This essay was written by upper-sixth former Archie Forsyth, and shortlisted for the 2020 Independent Learning Assignment. The following provides a short abstract to the full essay, which can be found at the bottom.

Estimated read time of abstract: 2 minutes
Estimated read time of essay: 20 minutes

In my ILA I explain the premises and applications of a variation of Newtonian mechanics called ‘Lagrangian’ mechanics and then go on to derive a differential equation that describes the motion of a double-sprung pendulum in three dimensions and then obtain its path of motion through coding a fourth order Runge-Kutta numerical solver. 

In short, Lagrangian mechanics uses Newton’s three laws of motion and slightly alters their form in order to make them more applicable to more complicated systems, including systems such as pendulums which are best described using polar coordinates. What makes this possible is the application of the Euler-Lagrange (E-L) equation, which involves differentiation, to the Lagrangian of the system. The Lagrange is simply the kinetic energy of the system minus the potential energies and when the E-L equation is applied to it, these energies are converted into an equation for the forces acting on the masses in the system and thus, dividing by the mass, a differential equation that describes the motion of the system. 

The next section of my ILA is a brief explanation of what a chaotic system is and that it is not always necessarily a complex system, for instance, take a double pendulum, i.e. a pendulum attached to the base of another pendulum. This is a very simple system however it is extremely chaotic, which is to say that the slightest change in its initial conditions, in this case angles from the equilibrium positions of the pendula, length of pendula and the greatness of the masses, greatly affect the system’s path of motion.  

From here the first major section of work begins as I derive a differential equation that describes the motion of first a double pendulum in polar coordinates (in 2-D) and then a double sprung pendulum in Cartesian coordinates (in 3-D). To demonstrate the effectiveness of Lagrangian mechanics, I derived the equation describing the sum of the forces acting on the masses in the double-sprung pendulum using both ordinary Newtonian mechanics, i.e. vector forces, and Lagrangian mechanics to show how much faster and more reliable it is to use the Lagrangian method. 

The final part of my ILA is the code that I made to find the path of the double-sprung pendulum’s motion. It is, as described before, a fourth order Runge-Kutta numerical solver, which uses an iterative method based on setting a fixed time difference and calculating the acceleration and velocities at the end of each of those time differences, which can be substituted back into the equations for acceleration to give a new coordinate, repeating this process many times so that you can find the coordinates of the masses after a given time. The code achieves this and allows for the choosing of the initial conditions, which are the spring constants, the unstretched lengths of the springs, the initial coordinates of the masses and the magnitude of the masses attached to the springs. 

To view Archie’s full article, follow this link below.

This essay was written by upper-sixth former Theo Lakin, and a finalist for the 2020 Independent Learning Assignment. The following provides a short abstract to the full essay, which can be found at the bottom.

Estimated read time of abstract: 3 minutes
Estimated read time of essay: 30 minutes

In my ILA I investigate the various aspects of Down’s syndrome, looking into not only the genetics but also looking at its influence on life, for that of the person with Down’s syndrome and those around them.  

Down’s Syndrome (DS) is a genetic condition which entails a set of physical, mental, and functional abnormalities as a result of an extra copy of chromosome 21 in the human genome, making 3 instead of the usual pair of two. This occurs during the creation of human sex cells (gametes) through meiotic division. It is a phenomenon known as trisomy 21, and it occurs in around 1 in 1,000 live births worldwide [THOMAS, 2019]. 

DS entails a set of very similar physical and mental characteristics for those who have it, albeit with some variation. Those with DS are also more likely to develop visual and aural impairments and are at an increased risk of leukaemia and Alzheimer’s disease. [NIA, 2017]. People with DS have an increased risk of cardiac disorders, most of which are congenital i.e. present from birth. Congenital cardiac disorders are present in around 40-60 percent of babies born with DS [PASCALL, 2015].  

