**Abstract:**

A series of experiments has been designed and conducted to study the effect of three operating factors, namely, coal feedrate, coal particle size, and steam/O2 ratio, and their interactions on the quality of syngas produced from ﬂuidized bed gasiﬁcation of lignite coal. The quality of syngas is evaluated based on ﬁve indices including carbon conversion, H2/CO ratio, CH4/H2 ratio, gas yield, and gasiﬁcation efﬁciency. The design of experiment tool based on the response surface methodology (RSM), which is believed to be more accurate than the common one-factor-at-a-time approach, is used to facilitate the comparison of the effect of all factors. The factors are tested in the ranges of 0.036–0.063 g/s, 70–500 lm, and 0.5– 1.0, for coal feedrate, coal particle size, and steam/O2 ratio, respectively. The carbon conversion, H2/CO ratio, CH4/H2 ratio, gas yield, and gasiﬁcation efﬁciency are found to range from 91% to 97%, 0.776 to 1.268, 0.0517 to 0.0702, 3.4 to 3.7 m3

gas/kg coal, and 56% to 67%, respectively. The effects of individual operating factors and their interactions on each syngas quality index are discussed using RSM tools. A set of operating conditions to achieve syngas with a desired quality for different applications is also proposed by optimization of the response surface of each index.

**Authors**: Karimipour, Gerspacher, Gupta, and Spiteri

**Download:** KarimipourEtAl2013

**Abstract:**

One of the most popular methods for solving the ordinary differential equations (ODEs) that describe the dynamic behaviour of myocardial cell models is known as the Rush– Larsen (RL) method. Its popularity stems from its improved stability over integrators such as the forward Euler (FE) method along with its easy implementation. The RL method partitions the ODEs into two sets: one for the gating variables, which are treated by an exponential integrator, and another for the

remaining equations, which are treated by the FE method. The success of the RL method can be understood in terms of its relatively good stability when treating the gating variables. However, this feature would not be expected to be of beneﬁt on cell models for which the stiffness is not captured by the gating equations. We demonstrate that this is indeed the case on a number of stiff cell models. We further propose a new partitioned method based on the combination of a ﬁrst-order generalization of the RL method with the FE method. This new method leads to simulations of stiff cell models that are often one or two orders of magnitude faster than the original RL method.

**Authors**: Megan E. Marsh, Saeed Torabi Ziaratgahi, Raymond J. Spiteri

**Download:** MarshEtAl2013

**Abstract:**

We use Monte Carlo simulations to study the dual-mode diﬀusion regime of binary and tertiary mixtures of hard spheres conﬁned in narrow cylindrical pores under the

inﬂuence of an imposed ﬂow. The ﬂow is introduced to the dynamics by adding a small bias directed along the long axis of the pore to the random displacement of each Monte Carlo move. As a result, the motion of the particles in all the components is dominated by a drift velocity that causes the mean squared displacements to increase quadratically in the long time limit. However, an analysis of the mean squared displacements at intermediate time scales shows that components of the mixture above and below their passing thresholds still exhibit behaviors consistent with normal and single-ﬁle diﬀusion, respectively. The diﬀerence between the mean squared displacements of the various components is shown to go though a maximum, suggesting there may be an optimal pore diameter for the separation of mixtures exhibiting dual-mode diﬀusion.

**Authors**: Wanasundara, Spiteri, and Bowles

**Download:** WanasundaraEtAl2012

**Abstract:**

In many parts of the world, snowmelt energetics are dominated by solar irradiance. This is particularly the case in the Canadian Rocky Mountains, where clear skies dominate the winter and spring. In mountains, solar irradiance at the snow surface is not only aﬀected by solar angles, atmospheric transmittance, and the slope and aspect of immediate topography but also by shadows from surrounding terrain. Accumulation of errors in estimating solar irradiation can lead to signiﬁcant errors in calculating the timing and rate of snowmelt due to the seasonal storage of internal energy in the snowpack. Gridded methods, which are often used to estimate solar irradiance in complex terrain, work best with highresolution digital elevation models (DEMs), such as those produced using LiDAR. However, such methods also introduce errors due to the rigid nature of the mesh as well as limiting the ability to represent basin characteristics. Unstructured triangular meshes are more eﬃcient in their use of DEM data than ﬁxed grids when producing solar irradiance information for spatially distributed snowmelt calculations and they do not suﬀer from the artefact problems of a gridded DEM. This paper demonstrates the increased accuracy of using a horizon-shading algorithm model with an unstructured mesh versus standard self-shading algorithms. A systematic over-prediction in irradiance is observed when only self-shadows are considered. The modelled results are diagnosed by comparison to measurements of mountain shadows by time-lapse digital cameras and solar irradiance by a network of radiometers in Marmot Creek Research Basin, Alberta, Canada. Results show that depending on the depth and aspect of the snowpack of the Mt. Allan cirque, 6.0% to 66.4% of the pre-melt snowpack could be prematurely melted. On average at a basin scale there was a 14.4 mm SWE diﬀerence in equivalent melt energy between the two shading algorithms with maximum diﬀerences over 100% of the total annual snowfall.

**Authors**: Marsh, Pomeroy, and Spiteri

**Download:** MarshEtAl2012

**Abstract:**

In areas of oil and gas exploration, seismic lines have been reported to alter the movement patterns of wolves (Canis lupus). We developed a mechanistic ﬁrst passage time model, based on an anisotropic elliptic partial differential equation, and used this to explore how wolf movement responses to seismic lines inﬂuence the encounter rate of the wolves with their prey. The model was parametrized using 5 min GPS location data. These data showed that wolves travelled faster on seismic lines and had a higher probability of staying on a seismic line once they were on it. We simulated wolf movement on a range of seismic line densities and drew implications for the rate of predator–prey interactions as described by the functional response. The functional response exhibited a more than linear increase with respect to prey density (type III) as well as interactions with seismic line density. Encounter rates were signiﬁcantly higher in landscapes with high seismic line density and were most pronounced at low prey densities. This suggests that prey at low population densities are at higher risk in environments with a high seismic line density unless they learn to avoid them.

