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Thesis (Ph.D. (Physics)) -- University of Limpopo, 2020 / This work presents a computational modelling workflow that uniquely combines several techniques, proposed as a means for studying and designing high-energy-density electrodes for the next-generation of rechargeable batteries within the era of the fourth industrial revolution (4IR). The Self-Consistent Charge Density Functional-based Tight Binding (SCC-DFTB) parameterisation scheme for the Li-Si and Na-Si systems is presented. By using the Li-Si system, a procedure for developing the Slater-Koster based potentials is shown. Using lessons learned from the Li-Si framework, the parameterisation of the Na-Si is reported. The Li-Si SCC-DFTB parameter set has been developed to handle environments that consist of Si-Si, Li-Si and Li-Li interactions; and the Na-Si SCC DFTB parameter set is developed for Na-Na, Na-Si, and Si-Si interactions. Validations and applications of the developed sets are illustrated and discussed. By calculating equilibrium lattice constants, the Li-Si set is shown to be compatible with various phases in the crystalline Li-Si system. The results were generally within a margin of less than 8% difference, with some values such as that of the cubic Li22Si5 being in agreement with experiments to within 1%. The volume expansion of Si as a function of Li insertion was successfully modelled via the Li-Si SCC-DFTB parameter set. It was shown that Si gradually expands in volume from 53.6% for the LiSi phase composed of 50 atm % Li, to 261.57% for Li15Si4 with 78.95 atm % Li, and eventually shoots over 300% for the Li22Si5 phase with the expansion at 316.45%, which agrees with experiments. Furthermore, the ability of the Li-Si SCC-DFTB parameter set to model the mechanical properties of Si is evaluated by calculating the mechanical properties of pristine cubic Si. The parameter set was able to produce the mechanical properties of Si, which agree with experiments to within 6%. The SCC-DFTB parameter set was then used to model the volume expansion of amorphous silicon (a-Si) as a result of lithiation within concentrations ranging from 33 – 50 atm % Li. Consistent with experiments, the a-Si was found to marginally expand in a linear form with increase in Li content. a-Si was observed to exhibit a lower expansion compared to c-Si. Additionally, the structural stability of the amorphous Li-Si alloys was examined, and observations agree with experiments.vi The Na-Si SCC-DFTB parameter set produced equilibrium lattice parameters that agree with experiments to within 4% for reference structures, and the transferability was tested on three Na-Si clathrate compounds (i.e. the Pm-3n Na8Si46, the Cmcm NaSi6 and Fd-3m Na24Si136). By employing the approach used when lithiating Si, the sodiation of crystalline silicon (c-Si) was modelled. It was predicted that c-Si expands by over 400% at 77 atm% Na and shoots above 500% for concentrations exceeding 80 atm% of Na. By comparing how c-Si expands as a result of lithiation to the expansion consequent to sodiation for concentrations ranging from 66.6 – 81.4 atm%, c-Si is shown to be unsuitable for Na-ion batteries. As a test, the ability of the developed Na-Si SCC DFTB parameter set to handle large and complex geometries was shown by modelling the expansion of a-Si at 33 atm% Na. It was deduced that a-Si would be more preferable for Na-ion batteries since at 33 atm% Na, a-Si expanded a lot less than when c-Si was used. Using the Li-Si and the Na-Si SCC-DFTB parameter sets, it was noted that amorphisation appears to lower the magnitude by which Si expands, therefore agreeing with experiments in that amorphous structures are reported to exhibit a buffering effect towards volume expansion. The material space for the Li-Si alloy system is explored through crystal structure predictions conducted via a machine learning powered cluster expansion (CE). Using the FCC and BCC – based parent lattice in the grid search, 12 thermodynamically stable Li-Si alloys were predicted by the genetic algorithm. Viz. the trigonal Li4Si (R-3m), tetragonal Li4Si (I4/m), tetragonal Li3Si (I4/mmm), cubic Li3Si (Fm-3m), monoclinic Li2Si3 (C2/m), trigonal Li2Si (P-3m1), tetragonal LiSi (P4/mmm), trigonal LiSi2 (P-2m1), monoclinic LiSi3 (P2/m), cubic LiSi3 (Pm-3m), tetragonal LiSi4 (I4/m) and monoclinic LiSi4 (C2/m). The structural stabilities of the predicted Li-Si alloys are further studied. With focus on pressure, the thermodynamic conditions under which the Li-rich phase, Li4Si (R 3m), would be stable are tested. Li4Si (R-3m) was subjected to pressures during geometry optimization and found to globally maintain its structural stability within the range 0 – 25GPa. Hence, Li4Si was predicted to be a low pressure phase. In studying the PDOS, the Li4Si (I4/m) was noted to be more stable around 40GPa and vii 45GPa, which is consistent with the prediction made from other works, wherein intelligence-based techniques were used. A test for exploring the Na-Si material space was done using insights acquired from the Li-Si framework. Three thermodynamically stable Na-Si (i.e. the I4/mmm Na3Si, P4/nmm NaSi and Immm NaSi2) were predicted. Using the Na-Si SCC-DFTB parameter set, a correlation of the total DOS in the vicinity of the Fermi level (Ef) with the structural stability of the three Na-Si alloys is done. NaSi (P4/nmm) was shown to be unstable at 0GPa, NaSi2 (Immm) is found to be stable, and the Na-rich Na3Si exhibited metastability. The stability of Na3Si was seen to improve when external pressure ranging from 2.5 – 25GPa was applied; hence, suggesting Na3Si (I4/mmm) to be a high-pressure phase. Furthermore, expanding on the groundwork laid from the Li-Si and Na-Si CE, the Mg-Si system was tested to illustrate that the approach can be used to rapidly screen for new materials. The ground-state crystal structure search predicted 4 thermodynamically stable Mg-Si alloys. Viz. Mg3Si (Pm-3m), MgSi (P4/mmm), MgSi2 (Immm) and MgSi3 (Pmmm). Lastly, to highlight the power of combining various computational techniques to advance material discovery and design, a framework linking SCC-DFTB and CE is illustrated. Candidate electrode materials with nano-architectural features were simulated by designing nanospheres comprised of more than 500 atoms, using the predicted Li-Si and Na-Si crystal structures. The stability of the nanospheres was examined using SCC-DFTB parameters developed herein. The workflow presented in this work paves the way for rapid material discovery, which is sought for in the era of the fourth industrial revolution. / National Cyber Infrastructure System: Center for High-Performance Computing (NICIS-CHPC) for computing resources, the National Research Foundation (NRF) and the University of Limpopo