Individuals with DS notably have behavioural and mental features as a result of their genes. These learning disabilities mean that it takes longer for them to develop certain skills, however level of ability certainly varies from person to person. In the past the impairment of learning ability has been overemphasised, and full potentials have only been realised in recent years due to an access to adequate education, and widespread societal acceptance.  

The genes of those with DS are the same as everyone else’s, just with an extra 1%. This is a very small amount in comparison to the whole human genome, meaning that all the rest of the genetic information is the same as it would be if the person did not have DS. [KESSLING, SAWTELL, 2002].  

People with DS are known for being particularly affectionate and happy, with an excellent outlook on life..  Over time, most teens and adults are competent with self-help and daily living skills which often allows them to lead semi-independent lives. With correct support and ambition, those with DS can strive for personal achievements such as being able to ride a bike, cooking their own meals, going to college, getting married and having a full-time job.  

A survey was completed in 1999 which concluded that teenagers with DS educated in mainstream schools are gaining considerable benefits in academic skills, communication skills and social independence [BUCKLEY, BIRD 99]. Information was collected on a wide range of issues including, health, behaviour, sexuality and social lives in addition to personal and social independence, communication skills and academic progress. The general trend showed that on average those with DS from a mainstream school were more competent with these tasks than those from the special schools. The other classmates also learn a great amount too, and it provides a valuable and eye-opening experience for everyone else within that school.  

There is no doubt that there is a truly special benefit these people with DS give to life for those around them. In a large-scale, population-based study, significantly lower divorce rates were found among families of children with Down syndrome (7.6%) compared with those of children with no identified disability (11.2%). [URBANO, HODAPP 07] This is a remarkable statistic as it shows that something like a disability does not break families apart, but instead seems to bring them closer together.  

When I was 5 years old, my younger sister, Lia, was born and diagnosed with Down’s syndrome.  While Lia (now 11) is a little different to others her age in some ways, most ways she is just like any other child. She is funny, ambitious, curious and just as annoying as my older sister. We share the same sense of humour and watching her take pride in her own achievements and activities is incredibly special. 

I hope you enjoy reading my ILA and seeing my conclusions I draw from various studies and scientific data.  

To view Theo’s full article, follow this link below.

This essay was written by upper-sixth former Ollie Jansen, and shortlisted for the 2020 Independent Learning Assignment. The following provides a short abstract to the full essay, which can be found at the bottom.

Estimated read time of abstract: 4 minutes
Estimated read time of essay: 20 minutes

How Has the Development of The da Vinci ® Surgical System Transformed the Future of Mitral Valve Repair Surgery?  

There have been monumental advancements in robotics over the last 20 years which have allowed for new and exciting innovation in the field of robotic surgery. The technology developed allows surgeons to perform a variety of complex procedures with more precision, flexibility and control than seen with conventional techniques. The surgeon is able to operate from a computer console next to the patient which provides a magnified 3D view of the surgical site and gives the surgeon complete control over the mechanical surgical instruments used to operate. The availability and potential of this technology poses a serious question: is it safe and effective for surgeons to operate on a patient’s heart with a surgical robot? Mitral valve repair (MVR) is the leading field of robotic heart surgery and this is the area of heart surgery that the da Vinci® surgical robot has had the biggest impact. This ILA evaluates the safety and efficacy of robotically assisted MVR, and how the development of this technology affects the future of MVR surgery.  

The procedure follows a similar technique to median sternotomy and right lateral minithoracotomy, with the major difference being the access ports and the instruments utilised. Access ports are placed through the right chest, including a 40mm minithoracotomy working port with a soft tissue retractor when a Chitwood clamp is used for aortic occlusion, and a 15 to 20mm working port when an intraortic balloon is used . The occlusion of the ascending aorta can be performed by either of these methods. Right internal jugular and femoral veins are cannulated for CPB . The left robotic arm is inserted through the third intercostal space in the anterior-axillary line and the right arm is inserted through the sixth intercostal space in the mid-axillary line . The chest cavity is flooded with CO₂ to mitigate intracavity air. Standard mitral valve repair techniques are used in the same way as conventional surgery. Posterior leaflet prolapse is treated by triangular or quadrangular leaflet resection, sliding repair , folding valvuloplasty and insertion of polytetrafluoroethylene (PTFE) chords. Anterior leaflet prolapse is mainly treated by the insertion of PTFE chords , with some cases treated by chordal transfer. All valve repairs include an insertion of a flexible annuloplasty band with a 2-0 polyester suture. A technique developed in 2009 allows for the annuloplasty band to be inserted using running annuloplasty sutures that require fewer steps than individual mattress sutures. This effective method allows for the annuloplasty band to be inserted much more swiftly, reducing aortic cross clamp and CPB times. 

