Studies of spatial clustering of inertial particles in turbulence

We present studies of the spatial clustering of inertial particles embedded in turbulent flow. A major part of the thesis is experimental, involving the technique of Phase Doppler Interferometry (PDI). The thesis also includes significant amount of simulation studies and some theoretical considerations. We describe the details of PDI and explain why it is suitable for study of particle clustering in turbulent flow with a strong mean velocity. We introduce the concept of the radial distribution function (RDF) as our chosen way of quantifying inertial particle clustering and present some original works on foundational and practical considerations related to it. These include methods of treating finite sampling size, interpretation of the magnitude of RDF and the possibility of isolating RDF signature of inertial clustering from that of large scale mixing. In experimental work, we used the PDI to observe clustering of water droplets in a turbulent wind tunnel. From that we present, in the form of a published paper, evidence of dynamical similarity (Stokes number similarity) of inertial particle clustering together with other results in qualitative agreement with available theoretical prediction and simulation results. We next show detailed quantitative comparisons of results from our experiments, direct-numerical-simulation (DNS) and theory. Very promising agreement was found for like-sized particles (mono-disperse). Theory is found to be incorrect regarding clustering of different-sized particles and we propose a empirical correction based on the DNS and experimental results. Besides this, we also discovered a few interesting characteristics of inertial clustering. Firstly, through observations, we found an intriguing possibility for modeling the RDF arising from inertial clustering that has only one (sensitive) parameter. We also found that clustering becomes saturated at high Reynolds number.

Systemic analysis of microarray data sets towards identifying genes regulating root development

Nitrogen and water are essential for plant growth and development. In this study, we designed experiments to produce gene expression data of poplar roots under nitrogen starvation and water deprivation conditions. We found low concentration of nitrogen led first to increased root elongation followed by lateral root proliferation and eventually increased root biomass. To identify genes regulating root growth and development under nitrogen starvation and water deprivation, we designed a series of data analysis procedures, through which, we have successfully identified biologically important genes. Differentially Expressed Genes (DEGs) analysis identified the genes that are differentially expressed under nitrogen starvation or drought. Protein domain enrichment analysis identified enriched themes (in same domains) that are highly interactive during the treatment. Gene Ontology (GO) enrichment analysis allowed us to identify biological process changed during nitrogen starvation. Based on the above analyses, we examined the local Gene Regulatory Network (GRN) and identified a number of transcription factors. After testing, one of them is a high hierarchically ranked transcription factor that affects root growth under nitrogen starvation. It is very tedious and time-consuming to analyze gene expression data. To avoid doing analysis manually, we attempt to automate a computational pipeline that now can be used for identification of DEGs and protein domain analysis in a single run. It is implemented in scripts of Perl and R.