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

Malignant phyllodes tumors display mesenchymal stem cell features and aldehyde dehydrogenase/disialoganglioside identify their tumor stem cells

INTRODUCTION: Although breast phyllodes tumors are rare, there is no effective therapy other than surgery. Little is known about their tumor biology. A malignant phyllodes tumor contains heterologous stromal elements, and can transform into rhabdomyosarcoma, liposarcoma and osteosarcoma. These versatile properties prompted us to explore their possible relationship to mesenchymal stem cells (MSCs) and to search for the presence of cancer stem cells (CSCs) in phyllodes tumors. METHODS: Paraffin sections of malignant phyllodes tumors were examined for various markers by immunohistochemical staining. Xenografts of human primary phyllodes tumors were established by injecting freshly isolated tumor cells into the mammary fat pad of non-obese diabetic-severe combined immunodeficient (NOD-SCID) mice. To search for CSCs, xenografted tumor cells were sorted into various subpopulations by flow cytometry and examined for their in vitro mammosphere forming capacity, in vivo tumorigenicity in NOD-SCID mice and their ability to undergo differentiation. RESULTS: Immunohistochemical analysis revealed the expression of the following 10 markers: CD44, CD29, CD106, CD166, CD105, CD90, disialoganglioside (GD2), CD117, Aldehyde dehydrogenase 1 (ALDH), and Oct-4, and 7 clinically relevant markers (CD10, CD34, p53, p63, Ki-67, Bcl-2, vimentin, and Globo H) in all 51 malignant phyllodes tumors examined, albeit to different extents. Four xenografts were successfully established from human primary phyllodes tumors. In vitro, ALDH(+) cells sorted from xenografts displayed approximately 10-fold greater mammosphere-forming capacity than ALDH(-) cells. GD2(+) cells showed a 3.9-fold greater capacity than GD2(-) cells. ALDH(+)/GD2(+)cells displayed 12.8-fold greater mammosphere forming ability than ALDH(-)/GD2(-) cells. In vivo, the tumor-initiating frequency of ALDH(+)/GD2(+) cells were up to 33-fold higher than that of ALDH(+) cells, with as few as 50 ALDH(+)/GD2(+) cells being sufficient for engraftment. Moreover, we provided the first evidence for the induction of ALDH(+)/GD2(+) cells to differentiate into neural cells of various lineages, along with the observation of neural differentiation in clinical specimens and xenografts of malignant phyllodes tumors. ALDH(+) or ALDH(+)/GD2(+) cells could also be induced to differentiate into adipocytes, osteocytes or chondrocytes. CONCLUSIONS: Our findings revealed that malignant phyllodes tumors possessed many characteristics of MSC, and their CSCs were enriched in ALDH(+) and ALDH(+)/GD2(+) subpopulations

Inflammatory Gene Regulatory Networks in Amnion Cells Following Cytokine Stimulation: Translational Systems Approach to Modeling Human Parturition

A majority of the studies examining the molecular regulation of human labor have been conducted using single gene approaches. While the technology to produce multi-dimensional datasets is readily available, the means for facile analysis of such data are limited. The objective of this study was to develop a systems approach to infer regulatory mechanisms governing global gene expression in cytokine-challenged cells in vitro, and to apply these methods to predict gene regulatory networks (GRNs) in intrauterine tissues during term parturition. To this end, microarray analysis was applied to human amnion mesenchymal cells (AMCs) stimulated with interleukin-1β, and differentially expressed transcripts were subjected to hierarchical clustering, temporal expression profiling, and motif enrichment analysis, from which a GRN was constructed. These methods were then applied to fetal membrane specimens collected in the absence or presence of spontaneous term labor. Analysis of cytokine-responsive genes in AMCs revealed a sterile immune response signature, with promoters enriched in response elements for several inflammation-associated transcription factors. In comparison to the fetal membrane dataset, there were 34 genes commonly upregulated, many of which were part of an acute inflammation gene expression signature. Binding motifs for nuclear factor-κB were prominent in the gene interaction and regulatory networks for both datasets; however, we found little evidence to support the utilization of pathogen-associated molecular pattern (PAMP) signaling. The tissue specimens were also enriched for transcripts governed by hypoxia-inducible factor. The approach presented here provides an uncomplicated means to infer global relationships among gene clusters involved in cellular responses to labor-associated signals