In a study conducted by Gillinov et al at the Cleveland clinic, published in 2017, the first 1000 cases of robotically assisted mitral valve repair were analysed. This study thus provides an unparalleled insight into the safety and effectiveness of this surgery. Mitral valve repair was achieved in 989/992 patients (99.5%), with 97.9% of these patients having no or mild mitral regurgitation at discharge. These outstanding results of the success rate of robotically assisted MVR are comparable to several other clinical trials with the same objective. In this trial, 20 patients were converted to a full sternotomy (mostly due to inadequate access due to excessive bleeding and inadequate repair). It is crucial that there should be a willingness to convert without hesitation from the robotic approach to a conventional approach if it appears to compromise surgical outcome.  

It is very clear that robotic mitral valve repair is a safe and effective alternative to conventional repair techniques. There are several key advantages that must be considered. Firstly, enhanced surgical dexterity is allowed, which results in increased precision in a tight area. A motion filter in the da Vinci® system prevents unintended movements caused by human tremor, which further enhances surgical precision. Secondly, high definition, 3D visualisation allows the surgeon to view the inside of the left atrium with line of vision parallel to the blood flow in the valve. This kind of visualisation is unattainable in other techniques and gives the surgeon an excellent roadmap to perform the repair. Thirdly, the cosmetic results are dramatically superior to alternative techniques due to discrete incisions used for access ports. Fourthly, because of the avoidance of median sternotomy and reduced surgical trauma, post-operative pain is much lower and recovery times are faster. The DaVinci® robot rotates around a pivot point near the patient’s ribs, minimizing physical pressure on sensitive nerves and tissues. Finally, the risks associated with postoperative infection are significantly decreased. When this is combined with standard practice broad spectrum antibiotics, the risk of infection is minimal. 

I believe that the introduction of the da Vinci® surgical system into mitral valve repair has completely transformed the field. It has led to a new standard of patient care amongst cardiothoracic surgeons: the thorough examination of the specific positive and negatives of each type of MVR surgery allows for surgeons to really evaluate what is best for their patients and discover how they can provide the highest standard of care. Furthermore, the confirmation that the da Vinci® surgical system is safe and effective bodes extremely well for the future. In the future, surgeons will become increasingly comfortable with using surgical robotics, which will allow for a seamless introduction of robotic techniques to other areas of cardiothoracic surgery. I think that if robotic mitral valve repair continues to persevere as an effective treatment, it absolutely sets the standard for the integration of surgical robotics into cardiothoracic surgery. Robotic mitral valve repair is so transformational to the future of mitral valve treatment: it creates a diverse armamentarium of surgical techniques allowing for the treatment of each patient to become even more individual to a patient’s needs. Robotic mitral valve repair completes an extraordinarily high-quality plethora of surgical options which enhances the ‘gold standard’ of mitral valve repair to an even higher level.  

To view Ollie’s full article, follow this link below.

This essay was written by upper-sixth former Chris Ratcliffe, and a finalist for the 2020 Independent Learning Assignment. The following provides a short abstract to the full essay, which can be found at the bottom.

