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We study an energy functional able to describe low energy configurations of a two dimensional lattice with dislocations in a nonlinear elasticity regime. The main result can be described as follows: configurations of energy comparable to the lattice spacing consist of piecewise constant microrotations with small angle grain boundaries between them. Moreover, we also give bounds to the energy of particular configurations describing a small angle symmetric tilt grain boundary.

Increasing relative semiconductor process variations are making the prediction of realistic worst-case integrated circuit delay or sign-off yield more difficult. As process geometries shrink, intra-die variations have become dominant and it is imperative to model them to obtain accurate timing analysis results. In addition, intra-die process variations are spatially correlated due to pattern dependencies in the manufacturing process. Any statistical static timing analysis (SSTA) tool is incomplete without a model for signal crosstalk, as critical path delays can increase or decrease depending on the switching of capacitively coupled nets. The coupled signal timing in turn depends on the process variations. This work describes an SSTA tool that models signal crosstalk and spatial correlation in intra-die process variations, along with gradients and inter-die variations.

Thèse de doctorat : Mathématiques : Metz : 2000. / Thèse soutenue sur ensemble de travaux. Bibliogr. Index.

Thesis (M.S.)--Worcester Polytechnic Institute. / Keywords: homogenization; calculus of variations. Includes bibliographical references (p. 21).

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published_or_final_version / Mathematics / Master / Master of Philosophy

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A review of the published music for solo bassoon suggests that there is relatively little solo literature for the instrument that dates from the late eighteenth and early nineteenth centuries. This document focuses on the creation of a modern performance edition and piano reduction of a recently uncovered work for solo bassoon and orchestra by Johann Dotzauer, VIII Variations for Bassoon and Orchestra, Op. 40 (originally published by Freiderich Hoffmeister Musikverlag in 1817).A comparison of Dotzauer's work with a comparable published work by Anton Reicha, reveals that the two works are similar in their treatment of phrase structure, form, harmonic and melodic language, range, and solo passagework. This comparison has shown that Dotzauer's piece is representative of the type of writing for solo bassoon that skilled composers employed in the early nineteenth century. Through the editing process, errors and inconsistencies found in the newly-uncovered Hoffmeister Edition of VIII Variations such as corrections to pitches and notation, articulation markings, dynamic markings, and other changes have been corrected in a manner that both reflects the integrity of the Hoffmeister Edition and adds clarification for those who will perform the work. VIII Variations for Bassoon and Orchestra, Op. 40 by Johann Dotzauer, is a well-crafted composition for solo bassoon that will help fill a void in the literature for bassoon now that it is more accessible through the creation of a new performance edition and piano arrangement.