Cell motility is closely linked to many important physiological and pathological events such as the immune response, wound healing, tissue differentiation, embryogenesis, in ammation, tumour invasion and metastasis. Understanding the ability of cells to alter their shape, deform and migrate is of vital importance in many biological studies. The rapid development in microscopy and imaging techniques has generated a huge amount of discrete data on migrating cells in vivo and in vitro. A key challenge is the use of discrete experimental observations to develop novel methods and algorithms that track cells and construct continuous trajectories of their motion as well as characterising key geometric quantities associated with cell migration. Therefore, in this work using robust numerical tools we focus on proposing and implementing mathematical methodologies for cell movement and apply them to model neutrophil cell migration. We derive and implement a computational framework that encompasses modelling of cell motility and cell tracking based on phase field and optimal control theory. The cell membrane is represented by an evolving curve and approximated by a diffuse interface; while the motion of the cell is driven by a force balance acting normal on the cell membrane. This approach allows us to characterise the locus of the centroid cell-surface position. In addition, we describe a surface partial differential equation framework that can be coupled with the phase-field framework, thereby offering a wholistic approach for modelling biochemical processes and biomechanics properties associated with cell migration.

RNA interference (RNAi), or Post-Transcriptional Gene Silencing (PTGS), is a biological process which uses small RNAs to regulate gene expression on a cellular level, typically by causing the destruction of specfic mRNA molecules. This biological pathway is found in both plants and animals, and can be used as an effective strategy in defending cells against parasitic nucleotide sequences, viruses and transposons. In the case of plants, it also constitutes a major component of the adaptive immune system. RNAi is characterised by the ability to induce sequence-specific degradation of target messenger RNA (mRNAs) and methylation of target gene sequences. The small interfering RNA produced within the initiated cell is not only used locally but can also be transported into neighbouring cells, thus acting as a mobile warning signal. In the first part of the thesis I develop and analyse a new mathematical model of the plant immune response to a viral infection, with particular emphasis on the role of RNA interference. The model explicitly includes two different time delays, one to represent the maturation period of undifferentiated cells, and another to account for the time required for the RNAi propagating signal to reach other parts of the plant, resulting in either recovery or warning of susceptible cells. Analytical and numerical bifurcation theory is used to identify parameter regions associated with recovery and resistant plant phenotypes, as well as possible chronic infections. The analysis shows that the maturation time plays an important role in determining the dynamics, and that long-term host recovery does not depend on the speed of the warning signal but rather on the strength of local recovery. At best, the warning signal can amplify and hasten recovery, but by itself it is not competent at eradicating the infection. In the second part of the thesis I derive and analyse a new mathematical model of plant viral co-infection with particular account for RNA-mediated cross-protection in a single plant host. The model exhibits four non-trivial steady states, i.e. a disease-free steady state, two one-virus endemic equilibria, and a co-infected steady state. I obtained the basic reproduction number for each of the two viral strains and performed extensive numerical bifurcation analysis to investigate the stability of all steady states and identified parameter regions where the system exhibits synergistic or antagonistic interactions between viral strains, as well as different types of host recovery. The results indicate that the propagating component of RNA interference plays a significant role in determining whether both viruses can persist simultaneously, and as such, it controls whether the plant is able to support some constant level of both infections. If the two viruses are sufficiently immunologically related, the least harmful of the two viruses becomes dominant, and the plant experiences cross-protection. In the third part of the thesis I investigate the properties of intracellular dynamics of RNA interference and its capacity as a gene regulator by extending a well known model of RNA interference with time delays. For each of the two amplification pathways of the model, I consider the cumulative effects of delay in dsRNA-primed synthesis associated with the non-instantaneous nature of chemical signals and component transportation delay. An extensive bifurcation analysis is performed to demonstrate the significance of different parameters, and to investigate how time delays can affect the bi-stable regime in the model.

The focus of this thesis is to propose and implement a highly efficient numerical method to study cell dynamics. Three key phases are covered: mathematical modelling, linear stability analytical theory and numerical simulations using the moving grid finite element method. This aim is to study cell deformation and cell movement by considering both the mechanical and biochemical properties of the cortical network of actin filaments and its concentration. These deformations are assumed to be a result of the cortical actin dynamics through its interaction with a protein known as myosin II in the cell cytoskeleton. The mathematical model that we consider is a continuum model that couples the mechanics of the network of actin filaments with its bio-chemical dynamics. Numerical treatment of the model is carried out using the moving grid finite element method. By assuming slow deformations of the cell boundary, we verify the numerical simulation results using linear stability theory close to bifurcation points. Far from bifurcation points, we show that the model is able to describe the deformation of cells as a function of the contractile tonicity of the complex formed by the association of actin filaments with the myosin II motor proteins. Our results show complex cell deformations and cell movements such as cell expansion, contraction, translation and protrusions in accordance with experimental observations. The migratory behaviour of cells plays a crucial role in many biological events such as immune response, wound healing, development of tissues, embryogenesis, inflammation and the formation of tumours.

M.A.

