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.

A multi-regional view on aging societies accounting for the existence of non-tradable goods

This thesis assesses the question, whether accounting for non-tradable goods sectors in a calibrated Auerbach-Kotlikoff multi-regional overlapping-generations-model significantly affects this model’s results when simulating the economic impact of demographic change. Non-tradable goods constitute a major part of up to 80 percent of GDP of modern economies. At the same time, multi-regional overlapping-generations-models presented by literature on demographic change so far ignored their existence and counterfactually assumed perfect tradability between model regions. Moreover, this thesis introduces the assumption of an increasing preference share for non-tradable goods of old generations. This fact-based as-sumption is also not part of models in relevant literature. rnThese obvious simplifications of common models vis-à-vis reality notwithstanding, this thesis concludes that differences in results between a model featuring non-tradable goods and a common model with perfect tradability are very small. In other words, the common simplifi-cation of ignoring non-tradable goods is unlikely to lead to significant distortions in model results. rnIn order to ensure that differences in results between the ‘new’ model, featuring both non-tradable and tradable goods, and the common model solely reflect deviations due to the more realistic structure of the ‘new’ model, both models are calibrated to match exactly the same benchmark data and thus do not show deviations in their respective baseline steady states.rnA variation analysis performed in this thesis suggests that differences between the common model and a model with non-tradable goods can theoretically be large, but only if the bench-mark tradable goods sector is assumed to be unrealistically small.rnFinally, this thesis analyzes potential real exchange rate effects of demographic change, which could occur due to regional price differences of non-tradable goods. However, results show that shifts in real exchange rate based on these price differences are negligible.rn

Distinct eosinophil cytokine expression patterns in skin diseases - the possible existence of functionally different eosinophil subpopulations

The function of eosinophils has been attributed to host defense, immunomodulation, and fibrosis. Although eosinophils are found among infiltrating cells in a broad spectrum of skin diseases, their pathogenic role remains uncertain. This study aimed to analyze the cytokine expression by eosinophils in different skin diseases.

ON THE EXISTENCE OF SHOCKS IN IRRADIATED EXOPLANETARY ATMOSPHERES

Supersonic flows are expected to exist in the atmospheres of irradiated exoplanets, but the question of whether shocks develop lingers. Specifically, it reduces to whether continuous flow in a closed loop may become supersonic and if some portions of the supersonic flow steepen into shocks. We first demonstrate that continuous, supersonic flow may exist in two flavors: isentropic and non-isentropic, with shocks being included in the latter class of solutions. Supersonic flow is a necessary but insufficient condition for shocks to develop. The development of a shock requires the characteristics of neighboring points in a flow to intersect. We demonstrate that the intersection of characteristics may be quantified via the knowledge of the Mach number. Finally, we examine three-dimensional simulations of hot Jovian atmospheres and demonstrate that shock formation is expected to occur mostly on the dayside hemisphere, upstream of the substellar point, because the enhanced temperatures near the substellar point provide a natural pressure barrier for the returning flow. Understanding the role of shocks in irradiated exoplanetary atmospheres is relevant to correctly modeling observables such as the peak offsets of infrared phase curves.

Comment on the existence of a long range correlation in the geomagnetic disturbance storm time (Dst) index

Very recently (Banerjee et al. in Astrophys. Space, doi:1007/s10509-011-0836-1, 2011) the statistics of geomagnetic Disturbance storm (Dst) index have been addressed, and the conclusion from this analysis suggests that the underlying dynamical process can be modeled as a fractional Brownian motion with persistent long-range correlations. In this comment we expose several misconceptions and flaws in the statistical analysis of that work. On the basis of these arguments, the former conclusion should be revisited.

