School of Mathematics and Statistics  Theses
http://hdl.handle.net/11343/295
20181015T12:38:32Z

Unsteady motion of small particles in fluid: from autonomous propulsion to the interrogation of liquidsolid interfaces
http://hdl.handle.net/11343/216669
Unsteady motion of small particles in fluid: from autonomous propulsion to the interrogation of liquidsolid interfaces
Collis, Jesse F.
Fluid flows at micro and nanometre length scales are governed by physical processes that are quite different to their macroscale counterparts. When these flows interact with suspended solid particles, a rich array of phenomena can occur. This thesis examines four such processes in which unsteadiness arises; due to both steady and oscillatory flow processes.
Axisymmetric particles immersed in shear flows undergo periodic rotational motions known as Jeffery orbits. While extensive measurements have been reported on these orbits, the axial rotation of the particles has been difficult to study. A new methodology and commensurate theory is developed to enable the observation of these axial rotations. Experimental measurements are performed to validate the proposed theory.
Hydrodynamic trapping of small particles in microvortices has been observed experimentally. These microvortices are generated by cylindrical nanorods rotating about their minor axis, driven by an external magnetic field. The physical mechanism underlying this phenomenon is currently unknown. Here, a hydrodynamic model based on a rotating disc is proposed in an attempt to explain these observations. An asymptotic expansion on the NavierStokes equations is used to include the effects of small fluid inertia in the system. Finite particle size and inertia effects are then included through use of a particle momentum equation. This model reveals a possible trapping mechanism due to the interaction of the particle with the surrounding nonuniform flow.
Nanorods suspended in acoustically actuated fluid chambers have been observed to undergo autonomous propulsion. These particles, which contain forandaft asymmetries due to both shape and density, create local streaming flows enabling their propulsion. A general theory is developed to describe their motion which is applied to a dumbbell model for analytic solution. This provides a significant advance on existing theory, by allowing axisymmetric particles of arbitrary shape and density distribution to be modelled. New physics is uncovered, demonstrating that these particles can change their propulsion direction at intermediate frequencies; this phenomena is yet to be observed experimentally.
The Navierslip condition is used widely to model noncontinuum flows. Its applicability to the gassolid interface is established from theory, while the liquidsolid interface does not enjoy such rigour. Here, a new experimental method for probing this boundary condition at the liquidsolid interface is developed, based on multimode measurements in Suspended Microchannel Resonators (SMRs). Analytic, numeric and statistic tools are formulated to enable interpretation of these measurements. A constant slip length (of 2.7 $\pm$ 0.6 nm) is measured for gold nanoparticles of varying radii, providing the first direct experimental evidence for Navier slip at the liquidsolid interface, i.e. the sliplength is a material parameter, independent of geometry. This array of measurements and theory advance our understanding of fluidstructure interactions of nanoparticles in fluid, and provide new information on the nature of the liquidsolid interface.
© 2018 Dr. Jesse F. Collis
20180101T00:00:00Z

The isoperimetric problem in block designs
http://hdl.handle.net/11343/214165
The isoperimetric problem in block designs
Surani, Muhammad Adib
This thesis focuses on the problem of determining the isoperimetric numbers of Levi graphs of balanced incomplete block designs. We study two versions of this: the vertexisoperimetric number and the edgeisoperimetric number. In the general case, we manage to obtain strong upper and lower bounds on these numbers for Levi graphs of arbitrary block designs. We also obtain stronger or even exact values for some families of graphs, particularly those arising from finite geometries or difference sets.
© 2018 Dr. Muhammad Adib Surani
20180101T00:00:00Z

