Norm-Resolvent Estimates and Perforated Domains

In this thesis we are concerned with norm-resolvent estimates for unbounded linear operators. The text is structured into four parts. The first two parts contain mathematical preliminaries, reviews of previous work and an introduction into the two results which constitute parts three and four. In the third part we are concerned with the non-normal Schrödinger operator H = −∆+V on L²(Rᵈ), where Re(V(x))≥c|x|²−b for some c,b>0. The spectrum of this operator is discrete and its real part is bounded below by −b. In general, the ε-pseudospectrum of H will have an unbounded component for any ε > 0 and thus will not approximate the spectrum in a global sense. By exploiting the fact that the semigroup exp(−tH) is immediately compact, we show a complementary result, namely that for every δ > 0, R > 0 there exists an ε > 0 such that the ε-pseudospectrum is contained in the union of the half plane {Re(z)>R} and disks of radius δ around the eigenvalues. In particular, the unbounded component of the pseudospectrum escapes towards +∞ as ε decreases. Additionally, we give two examples of non-selfadjoint Schrödinger operators outside of our class and study their pseudospectra in more detail. In Part IV, we prove norm-resolvent convergence, as ε→0, for the operator −∆ in domain perforated ε-periodically, to the limit operator −∆+μ on L²(Ω), where μ∈C is a constant depending on the choice of boundary conditions on the holes (we consider Dirichlet, Neumann and Robin boundary conditions). This is an improvement of previous results by [Cioranescu-Murat(1997)], [Kaizu(1985)], which show strong resolvent convergence. In particular, our result implies Hausdorff convergence of the spectrum of the resolvent for the perforated domain problem

Norm-Resolvent Estimates and Perforated Domains

In this thesis we are concerned with norm-resolvent estimates for unbounded linear operators. The text is structured into four parts. The first two parts contain mathematical preliminaries, reviews of previous work and an introduction into the two results which constitute parts three and four. In the third part we are concerned with the non-normal Schrödinger operator H = −∆+V on L²(Rᵈ), where Re(V(x))≥c|x|²−b for some c,b>0. The spectrum of this operator is discrete and its real part is bounded below by −b. In general, the ε-pseudospectrum of H will have an unbounded component for any ε > 0 and thus will not approximate the spectrum in a global sense. By exploiting the fact that the semigroup exp(−tH) is immediately compact, we show a complementary result, namely that for every δ > 0, R > 0 there exists an ε > 0 such that the ε-pseudospectrum is contained in the union of the half plane {Re(z)>R} and disks of radius δ around the eigenvalues. In particular, the unbounded component of the pseudospectrum escapes towards +∞ as ε decreases. Additionally, we give two examples of non-selfadjoint Schrödinger operators outside of our class and study their pseudospectra in more detail. In Part IV, we prove norm-resolvent convergence, as ε→0, for the operator −∆ in domain perforated ε-periodically, to the limit operator −∆+μ on L²(Ω), where μ∈C is a constant depending on the choice of boundary conditions on the holes (we consider Dirichlet, Neumann and Robin boundary conditions). This is an improvement of previous results by [Cioranescu-Murat(1997)], [Kaizu(1985)], which show strong resolvent convergence. In particular, our result implies Hausdorff convergence of the spectrum of the resolvent for the perforated domain problem

Secondary Electron Emission from Simple Metals: Comparative Studies for Al, Mg, and Be

In the secondary electron emission (SEE) from solids, the role of different excitation processes is now as ever of special interest from both the theoretical and the experimental points of view. Depending on the primary energy, the relative importance of different excitation mechanisms related to conduction as well as core electrons will be discussed for different simple metals. So far, first principles results are available only for Al for primary energies up to 10 keV. Starting from a microscopic description of the SEE based on the transport equation formalism, calculations were performed for other nearly-free-electron metals (Mg, Be) up to primary energies used in scanning electron microscopy. In this way, it is possible to obtain more general statements about the role of different excitation processes responsible for SEE. Special attention is devoted to the contribution of emitted electrons stemming from the excitation of conduction electrons by decay of bulk plasmons generated by the primary electron. The different strength of this excitation mechanism in Al, Mg, and Be is related to the different magnitude of the plasmon damping in these metals

