentz-violating background nonminimally coupled to a spinor and a gauge field is examined. Using an approach based on the self-adjoint extension method, an expression for the bound state energies is obtained in terms of the physics of the problem by determining the self-adjoint extension parameter.Comment: Matches published versio

The Influence of oral environment on diet choices in goats: a focus on saliva protein composition

There is ample evidence that ruminants are capable of making choices between different foods that provide a more balanced diet that would be obtained by eating at random. In the particular case of goats, they occupy a diversity of habitats and different breeds present variability of feeding behaviors resultant from adaptations to the existent plant species. In their food search activity, individuals are faced with variable amounts of plant secondary metabolites (PSMs), which may present some toxic and anti-nutritional effects depending on the individual’s ability to deal with it. The oral cavity has a key role in the recognition and decision processes of ingestion or rejection. In this chapter we will first consider how goats identify foods and behave according to the food items available. Focus will be done on the importance of taste sense in this process and the information available on the main structures involved in taste detection and perception in goats will be reviewed. In a second section we will focus on the characteristics of goat’s saliva, particularly in terms of their protein composition, presenting results obtained by our research team