Fabrication of photovoltaic laser energy converterby MBE

A laser-energy converter, fabricated by molecular beam epitaxy (MBE), was developed. This converter is a stack of vertical p-n junctions connected in series by low-resistivity, lattice matched CoSi2 layers to achieve a high conversion efficiency. Special high-temperature electron-beam (e-beam) sources were developed especially for the MBE growth of the junctions and CoSi2 layers. Making use of the small (greater than 1.2 percent) lattice mismatch between CoSi2 and Si layers, high-quality and pinhole-free epilayers were achieved, providing a capability of fabricating all the junctions and connecting layers as a single growth process with one pumpdown. Well-defined multiple p-n junctions connected by CoSi2 layers were accomplished by employing a low growth temperature (greater than 700 C) and a low growth rate (less than 0.5 microns/hour). Producing negligible interdiffusion, the low growth temperature and rate also produced negligible pinholes in the CoSi2 layers. For the first time, a stack of three p-n junctions connected by two 10(exp -5) Ohm-cm CoSi2 layers was achieved, meeting the high conversion efficiency requirement. This process can now be optimized for high growth rate to form a practical converter with 10 p-n junctions in the stack

Development of a numerical solution to the time dependent kinetic equation

A numerical solution was developed for the time dependent Fokker-Planck equation for arbitrary distributions of electrons injected into a magnetized plasma. The code which includes energy loss and pitch angle scattering due to Coulomb collisions and changes in pitch angle due to inhomogeneous magnetic fields was calibrated and tested. The numerical method is versatile so that other scattering or radiation terms can be easily included. Using this code many processes associated with the impulsive phase of solar flares will be investigated

Precompactness of solutions to the Ricci flow in the absence of injectivity radius estimates

Consider a sequence of pointed n-dimensional complete Riemannian manifolds {(M_i,g_i(t), O_i)} such that t in [0,T] are solutions to the Ricci flow and g_i(t) have uniformly bounded curvatures and derivatives of curvatures. Richard Hamilton showed that if the initial injectivity radii are uniformly bounded below then there is a subsequence which converges to an n-dimensional solution to the Ricci flow. We prove a generalization of this theorem where the initial metrics may collapse. Without injectivity radius bounds we must allow for convergence in the Gromov-Hausdorff sense to a space which is not a manifold but only a metric space. We then look at the local geometry of the limit to understand how it relates to the Ricci flow.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol7/paper14.abs.htm

Manifolds with 1/4-pinched flag curvature

We say that a nonnegatively curved manifold $(M,g)$ has quarter pinched flag curvature if for any two planes which intersect in a line the ratio of their sectional curvature is bounded above by 4. We show that these manifolds have nonnegative complex sectional curvature. By combining with a theorem of Brendle and Schoen it follows that any positively curved manifold with strictly quarter pinched flag curvature must be a space form. This in turn generalizes a result of Andrews and Nguyen in dimension 4. For odd dimensional manifolds we obtain results for the case that the flag curvature is pinched with some constant below one quarter, one of which generalizes a recent work of Petersen and Tao

Modelling the urban heat island in Birmingham, UK at the neighbourhood scale

Cities have higher peak temperatures compared to surrounding rural areas. The urban-rural surface air temperature difference is known as the urban heat island (UHI). As extreme heat exposure can lead to adverse health effects, information on UHI characteristics of cities is important for future urban climate planning strategies. This study applied the ADMS-Urban Temperature and Humidity model to investigate the key processes driving the UHI in Birmingham, UK, at the neighbourhood scale. This model was configured with a range of input datasets (such as meteorological data, landuse data, building data, anthropogenic heat sources etc) and run on the University of Birmingham’s BlueBEAR HPC. This urban climate modelling was evaluated against the temperature measurement datasets from UK Met Office and Weather Underground. The spatiotemporal variations of surface air temperature in Birmingham, UK were captured by this model. This modelling study can be further applied to explore the impacts of local urban head island mitigation strategies

On the spectra of the quantized action-variables of the compactified Ruijsenaars-Schneider system

A simple derivation of the spectra of the action-variables of the quantized compactified Ruijsenaars-Schneider system is presented. The spectra are obtained by combining Kahler quantization with the identification of the classical action-variables as a standard toric moment map on the complex projective space. The result is consistent with the Schrodinger quantization of the system worked out previously by van Diejen and Vinet.Comment: Based on talk at the workshop CQIS-2011 (Protvino, Russia, January 2011), 12 page

The quantization of the symplectic groupoid of the standard Podles sphere

We give an explicit form of the symplectic groupoid that integrates the semiclassical standard Podles sphere. We show that Sheu's groupoid, whose convolution C*-algebra quantizes the sphere, appears as the groupoid of the Bohr-Sommerfeld leaves of a (singular) real polarization of the symplectic groupoid. By using a complex polarization we recover the convolution algebra on the space of polarized sections. We stress the role of the modular class in the definition of the scalar product in order to get the correct quantum space.Comment: 33 pages; minor correction

IBM-1 description of the fission products 108,110,112^{108,110,112}Ru

IBM-1} calculations for the fission products $^{108,110,112}$Ru have been carried out. The even-even isotopes of Ru can be described as transitional nuclei situated between the U(5) (spherical vibrator) and SO(6) ($\gamma$-unstable rotor) symmetries of the Interacting Boson Model. At first, a Hamiltonian with only one- and two-body terms has been used. Excitation energies and $B$(E2) ratios of gamma transitions have been calculated. A satisfactory agreement has been obtained, with the exception of the odd-even staggering in the quasi-$\gamma$ bands of $^{110,112}$Ru. The observed pattern is rather similar to the one for a rigid triaxial rotor. A calculation based on a Hamiltonian with three-body terms was able to remove this discrepancy. The relation between the IBM and the triaxial rotor model was also examined.Comment: 22 pages, 8 figure

Building solids inside nano-space: from confined amorphous through confined solvate to confined ‘metastable’ polymorph

The nanocrystallisation of complex molecules inside mesoporous hosts and control over the resulting structure is a significant challenge. To date the largest organic molecule crystallised inside the nano-pores is a known pharmaceutical intermediate – ROY (259.3 g mol1). In this work we demonstrate smart manipulation of the phase of a larger confined pharmaceutical – indomethacin (IMC, 357.8 g mol1), a substance with known conformational flexibility and complex polymorphic behaviour. We show the detailed structural analysis and the control of solid state transformations of encapsulated molecules inside the pores of mesoscopic cellular foam (MCF, pore size ca. 29 nm) and controlled pore glass (CPG, pore size ca. 55 nm). Starting from confined amorphous IMC we drive crystallisation into a confined methanol solvate, which upon vacuum drying leads to the stabilised rare form V of IMC inside the MCF host. In contrast to the pure form, encapsulated form V does not transform into a more stable polymorph upon heating. The size of the constraining pores and the drug concentration within the pores determine whether the amorphous state of the drug is stabilised or it recrystallises into confined nanocrystals. The work presents, in a critical manner, an application of complementary techniques (DSC, PXRD, solid-state NMR, N2 adsorption) to confirm unambiguously the phase transitions under confinement and offers a comprehensive strategy towards the formation and control of nano-crystalline encapsulated organic solids