Acting the part : gender and performance in contemporary plays by women

Acknowledging performance as a process through which gender identities are constituted, the thesis explores attempts in women's theatre to subject these very constructs to creative deconstruction. It offers a study of plays by Caryl Churchill, Sarah Daniels and Timberlake Wertenbaker. Setting their work in the context of prevailing discourses of representation, the analysis delineates the ways in which plays by women interrogate the Western tradition of meaning and perception. The thesis proposes theatrical performance as a strategic engagement with the very means by which women's position is constituted. Therefore, it argues that in women's dramatic work, the possibility of resistance, of agency and choice occurs in the playful adaptation of dominant discourse, allowing for new figurations of subjectivity. Exploring the difficulties and limitations involved in this strategy, the study evaluates how plays by women release a potential for transgression which dislocates the structures of representation

Odi et Amo? Hobbes on the state of nature

Very few-if any-will doubt Hobbes's aversion to the state of nature and sympathy for civil society. On the other hand, it is not quite news that it would be inaccurate to claim that Hobbes rejected the state of nature entirely. Indeed, he embraced or at the very least tolerated the state of nature at the international level in order to escape from the individual state of nature. Hobbes's recommended exchange of an individual state of nature for an international one does seem to have a smack of contradiction, arguably first noted by Rousseau. There is yet another charge of contradiction lurking around Hobbes's account of the state of nature. Hobbes's political thought would still reflect an ambivalent attitude towards a third instantiation of the state of nature, i.e. civil war. This is one of the main reasons why the political allegiance of Thomas Hobbes has been an issue ever since the publication of De Cive at the very least. This paper deals with Hobbes's differential treatment of the original and the international states of nature and discusses the source of Hobbes's somewhat ambivalent attitude towards civil war. It is here argued that Hobbes can fairly hold his ground vis-à-vis Rousseau's criticism, in spite of the normative resemblance between the international state of nature and the initial state of nature, and that Hobbes ambivalent attitude of attraction and repulsion towards civil war is actually due not so much to opportunism on his part as to the normative autonomy he has granted to the state of nature.Fil: Rosler, Andres Bernardo. Universidad de Buenos Aires. Facultad de Filosofía y Letras. Departamento de Filosofía; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Semiconductor grade, solar silicon purification project

The conversion of metallurgical grade silicon into semiconductor grade silicon by way of a three step SiF2 polymer transport purification process was investigated. Developments in the following areas were also examined: (1) spectroscopic analysis and characterization of (SiF2) sub x polymer and Si sub x F sub y homologue conversion; (2) demonstration runs on the near continuous apparatus; (3) economic analysis; and (4) elemental analysis

Semiconductor Grade, Solar Silicon Purification Project

A low cost by-product, SiF4, is reacted with mg silicon to form SiF2 gas which is polymerized. The (SiF2)x polymer is heated forming volatile SixFy homologues which disproportionate on a silicon particle bed forming silicon and SiF4. The silicon analysis procedure relied heavily on mass spectroscopic and emission spectroscopic analysis. These analyses demonstrated that major purification had occured and some samples were indistinguishable from semiconductor grade silicon (except possibly for phosphorus). However, electrical analysis via crystal growth reveal that the product contains compensated phosphorus and boron

Semiconductor grade, solar silicon purification project

Experimental apparatus and procedures used in the development of a 3-step SiF2(x) polymer transport purification process are described. Both S.S.M.S. and E.S. analysis demonstrated that major purification had occured and some samples were indistinguishable from semiconductor grade silicon (except possibly for phosphorus). Recent electrical analysis via crystal growth reveals that the product contains compensated phosphorus and boron. The low projected product cost and short energy payback time suggest that the economics of this process will result in a cost less than the goal of $10/Kg(1975 dollars). The process appears to be readily scalable to a major silicon purification facility