Extensions of Modules over Schur Algebras, Symmetric Groups and Hecke Algebras

We study the relation between the cohomology of general linear and symmetric groups and their respective quantizations, using Schur algebras and standard homological techniques to build appropriate spectral sequences. As our methods fit inside a much more general context within the theory of finite-dimensional algebras, we develop our results first in that general setting, and then specialize to the above situations. From this we obtain new proofs of several known results in modular representation theory of symmetric groups. Moreover, we reduce certain questions about computing extensions for symmetric groups and Hecke algebras to questions about extensions for general linear groups and their quantizations.     

Analytic and numerical solutions in the theory of elastic plates

ABSTRACT

Numerical approximations of the solution of a boundary value problem when an exact solution is not available can be constructed by means of a variety of methods. In this paper, we present a technique that is based on the integral representation of the solution of an elliptic problem and the properties of the associated layer potentials. The procedure is illustrated in application to the mathematical model of bending of plates with transverse shear deformation in a finite domain, in the presence of Dirichlet, Neumann, and Robin conditions prescribed on the boundary.     

Error-tolerant RF litz coils for NMR/MRI.

A new class of NMR RF volume coils is being developed that permits improved tuning range, B(1) homogeneity, tuning stability, and sensitivity compared to birdcages over a wide range of practical conditions, especially for microscopy and wraparound flexible applications. They are denoted litz coils, as their flux transparency and current distribution is obtained from woven foil patterns with insulated crossovers. Contrary to the design criteria of phased arrays, the parallel routes in litz coils use high coupling coefficients to achieve optimal current distribution, which is highly independent of tuning, balancing, and matching adjustments and is compatible with multiple capacitive segmentation. Magnetic filling factors, loaded Q, and inhomogeneity measurements and calculations are presented for a variety of litz coils with frequency-diameter products from 7 to 20 MHz-m and are compared to similar birdcages.     

Photoluminescence spectroscopy of the molecular biexciton in vertically stacked InAs-GaAs quantum dot pairs

We present photoluminescence studies of the molecular neutral biexciton-exciton spectra of individual vertically stacked InAs/GaAs quantum dot pairs. We tune either the hole or the electron levels of the two dots into tunneling resonances. The spectra are described well within a few-level, few-particle molecular model. Their properties can be modified broadly by an electric field and by structural design, which makes them highly attractive for controlling nonlinear optical properties.     

Accuracy of existing atomic potentials for the CdTe semiconductor compound

CdTe and CdTe-based Cd(1-x)Zn(x)Te (CZT) alloys are important semiconductor compounds that are used in a variety of technologies including solar cells, radiation detectors, and medical imaging devices. Performance of such systems, however, is limited due to the propensity of nano- and micro-scale defects that form during crystal growth and manufacturing processes. Molecular dynamics simulations offer an effective approach to study the formation and interaction of atomic scale defects in these crystals, and provide insight on how to minimize their concentrations. The success of such a modeling effort relies on the accuracy and transferability of the underlying interatomic potential used in simulations. Such a potential must not only predict a correct trend of structures and energies of a variety of elemental and compound lattices, defects, and surfaces but also capture correct melting behavior and should be capable of simulating crystalline growth during vapor deposition as these processes sample a variety of local configurations. In this paper, we perform a detailed evaluation of the performance of two literature potentials for CdTe, one having the Stillinger-Weber form and the other possessing the Tersoff form. We examine simulations of structures and the corresponding energies of a variety of elemental and compound lattices, defects, and surfaces compared to those obtained from ab initio calculations and experiments. We also perform melting temperature calculations and vapor deposition simulations. Our calculations show that the Stillinger-Weber parameterization produces the correct lowest energy structure. This potential, however, is not sufficiently transferrable for defect studies. Origins of the problems of these potentials are discussed and insights leading to the development of a more transferrable potential suitable for molecular dynamics simulations of defects in CdTe crystals are provided.