Modeling and Simulation Group Meeting Old

Open Problems in Applied Math

Speaker: Alex Mogilner, Sophie Marbach, Rob Webber

Location: TBA

Date: Thursday, April 15, 2021, 12:30 p.m.


Sophie Marbach:

Title: Fractional noise in nanopores

Abstract: Fluctuations are ubiquitous in bio and artificial nanopores. Most of the time, fluctuations are seen as a negative feature that impedes for example signal measurements. Yet, biological pores are still able to achieve complex tasks in spite of fluctuations. To investigate the riddle of fluctuations in nanoporous transport, here I explore how fluctuations in the particle number within the pore affect signal measurements. I find that fractional noise emerges naturally as a striking and universal feature. In particular, I will show how fractional noise inherits from an intrinsic property of brownian walks.


Robert Webber:

Title: Rare event sampling in the Earth and planetary science

Abstract: In the Earth and planetary sciences, accurately estimating rare event probabilities is challenging yet scientifically significant. To estimate these rare probabilities, direct numerical simulations is often a limited tool with an unacceptably low benefit-cost ratio. As an alternative, we want to develop a non-intrusive Monte Carlo method that can be applied to a black box simulation model to improve rare probability estimates. Yet despite mathematical evidence that such a method can exist, developing this method for real-world applications is an ongoing challenge. In this talk, I introduce this open problem in applied mathematics and describe three examples involving heat waves, hurricanes, and Mercury's potential to be ejected from the solar system.
Alex Mogilner
Open problems of cell biology: how do 'macroscopic' forces and chirality emerge in stochastic gels?
Actin cytoskeleton is made of sub-micron size helical elastic fibers. These fibers keep turning over,
being randomly nucleated, grown and disassembled. They are interconnected into a gel randomly
and dynamically crosslinked by a host of small proteins. Remarkably, this gel sometimes self-organizes
into chiral structures on the cell scale, or generates either pushing or pulling forces of great magnitudes.
The chiral self-organization is a complete mystery, and many aspects of force generation are not clear.
I will describe open 'mathematical' problems related to these phenomena.