Morphology-based model for predicting osteocyte-like cell line (MLO-Y4) growth process

This work has led to the development of empirical mathematical models to quantitatively predicate the changes of morphology in osteocyte-like cell lines (MLO-Y4) in culture. MLO-Y4 cells were cultured at low density and the changes in morphology recorded over 11 hours. Cell area and three dimensional shape features including aspect ratio, circularity and solidity were then determined using widely accepted image analysis software (ImageJTM). Based on the data obtained from the imaging analysis, mathematical models were developed using the non-linear regression method. The developed mathematical models accurately predict the morphology of MLO-Y4 cells for different culture times and can, therefore, be used as a reference model for analyzing MLO-Y4 cell morphology changes within various biological/mechanical studies, as necessary.

Exponential integrators and a dual-scale model for wood drying

For the timber industry, the ability to simulate the drying of wood is invaluable for manufacturing high quality wood products. Mathematically, however, modelling the drying of a wet porous material, such as wood, is a diffcult task due to its heterogeneous and anisotropic nature, and the complex geometry of the underlying pore structure. The well{ developed macroscopic modelling approach involves writing down classical conservation equations at a length scale where physical quantities (e.g., porosity) can be interpreted as averaged values over a small volume (typically containing hundreds or thousands of pores). This averaging procedure produces balance equations that resemble those of a continuum with the exception that effective coeffcients appear in their deffnitions. Exponential integrators are numerical schemes for initial value problems involving a system of ordinary differential equations. These methods differ from popular Newton{Krylov implicit methods (i.e., those based on the backward differentiation formulae (BDF)) in that they do not require the solution of a system of nonlinear equations at each time step but rather they require computation of matrix{vector products involving the exponential of the Jacobian matrix. Although originally appearing in the 1960s, exponential integrators have recently experienced a resurgence in interest due to a greater undertaking of research in Krylov subspace methods for matrix function approximation. One of the simplest examples of an exponential integrator is the exponential Euler method (EEM), which requires, at each time step, approximation of φ(A)b, where φ(z) = (ez - 1)/z, A E Rnxn and b E Rn. For drying in porous media, the most comprehensive macroscopic formulation is TransPore [Perre and Turner, Chem. Eng. J., 86: 117-131, 2002], which features three coupled, nonlinear partial differential equations. The focus of the first part of this thesis is the use of the exponential Euler method (EEM) for performing the time integration of the macroscopic set of equations featured in TransPore. In particular, a new variable{ stepsize algorithm for EEM is presented within a Krylov subspace framework, which allows control of the error during the integration process. The performance of the new algorithm highlights the great potential of exponential integrators not only for drying applications but across all disciplines of transport phenomena. For example, when applied to well{ known benchmark problems involving single{phase liquid ow in heterogeneous soils, the proposed algorithm requires half the number of function evaluations than that required for an equivalent (sophisticated) Newton{Krylov BDF implementation. Furthermore for all drying configurations tested, the new algorithm always produces, in less computational time, a solution of higher accuracy than the existing backward Euler module featured in TransPore. Some new results relating to Krylov subspace approximation of '(A)b are also developed in this thesis. Most notably, an alternative derivation of the approximation error estimate of Hochbruck, Lubich and Selhofer [SIAM J. Sci. Comput., 19(5): 1552{1574, 1998] is provided, which reveals why it performs well in the error control procedure. Two of the main drawbacks of the macroscopic approach outlined above include the effective coefficients must be supplied to the model, and it fails for some drying configurations, where typical dual{scale mechanisms occur. In the second part of this thesis, a new dual{scale approach for simulating wood drying is proposed that couples the porous medium (macroscale) with the underlying pore structure (microscale). The proposed model is applied to the convective drying of softwood at low temperatures and is valid in the so{called hygroscopic range, where hygroscopically held liquid water is present in the solid phase and water exits only as vapour in the pores. Coupling between scales is achieved by imposing the macroscopic gradient on the microscopic field using suitably defined periodic boundary conditions, which allows the macroscopic ux to be defined as an average of the microscopic ux over the unit cell. This formulation provides a first step for moving from the macroscopic formulation featured in TransPore to a comprehensive dual{scale formulation capable of addressing any drying configuration. Simulation results reported for a sample of spruce highlight the potential and flexibility of the new dual{scale approach. In particular, for a given unit cell configuration it is not necessary to supply the effective coefficients prior to each simulation.

