SIAM Student Chapter Seminar: Difference between revisions

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*'''When:''' Every other Friday at 1:30 pm
*'''When:''' TBA
*'''Where:''' B333 Van Vleck Hall
*'''Where:''' Zoom
*'''Organizers:''' [http://www.math.wisc.edu/~xshen/ Xiao Shen]
*'''Organizers:''' [http://www.math.wisc.edu/~xshen/ Xiao Shen]
*'''Faculty advisers:''' [http://www.math.wisc.edu/~jeanluc/ Jean-Luc Thiffeault], [http://pages.cs.wisc.edu/~swright/ Steve Wright]  
*'''Faculty advisers:''' [http://www.math.wisc.edu/~jeanluc/ Jean-Luc Thiffeault], [http://pages.cs.wisc.edu/~swright/ Steve Wright]  
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== Spring 2020  ==
== Fall 2020  ==


{| cellpadding="8"
{| cellpadding="8"
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|-
|-
|Jan 31
|Jan 31
|[https://lorenzonajt.github.io/ Lorenzo Najt] (Math)
|[Yu Feng] (Math)
|''[[#Jan 31, Lorenzo Najt (Math)|Ensemble methods for measuring gerrymandering: Algorithmic problems and inferential challenges]]''
|''[[#TBA, Yu Feng (Math)|Phase separation in the advective Cahn--Hilliard equation]]''
|-
|-
|Feb 14
|[https://www.math.wisc.edu/~pollyyu/ Polly Yu] (Math)
|''[[#Feb 14, Polly Yu (Math)|Algebra, Dynamics, and Chemistry with Delay Differential Equations]]''
|-
|-
|Feb 21
|Gage Bonner (Physics)
|''[[#Feb 21, Gage Bonner (Physics)|Growth of history-dependent random sequences]]''
|-
|-
|-
|-
|
|
|}
|}
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== Abstracts ==
== Abstracts ==


=== Jan 31, Lorenzo Najt (Math) ===
=== TBA, Yu Feng (Math) ===
'''Ensemble methods for measuring gerrymandering: Algorithmic problems and inferential challenges'''
'''Phase separation in the advective Cahn--Hilliard equation'''
 
We will review some recent work regarding measuring gerrymandering by sampling from the space of maps, including two methods used in a recent amicus brief to the supreme court. This discussion will highlight some of the computational challenges of this approach, including some complexity-theory lower bounds and bottlenecks in Markov chains. We will examine the robustness of these statistical methods through their connection to phase transitions in the self-avoiding walk model, as well as their dependence on artifacts of discretization. This talk is largely based on https://arxiv.org/abs/1908.08881
 
=== Feb 14, Polly Yu (Math) ===
'''Algebra, Dynamics, and Chemistry with Delay Differential Equations'''
 
Delay differential equations (DDEs) can exhibit more complicated behavior than their ODE counterparts. What is stable in the ODE setting could exhibit oscillation in DDE. Where do delay equations show up anyway? In this talk, we’ll introduce DDEs, and how (sort-of-)linear algebra gives information about the stability of DDEs.
 


=== Feb 21, Gage Bonner (Physics) ===
The Cahn--Hilliard equation is a classic model of phase separation in binary mixtures that exhibits spontaneous coarsening of the phases. We study the Cahn--Hilliard equation with an imposed advection term in order to model the stirring and eventual mixing of the phases. The main result is that if the imposed advection is sufficiently mixing then no phase separation occurs, and the solution instead converges exponentially to a homogeneous mixed state. The mixing effectiveness of the imposed drift is quantified in terms of the dissipation time of the associated advection-hyperdiffusion equation, and we produce examples of velocity fields with a small dissipation time. We also study the relationship between this quantity and the dissipation time of the standard advection-diffusion equation.
''' Growth of history-dependent random sequences'''


Unlike discrete Markov chains, history-dependent random sequences are sequences of random variables whose "next" term depends on all others seen previously. For this reason, they can be difficult to analyze. I will discuss some simple and fun cases where the long-term behavior of the sequence can be computed explicitly in expectation.




Revision as of 05:17, 18 September 2020



Fall 2020

date speaker title
Jan 31 [Yu Feng] (Math) Phase separation in the advective Cahn--Hilliard equation

Abstracts

TBA, Yu Feng (Math)

Phase separation in the advective Cahn--Hilliard equation

The Cahn--Hilliard equation is a classic model of phase separation in binary mixtures that exhibits spontaneous coarsening of the phases. We study the Cahn--Hilliard equation with an imposed advection term in order to model the stirring and eventual mixing of the phases. The main result is that if the imposed advection is sufficiently mixing then no phase separation occurs, and the solution instead converges exponentially to a homogeneous mixed state. The mixing effectiveness of the imposed drift is quantified in terms of the dissipation time of the associated advection-hyperdiffusion equation, and we produce examples of velocity fields with a small dissipation time. We also study the relationship between this quantity and the dissipation time of the standard advection-diffusion equation.



Past Semesters

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