Yorgos Katsikis (Stanford University), Applied Mathematics Colloquium

Title:  Deadly parasites, whirligig toys and droplet computers: do the math!

Abstract:  I will present three problems on biophysics, low-cost diagnostic devices, and microfluidics from my research at the Prakash Lab at Stanford. First, I will talk about a mathematical “T-swimmer” model, based on slender-body theory, that we developed to study how submillimetre-scale parasites swim in freshwater to infect humans causing schistosomiasis, a disease comparable to malaria in global socio-economic impact. Juxtaposing this model with biological experiments and a robotic realization, I will show how these parasites break time-reversal symmetry and propagate at an optimal regime for efficient swimming. Second, I will describe an ultralow-cost (20 cents), lightweight (2 g), human-powered paper centrifuge designed on the basis of a mathematical model of a nonlinear, non-conservative oscillator inspired by the ancient whirligig toy. Our centrifuge achieves speeds of 125,000 r.p.m., separates pure plasma from whole blood in less than 1.5 min and isolates malaria parasites in 15 min. Finally, I will talk about a microfluidic platform that performs universal logic operations with droplets. Through a reduced-order model and scaling laws for understanding the underlying physics, I will demonstrate droplet-based AND, OR, XOR, NOT and NAND logic gates, fanouts, a full adder, a flip-flop and a finite-state machine.