Summer Research 2021 Poster Session
Summer 2021
Abstract: We expand on existing work and study the angular dynamics of isotropic and anisotropic particles in turbulence, and demonstrate capabilities in measuring the various quantities involved in these dynamics. We examine the shape-dependence of particle dynamics in turbulence by looking at disc-like triads and spherical tetrads. We see that large particles behave differently than … Read more
Poster Session Link Abstract: The speed and scale of urbanization brings tremendous challenges to the development of sustainable cities. We hope that our research will yield novel mathematical and computational tools to address major issues in urban planning such as traffic congestions and accessibility. To that end, we are studying the routes that Google Maps … Read more
Abstract: our objectives were (1) to develop a deeper understanding of the three branches of differential geometry, which are Riemannian, Contact, and Symplectic; (2) to study the applications of the theoretical concepts to Physics and other mathematical areas. No original results will be presented. We summarize the material we studied. Video: Live Poster Session: Thursday, … Read more
Abstract: Diophantine approximation studies how well real numbers can be approximated by rational numbers. Previous theorems, such as Khintchine’s theorem and the Duffin-Schaeffer conjecture, have implied that the inequalities |x-p/q| < a/q2, with p/q being Farey fractions, can accept infinitely many solutions for almost every x within the interval [0,1]. Our project studies a pertinent … Read more