Anisotropic Diffusion Approximations for Time-dependent Particle Transport.

In this thesis, we develop and numerically test new approximations to time-dependent radiation transport with the goal of obtaining more accurate solutions than the diffusion approximation can generate, yet requiring less computational effort than full transport. The first method is the nascent anisotropic diffusion (AD) approximation, which we extend to time-dependent problems in finite domains; the second is a novel anisotropic P_1-like (AP_1) approximation. These methods are ``anisotropic'' in that, rather than operating under the assumption of linearly anisotropic radiation, they incorporate an arbitrary amount of anisotropy via a transport-calculated diffusion coefficient. This anisotropic diffusion tensor is the second angular moment of a simple, purely absorbing transport problem. In this thesis, much of the computational testing of the new methods is performed in ``flatland'' geometry, a fictional two-dimensional universe that provides a realistic but computationally inexpensive testbed. As work ancillary to anisotropic diffusion and the numerical experiments, a complete description of flatland diffusion, including boundary conditions, is developed. Also, implementation details for both Monte Carlo and S_N transport in flatland are provided. The two new anisotropic methods, along with a ``flux limited'' modification to anisotropic diffusion, are tested in a variety of problems. Some aspects of the theory, including the newly formulated boundary conditions, are tested first with diffusive, steady-state problems. The new methods are compared against existing ones in linear, time-dependent radiation transport problems. Finally, the efficacy and performance of the anisotropic methods are investigated in several thermal radiative transfer (TRT) computational experiments. Our results demonstrate that for many multi-dimensional problems, the new anisotropic methods perform much better than their conventional counterparts. In every time-dependent test, the flux-limited anisotropic diffusion approach produced the most accurate solutions of the new methods. Based on our numerical testing, we believe this method to be a strong contender for accurate, inexpensive simulations of time-dependent transport and thermal radiative transfer problems.Ph.D.Nuclear Engineering & Radiological SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/91465/1/sethrj_1.pd

Dual Anion-Cation Ionic Liquid Crystal for Battery Applications

Ionic liquid crystals (ILCs) are a special class of compounds that not only contains mesogens group but also have cationic and/or anionic components. ILCs can self-organize into assemblies with varying degrees of orientational order resulting into formation of unique liquid crystal phases. Thermotropic ionic liquid crystals are special subclass of liquid crystal containing ionic liquid moiety that self- assemble with application of heat to form liquid crystal phases. Thermotropic ionic liquid crystal materials may exhibit several mesogenic phases at differing temperatures, distinguishable by the degree of order. This work mainly focuses on synthesis and characterization of Ionic liquid Crystals containing imidazolium and sulfonimide functional group attached to phenyl ring containing long chain alkyl group. In this presentation we will focus on how change in alkyl tail, change in ionic component (sulfonimide vs imidazolium) , and counter ion (i.e., triethyl ammonium vs Lithium cation) present in the compound, affect the liquid crystal properties. The synthesized ILCs was characterized by TGA, DSC and SAXS data. Keywords: Ionic liquids, Liquid crystals, Dual Cation-Anion, Batterie