Flexible fibers have a powerful role in microscopic biological phenomena. They can take the form of beating flagella that propel sperm cells and bacteria, or they can tangle into the vast, interconnected networks that make up the cellular cytoskeleton. In this talk I’ll discuss methods to numerically simulate flexible, inextensible microfilaments which are suspended in a viscous fluid; with special care taken to account for thermal fluctuations from the solvent. I’ll introduce a method where fibers are treated as a chain of beads and use it to interrogate experimental observations on magnetic filaments which are made to swim using an applied field. I’ll present ongoing work concerning a method more suited to fiber networks, in which inextensible fiber motions are parametrized as curves on the unit sphere. After writing down a stochastic differential equation governing the fluctuating fiber dynamics in the new, constrained coordinates, I’ll discuss temporal integration schemes which linearly scale in complexity with the number of fibers.
Stochastic to Continuous Epidemiology: How Network Structure Effects Spreading Phenomena
In this talk I will introduce 3 main tools: network epidemic simulations, SINDy (a model discovery tool), and the ICC curve. With these tools for simulating and analyzing epidemics, I will explore the impact of network structure on the stochastic simulations, the associated discovered models and theoretical explanations for these results. Finally, we will see what impact the structure has on the associated ICC curves and the statistical analysis.
