Analysis of models for quantum transport of electrons in graphene layers

We present and analyze two mathematical models for the self consistent quantum transport of electrons in a graphene layer. We treat two situations. First, when the particles can move in all the plane \RR^2, the model takes the form of a system of massless Dirac equations coupled together by a selfconsistent potential, which is the trace in the plane of the graphene of the 3D Poisson potential associated to surface densities. In this case, we prove local in time existence and uniqueness of a solution in H^s(\RR^2), for $s > 3/8$ which includes in particular the energy space H^{1/2}(\RR^2). The main tools that enable to reach $s\in (3/8,1/2)$ are the dispersive Strichartz estimates that we generalized here for mixed quantum states. Second, we consider a situation where the particles are constrained in a regular bounded domain $\Omega$. In order to take into account Dirichlet boundary conditions which are not compatible with the Dirac Hamiltonian $H_{0}$, we propose a different model built on a modified Hamiltonian displaying the same energy band diagram as $H_{0}$ near the Dirac points. The well-posedness of the system in this case is proved in $H^s_{A}$, the domain of the fractional order Dirichlet Laplacian operator, for $1/2\leq s<5/2$

High density limit of the stationary one dimensional Schrödinger-Poisson system

International audienceThe stationary one dimensional Schrödinger-Poisson system on a bounded interval is considered in the limit of a small Debye length (or small temperature). Electrons are supposed to be in a mixed state with the Boltzmann statistics. Using various reformulations of the system as convex minimization problems, we show that only the first energy level is asymptotically occupied. The electrostatic potential is shown to converge towards a boundary layer potential with a profile computed by means of a half space Schrödinger-Poisson system

Diffusion and guiding center approximation for particle transport in strong magnetic fields

International audienceThe diffusion limit of the linear Boltzmann equation with a strong magnetic field is performed. The giration period of particles around the magnetic field is assumed to be much smaller than the collision relaxation time which is supposed to be much smaller than the macroscopic time. The limiting equation is shown to be a diffusion equation in the parallel direction while in the orthogonal direction, the guiding center motion is obtained. The diffusion constant in the parallel direction is obtained through the study of a new collision operator obtained by averaging the original one. Moreover, a correction to the guiding center motion is derived

Etude mathématique et numérique de modèles de transport : application à la spintronique