Atrial fibrillation (AF) is the disordered activation of the atrial myocardium, which is a major cause of stroke. Currently, the most effective, minimally traumatic treatment for AF is percutaneous catheter ablation to isolate arrhythmogenic areas from the rest of the atrium. The standard in vitro evaluation of ablation catheters through lesion studies is a resource intensive effort due to tissue variability and visual measurement methods, necessitating large sample sizes and multiple prototype builds. A computational test bed for ablation catheter evaluation was built in SolidWorks® using the morphology and dimensions of the left atrium adjacent structures. From this geometry, the physical model was built in COMSOL Multiphysics®, where a combination of the laminar fluid flow, electrical currents, and bioheat transfer was used to simulate radiofrequency (RF) tissue ablation. Simulations in simplified 3D geometries led to lesions sizes within the reported ranges from an in-vivo ablation study. However, though the ellipsoid lesion morphologies in the full atrial model were consistent with past lesion studies, perpendicularly oriented catheter tips were associated with decreases of -91.3% and -70.0% in lesion depth and maximum diameter. On the other hand, tangentially oriented catheter tips produced lesions that were only off by -28.4% and +7.9% for max depth and max diameter. Preliminary investigation into the causes of the discrepancy were performed for fluid velocities, contact area, and other factors. Finally, suggestions for further investigation are provided to aid in determining the root cause of the discrepancy, such that the test bed may be used for other ablation catheter evaluations.

The self-organized nest construction behaviors of European paper wasps (Polistes dominula) show potential for adoption in artificial intelligence and robotic systems where centralized control proves challenging. However, P. dominula nest construction mechanisms are not fully understood. This research investigated how nest structures stimulate P. dominula worker action at different stages of nest construction. A novel stochastic site selection model, weighted by simple rules for cell age, height, and wall count, was implemented in a three-dimensional, step-by-step nest construction simulation. The simulation was built on top of a hexagonal coordinate system to improve precision and performance. Real and idealized nest data were used to evaluate simulated nests via two parameters: outer wall counts and compactness numbers. Structures generated with age-based rules were not significantly different from real nest structures along both parameters.

<p> The nervous system exists as our interface to the world, both integrating and interpreting sensory information and coordinating voluntary and involuntary movements. Given its importance, it has become a target for neuromodulatory therapies. The research to develop these therapies cannot be done purely on living tissues - animals, manpower, and equipment make that cost prohibitive and, given the cost of life required, it would be unethical to not search for alternatives. Computation modeling, the use of mathematics and modern computational power to simulate phenomena, has sought to provide such an alternative since the work of Hodgkin and Huxley in 1952. These models, though they cannot yet replace in-vivo and in-vitro experiments, can ease the burden on living tissues and provide details difficult or impossible to ascertain from them. This thesis iterates on previous frameworks for performing in-silico experiments for the purposes of mechanistic exploration and threshold prediction. To do so, an existing volume conductor model and validated nerve-fiber model were joined and a series of programs were developed around them to perform a set of in-silico experiments. The experiments are designed to predict changes in thresholds of behaviors elicited by bioelectric neuromodulation to parametric changes in experimental setup and to explore the mechanisms behind bioelectric neuromodulation, particularly surrounding the recently discovered Low Frequency Alternating Current (LFAC) waveform. This framework improved upon its predecessors through efficiency-oriented design and modularity, allowing for rapid simulation on consumer-grade computers. Results show a high degree of convergence with in-vivo experimental results, such as mechanistic alignment with LFAC and being within an order of magnitude of in-vivo pulse-stimulation threshold results for equivalent in-vivo and in-silico experimental designs. </p>

