Physics

Portfolio - Physics

As part of my undergraduate studies in physics, I worked on a range of independent research projects that can be grouped into two domains fields of physics corresponding to my interests in data and music. While I no longer do research directly pertaining to physics, what I have learned from these projects are invaluable to my current work; in particular, I still work with acoustics, and the frameworks and ways of thinking in quantum cosmology relates well to understanding machine learning approaches.

Application of the path integral approach to quantum physics

The following computational physics projects rely on the Path Integral formulation to solve certain forms of non-linear ordinary differential equations used in quantum physics. Due to the lack of a closed-form analytical solution, these were numerically solved as an optimisation problem using Mathematica.

Fluctuation about Cosmological Instantons

Supervisor: Dr Wang Qinghai

Co-Supervisor: A/P Gong Jiangbin

Done as an Honours Thesis; awarded the Outstanding Young Researcher Prize (Merit)

PDF copy of thesis is available at this link:
https://www.physics.nus.edu.sg/wp-content/uploads/sites/5/2020/08/hyp-201314-38.pdf

Abstract:

We studied the bounce solutions of self-interacting scalar fields coupled with gravity using a semi-classical approach. Our data suggests that bounce solutions not only have a minimum barrier curvature, but also a maximum barrier curvature. In addition, we propose a new class of bounce solutions, where the scalar field behaves like the Coleman-De Luccia bounce solutions, but the scale factor does not vanish at any finite Euclidean time. Unlike Coleman-De Luccia bounce solutions or oscillating bounce solutions, this cannot be considered a subset of the Hawking-Turok solution. However, like the Coleman-De Luccia bounce solutions, the quantum fluctuation about this new solution has only one negative mode, suggesting that it may also be associated with quantum tunnelling.

Some key findings from this project has been published as “Criteria of existence for bounce solutions in false vacuum decay with gravity” in IOPScience Classical and Quantum Gravity: https://iopscience.iop.org/article/10.1088/1361-6382/aaa4ea/meta

This publication has the following abstract:

The bounce solutions of self-interacting scalar fields coupled to gravity are studied using a semi-classical approach. We found that bounce solutions have a maximum required barrier curvature, in addition to the known minimum required barrier curvature. In particular, as the maximum barrier curvature is approached, the scale factor of the well-known Coleman–De Luccia (CDL) bounce solutions become divergent. Unlike the CDL or its more general oscillating bounce counterparts, this cannot be considered as a subset of the Hawking–Turok solution.

PT-Symmetric Quantum Mechanics

Supervisor: Dr Wang Qinghai

Co-Supervisor: A/P Gong Jiangbin

Done as a continuation of work from my Honours Thesis to follow up on investigating some of the interesting findings. The work done during this project contributed to the publication linked above.

Note: I completed my Honours Thesis a year early, and took my final year as an undergraduate to complete my minor in Psychology as well as to do additional research and study.

Project description:

This project seeked to build on the findings of Wong (2014). Using numerical methods, Wong (2014) found a new possible class of bounce solutions for self-interacting scalar fields coupled to gravity. We seek to understand the theoretical basis behind these solutions.

A Path Integral Approach to the Quantum Bouncer

Supervisor: Dr Yeo Ye

Done as an Independent Study Module in my first summer as an undergraduate student.

Abstract:

The propagator of a system provides a way to determine the dynamics of a system, i.e. how an initial wave function will evolve with time within a certain potential. While the propagator may be determined using the eigenfunctions associated with the system, this proves unwieldy for more complicated potentials, such as for the case of the quantum bouncer. Consequently, while the solution to the quantum bouncer is known, it is usually solved either numerically or approximated. We thus look at the Feynman path integral approach, and study similar cases, in an attempt to obtain a similar approach to the quantum bouncer.

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Musical acoustics

Inharmonicity of String Instruments

Supervisor: Dr Bernard Tan Tiong Gie

Done as an Independent Study Module

Abstract:

We seek to survey the effect of several factors on the inharmonicity of guitar strings. These factors are the thickness of the string and the method of excitation of the string, which may be categorized by the strength of the initial impulse, the location of the impulse and the implement used to create this impulse. It was found that the inharmonicity of plain steel guitar strings appears to correlate quite well to theoretical values. Also, some correlation with plucking strength was found, and the raw data suggests some kind of resonance with the guitar body. These appear to be suitable avenues for future study.

The Vibrating Behaviour of Coiled and Uncoiled Strings and their combination

Supervisor: Dr Bernard Tan Tiong Gie

Done as an Independent Study Module, as an extension of the previous project.

Abstract:

Inharmonicity describes the deviation from ideal harmonic behaviour in oscillating strings. The harmonic behaviour of ideal perfectly flexible strings assume small amplitude vibrations of infinitesimally thin strings with only a spring-like restoring force acting on each infinitesimal section of the string. The deviation from ideal perfectly flexible string behaviour is often taken to be the result of inherent stiffness in the string, and this stiffness arises from the thickness of the string. However, in practice there may be further deviation from this ideal stiff string behaviour, and in this report, we seek to outline some attempts to observe this deviation in musical instruments.

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Acoustics of Edge Blown, Free Reed and Lamellophone Instruments

Supervisor: Dr Bernard Tan Tiong Gie

Done as an Independent Study Module

Abstract:

We did a preliminary study into using fog visualization and high speed videography to directly observe the air flow in various aerophones so as to have a better overall understanding of the mechanism of sound production. This novel method was found to produce good qualitative observations of the dynamics of the system, and has an advantage over strobing when the system is not in a steady state. It may be extended to studying other systems where air oscillates rapidly.

As an extension of this project, I subsequently mentored an investigation into whether Schlieren Imaging can be used to visualise airflow better. While the airflow could be seen with Schlieren imaging, it also had a lot of major constraints that make it unsuitable for practical use.

The video below shows fog visualisation of a whistle, slowed down to approx. 4% speed.

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Portfolio - Physics

Application of the path integral approach to quantum physics

Musical acoustics

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