This thesis is decomposed into three parts. The main part is devoted to the study of spin polarized currents in semiconductor materials. An hierarchy of microscopic and macroscopic models are derived and analyzed. These models take into account the spin relaxation and precession mechanisms acting on the spin dynamics in semiconductors. We have essentially two mechanisms : the spin-orbit coupling and the spin-flip interactions. We begin by presenting a semiclassical analysis (via the Wigner transformation) of the Schr¨odinger equation with spin-orbit hamiltonian. At kinetic level, the spinor Vlasov (or Boltzmann) equation is an equation of distribution function with 2×2 hermitian positive matrix value. Starting then from the spinor form of the Boltzmann equation with different spin-flip and non spin-flip collision operators and using diffusion asymptotic technics, different continuum models are derived. We derive drift-diffusion, SHE and Energy-Transport models of two-components or spin-vector types with spin rotation and relaxation effects. Two numerical applications are then presented : the simulation of transistor with spin rotational effect and the study of spin accumulation effect in inhomogenous semiconductor interfaces. In the second part, the diffusion limit of the linear Boltzmann equation with a strong magnetic field is performed. The Larmor radius is supposed to be much smaller than the mean free path. The limiting equation is shown to be a diffusion equation in the parallel direction while in the orthogonal direction, the guiding center motion is obtained. The diffusion constant in the parallel direction is obtained through the study of a new collision operator obtained by averages of the original one. Moreover, a correction to the guiding center motion is derived. In the third part of this thesis, we are interested in the description of the confinement potential in two-dimensional electron gases. The stationary one dimensional Schr¨odinger?Poisson system on a bounded interval is considered in the limit of a small Debye length (or small temperature). Electrons are supposed to be in a mixed state with the Boltzmann statistics. Using various reformulations of the system as convex minimization problems, we show that only the first energy level is asymptotically occupied. The electrostatic potential is shown to converge towards a boundary layer potential with a profile computed by means of a half space Schrödinger?Poisson system.Ce travail de thèse comporte trois parties. La partie principale s'intéresse au transport des courants polarisés en spin dans des matériaux à base de semi-conducteurs. Nous dérivons et analysons une hiérarchie des modèles allant du niveau microscopique au niveau macroscopique et tenant compte des différents mécanismes de rotation et de relaxation du vecteur spin dans les semi-conducteurs. Les mécanismes essentiels pris en compte sont les couplages spin-orbite et les interactions avec renversement de spin (spin-flip interactions). Une analyse semi-classique (via la transformation de Wigner) de l'équation de Schrödinger avec hamiltonien spin-orbite est présentée. Au niveau cinétique, l'équation de Vlasov (ou Boltzmann) spinorielle est une équation à valeur dans l'ensemble des matrices carrées d'ordre deux hermitiennes et positives. Partant ensuite de la spinor forme de l'équation de Boltzmann (avec différents opérateurs de collisions avec et sans renversement du vecteur spin) et par des techniques d'asymptotiques de diffusion, nous dérivons et analysons plusieurs modèles macroscopiques. Ils sont de type dérive-diffusion, SHE, Energie-Transport, à deux composantes ou spinoriels conservant des effets de rotation et de relaxation du vecteur spin. Nous validons ensuite ces modèles par des cas tests numériques. Deux applications numériques sont présentées : la simulation d'un transistor à effet de rotation de spin et l'étude de l'effet d'accumulation de spin à l'interface entre deux couches semi-conductrices différemment dopées. Dans la seconde partie, nous considérons une équation cinétique de type Boltzmann linéaire dans des domaines où un champ magnétique fort est appliqué. Nous étudions la limite de diffusion en supposant que le champ magnétique est unidirectionnel et tend vers l'infini. Le modèle obtenu est un modèle macroscopique constitué d'une équation diffusive dans la direction parallèle au champ magnétique et d'une dérive représentant l'effet centre-guide en présence d'un champ électrique dans la direction perpendiculaire. Le terme de diffusion contient des moyennes de giration de l'opérateur de collisions utilisé. Nous prouvons la convergence en utilisant des techniques d'entropie pour traiter le comportement diffusif, et en conjuguant par les rotations locales induites par le champ magnétique pour tenir compte des oscillations. Dans la troisième partie de cette thèse, Nous nous intéressons à la description du potentiel de confinement dans des gas d'électrons bidimensionnels. Nous étudions la limite faible longueur de Debye (ou faible température) du système de Schrödinger-Poisson unidimensionnel stationnaire sur un intervalle borné. Les électrons sont supposés dans un mélange d'états avec une statistique de Boltzmann (ou de Fermi-Dirac). En utilisant différentes reformulations du système comme des problèmes de minimisation convexe, nous montrons qu'asymptotiquement seul le premier niveau d'énergie est occupé. Le potentiel électrostatique converge vers une couche limite avec un profil calculé à l'aide d'un système de Schrödinger-Poisson sur le demi axe réel

The Value of Plurality in 'The Network with a Thousand Entrances'

This contribution reflects on the value of plurality in the ‘network with a thousand entrances’ suggested by McCarty (http://goo.gl/H3HAfs), and others, in association with approaching time-honoured annotative and commentary practices of much-engaged texts. The question is how this approach aligns with tensions, today, surrounding the multiplicity of endeavour associated with modeling practices of annotation by practitioners of the digital humanities. Our work, hence, surveys annotative practice across its reflection in contemporary praxis, from the MIT annotation studio whitepaper (http://goo.gl/8NBdnf) through the work of the Open Annotation Collaboration (http://www.openannotation.org), and manifest in multiple tools facilitating annotation across the web up to and including widespread application in social knowledge creation suites like Wikipedia https://en.wikipedia.org/wiki/Web annotation

Comparison of Efficacy and Ocular Surface Disease Index Score between Bimatoprost, Latanoprost, Travoprost, and Tafluprost in Glaucoma Patients