Non-Newtonian natural convection flow along an isothermal horizontal circular cylinder using modified power-law model

Laminar two-dimensional natural convection boundary-layer flow of non-Newtonian fluids along an isothermal horizontal circular cylinder has been studied using a modified power-law viscosity model. In this model, there are no unrealistic limits of zero or infinite viscosity. Therefore, the boundary-layer equations can be solved numerically by using marching order implicit finite difference method with double sweep technique. Numerical results are presented for the case of shear-thinning as well as shear thickening fluids in terms of the fluid velocity and temperature distributions, shear stresses and rate of heat transfer in terms of the local skin-friction and local Nusselt number respectively.

Hierarchical multiscale model for biomechanics analysis of microfilament networks

The mechanisms of force generation and transference via microfilament networks are crucial to the understandings of mechanobiology of cellular processes in living cells. However, there exists an enormous challenge for all-atom physics simulation of real size microfilament networks due to scale limitation of molecular simulation techniques. Following biophysical investigations of constitutive relations between adjacent globular actin monomers on filamentous actin, a hierarchical multiscale model was developed to investigate the biomechanical properties of microfilament networks. This model was validated by previous experimental studies of axial tension and transverse vibration of single F-actin. The biomechanics of microfilament networks can be investigated at the scale of real eukaryotic cell size (10 μm). This multiscale approach provides a powerful modeling tool which can contribute to the understandings of actin-related cellular processes in living cells.

A comprehensive dual-scale wood torrefaction model : application to the analysis of thermal run-away in industrial heat treatment processes

A dual-scale model of the torrefaction of wood was developed and used to study industrial configurations. At the local scale, the computational code solves the coupled heat and mass transfer and the thermal degradation mechanisms of the wood components. At the global scale, the two-way coupling between the boards and the stack channels is treated as an integral component of the process. This model is used to investigate the effect of the stack configuration on the heat treatment of the boards. The simulations highlight that the exothermic reactions occurring in each single board can be accumulated along the stack. This phenomenon may result in a dramatic eterogeneity of the process and poses a serious risk of thermal runaway, which is often observed in industrial plants. The model is used to explain how thermal runaway can be lowered by increasing the airflow velocity, the sticker thickness or by gas flow reversal.

Numerical solutions for thin film flow down the outside and inside of a vertical cylinder

We consider a model for thin film flow down the outside and inside of a vertical cylinder. Our focus is to study the effect that the curvature of the cylinder has on the gravity-driven instability of the advancing contact line and to simulate the resulting fingering patterns that form due to this instability. The governing partial differential equation is fourth order with a nonlinear degenerate diffusion term that represents the stabilising effect of surface tension. We present numerical solutions obtained by implementing an efficient alternating direction implicit scheme. When compared to the problem of flow down a vertical plane, we find that increasing substrate curvature tends to increase the fingering instability for flow down the outside of the cylinder, whereas flow down the inside of the cylinder substrate curvature has the opposite effect. Further, we demonstrate the existence of nontrivial travelling wave solutions which describe fingering patterns that propagate down the inside of a cylinder at constant speed without changing form. These solutions are perfectly analogous to those found previously for thin film flow down an inclined plane.

An isoviscous, isothermal model investigating the influence of hydrostatic recesses on a spring-supported tilting pad thrust bearing

Tilting-pad hydrodynamic thrust bearings are used in hydroelectric power stations around the world, reliably supporting turbines weighing hundreds of tonnes, over decades of service. Newer designs incorporate hydrostatic recesses machined into the sector-shaped pads to enhance oil film thickness at low rotational speeds. External pressurisation practically eliminates wear and enhances service life and reliability. It follows that older generating plants, lacking such assistance, stand to benefit from being retrofitted with hydrostatic lubrication systems. The design process is not trivial however. The need to increase the groove size to permit spontaneous lifting of the turbine under hydrostatic pressure, conflicts with the need to preserve performance of the original plane pad design. A haphazardly designed recess can induce a significant rise in bearing temperature concomitant with reduced mechanical efficiency and risk of thermal damage. In this work, a numerical study of a sector-shaped pad is undertaken to demonstrate how recess size and shape can affect the performance of a typical bearing.

