Date of Award
8-2024
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Physics
Committee Chair/Advisor
Dr. Bradley S. Meyer
Committee Member
Dr. Murray Daw
Committee Member
Dr. Mark Leising
Committee Member
Dr. Endre Takacs
Abstract
Investigating equilibration in nucleosynthetic processes is crucial for understanding stellar chemical abundances in nuclear astrophysical scenarios. While current computational models are effective at predicting final species abundances at the end of these stellar processes, they fail to provide insights into the evolution of equilibrium. Without this deeper understanding, it is challenging to determine the impact of individual reaction rates on timescales and the resultant equilibrium.
In this work, we model nucleosynthetic processes as directed graphs. We develop theorems that allow us to express the mass fractions of species as spanning arborescences of these graphs. By obtaining eigenvalues in terms of these spanning branchings, we can formulate exact expressions for the eigenvectors. Under certain approximations, these eigenvalues enable us to compute the timescale for the system to reach equilibrium. Moreover, the eigenvalues allow us to compute the chemical abundances as the system evolves towards equilibrium.
We apply these concepts to some simple models to gain insights into interesting problems, such as understanding the effective transition rates in isomers and their evolution to equilibrium. We also investigate the timescales for clusters to evolve from quasi-static equilibrium (QSE) to nuclear static equilibrium (NSE).
Recommended Citation
Ghosh, Sayani, "Equilibria and Effective Transition Rates in Linear Networks" (2024). All Dissertations. 3682.
https://open.clemson.edu/all_dissertations/3682
Author ORCID Identifier
0000-0002-5040-4033