A numerical and analytical study of kinetic models for particle-wave interaction in plasmas

This dissertation presents a study of particle-wave interaction in plasmas. It focuses on a kinetic model called quasilinear theory, which is a reduction of VlasovMaxwell (or Vlasov-Poisson) system in the weak turbulence regime. The quantized waves in plasmas, known as plasmons, are absorbed or emitted by charged particles. Meanwhile, the particles change their states due to such emission/absorption process, therefore resulting in a nonlinear kinetic system for the pdf (probability density function) of particles and plasmons. The research presented here unfolds in two main topics: structure-preserving numerical solvers, and solvability of the kinetic model. On the first topic, we are interested in numerical simulation of non-uniform magnetized plasmas, which involves two processes: particle-wave interaction and wave propagation (plasmon advection). For particle-wave interaction in homogeneous magnetized plasmas, we propose a finite element scheme that preserves all the conservation laws. Firstly, an unconditionally conservative weak form is constructed. By “unconditional” we mean that conservation is independent of the transition probabilities. Then we design a discretization that preserves such unconditional conservation property, and discuss the conditions for positivity and stability. We present numerical examples with a “bump on tail” initial configuration, showing that the particle-wave interaction results in a strong anisotropic diffusion of the particles. We generalize the strategy to obtain a conservative DG (discontinuous Galerkin) scheme. The evolution of plasmon pdf is governed by a Liouville equation with additional reaction term caused by particle-wave interaction, where the dominant Poisson bracket term necessitates trajectorial average. Hence, we propose a Galerkin approach for trajectorial average in dynamical systems. The weak form of averaged equation is derived, and the concept of trajectory bundle is introduced. To compute and store the trajectory bundles, we propose a novel algorithm, named connection-proportion algorithm, which transforms a continuous topological problem into a discrete graph theory problem. The conservative DG scheme, combined with our trajectorial average method, renders a structure-preserving solver for particle-wave interaction in non-uniform magnetized plasmas. We demonstrate that discrete weak form with/without average differs only in the choice of test/trial spaces. The complexity of each procedure is analyzed. Finally, a numerical example for a non-uniform magnetized plasma in an infinitely long symmetric cylinder is presented. It is verified that the connectionproportion algorithm allows to distinguish different trajectory bundles, and the proposed DG scheme rigorously preserves all the conservation laws. On the second topic, the existence of global weak solution to quasilinear theory for electrostatic plasmas is proved. In the one-dimensional case, both the particle pdf and the plasmon pdf can be expressed with the same auxiliary function. The auxiliary function itself, is the solution of a porous medium equation with nonlinear source terms, defined on an unbounded domain. The solvability is then proved in two steps: Firstly, the equation on finite cut-off domain with Dirichlet’s boundary condition is solved. Next, the solution, extended by zero outside the cut-off domain, turns out to be a solution to the same equation on the unbounded domain.Computational Science, Engineering, and Mathematic

Luminous Intensity for Traffic Signals: A Scientific Basis for Performance Specifications

Humnan factors experiments on visual responses to simulated traffic signals using incandescent lamps and light-emitting diodes are described

Membrane Pre-treatment Using Chemical Disinfectants in Halide Impaired Waters

The use of membrane filtration processes for desalination, water reuse, and water reclamation techniques are becoming more prevalent given freshwater shortages. However, the treatment of these waters is challenging because of the membranes used in these processes. During nanofiltration and reverse osmosis the membranes undergo biofouling. Reverse osmosis and nanofiltration are high-pressure membrane filtration techniques that treat seawater, brackish waters, and industrial wastewaters. Because of the biofouling, the polyamide thin film needs to be pretreated with chlorine (HOCl/ OCl-) as a disinfectant, but this damages the polyamide membrane. When the free chlorine is in the presence of halide-impaired waters, it changes the chemistry of the membrane thus continuing to damage it. In order to find how halide concentration and other water quality parameters affect nanofiltration and reverse osmosis, this project requires liquid chromatography and mass spectrometry method to analyze different aromatic amine compounds (e.g. benzanilide) with similar structures to the polyamide membrane. The LC/MS is optimized in order to find the limits of detection for each of the compounds. The chlorination reactions are done to quantify how much these compounds react in the presence of free chlorine. Future research with regards to this includes kinetic measurements of compound degradation and by-product formation to see how these compounds are affected by free chlorine over time