Experimental and numerical study of water-filled road safety barriers

Portable water-filled road barriers (PWFB) are roadside structures placed on temporary construction zones to separate work site from moving traffic. Recent changes in governing standards require PWFB to adhere to strict compliance in terms of lateral displacement of the road barriers and vehicle redirectionality. Actual road safety barrier test can be very costly, thus researchers resort to Finite Element Analysis (FEA) in the initial designs phase prior to real vehicle test. There has been many research conducted on concrete barriers and flexible steel barriers using FEA, however not many is done pertaining to PWFB. This research probes a new method to model joint mechanism in PWFB. Two methods to model the joining mechanism are presented and discussed in relation to its practicality and accuracy to real work applications. Moreover, the study of the physical gap and mass of the barrier was investigated. Outcome from this research will benefit PWFB research and allow road barrier designers better knowledge in developing the next generation of road safety structures.

A RBF meshless approach for modeling a fractal mobile/immobile transport model

A fractional differential equation is used to describe a fractal model of mobile/immobile transport with a power law memory function. This equation is the limiting equation that governs continuous time random walks with heavy tailed random waiting times. In this paper, we firstly propose a finite difference method to discretize the time variable and obtain a semi-discrete scheme. Then we discuss its stability and convergence. Secondly we consider a meshless method based on radial basis functions (RBFs) to discretize the space variable. In contrast to conventional FDM and FEM, the meshless method is demonstrated to have distinct advantages: calculations can be performed independent of a mesh, it is more accurate and it can be used to solve complex problems. Finally the convergence order is verified from a numerical example which is presented to describe a fractal model of mobile/immobile transport process with different problem domains. The numerical results indicate that the present meshless approach is very effective for modeling and simulating fractional differential equations, and it has good potential in the development of a robust simulation tool for problems in engineering and science that are governed by various types of fractional differential equations.

Existence of travelling wave solutions for a model of tumour invasion

The existence of travelling wave solutions to a haptotaxis dominated model is analysed. A version of this model has been derived in Perumpanani et al. (1999) to describe tumour invasion, where diffusion is neglected as it is assumed to play only a small role in the cell migration. By instead allowing diffusion to be small, we reformulate the model as a singular perturbation problem, which can then be analysed using geometric singular perturbation theory. We prove the existence of three types of physically realistic travelling wave solutions in the case of small diffusion. These solutions reduce to the no diffusion solutions in the singular limit as diffusion as is taken to zero. A fourth travelling wave solution is also shown to exist, but that is physically unrealistic as it has a component with negative cell population. The numerical stability, in particular the wavespeed of the travelling wave solutions is also discussed.

Numerical study of lid-driven square cavity with heat generation using LBM

In this study, the mixed convection heat transfer and fluid flow behaviors in a lid-driven square cavity filled with high Prandtl number fluid (Pr = 5400, ν = 1.2×10-4 m2/s) at low Reynolds number is studied using thermal Lattice Boltzmann method (TLBM) where ν is the viscosity of the fluid. The LBM has built up on the D2Q9 model and the single relaxation time method called the Lattice-BGK (Bhatnagar-Gross-Krook) model. The effects of the variations of non dimensional mixed convection parameter called Richardson number(Ri) with and without heat generating source on the thermal and flow behavior of the fluid inside the cavity are investigated. The results are presented as velocity and temperature profiles as well as stream function and temperature contours for Ri ranging from 0.1 to 5.0 with other controlling parameters that present in this study. It is found that LBM has good potential to simulate mixed convection heat transfer and fluid flow problem. Finally the simulation results have been compared with the previous numerical and experimental results and it is found to be in good agreement.

