11 Utah Wave and Architected Materials Lab

Faculty Mentor: Pai Wang (Mechanical Engineering, University of Utah)

I have been fortunate enough to work in the Utah Waves & Architected Materials Lab since May 2023 under Dr. Wang’s supervision. I primarily have been researching expanding SSH (Su-SchriefferHeeger) model with non-local interactions to solve the inverse problem of dispersion curves. The inverse problem means that instead of trying to study a certain lattice/ connection of stiffness but to find a formula to specify the connections/ stiffness when target dispersion curves are given. With Dr. Wang, Dr. Fu, S. Paul, and I, we have discovered the formula for reconstructing target dispersion curves by deducing the connection/ stiffness and achieving dispersion curves that were not possible before due to the mathematical constraints of previous models. My ambition is to finish the research project and publish it before I graduate with my undergraduate degree. I have learned so many things from this research. First, I learned that the Block theorem applies to infinite periodic boundary conditions and that each degree of freedom of mass should have different amplitudes. I also learned how noticing complex conjugates simplifies computation drastically. How to use the orthogonality of trig functions to extract coefficients. Finally, I am attempting to learn how to solve a system of polynomials of degree two numerically to solve the research problem completely. I intend to research more on Phononic crystals, solid mechanics, and solid-state physics in my Ph.D. program in mechanical engineering at the University of Utah. After graduating with my doctoral degree, I plan to continue my research in academia or national research labs.