Entanglement control in one-dimensional s=1/2s=1/2 random XY spin chain

The entanglement in one-dimensional random XY spin systems where the impurities of exchange couplings and the external magnetic fields are considered as random variables is investigated by solving the different spin-spin correlation functions and the average magnetization per spin. The entanglement dynamics near particular locations of the system is also studied when the exchange couplings (or the external magnetic fields) satisfy three different distributions(the Gaussian distribution, double-Gaussian distribution, and bimodal distribution). We find that the entanglement can be controlled by varying the strength of external magnetic field and the different distributions of impurities. Moreover, the entanglement of some nearest-neighboring qubits can be increased for certain parameter values of the three different distributions.Comment: 13 pages, 4 figure

Two-soliton solution for the derivative nonlinear Schr\"odinger equation with nonvanishing boundary conditions

An explicit two-soliton solution for the derivative nonlinear Schr\"odinger equation with nonvanishing boundary conditions is derived, demonstrating details of interactions between two bright solitons, two dark solitons, as well as one bright soliton and one dark soliton. Shifts of soliton positions due to collisions are analytically obtained, which are irrespective of the bright or dark characters of the participating solitons.Comment: 11 pages, 4 figures. Phys. Lett. A 2006 (in press

Luminous Intensity for Traffic Signals: A Scientific Basis for Performance Specifications - Appendices

Luminous Intensity for Traffic Signals: A Scientific Basis for Performance Specifications - Appendice

Metagenomic analysis of ancient dental calculus reveals unexplored diversity of oral archaeal Methanobrevibacter

Background Dental calculus (mineralised dental plaque) preserves many types of microfossils and biomolecules, including microbial and host DNA, and ancient calculus are thus an important source of information regarding our ancestral human oral microbiome. In this study, we taxonomically characterised the dental calculus microbiome from 20 ancient human skeletal remains originating from Trentino-South Tyrol, Italy, dating from the Neolithic (6000–3500 BCE) to the Early Middle Ages (400–1000 CE). Results We found a high abundance of the archaeal genus Methanobrevibacter in the calculus. However, only a fraction of the sequences showed high similarity to Methanobrevibacter oralis, the only described Methanobrevibacter species in the human oral microbiome so far. To further investigate the diversity of this genus, we used de novo metagenome assembly to reconstruct 11 Methanobrevibacter genomes from the ancient calculus samples. Besides the presence of M. oralis in one of the samples, our phylogenetic analysis revealed two hitherto uncharacterised and unnamed oral Methanobrevibacter species that are prevalent in ancient calculus samples sampled from a broad range of geographical locations and time periods. Conclusions We have shown the potential of using de novo metagenomic assembly on ancient samples to explore microbial diversity and evolution. Our study suggests that there has been a possible shift in the human oral microbiome member Methanobrevibacter over the last millennia

Phase relationships in the La2O3-SrO-Nb2O5 system

The phase relationships in the La2O3---SrO---Nb2O5 system were studied. The isothermal section at 1400[deg]C of this system was determined. Within this system, two niobates, LaSr2Nb2O8.5 (1-2-2) with hexagonal structure and LaSr2NbO6 (1-2-1) with cubic structure occurred. Same family compounds, YSr2Nb2O8.5 and LaSr2Ta2O8.5, could be also synthesized. In the SrO-rich area of the SrO---Nb2O5 subsystem, a tetragonal solid solution with a composition range of Sr2-4NbO4.5-6.5 (i.e. 66.7-80 at.% SrO) was also observed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/29252/1/0000309.pd

Compound formation and melting behavior in theAB compound and rare earth oxide systems

Compound formation in the systems of the covalent compounds BeO, AlN, and SiC withR2O3(rare earth oxides) is described. Tentative phase diagrams of the AlNNd2O3 and AlNEu2O3 systems are presented.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/28688/1/0000507.pd