**Authors**: McKenzie, Merrill, Spiteri, and Lewis

**Download:** McKenzieEtAl2012

**Abstract:**

Splash-form tektites are glassy rocks ranging in size from roughly 1 to 100 mm that are believed to have formed from the splash of silicate liquid after a large terrestrial impact from which they are strewn over thousands of km. They are found in an array of shapes including spheres, oblate ellipsoids, dumb-bells, rods, and possibly fragments of tori. It has recently become appreciated that surface tension and centrifugal forces associated with the rotation of ﬂuid droplets are the main factors determining the shapes of these tektites. In this contribution, we compare the shape distribution of 1163 measured splashform tektites with the results of the time evolution of a 3D numerical model of a rotating ﬂuid drop with surface tension. We demonstrate that many aspects of the measured shape distribution can be explained by the results of the dynamical model.

**Authors**: Butler, Stauffer, Sinha, Lilly, and Spiteri

**Download:** ButlerEtAl2011

**Abstract:**

The electrophysiology in a cardiac cell can be modelled as a system of ordinary diﬀerential equations. The eﬃcient solution of these systems is important because they must be solved many times as sub-problems of tissue- or organ-level simulations of cardiac electrophysiology. The wide variety of existing cardiac cell models encompasses many diﬀerent properties, including the complexity of the model and the degree of stiﬀness. Accordingly, no single numerical method can be expected to be the most eﬃcient for every model. In this paper, we study the stiﬀness properties of a range of cardiac cell models and discuss the implications for their numerical solution. This analysis allows us to select or design numerical methods that are highly eﬀective for a given model and hence outperform commonly used methods.

**Authors**: Raymond J. Spiteri · Ryan C. Dean

**Download:** SpiteriDean2010.

**Abstract:**

We present a fully implicit ﬁnite diﬀerence method for the unsteady incompressible Navier–Stokes equations. It is based on the one-step θ-method for discretization in time and a special coordinate splitting (called vectorial operator splitting) for eﬃciently solving the nonlinear stationary problems for the solution at each new time level. The resulting system is solved in a fully coupled approach that does not require a boundary condition for the pressure. A staggered arrangement of velocity and pressure on a structured Cartesian grid combined with the fully implicit treatment of the boundary conditions help to preserve properties of the diﬀerential operators and thus lead to excellent stability of the overall algorithm. The convergence properties of the method are conﬁrmed via numerical experiments.

**Authors**: Rossitza S. Marinova, Raymond J. Spiteri, Eddy Essien

**Download:** MarinovaSpiteriEssien2010

**Abstract:**

We have determined the Arrhenius rate constants for 99 chemical reactions on palladium and solved the tightly coupled differential equations describing the chemical kinetics at a number of temperatures ranging from 350K to 700K. The rate equations were integrated to a week of reactor run-time. In this work we discuss the valuable insights that can be gained by closely examining the chemistry ongoing on the first differential slice of the plug flow reactor.

The two-component feed gas consisted of CO2 and CH4 with total pressure of 1 bar. The CO2 – CH4 partial pressures employed ranged from 20% – 80% to 80% – 20%. In these temperature and pressure ranges, the system performs in the low-coverage regime.

In addition to the feed gas, formaldehyde, methanol, molecular hydrogen, C2 hydrocarbons, formic acid, acetic acid, ketene, water, and carbon monoxide evolve from the catalyst surface in the first differential slice of the plug flow reactor. The relative amounts of the desorbing reaction products are dependent on the operating temperature and the relative pressures. The results of our simulations are consistent with results reported in the experimental literature.

**Authors**: Harrell Sellers, Raymond J. Spiteri, Michael Perrone

**Download:** SellersSpiteriPerrone2009

**Abstract:**

Mathematical models of electric activity in cardiac tissue are becoming increasingly powerful tools in the study of cardiac arrhythmias. Considered here are mathematical models based on ordinary differential equations (ODEs) and partial differential equations (PDEs) that describe the behaviour of this electrical activity. Generating an efficient numerical solution of these models is a challenging task, and in fact the physiological accuracy of tissue-scale models is often limited by the efficiency of the numerical solution process. In this thesis, we discuss two set of experiments that test ideas for making the numerical solution process more efficient. In the first set of experiments, we examine the numerical solution of four single cell cardiac electrophysiological models, which consist solely of ODEs. We study the efficiency of using implicit-explicit Runge–Kutta (IMEX-RK) splitting methods to solve these models. We find that variable step-size implementations of IMEX- RK methods (ARK3 and ARK5) that take advantage of Jacobian structure clearly outperform most methods commonly used in practice for two of the models, and they outperform all methods commonly used in practice for the remaining models. In the second set of experiments, we examine the solution of the bidomain model, a model consisting of both ODEs and PDEs that are typically solved separately. We focus these experiments on numerical methods for the solution of the two PDEs in the bidomain model. The most popular method for this task, Crank–Nicolson, produces unphysical oscillations; we propose a method based on a second-order L-stable singly diagonally implicit Runge–Kutta (SDIRK) method to eliminate these oscillations. We find that although the SDIRK method is able to eliminate these unphysical oscillations, it is only more efficient for crude error tolerances.

**Author:** Ryan C. Dean

**Advisor:** Raymond J. Spiteri

**Download:** rdean_msc_thesis