Graduation Year


Document Type

Honors Thesis

Degree Name

Bachelor of Arts


Biological and Physical Sciences

Faculty Advisor

Georgi Georgiev


An open question in science is how complex systems self-organize to produce emergent structures and properties. One aspect is to find the dependence of structure and organization on the size of a system. It has long been known that there is a quality-quantity relationship in natural systems, which is to say that the properties of system depend on its size. More recently, this has been termed the Size-Complexity Rule. In this Thesis paper, we study the average rates of nucleosynthesis and action efficiency of stars with varying initial metallicities and explosion energies from simulations (Nomoto, Tominaga, Umeda, Kobayashi, & Maeda, 2006) based on the Stellar Abundances for Galactic Archaeology database (Suda et al., 2008). Our goal is to study the size-complexity relation in stars of varying metallicities and explosion energies and to compare them with other complex systems. Here, as a measure of complexity of a star, we are using the grouping and approximate number of reactions of nucleons into heavier elements, because they increase the variety of elements and changes the structure of the star. Then we calculate the average rate of grouping of nucleons by multiplying each of them by their level of grouping, defined as how many of them are joined into a nucleus, and then divide by the lifetime of the star over which these isotopes were synthesized. As seen in our previous work, complexity, as measured by action efficiency grows exponentially in time and as a power law of all other characteristics of a system, including its size. Here we find that, as for the other systems studied, the complexity of a star in terms of grouping of its elements and the rate of increase of complexity is a power law of its size despite differing explosion energies and initial metalicities. As shown by these stars, the bigger a system is, the higher the levels of complexity it can reach even if the initial metallicity and explosion energy are different. This is seen in how each star’s progress, average rate, flow, and action efficiency of nucleosynthesis dramatically increase as a function of their initial number of nucleons. Our goal is to find how universal the size-complexity relation is, and whether there are any exceptions. We are planning to study other systems to find whether they obey the same rule and, as stellar evolution simulations improve, to study in detail not just the average rate, but the instantaneous rate of nucleosynthesis.

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