Aim. The purpose of this study is to evaluate and compare the efficacy of 4 prostaglandin analogues (PGAs) and to determine the incidence of ocular surface disease in newly diagnosed, primary open-angle glaucoma (POAG) patients started on one of those 4 PGAs: bimatoprost (benzalkonium chloride, BAK, 0.3 mg/mL), latanoprost (BAK 0.2 mg/mL), travoprost (polyquad), and tafluprost (BAK-free). Patients and Methods. In this single-center, open-label trial, 32 patients newly diagnosed with POAG were randomly started on one of the four PGAs. All patients underwent a complete ophthalmological exam at presentation and at 1, 3, and 6 months of follow-up. Dry eye disease (DED) was assessed using the original Ocular Surface Disease Index (OSDI) questionnaire, in order to evaluate the impact of the drops on the quality of life of patients. Results. The mean age was 60.06 years ± 11.76. All four drugs equally and significantly reduced the intraocular pressure (IOP) with respect to the baseline IOP. There was a trend for a slightly greater reduction of IOP with bimatoprost, but the difference was not found to be statistically significant when compared to other PGAs. OSDI scores were significantly superior for travoprost (10.68 ± 5.73) compared to the other three drugs (p<0.05). Latanoprost caused the most significant eyelash growth and iris discoloration. Conjunctival hyperemia and superficial keratitis occurrence were similar in the four groups. Conclusion. All prostaglandin analogues equally and significantly reduce the IOP in patients with POAG. According to the results of the OSDI score, latanoprost seems to be the least tolerated among the four drugs

Regulation of human dUTPase gene expression and p53-mediated transcriptional repression in response to oxaliplatin-induced DNA damage

Deoxyuridine triphosphate nucleotidohydrolase (dUTPase) catalyzes the hydrolysis of dUTP to dUMP and PPi. Although dUTP is a normal intermediate in DNA synthesis, its accumulation and misincorporation into DNA is lethal. Importantly, uracil misincorporation is a mechanism of cytotoxicity induced by fluoropyrimidine chemotherapeutic agents including 5-fluorouracil (5-FU) and elevated expression of dUTPase is negatively correlated with clinical response to 5-FU-therapy. In this study we performed the first functional characterization of the dUTPase promoter and demonstrate a role for E2F-1 and Sp1 in driving dUTPase expression. We establish a direct role for both mutant and wild-type forms of p53 in modulating dUTPase promoter activity. Treatment of HCT116 p53+/+ cells with the DNA-damaging agent oxaliplatin induced a p53-dependent transcriptional downregulation of dUTPase not observed in the isogenic null cell line. Oxaliplatin treatment induced enrichment of p53 at the dUTPase promoter with a concomitant reduction in Sp1. The suppression of dUTPase by oxaliplatin promoted increased levels of dUTP that was enhanced by subsequent addition of fluoropyrimidines. The novel observation that oxaliplatin downregulates dUTPase expression may provide a mechanistic basis contributing to the synergy observed between 5-FU and oxaliplatin in the clinic. Furthermore, these studies provide the first evidence of a direct transcriptional link between the essential enzyme dUTPase and the tumor suppressor p53

Global burden and strength of evidence for 88 risk factors in 204 countries and 811 subnational locations, 1990–2021: a systematic analysis for the Global Burden of Disease Study 2021