NMR spectroscopy in studies of light-induced structural changes in mammalian rhodopsin: Applicability of solution 19F NMR

We report high resolution solution 19F NMR spectra of fluorine-labeled rhodopsin mutants in detergent micelles. Single cysteine substitution mutants in the cytoplasmic face of rhodopsin were labeled by attachment of the trifluoroethylthio (TET), CF3-CH2-S, group through a disulfide linkage. TET-labeled cysteine mutants at amino acid positions 67, 140, 245, 248, 311, and 316 in rhodopsin were thus prepared. Purified mutant rhodopsins (6–10 mg), in dodecylmaltoside, were analyzed at 20°C by solution 19F NMR spectroscopy. The spectra recorded in the dark showed the following chemical shifts relative to trifluoroacetate: Cys-67, 9.8 ppm; Cys-140, 10.6 ppm; Cys-245, 9.9 ppm; Cys-248, 9.5 ppm; Cys-311, 9.9 ppm; and Cys-316, 10.0 ppm. Thus, all mutants showed chemical shifts downfield that of free TET (6.5 ppm). On illumination to form metarhodopsin II, upfield changes in chemical shift were observed for 19F labels at positions 67 (−0.2 ppm) and 140 (−0.4 ppm) and downfield changes for positions 248 (+0.1 ppm) and 316 (+0.1 ppm) whereas little or no change was observed at positions 311 and 245. On decay of metarhodopsin II, the chemical shifts reverted largely to those originally observed in the dark. The results demonstrate the applicability of solution 19F NMR spectroscopy to studies of the tertiary structures in the cytoplasmic face of intact rhodopsin in the dark and on light activation.

Evidence for the existence of a sulfonylurea-receptor-like protein in plants: Modulation of stomatal movements and guard cell potassium channels by sulfonylureas and potassium channel openers

Limitation of water loss and control of gas exchange is accomplished in plant leaves via stomatal guard cells. Stomata open in response to light when an increase in guard cell turgor is triggered by ions and water influx across the plasma membrane. Recent evidence demonstrating the existence of ATP-binding cassette proteins in plants led us to analyze the effect of compounds known for their ability to modulate ATP-sensitive potassium channels (K-ATP) in animal cells. By using epidermal strip bioassays and whole-cell patch-clamp experiments with Vicia faba guard cell protoplasts, we describe a pharmacological profile that is specific for the outward K+ channel and very similar to the one described for ATP-sensitive potassium channels in mammalian cells. Tolbutamide and glibenclamide induced stomatal opening in bioassays and in patch-clamp experiments, a specific inhibition of the outward K+ channel by these compounds was observed. Conversely, application of potassium channel openers such as cromakalim or RP49356 triggered stomatal closure. An apparent competition between sulfonylureas and potassium channel openers occurred in bioassays, and outward potassium currents, previously inhibited by glibenclamide, were partially recovered after application of cromakalim. By using an expressed sequence tag clone from an Arabidopsis thaliana homologue of the sulfonylurea receptor, a 7-kb transcript was detected by Northern blot analysis in guard cells and other tissues. Beside the molecular evidence recently obtained for the expression of ATP-binding cassette protein transcripts in plants, these results give pharmacological support to the presence of a sulfonylurea-receptor-like protein in the guard-cell plasma membrane tightly involved in the outward potassium channel regulation during stomatal movements.

On the existence of fractal strings whose set of dimensions of fractality is not perfect

In this paper we give an example of a nonlattice self-similar fractal string such that the set of real parts of their complex dimensions has an isolated point. This proves that, in general, the set of dimensions of fractality of a fractal string is not a perfect set.

On the existence of exponential polynomials with prefixed gaps

This paper shows that the conjecture of Lapidus and Van Frankenhuysen on the set of dimensions of fractality associated with a nonlattice fractal string is true in the important special case of a generic nonlattice self-similar string, but in general is false. The proof and the counterexample of this have been given by virtue of a result on exponential polynomials P(z), with real frequencies linearly independent over the rationals, that establishes a bound for the number of gaps of RP, the closure of the set of the real projections of its zeros, and the reason for which these gaps are produced.

A note on the effect of the HCl concentration on the heat of solution of thorium tetrachloride /

Work performed at the Argonne National Laboratory.

A note on the non-existence of multivalue A-stable methods of order greater than two /

Bibliography: leaf 3.

New method of solution of the traveling salesman problem /

"Supported in part jointly by the Atomic Energy Commission and the Advanced Research Projects Agency (ARPA) under AEC Contract AT(11-1)-1018."

On the existence of non-static plane symmetric space-times /

"July 30, 1958"

The existence of evil spirits proved; and their agency, particularly in relation to the human race, explained and illustrated.

Mode of access: Internet.