Mathematics Home / Research Seminars: Applied and Computational Mathematics
Time & Location: Typically talks will be in Gibson Hall 325 at 3:00 PM on a Friday.
Organizers: Punshon-Smith, Samuel and Buvoli, Tommaso
January 20
Title: Modeling microswimmers: the effects of cell shape and complex environments
Rudi Shuech | Tulane | Tulane University
Abstract:
In this two-part talk, first I will summarize my previous work on the effects of curved-rod bacterial shapes on swimming performance and other ecologically important tasks. We used a regularized Stokeslet boundary element method to compute the motion of curved-rod microswimmers propelled by rotating helical flagella. We then showed that Pareto-optimal tradeoffs between efficient swimming, chemotaxis, and cell construction cost can explain the morphological diversity of extant curved bacterial species.
In the second part, I will transition to thinking about the complex environments that microorganisms swim through, which are often composed of a viscous fluid with suspended microstructures such as elastic polymers and filamentous networks. These microstructures can have similar length scales to the microorganisms, leading to complex swimming dynamics. Some microorganisms are also known to remodel the viscoelastic networks they move through. To gain insight into the coupling between the dynamics of the swimmer and the network, we combined our computational framework for microswimmer motion with a model of a discrete viscoelastic network. The network is represented by a cloud of points with virtual Maxwell element links, whose properties (i.e., stiffness, relaxation time) can have non-obvious effects on the swimmer dynamics. We model enzymatic dissolution of the network by bacteria or microrobots by breaking links based on their distance to the microswimmer. We investigate how swimming performance is affected by properties of the network and swimmer.
If time allows, I will also introduce our new work on microswimmers penetrating thin, membrane-like interfaces.
Time: 3:00
Location: Stanley Thomas 316
January 27
Title: The hydrodynamics of dinoflagellate motility
Rudi Shuech | Tulane | Tulane University
Abstract:
Flagella are crucial to the interactions of many microorganisms with their surrounding fluid environment. The single-celled dinoflagellates have a unique but remarkably conserved flagellation morphology: a trailing longitudinal flagellum and an exquisitely complex transverse flagellum that encircles the cell. What are the selective advantages offered by this arrangement? We investigated the dinoflagellate design in silico using a high-performance regularized Stokeslet boundary element method, comparing to µPIV observations of swimming cells and quantifying how the morphology affects swimming performance. We found that the helical transverse flagellum provides most forward thrust and, despite its near-cell position, is more hydrodynamically efficient than the trailing flagellum; however, the latter is nonetheless required to enable steering. Flagellar hairs and the sheet-like structure of the transverse flagellum allow dinoflagellates to exert strong propulsive forces and maintain high clearance rates without extending a long conventional flagellum far into the surroundings. This unique morphology has thus been essential to the evolution of the generally large, fast-swimming dinoflagellates.
Time: 3:00
Location: Stanley Thomas 316
February 3
Title: Analysis of solitonic interactions, and an initial connection to random matrix theory
Ken McLaughlin | Tulane University
Abstract: I will describe the interaction between a single soliton and a gas of solitons, providing for the first time a mathematical justification for the kinetic theory as posited by Zakharov in the 1970s. Then, if time permits, I will explain an initial connection to random matrix theory, in order to introduce randomness into a large collection of solitons. This is joint work with Manuela Girotti, Tamara Grava, Robert Jenkins, and Alexander Minakov.
Time: 3:00
Location: Gibson Hall 325
February 24
Title: Phase transitions and log Sobolev inequalities
Matias Delgadino | University Texas Austin
Abstract: In this talk, we will study the mean field limit of weakly interacting diffusions for confining and interaction potentials that are not necessarily convex. We explore the relationship between the large N limit of the constant in the logarithmic Sobolev inequality (LSI) for the N-particle system, and the presence or absence of phase transitions for the mean field limit. The non-degeneracy of the LSI constant will be shown to have far reaching consequences, especially in the context of uniform-in-time propagation of chaos and the behaviour of equilibrium fluctuations. This will be done by employing techniques from the theory of gradient flows in the 2-Wasserstein distance, specifically the Riemannian calculus on the space of probability measures.
Time: 3:00
Location: Gibson Hall 325
March 3
Title: TBA
David Herzog | Iowa State University
Abstract: TBA
Time: 3:00
Location: Gibson Hall 325
March 10
Title: TBA
Speaker | Tulane University
Abstract: TBA
Time: 3:00
Location: Gibson Hall 325
March 17
Title: TBA
Angel Pineda | Manhattan College
Abstract: TBA
Time: 3:00
Location: Gibson Hall 325
March 24
Title: TBA
Stuart Humphries | University of Lincoln, UK
Abstract: TBA
Time: 3:00
Location: Gibson Hall 325
March 31
Title: TBA
Speaker | Tulane University
Abstract: TBA
Time: TBA
Location: Gibson Hall 325
April 7
Title: TBA
Speaker | Tulane University
Abstract: TBA
Time: 3:00
Location: Gibson Hall 325
April 14
Title: TBA
Ben Southworth | Los Alamos National Labs
Abstract: TBA
Time: 3:00
Location: Gibson Hall 325
April 21
Title: TBA
Greg Lyng | Optum Labs
Abstract: TBA
Time: 3:00
Location: Gibson Hall 325
April 28
Title: TBA
Speaker | Tulane University
Abstract: TBA
Time: 3:00
Location: Gibson Hall 325
May 3
Last day of Class