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Date Time |
Location | Speaker |
Title – click for abstract |
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02/03 4:00pm |
Zoom |
Peter Miller University of Michigan |
Universality in the Small-Dispersion Limit of the Benjamin-Ono Equation
This talk concerns the Benjamin-Ono (BO) equation of internal wave theory, and properties of the solution of the Cauchy initial-value problem in the situation that the initial data is fixed but the coefficient of the nonlocal dispersive term in the equation is allowed to tend to zero (i.e., the zero-dispersion limit). It is well-known that existence of a limit requires the weak topology because high-frequency oscillations appear even though they are not present in the initial data. Physically, this phenomenon corresponds to the generation of a dispersive shock wave. In the setting of the Korteweg-de Vries (KdV) equation, it has been shown that dispersive shock waves exhibit a universal form independent of initial data near the two edges of the dispersive shock wave, and also near the gradient catastrophe point for the inviscid Burgers equation from which the shock wave forms. In this talk, we will present corresponding universality results for the BO equation. These have quite a different character than in the KdV case; while for KdV one has universal wave profiles expressed in terms of solutions of Painlevé-type equations, for BO one instead has expressions in terms of classical Airy functions and Pearcey integrals. These results are proved for general rational initial data using a new approach based on an explicit formula for the solution of the Cauchy problem for BO. This is joint work with Elliot Blackstone, Louise Gassot, Patrick Gérard, and Matthew Mitchell. Abstract |
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02/17 4:00pm |
Zoom: https://ta |
Andrea Bertozzi UCLA |
High-throughput optimization of DNA-aptamer secondary structure for classification and machine learning intepretability
We consider the secondary structures for aptamers, single
stranded DNA sequences that often fold on themselves and can be designed
to bind to small molecules. Given a specific aptamer sequence, there are
well-established computational tools to identify the lowest energy
secondary structure. However there is a need for a high-throughput process
whereby thousands of DNA structures can be calculated in real time for use
in an interactive setting, in particular when combined with aptamer
selection processes in which thousands of candidate molecules are screened
in the lab. We present a new method called GMfold, which algorithmically
uses subgraph matching ideas, in which the DNA chain is a graph with
nucleotides as graph nodes and adjacency along the chain to define edges
in the primary DNA structure. This allows us to cluster thousands of DNA
strands using modern machine learning algorithms. We present examples
using data from in vitro systematic evolution of ligands by exponential
enrichment (SELEX). This work is intended to serve as a building block for
future machine-learning informed DNA-aptamer selection processes for
target binding and medical therapeutics.
The Seminar will be via Zoom: https://tamu.zoom.us/j/94220070032 Abstract |
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03/03 4:00pm |
Zoom |
Michael Siegel New Jersey Institute of Technology, Newark |
A fast mesh-free boundary integral method for two-phase flow with soluble surfactant
We present an accurate and efficient boundary integral (BI) method to simulate the deformation of drops and bubbles in Stokes flow with soluble surfactant. Soluble surfactant advects and diffuses in bulk fluids while adsorbing and desorbing from interfaces. Since the fluid velocity depends on the bulk surfactant concentration C, the advection-diffusion equation governing C is
nonlinear, which precludes the Green’s function formulation necessary for a
BI method. However, in the physically representative large Peclet number
limit an analytical reduction of the surfactant dynamics surprisingly permits
a Green’s function formulation. Despite this, existing fast algorithms for
similar BI formulations, such as those developed for the heat equation, do
not readily apply. To address this challenge, we present a new fast algorithm
for our formulation which gives a mesh-free solution to the fully coupled
moving interface problem, including soluble surfactant effects. The method
extends to other problems involving advection-diffusion in the large Peclet
number limit. This is joint work with Michael Booty (NJIT), Samantha Evans (NJIT), and Johannes Tausch (SMU).
Zoom: https://tamu.zoom.us/j/94220070032 |
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03/24 4:00pm |
Zoom |
Andre Nachbin WPI, Worcester, MA |
Water waves on graphs
We have deduced a weakly nonlinear, weakly dispersive Boussinesq system for water waves on a 1D branching channel, namely on a graph. The model required a new compatibility condition at the graph’s node, where the main reach bifurcates into two reaches. The new nonlinear compatibility condition generalizes the well-known Neumann-Kirchhoff condition and includes forking angles in a systematic fashion. We present numerical simulations comparing solitary waves on the 1D (reduced) graph model with results of the (parent) 2D model, where a compatibility condition is not needed. We will comment on new problems that arise.
Join :https://tamu.zoom.us/j/94220070032 |
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03/31 4:00pm |
Zoom |
Dimitris Papageorgiou Imperial College, London |
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04/14 4:00pm |
BLOC 628 |
John Lowengrub UC Irvine |
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04/21 4:00pm |
BLOC 628 |
Todd Arbogast UT, Austin |
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04/28 4:00pm |
Zoom |
Christoph Borgers Tufts University, Medford, MA |
The yard-sale convergence theorem
Suppose n identical agents engage in a sequence of trades. Each trade involves a random pair of agents, and as a result of the trade, one agent gains some amount of wealth, and the other loses the same amount. The total amount of wealth is conserved, call it W. The amount of wealth transferred is a small fraction of the poorer trading partner’s pre-trade wealth, so nobody ever goes bankrupt. The direction of wealth transfer is random with both possibilities equally likely. The yard-sale convergence theorem states that with probability 1, the wealth of one agent will converge to W, and the wealth of all others will therefore converge to 0. For short, randomness that is fair in expectation inescapably leads to total oligarchy. This was first observed by Anirban Chakraborti 25 years ago. It is an immediate consequence of the martingale convergence theorem. However, I will give a more elementary proof, using nothing heavier than the Borel-Cantelli lemma, of a stronger result. This is joint work with Claude Greengard. |