Estimated read time of abstract: 1 minute
Estimated read time of essay: 30 minutes

In this project I explored the possibilities of converting a Boeing 737800 Commercial Jet to battery power. Beginning with finding the minimum power requirements for flight by two methods; calculation and then modelling to improve the accuracy. Then finding the necessary battery requirements within a weight limit that would replace the fuel load directly to see if the conversion is feasible. In addition, an investigation into aerofoil design was undertaken as the electric plane was found to be most efficient at slower speeds. In order for this to be possible, a wing shape optimised for slower speeds was designed. 

To view Chris’ full article, follow this link below.

This essay was written by upper-sixth former Ben Perryman, and shortlisted for the 2020 Independent Learning Assignment. The following provides a short abstract to the full essay, which can be found at the bottom.

Estimated read time of abstract: 2 minutes
Estimated read time of essay: 20 minutes

Encryption

Encryption is a vital tool in many different aspects of life both today and in the past. I wanted to do an ILA on the topic to expand my own knowledge of both the concepts involved and different historical events where encryption and decryption were vital, such as the execution of Mary Queen of Scots or the Battle of Britain. Additionally I wanted to use the opportunity to expand on my knowledge of computer science and I endeavoured to create most of the ciphers that I studied using python. 

First I looked into the different methods of keeping information secure, and narrowed the scope of my ILA to just look at forms of encryption that involved a key. The first of these was the Caesar Cipher, named because Julius Caesar used it in his private communication to keep his servants from reading his messages. This involves shifting the entire alphabet by a few spaces, and then changing each letter accordingly. This is an easy cipher to use, and just as easy to decipher as there are only 25 ways of hiding your message.  

Caesar Ciphers were not secure enough for formal communications as the need for secrecy increased and so the permutation cipher was developed. To encrypt a message with a permutation cipher you create a map which links all letters to other letters, for example A could be linked to Q. This makes it much harder to check all combinations, but each letter is still mapped to another letter, and so if you find out a few letters, you can quickly decipher the whole message. Permutation ciphers were used for thousands of years, with examples being seen in ancient times and up to the 1900s, however generally they became obsolete in the 16^th century and were replaced by the Vigenère cipher. This used a combination of Caesar ciphers, but it used a key phrase to determine which alphabet to use and the phrase was only known to the users of the message. This could only be deciphered if you knew the message, however when it was used on a large scale, such as in the American Civil War, finding out the phrase could be done with a single captured soldier and changing the phrase took days. This was the hardest cipher for me to code as it involved a lot of linear algebra and matrices. 

Modern Encryption is built upon public-key and other forms of RSA encryption, because the internet relies upon fast transmission of data and this data must be kept secure. RSA is the perfect cipher for this as it is able to encrypt data efficiently. To decipher RSA one must factorise a number with thousands of digits, which cannot be done with computers in a reasonable timeframe. Quantum computing presents a threat to this, as it is able to factorise numbers very quickly, but for now quantum computers are not powerful enough to decipher RSA. A question I wanted to answer with my ILA was whether or not encryption was at risk of being widely broken; however looking at futuristic forms of encryption such as quantum encryption showed me that even though new methods of deciphering messages were being developed, encryption was developing at an even faster rate. Quantum encryption was the only form of encryption I didn’t write using code, as it relies on the quantum laws of uncertainty to work, and these are very difficult to model. Furthermore it has only sent messages a short distance, but quantum encryption is an amazing form of encryption, because it is built upon the laws of physics, so unless the laws are wrong, it is theoretically unbreakable. 

To view Ben’s full article, follow this link below.

This essay was written by upper-sixth former Alex Thow, and a finalist for the 2020 Independent Learning Assignment. The following provides a short abstract to the full essay, which can be found at the bottom.

Estimated read time of abstract: 5 minutes
Estimated read time of essay: 45 minutes

Quantum mechanics is difficult. It is confusing. It is illogical. Albert Einstein himself hated the concept, stating, “If it is correct, it signifies the end of physics as a science”. Erwin Schrödinger, one of the great names in early quantum mechanics, said, “I do not like it, and I am sorry I ever had anything to do with it”. Even Richard Feynman, one of the greatest teachers physics has ever seen, went so far as to say, “I think I can safely say nobody understands quantum mechanics.” Despite all this, it manages to answer some of the most interesting questions out there in a beautiful way. In my ILA I explored the answer to the question of how it is certain molecules have colour.

