Physics
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Item LARGE SYSTEMS OF MANY INTERCONNECTED DYNAMICAL UNITS: GENE NETWORK INFERENCE, EPIGENETIC HERITABILITY, AND EMERGENT BEHAVIOR IN OSCILLATOR SYSTEMS(2014) Ku, Wai Lim; Ott, Edward; Girvan, Michelle; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)In this thesis, which consists of three parts, we investigate problems related to systems biology and collective behavior in complex systems. The first part studies genetic networks that are inferred using gene expression data. Here we use established transcriptional regulatory interactions (TRIs) in combination with microarray expression data from both Escherichia coli (a prokaryote) and Saccharomyces cerevisiae (a eukaryote) to assess the accuracy of predictions of coregulated gene pairs and TRIs from observations of coexpressed gene pairs. We find that highly coexpressed gene pairs are more likely to be coregulated than to share a TRI for Saccharomyces cerevisiae, while the incidence of TRIs in highly coexpressed gene pairs is higher for Escherichia coli. The data processing inequality (DPI) of information theory has previously been applied for the inference of TRIs. We consider the case where a transcription factor gene is known to regulate two genes (one of which is a transcription factor gene) that are known not to regulate one another. According to the DPI if certain conditions hold, the non-interacting gene pairs should have the smallest mutual information among all pairs in the triplets. While we observe that this is sometimes the case for Escherichia coli, we find that it is almost always not the case for Saccharomyces cerevisiae, thus indicating that the assumed conditions under which the DPI was derived do not hold. The second part of this dissertation is related to the dynamical process of epigentic heritability. Epigenetic modifications to histones may promote either activation or repression of the transcription of nearby genes. Recent experimental studies show that the promoters of many lineage-control genes in stem cells have "bivalent domains" in which the nucleosomes contain both active (H3K4me3) and repressive (H3K27me3) marks. Here we formulate a mathematical model to investigate the dynamic properties of bivalent histone modification patterns, and we predict some interesting and potentially experimental observable features. The third part of this dissertation studies dynamical systems in which a large number $N$ of identical Landau-Stuart oscillators are globally coupled via a mean-field. Previously, it has been observed that this type of system can exhibit a variety of different dynamical behaviors including clumped states (in which each oscillator is in one of a small number of groups for which all oscillators in each group have the same state which is different from group to group), as well as extensive chaos (a situation in which all oscillators have different states and the macroscopic dynamics of the mean field is chaotic). One of our foci is the transition between clumped states and extensive chaos as the system is subjected to slow adiabatic parameter change. We observe and analyze explosive discontinuous transitions between the clumped states and the extensively chaotic states. Also, we study the fractal structures of the extensively chaotic attractors.Item Non-linear Development of Streaming Instabilities in Magnetic Reconnection with a Strong Guide Field(2009) Che, Haihong; Drake, James F.; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Magnetic reconnection is recognized as a dominant mechanism for converting magnetic energy into the convective and thermal energy of particles, and the driver of explosive events in nature and laboratory. Magnetic reconnection is often modeled using resistive magnetohydrodynamics, in which collisions play the key role in facilitating the release of energy in the explosive events. However, in space plasma the collisional resistivity is far below the required resistivity to explain the observed energy release rate. Turbulence is common in plasmas and the anomalous resistivity induced by the turbulence has been proposed as a mechanism for breaking the frozen-in condition in magnetic reconnection. Turbulence-driven resistivity has remained a poorly understood, but widely invoked mechanism for nearly 50 years. The goal of this project is to understand what role anomalous resistivity plays in fast magnetic reconnection. Turbulence has been observed in the intense current layers that develop during magnetic reconnection in the Earth's magnetosphere. Electron streaming is believed to be the source of this turbulence. Using kinetic theory and 3D particle-in-cell simulations, we study the nonlinear development of streaming instabilities in 3D magnetic reconnection with a strong guide field. Early in time an intense current sheet develops around the x-line and drives the Buneman instability. Electron holes, which are bipolar spatial localized electric field structures, form and then self-destruct creating a region of strong turbulence around the x-line. At late time turbulence with a characteristic frequency in the lower hybrid range also develops, leading to a very complex mix of interactions. The difficulty we face in this project is how to address a long-standing problem in nonlinear kinetic theory: how to treat large amplitude perturbations and the associated strong wave-particle interactions. In my thesis, I address this long-standing problem using particle-in-cell simulations and linear kinetic theory.Some important physics have been revealed. 1: The lower hybrid instability (LHI) dominates the dynamics in low $beta$ plasma in combination with either the electron-electron two-stream instability (ETS) or the Buneman instability (BI), depending on the parallel phase speed of the LHI. 2: An instability with a high phase speed is required to tap the energy of the high velocity electrons. The BI with its low phase speed, can not do this. The ETS and the LHI both have high phase speed. 3: The condition for the formation of stable electron holes requires $|v_p -v_g|< sqrt{2e|phi|/m_e}$, where $|phi|$ is the amplitude of the electric potential, and $v_p$ and $v_g$ are the phase and group velocity of the relevant waves. Like ETS and BI, LHI all can form electron holes. 4: The overlapping resonance in phase space is the dominant mechanism for transporting the momentum and energy from high velocity electrons to low velocity electrons, which then couple to the ions.