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A family of low-density lattice codes (LDLC) is studied based on Construction-A for lattices. The family of Construction-A codes is already known to contain a large capacity-achieving subset. Parallels are drawn between coset non-binary low-density parity-check (LDPC) codes and nested low-density Construction-A lattices codes. Most of the related research in LDPC domain assumes optimal power allocation to encoded codeword. The source coding problem of mapping message to power optimal codeword for any LDPC code is in general, NP-hard. In this thesis, we present a novel method for encoding and decoding lattice based on non-binary LDPC codes using message-passing algorithms. / text

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Reaction-diffusion-convection (R-D-C) problems are governed by wide spectrum of spatio-temporal scales associated with ranges of physical and chemical processes. Such Problems are called multiscale, multiphysics problems. The challenge associated with R-D-C problems is to bridge these scales and processes as seamlessly as possible. For this purpose, we develop a wavelet-based multiscale simulation framework that couples diverse scales and physics.In a first stage we focus on R-D models. We treat the `fine' reaction-scales stochastically, with kinetic Monte Carlo (kMC). The transport via diffusion possesses larger spatio-temporal scales which are bridged to the kMC with the Compound Wavelet Matrix (CWM) formalism. Since R-D-C problems are dynamical we extend the CWM method via the dynamic-coupling of the kMC and diffusion models. The process is approximated by sequential increments, where the CWM on each increment is used as the starting point for the next, providing better exploration of phase-space. The CWM is extended to two-dimensional diffusion with a reactive line-boundary to show that the computational gain and error depends on the scale-overlap and wavelet-filtering. We improve the homogenization by a wavelet-based scheme for the exchange of information between a reactive and diffusive field by passing information along fine to coarse (up-scaling) and coarse to fine (down-scaling) scales by retaining the fine-scale statistics (higher-order moments, correlations). Critical to the success of the scheme is the identification of dominant scales. The efficiency of the scheme is compared to the homogenization and benchmark model with scale-disparity.To incorporate transport by convection, we then couple the Lattice Boltzmann Model (LBM) and kMC operating at diverse scales for flows around reactive block. Such model explores markedly different physics due to strong interplay between these time-scales. `Small' reaction induced temperature variations are considered for multiscale coupling of the reactions with the flow, showing the discrepancies in the evolutions and yield comparing to the conventional model. The same framework is used to study the reactions induced by hydrodynamic bubble collapse which shows the similar features of the kinetics and yield comparing to conventional models.We culminate to some problems that could be solved using the developed framework and preliminary results are presented as "proof of concept."

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We use normal mode decomposition to obtain phonon properties from quasi-harmonic lattice dynamics calculations and classical molecular dynamics simulations in unstrained Lennard-Jones argon superlattices with perfect and mixed interfaces. Debye scaling of phonon lifetimes at low frequencies in both perfect and mixed superlattices and Rayleigh scaling for intermediate frequencies in mixed superlattices is observed. For short period mixed superlattices, lifetimes below the Ioffe-Regel limit are observed. The relaxation-time approximation of the Boltzmann transport equation is used to predict cross-plane and in-plane thermal conductivity. We find that using a dispersion relation which includes the secondary periodicity is required to predict thermal conductivity. The assumption of perturbative disorder, where Tamura elastic mass defect scattering theory can be applied, was found to be valid for predicting cross-plane thermal conductivities but not in-plane thermal conductivities in mixed superlattices.

Zircaloy-2 is used extensively in the nuclear industry as a structural material for the reactor core in both light and heavy water reactors. The intergranular strains and texture greatly affect the mechanical properties of the material while in operation. Understanding the plastic deformation of Zircaloy-2 will improve on current plastic deformation models, particularly for twinning mechanisms, which are more active at lower temperatures, and are not yet well understood. For this study, neutron diffraction was used to track the lattice spacing and peak intensity in warm-rolled and recrystallized Zircaloy-2 slab for various crystallographic orientations at 77 K. Tests were performed in all three principle directions under tension and compression. The texture was measured for the deformed samples to help interpret the dominant deformation systems and then Electron Back Scattering Diffraction was used to identify and image the active twinning modes. Prism <a> slip, basal <a> slip, {10-12} and {11-2 1} tensile twinning, and {11-2 2} compression twinning were found to be contributing deformation systems in Zircaloy-2 at 77K. In this study, the diffraction elastic constants for Zircaloy-2 at room temperature and 77K are reported for the first time in open literature. These values will be useful in future experimental work by allowing a conversion between lattice spacing and residual stress. / Thesis (Master, Mechanical and Materials Engineering) -- Queen's University, 2009-09-24 13:41:25.371

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