The purpose of this investigation was to evaluate the ease of obtaining and reproducing diffusion coefficients for carbon dioxide and oxygen in water at 25°C using a quiescent liquid absorption apparatus. Absorption curves were obtained for carbon dioxide in water using both a zero initial concentration and specific initial concentration of carbon dioxide. The evacuation pressure, operating pressure, initial concentration, and pressure increment were varied. The zero initial concentration tests gave values for the diffusion coefficient consistently lower than expected. In addition the values were not reproducible and could not be correlated to the variation of parameters for the system. The cause of this variation was considered to be a combination of the evacuation procedure and the condensation phenomena. The interrelation of these effects was not determined. Tests made with specific initial concentrations gave good agreement for the value of the diffusion coefficient. A value of 1.95 ± 0.15 x 10⁻⁵ square centimeters per second was determined to represent the diffusion coefficient for carbon dioxide at 25°C. A slight trend toward lower values of the diffusion coefficient at higher pressure gradients was observed. The effect of the evacuation pressure and condensation were considered to be minimal in these tests. In both zero and specific initial concentration tests, convection appeared between 4 and 6 minutes after the start of the absorption. test. The absorption of oxygen in water at 25°C is nearly 15 times less than that of carbon dioxide. As a result, the absorption of oxygen was considered to be out of the applicable range for measurement of diffusion, coefficients with this apparatus. The quiescent liquid system was considered to be a rapid and reasonably accurate method for measuring the absorption of very soluble gases, such as carbon dioxide, over a limited range. The adaptability of the apparatus to less soluble gases is rather limited. However, for repeated measurements for a few chosen gases the system would be ari inexpensive, competitive apparatus. / Master of Science

A method for solving general compressible three-dimensional boundary-layer flows is developed. The equations are initially placed in a Crocco-type form which makes use of similarity variables. A general solution technique which employs an implicit finite-difference scheme that is stable for negative transverse velocities is developed. The solutions for some 10° vertical half-angle elliptical cones of varying ellipticity ratios at up to 8° angle of attack at a Mach number of 7.95 are presented. Skin friction and heat-transfer-rate distributions are presented for all cases. Good agreement has been found with experiment for the heat-transfer rates on circular cones at angle of attack. It has also been determined that increasing ellipticity tended to produce large heat-transfer-rate gradients, and large increases in the peak heat-transfer rates and peak skin frictions. It has also been found that for even moderate angles of attack and small ellipticity ratios the peak heat-transfer rate and peak longitudinal skin friction fall close to the major axis of the cone. / Master of Science

A study was made to ascertain the mechanism by which ortho-positronium reacts with nitroaromatics in solution. These reactions are two to three orders of magnitude faster than expected by simple pickoff. Conjugation of the nitro group with the aromatic ring was found to be a necessary condition for this behavior. The rate constant for each of these reactions was measured in suitable solvents over a wide temperature range, 200-500°K. Distinct departure from the Arrhenius law was found. In general, the rate constant increased linearly with increasing temperature up to a point, and then decreased linearly as the temperature was raised further. The following mechanism is postulated: Ps + M [stacked right and left arrows with k₁ above and k₋₁ below] PsM [right arrow with k₂ above] M + 2γ. Ortho-Positronium reacts with the nitroaromatic, M, to form a complex in a reversible step. The complex may either decompose into a positronium atom and nitroaromatic molecule or it may go on to annihilate the positron. A steady-state concentration ot the complex is assumed and the observed rate constant for the process is K_obs = k₁k₂ /(k₋₁+ k₂) The two limiting cases are: (1) k₂ >> k₋₁ causing k_obs = k₁ . Typical Arrhenius behavior is expected and observed in this region, and (2) k₋₁ >> k₂ causing k_obs = K_EQk₂ . In this region H_EQ + E_a(2) <O and the observed rate constant decreases with increasing temperature. This corresponds to a stable but temperature sensitive PsM complex. An approximate molecular orbital study has been made to study the possible existence of positron and positronium complexes with a select number of organic molecules. The CND0/2 approximation is used for all electronic integrals and for electron positron Coulomb integrals. The core Hamiltonian matrix elements for the positron were estimated by combining the Wolfsberg-Helmholtz and Cusachs-Cusachs approximations. This approach shows that the positron should become bound to the molecules. Using the same criteria, the formation of stable positronium complexes is more improbable. The calculated binding energies are strongly dependent on the value of the Wolfsberg-Helmholtz proportionality constant for positrons. / Doctor of Philosophy

A highway driving simulator with a computer-generated visual display, physical motion cues of roll, yaw, and lateral translation, and velocity dependent sound/vibration cues was used to investigate the influence of these cues on driver performance. Forty-eight student subjects were randomly allocated to six experimental groups. Each group of eight subjects experienced a unique combination of the motion and audio cues. The control group performed under a full simulation condition while each of the remaining five groups performed with certain combinations of motion and sound deleted. Each driver generated nine minutes of continuous data from which five performance measures were derived. Results indicate that the performance measures of yaw, lateral and velocity deviation are significantly affected by the deletion of cues. In support of the hypothesis that driver performance is augmented by the addition of motion cues, significant negative correlations were shown between the number of motion cues present and the measures of yaw and lateral deviation. With respect to motion and audio cues, recommendations were made regarding simulator design criteria and relative simulator fidelity comparisons. / Master of Science

R.J. Hull and H.H. Stroke. / "November 1, 1961." "Reprinted from Journal of the Optical Society of America, vol.51, no. 11, 1203-1212, November, 1961." / Includes bibliographical references. / Army Signal Corps Contract DA36-0390-sc-78108. Dept. of the Army Task 3-99-20-001 and Project 3-99-00-000.

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