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(2023)ThesisThe magnitude of the diffusivity that characterizes lateral mixing in the ocean is about 106 -108 times larger than that of vertical mixing. The lateral direction is along the direction of the neutral tangent plane (same as the direction of the locally referenced potential density surface). However, due to the helical nature of the neutral trajectories (the normal vector of the neutral tangent plane is not curl-free), well-defined neutral surfaces do not exist. Well-defined but only approximately neutral surfaces have traditionally been chosen based on either (i) constructing a three-dimensional density variable whose iso-surface (the surface with a constant density value of the density variable) describes the lateral direction, or (ii) creating a two-dimensional approximately neutral surfaces (ANS), which are normally more neutral than the iso-surfaces of the three-dimensional density variable A three-dimensional neutral density variable is here derived called rSCV, which is an improvement on the neutral density rn of Jackett and McDougall (1997). Compared with rn, rSCV is independent of pressure and thus is insensitive to the ubiquitous vertical heaving motions of waves and eddies, and has similar neutrality as rn. The material derivatives (the rate of change of the density variables) of rSCV and rn have also been derived using numerical methods. The material derivative of rSCV is shown to be close to that of rn. Oceanographers have traditionally estimated the quality of an ANS by focusing on the fictitious vertical diffusion caused by lateral diffusion being applied in the wrong direction. This thesis shows that the spurious advection through an ANS is another important consideration that limits the accuracy and usefulness of an ANS. Because of this concern, a two-dimensional approximately neutral surface is constructed called the Wu.s-surface, which minimizes the spurious dia-surface advection through the surface. The spurious dia-surface advection through the Wu.s-surface is more than a hundred times smaller than that on the most neutral ANS to date, however, the fictitious diapycnal diffusion on it is larger. Therefore, the Wu.s+s2-surface is created to control both the spurious dia-surface advection and the fictitious diapycnal diffusion on the surface. It is shown that minimizing the fictitious diffusion and the spurious dia-surface advection is important for using such surfaces in inverse studies. Hence the Wu.s+s2-surface is the best choice of surface for such studies.
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(2024)ThesisOsteochondral tissue comprises of complex chemical, cellular and physical gradients which pose an immense challenge for repair via traditional tissue engineering approaches. Granular hydrogels have emerged as an exciting new opportunity for control of micro- and macro- scale properties for fabrication of complex tissue environments. This thesis explores the utility of gelMA-microgel based granular scaffolds for tissue engineering, with a focus on the osteochondral interface. First, scaffolds were optimised for MSC chondrogenesis by manipulating interstitial filler volume. Higher volumes were found to promote cell sphericity, proliferation, and aggregation, which led to enhanced chondrogenic matrix deposition. Second, incorporation of bioactive Laponite® -RD and -XLG nanosilicates is explored for MSC osteogenesis. Nanosilicate inclusion significantly enhanced MSC osteogenesis but was not found to be osteo-inductive. Third, embedded extrusion printing was utilised for deposition of a bone-mimetic ink in optimised MSC-laden microgel suspensions. Photo-crosslinkable gelMA microgels allowed tuning of ink properties, thus improving robustness. Over 21 days, MSCs exhibited gradient-like chondrogenic ECM deposition away from the bone and mineralisation close to it. Lastly, vascular structures were fabricated using a casting approach for straight channels and direct writing with a sacrificial ink for complex geometries. Design of a novel PDMS-based reactor allowed channel fabrication and long-term perfusion of constructs within the same setup. Taken together, this thesis demonstrates the modularity and versatility of gelMA microgel based granular suspensions and lays the foundation for their use in the fabrication of complex tissue models replete with vasculature.