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

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

Optical realization of universal quantum cloning

Beyond the no-cloning theorem, the universal symmetric quantum cloning machine was first addressed by Buzek and Hillery. Here, we realized the one-to-two qubits Buzek-Hillery cloning machine with linear optical devices. This method relies on the representation of several qubits by a single photon. We showed that, the fidelities between the two output qubits and the original qubit are both 5/6 (which proved to be the optimal fidelity of one-to-two qubits universal cloner) for arbitrary input pure states.Comment: 5 Pages, 2 Figure

The entanglement in one-dimensional random XY spin chain with Dzyaloshinskii-Moriya interaction

The impurities of exchange couplings, external magnetic fields and Dzyaloshinskii--Moriya (DM) interaction considered as Gaussian distribution, the entanglement in one-dimensional random $XY$ spin systems is investigated by the method of solving the different spin-spin correlation functions and the average magnetization per spin. The entanglement dynamics at central locations of ferromagnetic and antiferromagnetic chains have been studied by varying the three impurities and the strength of DM interaction. (i) For ferromagnetic spin chain, the weak DM interaction can improve the amount of entanglement to a large value, and the impurities have the opposite effect on the entanglement below and above critical DM interaction. (ii) For antiferromagnetic spin chain, DM interaction can enhance the entanglement to a steady value. Our results imply that DM interaction strength, the impurity and exchange couplings (or magnetic field) play competing roles in enhancing quantum entanglement.Comment: 12 pages, 3 figure

The controlled teleportation of an arbitrary two-atom entangled state in driven cavity QED

In this paper, we propose a scheme for the controlled teleportation of an arbitrary two-atom entangled state $|\phi>_{12}=a|gg>_{12}+b|ge>_{12}+c|eg>_{12}+d|ee>_{12}$ in driven cavity QED. An arbitrary two-atom entangled state can be teleported perfectly with the help of the cooperation of the third side by constructing a three-atom GHZ entangled state as the controlled channel. This scheme does not involve apparent (or direct) Bell-state measurement and is insensitive to the cavity decay and the thermal field. The probability of the success in our scheme is 1.0.Comment: 10 page