Background: Understanding the health consequences associated with exposure to risk factors is necessary to inform public health policy and practice. To systematically quantify the contributions of risk factor exposures to specific health outcomes, the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2021 aims to provide comprehensive estimates of exposure levels, relative health risks, and attributable burden of disease for 88 risk factors in 204 countries and territories and 811 subnational locations, from 1990 to 2021. Methods: The GBD 2021 risk factor analysis used data from 54 561 total distinct sources to produce epidemiological estimates for 88 risk factors and their associated health outcomes for a total of 631 risk–outcome pairs. Pairs were included on the basis of data-driven determination of a risk–outcome association. Age-sex-location-year-specific estimates were generated at global, regional, and national levels. Our approach followed the comparative risk assessment framework predicated on a causal web of hierarchically organised, potentially combinative, modifiable risks. Relative risks (RRs) of a given outcome occurring as a function of risk factor exposure were estimated separately for each risk–outcome pair, and summary exposure values (SEVs), representing risk-weighted exposure prevalence, and theoretical minimum risk exposure levels (TMRELs) were estimated for each risk factor. These estimates were used to calculate the population attributable fraction (PAF; ie, the proportional change in health risk that would occur if exposure to a risk factor were reduced to the TMREL). The product of PAFs and disease burden associated with a given outcome, measured in disability-adjusted life-years (DALYs), yielded measures of attributable burden (ie, the proportion of total disease burden attributable to a particular risk factor or combination of risk factors). Adjustments for mediation were applied to account for relationships involving risk factors that act indirectly on outcomes via intermediate risks. Attributable burden estimates were stratified by Socio-demographic Index (SDI) quintile and presented as counts, age-standardised rates, and rankings. To complement estimates of RR and attributable burden, newly developed burden of proof risk function (BPRF) methods were applied to yield supplementary, conservative interpretations of risk–outcome associations based on the consistency of underlying evidence, accounting for unexplained heterogeneity between input data from different studies. Estimates reported represent the mean value across 500 draws from the estimate's distribution, with 95% uncertainty intervals (UIs) calculated as the 2·5th and 97·5th percentile values across the draws. Findings: Among the specific risk factors analysed for this study, particulate matter air pollution was the leading contributor to the global disease burden in 2021, contributing 8·0% (95% UI 6·7–9·4) of total DALYs, followed by high systolic blood pressure (SBP; 7·8% [6·4–9·2]), smoking (5·7% [4·7–6·8]), low birthweight and short gestation (5·6% [4·8–6·3]), and high fasting plasma glucose (FPG; 5·4% [4·8–6·0]). For younger demographics (ie, those aged 0–4 years and 5–14 years), risks such as low birthweight and short gestation and unsafe water, sanitation, and handwashing (WaSH) were among the leading risk factors, while for older age groups, metabolic risks such as high SBP, high body-mass index (BMI), high FPG, and high LDL cholesterol had a greater impact. From 2000 to 2021, there was an observable shift in global health challenges, marked by a decline in the number of all-age DALYs broadly attributable to behavioural risks (decrease of 20·7% [13·9–27·7]) and environmental and occupational risks (decrease of 22·0% [15·5–28·8]), coupled with a 49·4% (42·3–56·9) increase in DALYs attributable to metabolic risks, all reflecting ageing populations and changing lifestyles on a global scale. Age-standardised global DALY rates attributable to high BMI and high FPG rose considerably (15·7% [9·9–21·7] for high BMI and 7·9% [3·3–12·9] for high FPG) over this period, with exposure to these risks increasing annually at rates of 1·8% (1·6–1·9) for high BMI and 1·3% (1·1–1·5) for high FPG. By contrast, the global risk-attributable burden and exposure to many other risk factors declined, notably for risks such as child growth failure and unsafe water source, with age-standardised attributable DALYs decreasing by 71·5% (64·4–78·8) for child growth failure and 66·3% (60·2–72·0) for unsafe water source. We separated risk factors into three groups according to trajectory over time: those with a decreasing attributable burden, due largely to declining risk exposure (eg, diet high in trans-fat and household air pollution) but also to proportionally smaller child and youth populations (eg, child and maternal malnutrition); those for which the burden increased moderately in spite of declining risk exposure, due largely to population ageing (eg, smoking); and those for which the burden increased considerably due to both increasing risk exposure and population ageing (eg, ambient particulate matter air pollution, high BMI, high FPG, and high SBP). Interpretation: Substantial progress has been made in reducing the global disease burden attributable to a range of risk factors, particularly those related to maternal and child health, WaSH, and household air pollution. Maintaining efforts to minimise the impact of these risk factors, especially in low SDI locations, is necessary to sustain progress. Successes in moderating the smoking-related burden by reducing risk exposure highlight the need to advance policies that reduce exposure to other leading risk factors such as ambient particulate matter air pollution and high SBP. Troubling increases in high FPG, high BMI, and other risk factors related to obesity and metabolic syndrome indicate an urgent need to identify and implement interventions

DIFFUSION MODELS FOR SPIN TRANSPORT DERIVED FROM THE SPINOR BOLTZMANN EQUATION

Abstract. The aim of this paper is to derive and analyse diffusion models for semiconductor spintronics. We begin by presenting and studying the so called ”spinor ” Boltzmann equation. Starting then from a rescaled version of linear Boltzmann equation with different spin-flip and non spin-flip collision operators, different continuum (drift-diffusion) models are derived. By comparing the strength of the spin-orbit scattering with the scaled mean free paths, we explain how some models existing in the literature (like the two-component models) can be obtained from the spinor Boltzmann equation. A new spin-vector drift-diffusion model keeping spin relaxation and spin precession effects due to the spin-orbit coupling in semiconductor structures is derived and some of its mathematical properties are checked. Key words. Spinor Boltzmann equation, spin-orbit coupling, spin-flip interactions, diffusion limit, decoherence limit, two-component drift-diffusion model, spin-vector drift-diffusion model. Subject classifications. hal-00624338, version 1- 17 Sep 2011 1. Introduction. Th