To begin we must mention molecular orbitals (MOs). Some of the mathematics behind these MOs is discussed in the main text, but unfortunately it is too complicated to go into here, so the results will have to speak for themselves. Electrons in molecules are never in one place – we have quantum mechanics to thank for that. They are spread out unevenly around the molecule and the regions that they occupy are the MOs. There are many MOs in each molecule to accommodate all the electrons, as only two electrons can occupy any given orbital due to an effect called the Pauli exclusion principle. The different distribution of electron density within each MO leads to the MOs having different energies. The highest energy MO with an electron in it is called the HOMO (highest energy occupied molecular orbital) and the lowest energy MO that does not contain an electron is called the LUMO (lowest energy unoccupied molecular orbital). These orbitals are key in so many areas of chemistry, including the chemistry of colour, as it turns out that an electron in the HOMO can absorb the energy in a photon and jump up the LUMO. The energy of a photon of light is directly proportional to the frequency of the light, and so the energy gap between the HOMO and the LUMO determines the colour of light that is absorbed. The colour we see is simply the complementary colour to what is absorbed, as the rest of the spectrum is reflected.

Now, my ILA would have been a lot shorter if it were simple for the HOMO-LUMO energy gap to be in the right range for visible light to be absorbed, but unfortunately this is not the case for most molecules as they generally absorb UV light. The main structural feature that coloured molecules require is something called a conjugated system, which is a chain of alternating double and single bonds (these are generally bonds between carbon atoms as the molecules we are interested in are organic). A clear example of this is in beta-carotene, the molecule that gives carrots their orange colour.

A structure like this results in an important phenomenon called delocalisation, which spreads out the MOs over the chain, allowing the electrons to move freely across it. It is actually possible to come up with an expression relating the length of the chain to the absorbed wavelength, which was done in my ILA. The result is that a molecule needs a conjugated system with at least five or six double bonds before it can absorb visible light, and hence we see why most molecules are in fact colourless.

The synthesis of dyes requires an understanding of their structure. We already know that they must contain a conjugated system, and this part of the dye is called the chromophore. Any additional groups attached slightly alter the colour of the dye and are called auxochromes. The variety of structures this vary broad description allows is immense. A number of the chromophores explored in my ILA are shown below to show just how varied the dyes can be.

It is all well and good being able to create dyes, but they are useless if we have no way of attaching them to materials. Material structure is very diverse, but often the materials we dye have polymer structures. For example, plant fibres are composed of cellulose, a polymer of glucose. Animal fibres are made of proteins which are chains of amino acids. Even synthetic materials such as nylon are polymers. These polymers can stack together and align, creating a fibrous structure with pores running through it. The dye molecules are able to travel through these pores and attach themselves to the material through different kinds of bonding.

Direct dyes are the simplest to apply as these form strong enough interactions, often ionic or strong dispersion forces, to hold the dye in place without any other input. Another type of dyes called reactive dyes can quite literally react with the material, forming strong covalent bonds to it. An example of this is shown below.

There are, however, situations when the dye cannot hold itself onto the material well enough, and a mordant must be used. Mordants are inorganic metal salts that help fix a dye to a material. The metal ion in the mordant forms something called a chelation with both the dye molecule and the material, acting as a bridge between them, holding them together. The structure of one of these chelations is shown here.

Dyes are not just useful in the chemical world; they occur all the time in nature too. Two interesting examples I covered in my ILA were retinal and chlorophyll. Retinal is able to harness its ability to absorb visible light to help us see colour by altering its structure when it absorbs light. Chlorophyll is able to use the energy it absorbs from visible light to help plants photosynthesise. So, it really is impossible to go anywhere without seeing, wearing, or using dyes in some shape or form and it is impossible to deny their importance in our world.

To view Alex’s full article, follow this link below.