The Locus of Mid-Tangent Points of Planar Curves
In this project, we defined a mid-tangent point with respect to a fixed point X and a tangent at a point Y on a planar curve C as a point on the tangent that is equidistant from X and Y. We studied the locus of mid-tangent points of conic sections. We found that the locus of mid-tangent points of most conic sections are non-linear curves. However, we observed and proved by using Euclidean geometry that the locus of mid-tangent points of circles are straight lines. The mapping defined by mid-tangent points was studied further. The similarity between a mid-tangent mapping and a stereographic projection was displayed as a one – to – one correspondence function. We also extended the concept of mid-tangent points to three dimensional space and found that the similarity with the stereographic projection was retained in higher dimensions. Finally, we studied the locus of mid-tangent points of a sphere to create a mapping of the sphere to a plane.
A Novel Selection Process for the Conversion of Conventional Bacteria into Electrotrophs
The redox reactions of bacteria metabolism have been extrinsically studied. These mechanisms allow certain types of bacteria to be able to synthesize extremely valuable extracellular byproducts. Other types of bacteria are able to extract toxic metals from water by donating electrons directly to those aqueous metal ions, thus turning them into solid precipitates. However, the problem of these microorganisms is that their efficiency rates and production speeds are exceptionally low. This study focuses on the properties of electrotrophs, which are bacteria that can feed on pure electrons directly from an electrode (Rabaey et al 2010). Compared to normal organic-feeding bacteria, electrotrophs direct the majority of the electrons obtained to the production of metabolic byproducts (Nevin et al 2010). Therefore, when electrotrophs are employed in bioelectrochemical systems (BESs) their metabolic redox reaction efficiency rates are dramatically increased. This makes it possible to produce large quantities of valuable compounds such as hydrocarbons, plastics and medicine or efficiently remediating the environment (He et al 2016). Moreover, the usage of electricity as an energy source compared to conventional organic substrates is immensely cheaper (Rabaey et al 2010). However, not all bacteria are electrotrophs nor do all electrotrophs have favourable metabolic traits. Thus, there is a need for a novel procedure to turn conventional bacteria into electrotrophs which is a crucial step to making the BES an aggressive competitor in the sustainable energy industry.
How to spill your coffee
We all do it – walk along with a cup in hand, and carelessly spill it. While it’s usually more annoying than anything else, it happens to affect almost all of us, and little is done to minimise the likelihood of it occurring. So my aim was to explain the physics behind why we spill drinks when we walk, and to investigate how we can minimise the likelihood of this occurring. I broke this investigation into two distinct parts, explaining the system of the cup, and explaining the effect of walking. From initial observations, it was clear that the cup was a resonating system. Like any resonating system, the cup has a natural frequency. When the cup is oscillated – moved back and forth – at near this frequency, the size of the liquid oscillations is very large. This is because the acceleration is in phase with the motion of the liquid, so in each cycle maximum energy is input into the system. In my investigation I experimentally measured this natural frequency, and created a mathematical model to explain this frequency. It was also found that as the size of liquid oscillations in the cup increases, so does distortion of the fluid surface, possibly enabling spilling. To systematically analyse the effect of walking, I had subjects walk on a treadmill, so walking surface and speed were controlled. However, I also needed an accurate way of measuring the motion of a carried cup. Firstly, I tried to use video analysis; however I found this far too imprecise for measuring small changes in velocity of a cup. In the end I used a smartphone to record the acceleration of a carried cup, as acceleration is what causes the movement of liquid in a cup. This allowed surprisingly accurate measurements to be made, and allowed both the size and frequency of the acceleration to be recorded. In order to relate the system of the cup and the oscillation provided whilst walking I conducted a qualitative experiment into the effect of stride frequency on the likelihood of spilling. When stride frequency was very close to the natural frequency of the cup, spilling occurred almost instantly, while it did not occur if stride frequency was much higher or lower. In the end, my research showed that to minimise the likelihood of spilling your drink walk slowly, use a narrow cup, focus on walking smoothly, and fill the cup well below the rim. Despite this, some people happen to be much smoother cup carriers than others, likely due to their individual biomechanics. And, if you really don’t want to spill your drink, you can always use a lid.
聚乳酸/天然纖維複合材料之研究-探討加入玉米葉纖維對機械性質之影響
本研究以玉米葉纖維做為聚乳酸纖維的補強材料，並以加入的玉米葉纖維長度為操縱變因，探討其對聚乳酸/玉米葉纖維複合材料機械性質的影響。實驗設計以純聚乳酸為對照組，以加入1mm, 2mm, 5mm, 13mm玉米葉纖維的聚乳酸複合材料為實驗組。本研究以拉伸強度和耐衝擊值來判斷機械性質的強度。 實驗數據顯示，實驗組的拉伸強度與對照組差距不大，但在耐衝擊值卻比對照組高出許多。除此之外，拉伸強度和耐衝擊值都顯示加入2mm玉米葉纖維在實驗組擁有最佳的數值。另外，加入越長的玉米葉纖維反而不會擁有較佳的機械性質。未來期待聚乳酸複合材料能夠應用在更廣的層面。
VERMICOMPOSTING-EFFICIENT DAIRY SLUDGE MANAGEMENT
The continued growth of dairy farming in NZ and the move toward keeping cows on stand-off pads has seen a major increase in two significant waste streams, the wood fibre that is scrapped off the surface of the standing pads and the effluent that is now concentrated at the site of these pads. In combination these waste streams offer the farmer an opportunity to recycle valuable nutrients back into the soil as an up-valued soil conditioner. This investigation explores vermicomposting as a tool to efficiently manage these two significant waste streams. Sludge was removed from a settling pond and mixed with a range of carbon products that are recommended by Dairy NZ for use in stand-off pads: wood chips, post peeling, sawdust and also wood shavings (used in calf sheds). The wood fibre/sludge mixtures were assessed on their acceptability to tiger worms (Eisenia fetida) by measuring the pH of the mixture and seeing if they corresponded with the preferred pH for tiger worms. The vertical spatial distribution of tiger worms was measured over a period of 15 days and the rate at which the worms moved into the different mixtures was assessed. The worm mass before and after this 15 day period was also measured to ascertain the mixtures’ ability to support worm growth. Finally, different ratios of sludge and post peelings removed from a calf shed were used in a choice chamber experiment to establish the worms’ preference. Tiger worms were used throughout the investigation as they represent the worm species most widely used in vermicomposting in New Zealand. Tiger worms feed on decomposing organic matter, bacteria and fungi in the upper organic horizon of soil. All of the unused wood fibre and dairy sludge tested lay within the acceptable pH range for tiger worms. Wood fibre exposed to large amounts of urine ie calf shed post peelings, that lie outside the acceptable range can be favourably adjusted with the addition of dairy sludge. All the particle sizes of the wood fibre tested were found to be acceptable to tiger worms and capable of supporting increase in their body mass beyond that of the compost. Due to the observation that the worms did not integrate themselves as fully in sawdust as the other fibres tested it is recommended that further investigation should be carried out before sawdust is used for vermicomposting. While a comparison of the average worm density in each mixture may indicate a preference for post peelings this cannot be statistically proven and more trials are recommended. The preferred ratio within the limits that were tested is 1:3 calf shed post peelings to sludge (41% dry weight). Vermicomposting can therefore be recommended as a possible onsite technology to process the twin waste streams of wood fibre and effluent generated by dairy farms. The next step would be to implement medium scale field trials with a continuous windrow system, testing resulting compost for its nutrient content and then comparing this output to that of current practises