Statistical models for the location of lightningcaused wildfire ignitions
http://hdl.handle.net/11343/214157
Statistical models for the location of lightningcaused wildfire ignitions
Read, Nicholas
Lightningcaused wildfire is a significant concern for fire management agencies worldwide. Unlike other ignition sources, lightning fires often occur in remote and inaccessible locations making detection and suppression particularly challenging. Furthermore, individual lightning storms result in a large number of fires clustered in space and time which can overwhelm suppression efforts. Victoria, Australia, is one of the most fire prone environments in the world and the increased frequency of largescale landscape fires over the last decade is of particular concern to local wildfire management authorities.
This thesis is concerned with modeling lightningcaused wildfire ignition locations in Victoria. Such models could be used for predicting daily lightningcaused ignition likelihood as well as simulating realistic point patterns for use in fire spread models for risk analyses.
The first half of this thesis looks at regression models. We review methods for the model selection, validation, approximation and interpretation of generalised additive models. A review of performance metrics, such as the AUC, shows the difficulties and subtleties involved in evaluating the predictive performance of models.
We apply this theory to construct a nonlinear logistic regression model for lightningcaused wildfires in Victoria. The model operates on a daily time scale, with a spatial resolution of 20 km and uses covariate data including fuel moisture indices, vegetation type, a lightning potential index and weather. We develop a simple method to deconstruct model output into contributions from each of the individual covariates, allowing predictions to be explained in terms of the weather conditions driving them. Using these ideas, we discuss ranking the relative 'importance' of covariates in the model, leading to an approximating model with similar performance to the full model.
The second half of this thesis looks at point process models for lightningcaused ignitions. We introduce general theory for point processes, focusing on the inhomogeneous Poisson process, cluster processes and replicated point patterns. The Kfunction is a useful summary function for describing the spatial correlation point patterns and for fitting models. We present a method for pooling multiple estimates of the Kfunction, such as those that arise when using replicated point patterns, intended to reduce bias.
We fit an inhomogeneous Poisson process model as well as a Thomas and Cauchy cluster process model to the Victorian lightningcaused ignition data set. The cluster process models prove to have significantly better fit than the Poisson process model, but still struggle to reproduce the complex behaviour of the physical process.
© 2018 Dr. Nicholas Read
20180101T00:00:00Z

Quantifying interactions between nanoengineered particles and cells
http://hdl.handle.net/11343/212536
Quantifying interactions between nanoengineered particles and cells
Faria, Matthew
Nanoengineering has recently emerged as a promising technology for the understanding, treatment, and diagnosis of disease. One of its most compelling potential uses is in the design of particles with controlled interactions with particular cell types. Significant research effort has been devoted to developing particles that exhibit a variety of interesting behaviors, including stealth, targeting, cargo carrying capabilities, or responsiveness to biological environments.
In vitro experiments with cultured cells are fundamental to understanding and studying the interface between nanoengineered particles and biological systems. However, partially due to the wide range of physicochemical properties nanomaterials exhibit, quantification and generalization of data from in vitro bionano experiments has unique challenges when compared to traditional smallmolecule drugs or materials in bulk. As the fields of bionano research and nanomedicine have matured, in vitro quantification has become a significant barrier to understanding, characterizing, and comparing newly developed particle systems.
This thesis addresses three interrelated areas that are necessary to accurately quantify in vitro interactions between nanoengineered particles and cells. First, particledependent variation between the amount of material administered and that which reaches the surface of cells (in vitro dosimetry) is studied. Second, instrument independent quantification of cellparticle association is used to study differences in association induced by labeling and cytometry technique. Third, a theoretical framework to isolate the biological kinetics of association is developed, and is used to compare cellparticle association results from experiments varying in particle type and cell line. Though the primary focus of this thesis is computational, a mixture of experimental, mathematical, and computational strategies are utilized.
This thesis addresses three interrelated areas that are necessary to accurately quantify in vitro interactions between nanoengineered particles and cells. First, particledependent variation between the amount of material administered and that which reaches the surface of cells (in vitro dosimetry) is studied. Second, instrument independent quantification of cellparticle association is used to study differences in association induced by labeling and cytometry technique. Third, a theoretical framework to isolate the biological kinetics of association is developed, and is used to compare cellparticle association results from experiments varying in particle type and cell line. Though the primary focus of this thesis is computational, a mixture of experimental, mathematical, and computational strategies are utilized.
© 2018 Dr Matthew Faria
20180101T00:00:00Z