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.

GENETIC VARIATION, LOCAL ADAPTATION AND POPULATION STRUCTURE IN NORTH AMERICAN RED OAK SPECIES, QUERCUS RUBRA L. AND Q. ELLIPSOIDALIS E. J. HILL

Forest trees, like oaks, rely on high levels of genetic variation to adapt to varying environmental conditions. Thus, genetic variation and its distribution are important for the long-term survival and adaptability of oak populations. Climate change is projected to lead to increased drought and fire events as well as a northward migration of tree species, including oaks. Additionally, decline in oak regeneration has become increasingly concerning since it may lead to decreased gene flow and increased inbreeding levels. This will in turn lead to lowered levels of genetic diversity, negatively affecting the growth and survival of populations. At the same time, populations at the species’ distribution edge, like those in this study, could possess important stores of genetic diversity and adaptive potential, while also being vulnerable to climatic or anthropogenic changes. A survey of the level and distribution of genetic variation and identification of potentially adaptive genes is needed since adaptive genetic variation is essential for their long-term survival. Oaks possess a remarkable characteristic in that they maintain their species identity and specific environmental adaptations despite their propensity to hybridize. Thus, in the face of interspecific gene flow, some areas of the genome remain differentiated due to selection. This characteristic allows the study of local environmental adaptation through genetic variation analyses. Furthermore, using genic markers with known putative functions makes it possible to link those differentiated markers to potential adaptive traits (e.g., flowering time, drought stress tolerance). Demographic processes like gene flow and genetic drift also play an important role in how genes (including adaptive genes) are maintained or spread. These processes are influenced by disturbances, both natural and anthropogenic. An examination of how genetic variation is geographically distributed can display how these genetic processes and geographical disturbances influence genetic variation patterns. For example, the spatial clustering of closely related trees could promote inbreeding with associated negative effects (inbreeding depression), if gene flow is limited. In turn this can have negative consequences for a species’ ability to adapt to changing environmental conditions. In contrast, interspecific hybridization may also allow the transfer of genes between species that increase their adaptive potential in a changing environment. I have studied the ecologically divergent, interfertile red oaks, Quercus rubra and Q. ellipsoidalis, to identify genes with potential roles in adaptation to abiotic stress through traits such as drought tolerance and flowering time, and to assess the level and distribution of genetic variation. I found evidence for moderate gene flow between the two species and low interspecific genetic differences at most genetic markers (Lind and Gailing 2013). However, the screening of genic markers with potential roles in phenology and drought tolerance led to the identification of a CONSTANS-like (COL) gene, a candidate gene for flowering time and growth. This marker, located in the coding region of the gene, was highly differentiated between the two species in multiple geographical areas, despite interspecific gene flow, and may play a role in reproductive isolation and adaptive divergence between the two species (Lind-Riehl et al. 2014). Since climate change could result in a northward migration of trees species like oaks, this gene could be important in maintaining species identity despite increased contact zones between species (e.g., increased gene flow). Finally I examined differences in spatial genetic structure (SGS) and genetic variation between species and populations subjected to different management strategies and natural disturbances. Diverse management activities combined with various natural disturbances as well as species specific life history traits influenced SGS patterns and inbreeding levels (Lind-Riehl and Gailing submitted).

SCALABLE APPROXIMATION OF KERNEL FUZZY C-MEANS

Virtually every sector of business and industry that uses computing, including financial analysis, search engines, and electronic commerce, incorporate Big Data analysis into their business model. Sophisticated clustering algorithms are popular for deducing the nature of data by assigning labels to unlabeled data. We address two main challenges in Big Data. First, by definition, the volume of Big Data is too large to be loaded into a computer’s memory (this volume changes based on the computer used or available, but there is always a data set that is too large for any computer). Second, in real-time applications, the velocity of new incoming data prevents historical data from being stored and future data from being accessed. Therefore, we propose our Streaming Kernel Fuzzy c-Means (stKFCM) algorithm, which reduces both computational complexity and space complexity significantly. The proposed stKFCM only requires O(n2) memory where n is the (predetermined) size of a data subset (or data chunk) at each time step, which makes this algorithm truly scalable (as n can be chosen based on the available memory). Furthermore, only 2n2 elements of the full N × N (where N >> n) kernel matrix need to be calculated at each time-step, thus reducing both the computation time in producing the kernel elements and also the complexity of the FCM algorithm. Empirical results show that stKFCM, even with relatively very small n, can provide clustering performance as accurately as kernel fuzzy c-means run on the entire data set while achieving a significant speedup.

Improving the performance of GIS/spatial analysts though novel applications of the Emotiv EPOC EEG headset

Geospatial information systems are used to analyze spatial data to provide decision makers with relevant, up-to-date, information. The processing time required for this information is a critical component to response time. Despite advances in algorithms and processing power, we still have many “human-in-the-loop” factors. Given the limited number of geospatial professionals, analysts using their time effectively is very important. The automation and faster humancomputer interactions of common tasks that will not disrupt their workflow or attention is something that is very desirable. The following research describes a novel approach to increase productivity with a wireless, wearable, electroencephalograph (EEG) headset within the geospatial workflow.

Effect of high order interpolation in the stability and efficiency of the time-integration process in vorticity-velocity CFD algorithms

The numerical solution of the incompressible Navier-Stokes Equations offers an effective alternative to the experimental analysis of Fluid-Structure interaction i.e. dynamical coupling between a fluid and a solid which otherwise is very complex, time consuming and very expensive. To have a method which can accurately model these types of mechanical systems by numerical solutions becomes a great option, since these advantages are even more obvious when considering huge structures like bridges, high rise buildings, or even wind turbine blades with diameters as large as 200 meters. The modeling of such processes, however, involves complex multiphysics problems along with complex geometries. This thesis focuses on a novel vorticity-velocity formulation called the KLE to solve the incompressible Navier-stokes equations for such FSI problems. This scheme allows for the implementation of robust adaptive ODE time integration schemes and thus allows us to tackle the various multiphysics problems as separate modules. The current algorithm for KLE employs a structured or unstructured mesh for spatial discretization and it allows the use of a self-adaptive or fixed time step ODE solver while dealing with unsteady problems. This research deals with the analysis of the effects of the Courant-Friedrichs-Lewy (CFL) condition for KLE when applied to unsteady Stoke’s problem. The objective is to conduct a numerical analysis for stability and, hence, for convergence. Our results confirmthat the time step ∆t is constrained by the CFL-like condition ∆t ≤ const. hα, where h denotes the variable that represents spatial discretization.

SPATIAL UNDERSTANDING OF MATRIX INVERSION FOR INVERSE FORCE ESTIMATION

A basic approach to study a NVH problem is to break down the system in three basic elements – source, path and receiver. While the receiver (response) and the transfer path can be measured, it is difficult to measure the source (forces) acting on the system. It becomes necessary to predict these forces to know how they influence the responses. This requires inverting the transfer path. Singular Value Decomposition (SVD) method is used to decompose the transfer path matrix into its principle components which is required for the inversion. The usual approach to force prediction requires rejecting the small singular values obtained during SVD by setting a threshold, as these small values dominate the inverse matrix. This assumption of the threshold may be subjected to rejecting important singular values severely affecting force prediction. The new approach discussed in this report looks at the column space of the transfer path matrix which is the basis for the predicted response. The response participation is an indication of how the small singular values influence the force participation. The ability to accurately reconstruct the response vector is important to establish a confidence in force vector prediction. The goal of this report is to suggest a solution that is mathematically feasible, physically meaningful, and numerically more efficient through examples. This understanding adds new insight to the effects of current code and how to apply algorithms and understanding to new codes.