Hypertrophic cardiomyopathy (HCM) is the most common monogenic disorder and the leading cause of sudden arrhythmic death in children and young adults. It is typically asymptomatic and first manifests itself during cardiac arrest, making it a challenge to diagnose in advance. Computational models can explore and reveal underlying molecular mechanisms in cardiac electrophysiology by allowing researchers to alter various parameters such as tissue size or ionic current amplitudes. The goal of this thesis is to develop a computational model in MATLAB and to determine if this model can accurately indicate cases of hypertrophic cardiomyopathy. This goal is achieved by combining a three-dimensional network of the bidomain model with the Beeler-Reuter model and then by manually varying the thickness of that tissue and recording the resulting membrane potential with respect to time. The results of this analysis demonstrated that the developed model is able to depict variations in tissue thickness through the difference in membrane potential recordings. A one-way ANOVA analysis confirmed that the membrane potential recordings of the different thicknesses were significantly different from one another. This study assumed continuum behavior, which may not be indicative of diseased tissue. In the future, such a model might be validated through in vitro experiments that measure electrical activity in hypertrophied cardiac tissue. This model may be useful in future applications to study the ionic mechanisms related to hypertrophic cardiomyopathy or other related cardiac diseases.

The kinetics of milk coagulation are complex and still not well understood. A deeper understanding of coagulation and the impact of the relevant factors would aid in both cheese manufacturing and also in determining the nutritional benefits of dairy products. A method using confocal microscopy was developed to follow the movement of milk fat globules and the formation of a milk protein network during the enzyme-induced coagulation of milk. Image processing methods were then used to quantify the rate of coagulation. It was found that the texture of the protein network is an indicator of the current status of the milk gelation, and hence can be used to monitor the coagulation process. The imaging experiment was performed on milk gels with different concentrations of the coagulation enzyme, chymosin. Rheological measurements were taken using free oscillation rheometry to validate the imaging results. Both methods showed an inverse relationship between rennet concentration and the coagulation time. The results from the imaging study were used to create a computational model, which created simulated images of coagulating milk. The simulated images were then analyzed using the same image analysis algorithm. The temporal protein network texture behavior in the simulated images followed the same pattern as the protein texture in the confocal imaging data. The model was developed with temperature and rennet concentration as user inputs so that it could be implemented as a predictive tool for milk coagulation.

<p>  </p> <p>Laser powder bed fusion (L-PBF) is a relatively young metallurgical processing method which has many advantages over traditional casting and wrought based methods. Alloy systems suitable for this additive manufacturing (AM) process include Ti-6Al-4V, 316 stainless steel, Inconel 718 and 625 making it attractive for automotive, aerospace, and biomedical applications. Despite the potential, L-PBF is plagued by defects and inconsistent build qualities which make certification of critical components onerous. Additionally, experimental studies are difficult due to the cost of laser systems and feedstock material. Many researchers have turned to computational modeling as this allows for rigorous examination and isolation of the underlying physics to better understand where problems may arise, and where improvements can be made. However, models often fail to consider the role of systematic and statistical uncertainty while also relying heavily on assumptions and simplifications for computational efficiency. As such, there is no quantifiable metric for how reliable these models are. This work applies an uncertainty quantification (UQ) framework to computational models for L-PBF to understand the role of uncertainty and assumptions on model reliability as this provides insight into their limitations and potential areas of improvement.</p> <p>First, the UQ framework is applied to a finite volume melt pool transport model to evaluate the role of uncertainty and model assumptions on melt pool shapes and solidification dynamics. This includes the role of simulating the powder bed thermophysical properties, surface tension driven Marangoni convection, and the thermodynamic relation dictating latent heat release. The transport model is then weakly coupled to a cellular automata (CA) grain evolution model to propagate and quantify the uncertainty in the as-built microstructure including crystallographic texture formation. Further propagation of melt pool and microstructure uncertainty to the resulting mechanical properties to close the process-microstructure-property relations are discussed. Lastly, recommendations for future model development and research are presented. </p>