Manufacturing and Material Property Verification of Short Fiber Particle Reinforced Composites

This thesis investigates the manufacturing, testing, and material property verification of short fiber and particle reinforced polymer composites intended for use in flywheel energy storage systems. Composite tensile specimens were fabricated using controlled mold geometries and autoclave-assisted curing to improve consolidation quality and reduce void content. Short carbon fibers and particulate reinforcements were selected to balance mechanical performance, manufacturability, and isotropy for high-speed rotor applications. Tensile testing was performed using a tensile testing machine, and machine compliance effects were quantified and removed to obtain accurate elastic moduli. Experimental results were compared against analytical micromechanics predictions to evaluate stiffness trends and reinforcement efficiency. Heat transfer modeling and PID control of the autoclave were developed to ensure repeatable curing conditions and consistent material quality. The results demonstrate the influence of reinforcement type and processing conditions on elastic response and highlight limitations associated with specimen fabrication and testing. This work provides validated material property data and manufacturing insights that support the development of composite flywheel rotors for high-energy-density storage applications

Gliders on the SCA Model

The Stranded Cellular Automata (SCA) model consists of a grid of cells which can each contain between zero and two strands apiece and two turning rules that control when strands turn and when they cross. While patterns on this model have been studied previously, such research has not needed an algebraic description of the model. We provide a formal algebraic definition of patterns on the model, define gliders on the model in a way which is semi-compatible with definitions of gliders in other cellular automata models, and classify all 1- and 2-stranded gliders on this model. In addition, we prove an equivalence of two classes of gliders and design an algorithm to generate all such elements of that class

Graph Theoretical Modeling of Self-Assembling DNA of the Double Cone Graph

The unique properties of double-stranded DNA molecules make DNA a valuable structural material with which to form nanostructures, and the field of DNA nanotechnology is largely based on this premise. By modeling nanostructures with discrete graphs, efficient DNA self-assembly becomes a mathematical puzzle. These nanostructures have wide-ranging applications, such as containers for the transport and release of nano-cargos, templates for the controlled growth of nano-objects, and in drug-delivery methods. This research centers around exploring graph theoretical and combinatorial properties of DNA self-assembly to optimize the nanostructure construction for the Double Cone Graph

Objections to the Use of the Axiom of Choice to Model the Physical World

We look at platonistic mathematics and the application of this perspective in the physical world. We recognize paradoxes within Zermelo–Fraenkel set theory with the axiom of choice (ZFC) that conflict with physical reality, giving us reason to question if the axiom of choice should be so freely applied in theories of the physical world especially since it appears to enable a deterministic perspective. In theories of quantum physics, the axiom of choice is used to assume noncomputable numbers as initial conditions. This is equivalent to assuming a finite system contains an infinite amount of information at an instant in time; however, we know the world behaves probabilistically at the subatomic level. Our main purpose is to question the use of the axiom of choice when describing the physical world and advocate for alternate views of math, such as intuitionist mathematics, that avoid the assumption of determinism

Summer 2025

https://scholar.rose-hulman.edu/rose_echoes/1125/thumbnail.jp