Applied/GPS
Graduate Applied Math Seminar
The Graduate Applied Math Seminar is one of the main tools for bringing together applied grad students in the department and building the community. You are encouraged to get involved! It is weekly seminar run by grad students for grad students. If you have any questions, please contact Peter Mueller (mueller (at) math.wisc.edu).
The seminar schedule can be found here. We meet in Van Vleck 901 from 3:40pm to 4:30pm on Mondays.
Spring 2014
| date | speaker | title |
|---|---|---|
| February 3 | Jim Brunner | "Chemical reaction networks" |
| February 17 | Peter Mueller | "Optimal swimming and evolution" |
| March 10 | Xiaoqian Xu | "Mixing on the torus" |
| March 17 | Zhennan Zhou | |
| April 7 | Will Mitchell | "Pade Approximants: How does your machine compute exp(A), with A a matrix?" |
Abstracts
Please add your abstracts here.
Monday, Feb 3: Jim Brunner
"Chemical reaction networks"
Abstract: Jim will be using Jeremy Gunawardena's notes to introduce the topic: http://www.jeremy-gunawardena.com/papers/crnt.pdf and then transition into talking about what Prof. Craciun is looking at.
Monday, Feb 17: Peter Mueller
"Optimal swimming and evolution"
Abstract: We will be going over Christophe Eloy's paper: "On the best results for undulatory swimming" (https://www.irphe.fr/~eloy/PDF/JFM2013a.pdf).
Monday, Mar 10: Xiaoquan Xu
"Mixing on the torus"
Abstract: Consider a diffusion-free passive scalar $\theta$ being mixed by an incompressible flow $u$ on the torus $T^d$. Our aim is to study how well this scalar can be mixed under an enstrophy constraint on the advecting velocity field. Our main result shows that the mix-norm ($||\theta(t)||_{H^{-1}$) is bounded below by an exponential function of time. We will also perform numerical simulations and confirm that the numerically observed decay rate scales similarly to the rigorous lower bound, at least for a significant initial period of time. This is the joint work with Gautam Iyer and Alexander Kiselev.
Fall 2013
| date | speaker | title |
|---|---|---|
| September 20 | Peter Mueller | "Fluid dynamics crash course" |
| September 27 | Peter Mueller | "Solutions to Stokes flow" |
| October 25 | Zhennan Zhou | "Numerical approximation of the Schrodinger equation with the electromagnetic field by the
Hagedorn wave packets" |
| November 1 | Zhennan Zhou | Part 2: "Numerical approximation of the Schrodinger equation with the electromagnetic field by the
Hagedorn wave packets" |
| November 8 | Will Mitchell | "How do we make a mesh? Two fundamental schemes" |
| November 22 | David Dynerman | "Semi-algebraic geometry of common lines" |
Abstracts
Please add your abstracts here.
Friday, Sept 20: Peter Mueller
"Fluid dynamics crash course"
Abstract: Deriving fundamental solutions to Stokes flow and using complex variable tricks to solve two-dimensional problems.
Friday, Sept 27: Peter Mueller
"Solutions to Stokes flow"
Abstract: We will slowly traverse the steps to exactly solve flow past a cylinder (2D) or sphere (3D).
Friday, Oct 25 and Nov 1: Zhennan Zhou
"Numerical approximation of the Schrodinger equation with the electromagnetic field by the Hagedorn wave packets"
Abstract: In this paper, we approximate the semi-classical Schrodinger equation in the presence of electromagnetic field by the Hagedorn wave packets approach. By operator splitting, the Hamiltonian is divided into the modified part and the residual part. The modified Hamiltonian, which is the main new idea of this paper, is chosen by the fact that Hagedorn wave packets are localized both in space and momentum so that a crucial correction term is added to the truncated Hamiltonian, and is treated by evolving the parameters associated with the Hagedorn wave packets. The residual part is treated by a Galerkin approximation. We prove that, with the modified Hamiltonian only, the Hagedorn wave packets dynamics gives the asymptotic solution with error O(eps^{1/2}), where eps is the the scaled Planck constant. We also prove that, the Galerkin approximation for the residual Hamiltonian can reduce the approximation error to O( eps^{k/2}), where k depends on the number of Hagedorn wave packets added to the dynamics. This approach is easy to implement, and can be naturally extended to the multidimensional cases. Unlike the high order Gaussian beam method, in which the non-constant cut-off function is necessary and some extra error is introduced, the Hagedorn wave packets approach gives a practical way to improve accuracy even when eps is not very small.
