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The coffee cup system can be simplified and modeled by a cart-and-pendulum system. Bazzi et al. and Maurice et al. present two different cart-and-pendulum systems to represent the coffee cup system [1],[2]. The purpose of this project was to build upon these systems and to gain a better understanding of the coffee cup system and to determine where chaos existed within the system. The honors thesis team first worked with their senior design group to develop a mathematical model for the cart-and-pendulum system based on the Bazzi and Maurice papers [1],[2]. This system was analyzed and then built upon by the honors thesis team to build a cart-and-two-pendulum model to represent the coffee cup system more accurately.
Analysis of the single pendulum model showed that there exists a low frequency region where the pendulum and the cart remain in phase with each other and a high frequency region where the cart and pendulum have a π phase difference between them. The transition point of the low and high frequency region is determined by the resonant frequency of the pendulum. The analysis of the two-pendulum system also confirmed this result and revealed that differences in length between the pendulum cause the pendulums to transition to the high frequency regions at separate frequency. The pendulums have different resonance frequencies and transition into the high frequency region based on their own resonant frequency. This causes a range of frequencies where the pendulums are out of phase from each other. After both pendulums have transitioned, they remain in phase with each other and out of phase from the cart.
However, if the length of the pendulum is decreased too much, the system starts to exhibit chaotic behavior. The short pendulum starts to act in a chaotic manner and the phase relationship between the pendulums and the carts is no longer maintained. Since the pendulum length represents the distance between the particle of coffee and the top of the cup, this implies that coffee near the top of the cup would cause the system to act chaotically. Further analysis would be needed to determine the reason why the length affects the system in this way.
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Vaccines are one of the most effective ways of combating infectious diseases and developing vaccine platforms that can be used to produce vaccines can greatly assist in combating global public health threats. This dissertation focuses on the development and pre-clinical testing of vaccine platforms that are highly immunogenic, easily modifiable, economically viable to produce, and stable. These criteria are met by the recombinant immune complex (RIC) universal vaccine platform when produced in plants. The RIC platform is modeled after naturally occurring immune complexes that form when an antibody, a component of the immune system that recognizes protein structures or sequences, binds to its specific antigen, a molecule that causes an immune response. In the RIC platform, a well-characterized antibody is linked via its heavy chain, to an antigen tagged with the antibody-specific epitope. The RIC antibody binds to the epitope tags on other RIC molecules and forms highly immunogenic complexes. My research has primarily focused on the optimization of the RIC platform. First, I altered the RIC platform to enable an N-terminal antigenic fusion instead of the previous C-terminal fusion strategy. This allowed the platform to be used with antigens that require an accessible N-terminus. A mouse immunization study with a model antigen showed that the fusion location, either N-terminal or C-terminal, did not impact the immune response. Next, I studied a synergistic response that was seen upon co-delivery of RIC with virus-like particles (VLP) and showed that the synergistic response could be produced with either N-terminal or C-terminal RIC co-delivered with VLP. Since RICs are inherently insoluble due to their ability to form complexes, I also examined ways to increase RIC solubility by characterizing a panel of modified RICs and antibody-fusions. The outcome was the identification of a modified RIC that had increased solubility while retaining high immunogenicity. Finally, I modified the RIC platform to contain multiple antigenic insertion sites and explored the use of bioinformatic tools to guide the design of a broadly protective vaccine.
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Heart disease is the leading cause of death in the developed world and often occurs following myocardial infarction. Apelin is an endogenous prepropeptide that has been studied for its role in improving cardiac contractility and vasodilation but suffers from a short half-life in the body. By encasing apelin in a nanoparticle patch, we were able to slowly release apelin to cardiac tissue and observe its effects for one month following induced myocardial infarction surgery in mice. This study demonstrates that the apelin nanoparticles can protect the heart from myocardial-induced heart failure, observing overall improved cardiac function and reduction of fibrotic scarring associated with post-myocardial infarction compared to a nontreated group.