Existence of solutions and asymtptotic limits of the Euler-Poisson and the quantum drift-diffusion systems

My work concerns two different systems of equations used in the mathematical modeling of semiconductors and plasmas: the Euler-Poisson system and the quantum drift-diffusion system. The first is given by the Euler equations for the conservation of mass and momentum, with a Poisson equation for the electrostatic potential. The second one takes into account the physical effects due to the smallness of the devices (quantum effects). It is a simple extension of the classical drift-diffusion model which consists of two continuity equations for the charge densities, with a Poisson equation for the electrostatic potential. Using an asymptotic expansion method, we study (in the steady-state case for a potential flow) the limit to zero of the three physical parameters which arise in the Euler-Poisson system: the electron mass, the relaxation time and the Debye length. For each limit, we prove the existence and uniqueness of profiles to the asymptotic expansion and some error estimates. For a vanishing electron mass or a vanishing relaxation time, this method gives us a new approach in the convergence of the Euler-Poisson system to the incompressible Euler equations. For a vanishing Debye length (also called quasineutral limit), we obtain a new approach in the existence of solutions when boundary layers can appear (i.e. when no compatibility condition is assumed). Moreover, using an iterative method, and a finite volume scheme or a penalized mixed finite volume scheme, we numerically show the smallness condition on the electron mass needed in the existence of solutions to the system, condition which has already been shown in the literature. In the quantum drift-diffusion model for the transient bipolar case in one-space dimension, we show, by using a time discretization and energy estimates, the existence of solutions (for a general doping profile). We also prove rigorously the quasineutral limit (for a vanishing doping profile). Finally, using a new time discretization and an algorithmic construction of entropies, we prove some regularity properties for the solutions of the equation obtained in the quasineutral limit (for a vanishing pressure). This new regularity permits us to prove the positivity of solutions to this equation for at least times large enough.

In-situ DRIFT/MS study of the conversion of ethanol on mixed Mg/Si oxides

Due to the high price of natural oil and harmful effects of its usage, as the increase in emission of greenhouse gases, the industry focused in searching of sustainable types of the raw materials for production of chemicals. Ethanol, produced by fermentation of sugars, is one of the more interesting renewable materials for chemical manufacturing. There are numerous applications for the conversion of ethanol into commodity chemicals. In particular, the production of 1,3-butadiene whose primary source is ethanol using multifunctional catalysts is attractive. With the 25% of world rubber manufacturers utilizing 1,3-butadiene, there is an exigent need for its sustainable production. In this research, the conversion of ethanol in one-step process to 1,3-butadiene was studied. According to the literature, the mechanisms which were proposed to explain the way ethanol transforms into butadiene require to have both acid and basic sites. But still, there are a lot of debate on this topic. Thus, the aim of this research work is a better understanding of the reaction pathways with all the possible intermediates and products which lead to the formation of butadiene from ethanol. The particular interests represent the catalysts, based on different ratio Mg/Si in comparison to bare magnesia and silica oxides, in order to identify a good combination of acid/basic sites for the adsorption and conversion of ethanol. Usage of spectroscopictechniques are important to extract information that could be helpful for understanding the processes on the molecular level. The diffuse reflectance infrared spectroscopy coupled to mass spectrometry (DRIFT-MS) was used to study the surface composition of the catalysts during the adsorption of ethanol and its transformation during the temperature program. Whereas, mass spectrometry was used to monitor the desorbed products. The set of studied materials include MgO, Mg/Si=0.1, Mg/Si=2, Mg/Si=3, Mg/Si=9 and SiO2 which were also characterized by means of surface area measurements.

Development of an X-ray spectrometric system and feasibility tests of Silicon Drift Detector for medical and space applications

The thesis work concerns X-ray spectrometry for both medical and space applications and is divided into two sections. The first section addresses an X-ray spectrometric system designed to study radiological beams and is devoted to the optimization of diagnostic procedures in medicine. A parametric semi-empirical model capable of efficiently reconstructing diagnostic X-ray spectra in 'middle power' computers was developed and tested. In addition, different silicon diode detectors were tested as real-time detectors in order to provide a real-time evaluation of the spectrum during diagnostic procedures. This project contributes to the field by presenting an improved simulation of a realistic X-ray beam emerging from a common X-ray tube with a complete and detailed spectrum that lends itself to further studies of added filtration, thus providing an optimized beam for different diagnostic applications in medicine. The second section describes the preliminary tests that have been carried out on the first version of an Application Specific Integrated Circuit (ASIC), integrated with large area position-sensitive Silicon Drift Detector (SDD) to be used on board future space missions. This technology has been developed for the ESA project: LOFT (Large Observatory for X-ray Timing), a new medium-class space mission that the European Space Agency has been assessing since February of 2011. The LOFT project was proposed as part of the Cosmic Vision Program (2015-2025).

