Numerical analysis of the planewave discretization of some orbital-free and Kohn-Sham models

We provide a priori error estimates for the spectral and pseudospectral Fourier (also called planewave) discretizations of the periodic Thomas-Fermi-von Weizs\"{a}cker (TFW) model and for the spectral discretization of the Kohn-Sham model, within the local density approximation (LDA). These models allow to compute approximations of the ground state energy and density of molecular systems in the condensed phase. The TFW model is stricly convex with respect to the electronic density, and allows for a comprehensive analysis. This is not the case for the Kohn-Sham LDA model, for which the uniqueness of the ground state electronic density is not guaranteed. Under a coercivity assumption on the second order optimality condition, we prove that for large enough energy cut-offs, the discretized Kohn-Sham LDA problem has a minimizer in the vicinity of any Kohn-Sham ground state, and that this minimizer is unique up to unitary transform. We then derive optimal a priori error estimates for the spectral discretization method.Comment: 50 page

F-term Braneworld inflation in Light of Five-year WMAP observations

We consider a supersymmetric hybrid inflation in the framework of the Randall-Sundrum type II Braneworld model. We drive an analytical expression for the scalar potential and find that the F-term dominates hybrid inflation process. We show that for some value of Brane tension we can eliminate the fine tuning problem related to coupling constant k of the potential: We also calculate all known spectrum inflation parameters and show that observational bounds from WMAP5, BAO and SN observations are satisfied.Comment: 7 pages, no figure

Global Stability Analysis of Healthy Situation for a Coupled Model of Healthy and Cancerous Cells Dynamics in Acute Myeloid Leukemia

In this paper we aim to study the global stability of a coupled model of healthy and cancerous cells dynamics in healthy situation of Acute Myeloid Leukemia. We also clarify the effect of interconnection between healthy and cancerous cells dynamics on the global stability The interconnected model is obtained by transforming the PDE-based model into a nonlinear distributed delay system. Using Lyapunov approach, we derive necessary and sufficient conditions for global stability for a selected equilibrium point of particular interest (healthy situation). Simulations are conducted to illustrate the obtained results

On Chaplygin Gas Braneworld Inflation with Monomial Potential

In this paper we study the Chaplygin gas model as a candidate for inflation in the framework of the Randall Sundrum type-II braneworld model. We consider the original and generalized Chaplygin gas model in the presence of monomial potential. The inflationary spectrum perturbation parameters are reformulated and evaluated in the high-energy limit and we found that they depend on several parameters. We also showed that these perturbation parameters are widely compatible with the recent Planck data for a particular choice of the parameters space of the model. A suitable observational central value of $n_{s}\simeq$ $0.965$ is also obtained in the case of original and generalized Chaplygin gas.Comment: 7 figures. arXiv admin note: text overlap with arXiv:0805.1005 by other author

Crop Insurance and Pesticides in French agriculture: an empirical analysis of multiple risks management

This paper investigates the determinants of rapeseed hail insurance and chemical input decisions using individual panel data set of French farms covering the period from 1993 to 2004. Economic theory suggests that insurance and prevention decisions are not independent due to risk reduction and/or moral hazard eff ects. We propose a theoretical framework that integrates two statistically independent sources of risk faced by farmers of our sample hail risk and pest risk. Statistical tests confi rm that chemical and insurance demands are endogenous to each other and simultaneously determined. An econometric model involving two simultaneous equations with mixed censored/continuous dependent variables is thus estimated for rapeseed. Estimation results show that rapeseed insurance demand has a positive and signi cant eff ect on pesticide use and vice versa. Insurance demand is also positively in uenced by the yield's coeffi cient of variation and the loss ratio, and negatively infl uenced by proxies for wealth (including CAP subsidies) and activity diversi cation

Computational analysis of the behavior of atmospheric pollution due to demographic, structural factors, vehicular flow and commerce activities

According to the latest assessments made by the world health organization (WHO2016), the atmospheric pollution (air), has become one of the main causes of morbidity and mortality in the world, with a steep growth of respiratory diseases, increase in lung cancer, ocular complications, and dermis diseases [1,2,3]. Currently, there are governments which still underestimate investments in environmental care, turning their countries into only consumers and predators of the ecosystem [1,2,3]. Worldwide, several cities have been implementing different regional strategies to decrease environmental pollution, however, these actions have not been effective enough and significant indices of contamination and emergency declarations persist [1,2,3]. Medellín is one of the cities most affected by polluting gases in Latin America due to the high growth of construction sector, high vehicular flow, increase in commerce, besides a little assertive planting trees system, among other reasons [1,2,3]. With the purpose of providing new researching elements which benefit the improvement of air quality in the cities of the world, it is pretended to mathematically model and computationally implement the behavior of the flow of air, e.g., in zones in the city of Medellín to determine the extent of pollution by tightness, impact of current architectural designs, vehicular transport, high commerce flow, and confinement in the public transport system. The simulations allowed to identify spotlights of particulate tightness caused by architectural designs of the city which do not benefit air flow. Also, recirculating gases were observed in different zones of the city. This research can offer greater knowledge around the incidence of pollution generated by structures and architecture. Likewise, these studies can contribute to a better urban, structural and ecological reordering in cities, the implementation of an assertive arborization system, and the possibility to orientate effective strategies over cleaning (purification) and contaminant extracting systems