Bucket attack on numeric set watermarking model and safeguards

Numeric set watermarking is a way to provide ownership proof for numerical data. Numerical data can be considered to be primitives for multimedia types such as images and videos since they are organized forms of numeric information. Thereby, the capability to watermark numerical data directly implies the capability to watermark multimedia objects and discourage information theft on social networking sites and the Internet in general. Unfortunately, there has been very limited research done in the field of numeric set watermarking due to underlying limitations in terms of number of items in the set and LSBs in each item available for watermarking. In 2009, Gupta et al. proposed a numeric set watermarking model that embeds watermark bits in the items of the set based on a hash value of the items’ most significant bits (MSBs). If an item is chosen for watermarking, a watermark bit is embedded in the least significant bits, and the replaced bit is inserted in the fractional value to provide reversibility. The authors show their scheme to be resilient against the traditional subset addition, deletion, and modification attacks as well as secondary watermarking attacks. In this paper, we present a bucket attack on this watermarking model. The attack consists of creating buckets of items with the same MSBs and determine if the items of the bucket carry watermark bits. Experimental results show that the bucket attack is very strong and destroys the entire watermark with close to 100% success rate. We examine the inherent weaknesses in the watermarking model of Gupta et al. that leave it vulnerable to the bucket attack and propose potential safeguards that can provide resilience against this attack.

Radiative and total heat transfer measurements to a Titan Explorer model

Radiative and total heat transfer at the flow stagnation point of a 1:40.8 binary scaled model of the Titan Explorer vehicle were measured in the X3 expansion tube. Results from the current study illustrated that with the addition of CH4 into a N2 test gas radiative heat transfer could be detected. For a test gas of 5% CH4 and 95% N2, simulating an atmospheric model for Titanic aerocapture, approximately 4% of the experimentally measured total stagnation point heat transfer was found to be due to radiation. This was in comparison to < 1% measured for a test gas of pure nitrogen. When scaled to the flight vehicle, experimental results indicate a 64% contribution of radiation (test gas 5% CH4/95% N2). Previous numerical results however have predicted this contribution to be between 80-92%. Thus, experimental results from the current study suggest that numerical analyses are over-predicting the radiative heat transfer on the flight vehicle.

Numerical investigation of the influence of topography on simulated downburst wind fields

A, dry, non-hydrostatic sub-cloud model is used to simulate an isolated stationary downburst wind event to study the influence topographic features have on the near-ground wind structure of these storms. It was generally found that storm maximum wind speeds could be increased by up to 30% because of the presence of a topographic feature at the location of maximum wind speeds. Comparing predicted velocity profile amplification with that of a steady flow impinging jet, similar results were found despite the simplifications made in the impinging jet model. Comparison of these amplification profiles with those found in the simulated boundary layer winds reveal reductions of up to 30% in the downburst cases. Downburst and boundary layer amplification profiles were shown to become more similar as the topographic feature height was reduced with respect to the outflow depth.

Numerical simulation of downburst winds

The wind field of an intense idealised downburst wind storm has been studied using an axisymmetric, dry, non-hydrostatic numerical sub-cloud model. The downburst driving processes of evaporation and melting have been paramaterized by an imposed cooling source that triggers and sustains a downdraft. The simulated downburst exhibits many characteristics of observed full-scale downburst events, in particular the presence of a primary and counter rotating secondary ring vortex at the leading edge of the diverging front. The counter-rotating vortex is shown to significantly influence the development and structure of the outflow. Numerical forcing and environmental characteristics have been systematically varied to determine the influence on the outflow wind field. Normalised wind structure at the time of peak outflow intensity was generally shown to remain constant for all simulations. Enveloped velocity profiles considering the velocity structure throughout the entire storm event show much more scatter. Assessing the available kinetic energy within each simulated storm event, it is shown that the simulated downburst wind events had significantly less energy available for loading isolated structures when compared with atmospheric boundary layer winds. The discrepancy is shown to be particularly prevalent when wind speeds were integrated over heights representative of tall buildings. A similar analysis for available full scale measurements led to similar findings.