Asymmetric drift and halo flattening in disk galaxies

The main result in this work is the solution of the Jeans equations for an axisymmetric galaxy model containing a baryonic component (distributed according to a Miyamoto-Nagai profile) and a dark matter halo (described by the Binney logarithmic potential). The velocity dispersion, azimuthal velocity and some other interesting quantities such as the asymmetric drift are studied, along with the influence of the model parameters on these (observable) quantities. We also give an estimate for the velocity of the radial flow, caused by the asymmetric drift. Other than the mathematical beauty that lies in solving a model analytically, the interest of this kind of results can be mainly found in numerical simulations that study the evolution of gas flows. For example, it is important to know how certain parameters such as the shape (oblate, prolate, spherical) of a dark matter halo, or the flattening of the baryonic matter, or the mass ratio between dark and baryonic matter, have an influence on observable quantities such as the velocity dispersion. In the introductory chapter, we discuss the Jeans equations, which provide information about the velocity dispersion of a system. Next we will consider some dynamical quantities that will be useful in the rest of the work, e.g. the asymmetric drift. In Chapter 2 we discuss in some more detail the family of galaxy models we studied. In Chapter 3 we give the solution of the Jeans equations. Chapter 4 describes and illustrates the behaviour of the velocity dispersion, as a function of the several parameters, along with asymptotic expansions. In Chapter 5 we will investigate the behaviour of certain dynamical quantities for this model. We conclude with a discussion in Chapter 6.

Design and operation of ARGONTUBE: a 5 m long drift liquid argon TPC

The Liquid Argon Time Projection Chamber (LArTPC) is a prime type of detector for future large-mass neutrino observatories and proton decay searches. In this paper we present the design and operation, as well as experimental results from ARGONTUBE, a LArTPC being operated at the AEC-LHEP, University of Bern. The main goal of this detector is to prove the feasibility of charge drift over very long distances in liquid argon. Many other aspects of the LArTPC technology are also investigated, such as a voltage multiplier to generate high voltage in liquid argon (Greinacher circuit), a cryogenic purification system and the application of multi-photon ionization of liquid argon by a UV laser. For the first time, tracks induced by cosmic muons and UVlaser beam pulses have been observed and studied at drift distances of up to 5 m, the longest reached to date.

First measurements with ARGONTUBE, a 5m long drift Liquid Argon TPC

The Liquid Argon Time Projection Chamber (LAr TPC) technique is a promising technology for future neutrino detectors. At LHEP of the University of Bern (Switzerland), an R&D program towards large detectors are on-going. The main goal is to show the feasibility of long drift paths over many meters. Therefore, a liquid Argon TPC with 5m of drift distance was constructed. Many other aspects of the liquid Argon TPC technology are also investigated, such as a new device to generate high voltage in liquid Argon (Greinacher circuit), a recirculation filtering system and the multi-photon ionization of liquid Argon with a UV laser. Two detectors are built: a medium size prototype for specific detector technology studies, and ARGONTUBE, a 5m long device.

Measurement of the drift field in the ARGONTUBE LAr TPC with 266 nm pulsed laser beams

ARGONTUBE is a liquid argon time projection chamber (LAr TPC) with a drift field generated in-situ by a Greinacher voltage multiplier circuit. We present results on the measurement of the drift-field distribution inside ARGONTUBE using straight ionization tracks generated by an intense UV laser beam. Our analysis is based on a simplified model of the charging of a multi-stage Greinacher circuit to describe the voltages on the field cage rings.

TUMOR PROGRESSION: ANALYSIS OF THE INSTABILITY OF THE METASTATIC PHENOTYPE, SENSITIVITY TO RADIATION AND CHEMOTHERAPY (PHENOTYPIC DRIFT, BREAST CANCER)

The major complications for tumor therapy are (i) tumor spread (metastasis); (ii) the mixed nature of tumors (heterogeneity); and (iii) the capacity of tumors to evolve (progress). To study these tumor characteristics, the rat 13762NF mammary adenocarcinoma was cloned and studied for metastatic properties and sensitivities to therapy (chemotherapy, radiation and hyperthermia). The cell clones were heterogeneous and no correlation between metastatic potential and therapeutic sensitivities was observed. Further, these phenotypes were unstable during passage in vitro; yet, the changes were clone dependent and reproducible using different cryoprotected cell stocks. To understand the phenotypic instability, subclones were isolated from low and high passage cell clones. Each subclone possessed a unique composite phenotype. Again, no apparent correlation was seen between metastatic potential and sensitivity to therapy. The results demonstrated that (1) tumor cells are heterogeneous for multiple phenotypes; (2) tumor cells are unstable for multiple phenotypes; (3) the magnitude, direction and time of occurrence of phenotypic drift is clone dependent; (4) the sensitivity of cell clones to ionizing radiation (gamma or heat) and chemotherapy agents is independent of their metastatic potential; (5) shifts in metastatic potential and sensitivity to therapy may occur simultaneously but are not linked; and (6) tumor cells independently diverge to form several subpopulations with unique phenotypic profiles. ^

Exact moment calculations for genetic models with migration, mutation, and drift

Using properties of moment stationarity we develop exact expressions for the mean and covariance of allele frequencies at a single locus for a set of populations subject to drift, mutation, and migration. Some general results can be obtained even for arbitrary mutation and migration matrices, for example: (1) Under quite general conditions, the mean vector depends only on mutation rates, not on migration rates or the number of populations. (2) Allele frequencies covary among all pairs of populations connected by migration. As a result, the drift, mutation, migration process is not ergodic when any finite number of populations is exchanging genes. in addition, we provide closed form expressions for the mean and covariance of allele frequencies in Wright's finite-island model of migration under several simple models of mutation, and we show that the correlation in allele frequencies among populations can be very large for realistic rates of mutation unless an enormous number of populations are exchanging genes. As a result, the traditional diffusion approximation provides a poor approximation of the stationary distribution of allele frequencies among populations. Finally, we discuss some implications of our results for measures of population structure based on Wright's F-statistics.