Fast numerical methods for mixed, singular Helmholtz boundary value problems and Laplace eigenvalue problems - with applications to antenna design, sloshing, electromagnetic scattering and spectral geometry

This thesis presents a novel class of algorithms for the solution of scattering and eigenvalue problems on general two-dimensional domains under a variety of boundary conditions, including non-smooth domains and certain "Zaremba" boundary conditions - for which Dirichlet and Neumann conditions are specified on various portions of the domain boundary. The theoretical basis of the methods for the Zaremba problems on smooth domains concern detailed information, which is put forth for the first time in this thesis, about the singularity structure of solutions of the Laplace operator under boundary conditions of Zaremba type. The new methods, which are based on use of Green functions and integral equations, incorporate a number of algorithmic innovations, including a fast and robust eigenvalue-search algorithm, use of the Fourier Continuation method for regularization of all smooth-domain Zaremba singularities, and newly derived quadrature rules which give rise to high-order convergence even around singular points for the Zaremba problem. The resulting algorithms enjoy high-order convergence, and they can tackle a variety of elliptic problems under general boundary conditions, including, for example, eigenvalue problems, scattering problems, and, in particular, eigenfunction expansion for time-domain problems in non-separable physical domains with mixed boundary conditions.

Fast Lattice Green's Function Methods for Viscous Incompressible Flows on Unbounded Domains

In this thesis, a collection of novel numerical techniques culminating in a fast, parallel method for the direct numerical simulation of incompressible viscous flows around surfaces immersed in unbounded fluid domains is presented. At the core of all these techniques is the use of the fundamental solutions, or lattice Green’s functions, of discrete operators to solve inhomogeneous elliptic difference equations arising in the discretization of the three-dimensional incompressible Navier-Stokes equations on unbounded regular grids. In addition to automatically enforcing the natural free-space boundary conditions, these new lattice Green’s function techniques facilitate the implementation of robust staggered-Cartesian-grid flow solvers with efficient nodal distributions and fast multipole methods. The provable conservation and stability properties of the appropriately combined discretization and solution techniques ensure robust numerical solutions. Numerical experiments on thin vortex rings, low-aspect-ratio flat plates, and spheres are used verify the accuracy, physical fidelity, and computational efficiency of the present formulations.

Natural cone formation for fast ignition of laser fusion

We propose to utilize the leading pulse of a petawatt class laser to create a conic plasma channel in the dense plasmas. This plasma channel could serve as a natural cone to guide the main pulse to the cone tip, as behaves similarly to the physical Au cone. We estimate that the leading pulse of a petawatt laser could create a natural cone with cone tip only about 100 mu m away from the edge of compressed core plasma. The natural cone formation should be compatible for a good uniform compression and efficient fast heating of the imploded fuel.

Fast and Efficient Neural Conversion of Human Hematopoietic Cells

Neurons obtained directly from human somatic cells hold great promise for disease modeling and drug screening. Available protocols rely on overexpression of transcription factors using integrative vectors and are often slow, complex, and inefficient. We report a fast and efficient approach for generating induced neural cells (iNCs) directly from human hematopoietic cells using Sendai virus. Upon SOX2 and c-MYC expression, CD133-positive cord blood cells rapidly adopt a neuroepithelial morphology and exhibit high expansion capacity. Under defined neurogenic culture conditions, they express mature neuronal markers and fire spontaneous action potentials that can be modulated with neurotransmitters. SOX2 and c-MYC are also sufficient to convert peripheral blood mononuclear cells into iNCs. However, the conversion process is less efficient and resulting iNCs have limited expansion capacity and electrophysiological activity upon differentiation. Our study demonstrates rapid and efficient generation of iNCs from hematopoietic cells while underscoring the impact of target cells on conversion efficiency.

Preparation, characterization and gas sensing properties of high soluble metal (II) phthalocyanine thin films by spin-coating method

Three novel metal (II) phthalocyanine complexes were synthesized by cyclic tetramerisation reaction of a dicyano benzene component and different metal ions (Pd2+, Co2+, Zn2+). The structure of complexes was confirmed by elemental analysis, mass and IR spectrum. The excellent solubility of the complexes in benzene enabled us to obtain films by a spin-coating method. The films were characterized by IR, electronic spectral and AFM. The gas sensing properties to NO2 of the metal (II) phthalocyanine complex films were studied. In addition, the effects of different metal ions and the gas sensing temperature on the sensing properties were studied. (C) 2005 Elsevier B.V. All rights reserved.

Preparation, characterization and gas sensing properties of lead tetra-(tert-butyl)-5,10,1 5,20-tetraazaporphyrin spin-coating films

A spin-coated film of lead tetra-(tert-butyl)-5,10,15,20-tetraazaporphyrin complex (PbTAP(t-Bu)(4)) was obtained and characterized by IR spectra, absorption spectra and atomic force microscopy. The response and recovery characteristics of the film to NH3, NO2 and C2H5OH vapor were investigated at room temperature. In addition, the reversibility and stability of the film to NH3 were also studied. The results indicate that the PbTAP(t-Bu)(4) derivative can be exploited as an NH3 sensor at room temperature. (c) 2007 Elsevier B.V. All rights reserved.