Friday, Nov 8: Will Mitchell
"How do we make a mesh? Two fundamental schemes"
Abstract: Meshing a bounded 2D or 3D region using triangles or tetrahedra is a fundamental problem in numerical mathematics and an area of active research. In this talk I'll discuss two now-classical (although only 10-year-old) algorithms which can succeed in addressing the challenges of irregular boundaries and variable densities. For those wishing to read ahead, see:
1) Persson and Strang, "A simple mesh generator in Matlab," SIAM Review, 2004
2) Du et al, "Constrained centroidal Voronoi tesselations for surfaces," SIAM Journal on Scientific Computing, 2003.
Friday, Nov 22: David Dynerman
"Semi-algebraic geometry of common lines"
Abstract: Cryo-electron microscopy (cryo-EM) is a technique for discovering the 3D structures of small molecules. To perform this 3D reconstruction a large number of 2D images taken from unknown microscope positions must be correctly positioned back in 3D space. Although these microscope positions are unknown, the common lines of intersection of the image planes can be detected and used in 3D reconstruction. A major difficulty in this process is large amounts of noise in the common line data.
The set of all noiseless common lines forms a semi-algebraic set (a set defined by polynomial equalities and inequalities). We define and describe the geometry of this set, and briefly discuss applications.
Spring 2013
| date | speaker | title |
|---|---|---|
| February 1 | Bryan Crompton | "The surprising math of cities and corporations" |
| February 8 | Peter Mueller | Mandelbrot's TED talk |
| February 15 | Jim Brunner | "Logical Models, Polynomial Dynamical Systems, and Iron Metabolism" |
| February 22 | Leland Jefferis | Video lecture on intro quantum mechanics + The postulates of quantum mechanics + Spin 1/2 systems |
| February 29 | Leland Jefferis | Topics in quantum mechanics: Spin 1/2 systems + Uncertainty relations + Quantum harmonic oscillators + ... |
| March 15 | Will Mitchell | FEniCS, my favorite finite element software package |
| March 22 | ||
| April 5 | Bryan Crompton | TBD |
| April 26 | Peter Mueller | Stokeslets, flagella, and stresslet swimmers |
Abstracts
Please add your abstracts here.
Friday, Feb 1: Bryan Cromtpon
"The surprising math of cities and corporations"
Abstract: We'll watch Geoffrey West's TED talk and discuss some of the math in his papers.
Friday, Feb 15: Jim Brunner
"Logical Models, Polynomial Dynamical Systems, and Iron Metabolism"
Abstract: I will introduce logical models and polynomial dynamical systems in the context of a model of iron metabolism in an epithelial cell.
Friday, Feb 22 & Feb 29: Leland Jefferis
"Topics in Quantum Mechanics"
Abstract: I will introduce the key ideas of quantum mechanics and expose the fascinating mathematical framework behind the theory.
Friday, Mar 15: Will Mitchell
"FEniCS, my favorite finite element software"
Abstract: The finite element method is mathematically elegant but can be thorny to code from scratch. The free, open-source FEniCS software takes care of the worst implementation details without constraining the freedom of the user to specify methods. I'll review the finite element method and then give some examples of FEniCS code.
Friday, Apr 6: Bryan Crompton
"Fractional Calculus and the Fractional Diffusion Wave Equation"
Abstract: I'll talk about the equivalent formulations, the Grundwald-Letnikov and Riemann-Liouville, of fractional calculus. I will give some examples of fractional derivatives (and integrals) and then discuss the fundamental solutions to the fractional diffusion wave equation. Derivations will be done non-rigorously.
Friday, Apr 26: Peter Mueller
"Stokeslets, flagella, and stresslet swimmers"
Abstract: I will be discussing time-dependent swimmers involving stokeslets as an approximation to flagella. We will then approximate the far-field by an oscillating stresslet and discuss some questionable results.