Quantum transition state theory and solving a first order master equation for complex reactions numerically

The field of chemical kinetics is an exciting and active field. The prevailing theories make a number of simplifying assumptions that do not always hold in actual cases. Another current problem concerns a development of efficient numerical algorithms for solving the master equations that arise in the description of complex reactions. The objective of the present work is to furnish a completely general and exact theory of reaction rates, in a form reminiscent of transition state theory, valid for all fluid phases and also to develop a computer program that can solve complex reactions by finding the concentrations of all participating substances as a function of time. To do so, the full quantum scattering theory is used for deriving the exact rate law, and then the resulting cumulative reaction probability is put into several equivalent forms that take into account all relativistic effects if applicable, including one that is strongly reminiscent of transition state theory, but includes corrections from scattering theory. Then two programs, one for solving complex reactions, the other for solving first order linear kinetic master equations to solve them, have been developed and tested for simple applications.

Optimization of three-dimensional branching networks of microchannels for thermal management of microelectronics

The aim of this work is to present a methodology to develop cost-effective thermal management solutions for microelectronic devices, capable of removing maximum amount of heat and delivering maximally uniform temperature distributions. The topological and geometrical characteristics of multiple-story three-dimensional branching networks of microchannels were developed using multi-objective optimization. A conjugate heat transfer analysis software package and an automatic 3D microchannel network generator were developed and coupled with a modified version of a particle-swarm optimization algorithm with a goal of creating a design tool for 3D networks of optimized coolant flow passages. Numerical algorithms in the conjugate heat transfer solution package include a quasi-ID thermo-fluid solver and a steady heat diffusion solver, which were validated against results from high-fidelity Navier-Stokes equations solver and analytical solutions for basic fluid dynamics test cases. Pareto-optimal solutions demonstrate that thermal loads of up to 500 W/cm2 can be managed with 3D microchannel networks, with pumping power requirements up to 50% lower with respect to currently used high-performance cooling technologies.

Modeling of a Heat-Induced Buckling of Plates Using the Mesh-free Method

In the process of engineering design of structural shapes, the flat plate analysis results can be generalized to predict behaviors of complete structural shapes. In this case, the purpose of this project is to analyze a thin flat plate under conductive heat transfer and to simulate the temperature distribution, thermal stresses, total displacements, and buckling deformations. The current approach in these cases has been using the Finite Element Method (FEM), whose basis is the construction of a conforming mesh. In contrast, this project uses the mesh-free Scan Solve Method. This method eliminates the meshing limitation using a non-conforming mesh. I implemented this modeling process developing numerical algorithms and software tools to model thermally induced buckling. In addition, convergence analysis was achieved, and the results were compared with FEM. In conclusion, the results demonstrate that the method gives similar solutions to FEM in quality, but it is computationally less time consuming.

Meshfree Method for Prediction of Thermal Properties of Porous Ceramic Materials

In the presented thesis work, meshfree method with distance fields is applied to create a novel computational approach which enables inclusion of the realistic geometric models of the microstructure and liberates Finite Element Analysis(FEA) from thedependance on and limitations of meshing of fine microstructural feature such as splats and porosity.Manufacturing processes of ceramics produce materials with complex porosity microstructure.Geometry of pores, their size and location substantially affect macro scale physical properties of the material. Complex structure and geometry of the pores severely limit application of modern Finite Element Analysis methods because they require construction of spatial grids (meshes) that conform to the geometric shape of the structure. As a result, there are virtually no effective tools available for predicting overall mechanical and thermal properties of porous materials based on their microstructure. This thesis is a separate handling and controls of geometric and physical computational models that are seamlessly combined at solution run time. Using the proposedapproach we will determine the effective thermal conductivity tensor of real porous ceramic materials featuring both isotropic and anisotropic thermal properties. This work involved development and implementation of numerical algorithms, data structure, and software.

Development of a Coupling Model for Fluid-Structure Interaction using the Mesh-free Finite Element Method and the Lattice Boltzmann Method

In the presented thesis work, the meshfree method with distance fields was coupled with the lattice Boltzmann method to obtain solutions of fluid-structure interaction problems. The thesis work involved development and implementation of numerical algorithms, data structure, and software. Numerical and computational properties of the coupling algorithm combining the meshfree method with distance fields and the lattice Boltzmann method were investigated. Convergence and accuracy of the methodology was validated by analytical solutions. The research was focused on fluid-structure interaction solutions in complex, mesh-resistant domains as both the lattice Boltzmann method and the meshfree method with distance fields are particularly adept in these situations. Furthermore, the fluid solution provided by the lattice Boltzmann method is massively scalable, allowing extensive use of cutting edge parallel computing resources to accelerate this phase of the solution process. The meshfree method with distance fields allows for exact satisfaction of boundary conditions making it possible to exactly capture the effects of the fluid field on the solid structure.

Optimizing the radiation pattern of smart antennas using genetic algorithms

This work is directed towards optimizing the radiation pattern of smart antennas using genetic algorithms. The structure of the smart antennas based on Space Division Multiple Access (SDMA) is proposed. It is composed of adaptive antennas, each of which has adjustable weight elements for amplitudes and phases of signals. The corresponding radiation pattern formula available for the utilization of numerical optimization techniques is deduced. Genetic algorithms are applied to search the best phase-amplitude weights or phase-only weights with which the optimal radiation pattern can be achieved. ^ One highlight of this work is the proposed optimal radiation pattern concept and its implementation by genetic algorithms. The results show that genetic algorithms are effective for the true Signal-Interference-Ratio (SIR) design of smart antennas. This means that not only nulls can be put in the directions of the interfering signals but also simultaneously main lobes can be formed in the directions of the desired signals. The optimal radiation pattern of a smart antenna possessing SDMA ability has been achieved. ^ The second highlight is on the weight search by genetic algorithms for the optimal radiation pattern design of antennas having more than one interfering signal. The regular criterion for determining which chromosome should be kept for the next step iteration is modified so as to improve the performance of the genetic algorithm iteration. The results show that the modified criterion can speed up and guarantee the iteration to be convergent. ^ In addition, the comparison between phase-amplitude perturbations and phase-only perturbations for the radiation pattern design of smart antennas are carried out. The effects of parameters used by the genetic algorithm on the optimal radiation pattern design are investigated. Valuable results are obtained. ^