Strengths

Delving into tensor mathematics in general relativity, modelling systems with Python and analysing dynamic systems has reframed my view of the world and exponentially increased my mathematical knowledge; these would be areas where I would love to deepen my understanding and gain practical experience. I have completed a wide breadth of mathematical modules, including topics such as tensors, Fourier analysis, integral transformation, dynamic systems, Sturm-Liouville theory, complex analysis, linear ODEs and PDEs, numerical methods, General and Special Relativity, and fluid mechanics; I thrive on the logical nature of Mathematics and continue to develop my skills, furthering my competency in Physics.
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Through my Physics degree and Chemistry and Mathematics/ Statistics A-levels, I can interpret and analyse many different forms of data, including chromatography, proton and carbon NMR, mass spectrometry, and IR spectrometry. In addition, I'm knowledgeable about statistical analysis and models, including Gaussian, Poisson, and Binomial distributions, as well as particle detector data such as cross-sections, the centre of mass energies and hadronic jet information. Moreover, in my university studies, I have engaged in practical Physics lab work; the knowledge and skills gained were invaluable and further developed my technical abilities and taught me essential inference tools. The series of experiments undertaken at university focused on skill acquisition equipping me with practical skills to become a perspicacious physicist. I developed ingenuity and critical thinking when mitigating problems such as faulty experimental setup, organisation and clarity of literary communication when keeping a methodical log, and analytical abilities in composing a formal lab report and comparing results critically. I can think of nothing more rewarding than furthering these skills.
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Alongside this, within my degree, I have developed my computational abilities, learning to code in both Python and Mathematica and completing models in Computational Physics and Machine learning; I've produced reports on 'Convolutional Neural Networks as Applied to NOVA data' and 'Ant Colony Optimization Algorithms as applied to path minimisation in Graph Theory' as well as modelling various systems from spin interactions in atoms, thermal diffusion, and wave propagation through media that can be viewed on my GitHub page "https://github.com/Joshua-Giblin-Burnham". Computational modelling and analysis have become one of my favourite areas of physics as I find computational work profoundly satisfying and fascinating; I hope to gain further experience and prospectively look towards computational work when considering a research career.
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My master's research project focuses on a computational simulation of the mechanics of imaging biomolecules via Atomic Force Microscopy (AFM). Collaborating with UCL's mechanical engineering department, we aim to use finite element analysis and the commercial ABAQUS software to simulate the mechanical indentation of biological surfaces. Therefore, I learned how to apply finite element analysis via Python scripting and required extensive research of AFM techniques. The main technical challenges come from using finite element modelling while accurately emulating the dynamics of AFM raster scanning and biological molecule-substrate ensemble.

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In addition, I have completed summer research simulating the structure and STM appearance of various proposed defects in ZrSe2 using density functional theory (DFT). The project used the CONQUEST DFT code developed in UCL by Prof David Bowler for the DFT calculations. It expanded my understanding of the basics of atomic modelling. Through the project, I gained experience using and coding in Unix, alongside skills in high-performance computing and data presentation. I have also completed research under Professor Jon Butterworth; I compared predictions of the Gildener-Weinberg Higgs Bosons model with the SM using RIVET/ CONTUR code. My analysis refined the constraints using new data and improved the treatment of error correlations in CONTUR.
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I thrive in a scientific setting and look forward to future collaborative work. Previously, I have led multiple group projects at university, including producing a science education proposal. We created a proposal for a physics "egg hunt" mobile app, which we then pitched for STFC public engagement small award. The project required extensive research, problem-solving and teamwork to produce a viable pitch. Additionally, I have led a group project researching transparent conducting oxides (TCOs), conducting a theoretical analysis of the concepts underpinning the physical properties of TCOs and, subsequently, an experimental study into the structure and band gap of scandium-doped zinc oxide (ZnO: Sc) conducted in UCL's Chemistry Department. I have also worked collaboratively in the Hoogenboom lab alongside extensive collaboration with UCL mechanical engineering in my master's project.