2 resultados para Elementary Methods In Number Theory

em Digital Commons - Michigan Tech


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It has been proposed that inertial clustering may lead to an increased collision rate of water droplets in clouds. Atmospheric clouds and electrosprays contain electrically charged particles embedded in turbulent flows, often under the influence of an externally imposed, approximately uniform gravitational or electric force. In this thesis, we present the investigation of charged inertial particles embedded in turbulence. We have developed a theoretical description for the dynamics of such systems of charged, sedimenting particles in turbulence, allowing radial distribution functions to be predicted for both monodisperse and bidisperse particle size distributions. The governing parameters are the particle Stokes number (particle inertial time scale relative to turbulence dissipation time scale), the Coulomb-turbulence parameter (ratio of Coulomb ’terminalar speed to turbulence dissipation velocity scale), and the settling parameter (the ratio of the gravitational terminal speed to turbulence dissipation velocity scale). For the monodispersion particles, The peak in the radial distribution function is well predicted by the balance between the particle terminal velocity under Coulomb repulsion and a time-averaged ’drift’ velocity obtained from the nonuniform sampling of fluid strain and rotation due to finite particle inertia. The theory is compared to measured radial distribution functions for water particles in homogeneous, isotropic air turbulence. The radial distribution functions are obtained from particle positions measured in three dimensions using digital holography. The measurements support the general theoretical expression, consisting of a power law increase in particle clustering due to particle response to dissipative turbulent eddies, modulated by an exponential electrostatic interaction term. Both terms are modified as a result of the gravitational diffusion-like term, and the role of ’gravity’ is explored by imposing a macroscopic uniform electric field to create an enhanced, effective gravity. The relation between the radial distribution functions and inward mean radial relative velocity is established for charged particles.

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Important food crops like rice are constantly exposed to various stresses that can have devastating effect on their survival and productivity. Being sessile, these highly evolved organisms have developed elaborate molecular machineries to sense a mixture of stress signals and elicit a precise response to minimize the damage. However, recent discoveries revealed that the interplay of these stress regulatory and signaling molecules is highly complex and remains largely unknown. In this work, we conducted large scale analysis of differential gene expression using advanced computational methods to dissect regulation of stress response which is at the heart of all molecular changes leading to the observed phenotypic susceptibility. One of the most important stress conditions in terms of loss of productivity is drought. We performed genomic and proteomic analysis of epigenetic and miRNA mechanisms in regulation of drought responsive genes in rice and found subsets of genes with striking properties. Overexpressed genesets included higher number of epigenetic marks, miRNA targets and transcription factors which regulate drought tolerance. On the other hand, underexpressed genesets were poor in above features but were rich in number of metabolic genes with multiple co-expression partners contributing majorly towards drought resistance. Identification and characterization of the patterns exhibited by differentially expressed genes hold key to uncover the synergistic and antagonistic components of the cross talk between stress response mechanisms. We performed meta-analysis on drought and bacterial stresses in rice and Arabidopsis, and identified hundreds of shared genes. We found high level of conservation of gene expression between these stresses. Weighted co-expression network analysis detected two tight clusters of genes made up of master transcription factors and signaling genes showing strikingly opposite expression status. To comprehensively identify the shared stress responsive genes between multiple abiotic and biotic stresses in rice, we performed meta-analyses of microarray studies from seven different abiotic and six biotic stresses separately and found more than thirteen hundred shared stress responsive genes. Various machine learning techniques utilizing these genes classified the stresses into two major classes' namely abiotic and biotic stresses and multiple classes of individual stresses with high accuracy and identified the top genes showing distinct patterns of expression. Functional enrichment and co-expression network analysis revealed the different roles of plant hormones, transcription factors in conserved and non-conserved genesets in regulation of stress response.