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

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

Modeling Corner Solutions with Panel Data: Application to Industrial Energy Demand in France

This paper is providing an initial empirical application of Lee and Pitt's approach to the problem of corner solutions with panel data. This approach deals with corner solutions in a manner consistent with behavioral theory. Furthermore it allows the use of flexible form cost functions and general error structure. In this model energy demand, at industrial plant level, is the result of a discrete choice of type of energy to consume and a continuous choice to define the demand level. The econometric model is essentially an endogenous switching regime model which require the evaluation of multivariate probability integrals. We estimate the random effect model by maximum likelihood using a panel of industrial French plants. We verify that estimations predict globally well the model and we simulate the effects of prices variations and a CO2 tax on energy demand.

Quasi 1D modelling of a Scramjet engine cycle using Heiser-Pratt approach

Scramjet engines are key for sustained hypersonic flights. Analytic models play a critical role in the preliminary design of a scramjet engine configuration. The objective of this research is to develop and validate a quasi-1D model for the scramjet engine encompassing inlet, isolator and combustor, to evaluate the impact of flight conditions and design parameters on the engine functionality. The model is developed assuming isentropic flow in the inlet with a single turn; modified Fanno-flow equations in the isolator that account for the area change of the core flow; and the combustor is modeled using Heiser-Pratt equations accounting for the fuel mixing efficiency. The isolator and combustor models are validated against experimental results. The model accounts for twelve parameters allowing for a decent range of possible configurations. Finally, the model was applied to five sets of parametric studies to evaluate the effect of multiple parameters on the engine functionality

Overt hyperthyroidism and venous thrombosis: what is the association?

Introduction: Patients that present overt hyperthyroidism, are more prone to a venous or arterial thrombosis1-3. Multiple mechanisms can explain the procoagulant changes in the hemostatic system in this population. Hereby, we report the case of a patient with Grave’s disease, presenting overt hyperthyroidism, associated with pulmonary embolism. The aim of this report is to emphasize the pathophysiological patterns responsible of the emergence of venous thrombosis (VT) in hyperthyroidism, as well as to discuss the increased probability of VT in this population. Case report: 44-year-old woman, with a past medical history of Grave’s disease, treated during the previous year before her admission by carbimazole 30 mg daily, presented to the emergency department with a fever, productive cough, hemoptysis and painful breathing during the last couple of days. In the previous weeks she had noticed swelling and redness of her right leg. The diagnosis of VT of the lower limb was confirmed by a venous ultrasound of the lower extremities and she was put on vitamin K antagonists 10 days before she presented to the emergency department for her exertional dyspnea. No risk factors for venous thrombosis were present. On physical examination she had a breathing frequency of 30 per minute, an air saturation of 92%, a temperature of 38.6 °C and, pulse rate of 120 beats per minute. The ECG showed a sinus tachycardia of 120 bpm and an S1Q3 aspect. CT scan has shown proximal right pulmonary emboli in the right upper and lower lobe with infarction of the basal right lung. Laboratory data revealed a TSH of 0.005mE/l and FT4 of >70 pmol/l. The thrombophilic tests were negative. The patient received heparin, followed by oral anticoagulant therapy with a vitamin K antagonist with a favorable evolution. By presenting this case, our aim is to emphasize the fact that hyperthyroidism can be a risk factor for venous thromboembolism, as indicated previously by a small number of retrospective studies. This patient had no identifiable risk factors for VTE. Possible predisposing factors for the development of VT and PE in patients with thyrotoxicosis are also in line with Virchow’s triad. Conclusion: Patients with hyperthyroidism may often have accompanying endothelial dysfunction, decreased fibrinolytic activity, and hypercoagulable states which contribute to the development of VT