Throughout this summer, I have gained valuable insight into mathematics research. Coming in with little knowledge of dynamical systems, I began by reading and learning all about the topic. Participating in a reading group helped me understand the material quickly and in depth, since other students and I tackled and solved practice problems together.
Towards the end of this summer I was able to reproduce fluorescence quenching on bare nanoparticles. Upon photoexcitation by the laser (or sunlight), there is a locally enhanced electromagnetic field produced around the nanoparticle. As mentioned in previous posts, a fluorophore oriented closer to the surface of a plasmonic particle will experience a greater EM field. However, fluorophores located too close or touching the surface of a particle will undergo quenching of fluorescence because of the significantly stronger EM field. To save some time, I will not go into a lengthy discussion on the exact science behind quenching, mainly because I don’t understand most of it. In this context all we are concerned with is the fact that fluorophores located on the surface of bare nanoparticles are showing a decreased fluorescence enhancement. As opposed to positive ratios, the quenched particles show up as dark spots on a bright background, meaning these particles are emitting less photons than the background dye. A typical correlated fluorescence scan and LSPR image of bare NPs can be seen below. After analyzing 25 particles, the average enhancement was 0.84 ± 0.07. 25 particles isn’t necessarily a substantial amount, but the quenching measurements thus far prove the background theory.
Sorry for the long hiatus, the last few weeks of research were quite hectic. Simultaneously trying to wrap-up experimentation for the summer, compiling tons of data, and preparing for the coming semester is a daunting task.
My project took a new direction after my presentation. I had the idea to implement partitions along the time series points instead of using uniform partitions. The reason behind this new approach is that the finite representation given by it would be true to the time series. This approach would also improve the quality of the finite representation, bringing it closer to an outer approximation. Since every time series point is on a partition, every interval and their image gets picked up by the finite representation.
As I have mentioned before, I am part of a group of research students, each with their own individual projects, mentored by Professor Day and/or Professor LaMar. We all meet once a week to hear a talk on someone’s research. In preparing for my talk, I read various articles on giving talks, most of which included the following,