Difference between revisions of "Applied/GPS"

From UW-Math Wiki
Jump to: navigation, search
m (Friday, April 1: Will Mitchell)
 
(60 intermediate revisions by 7 users not shown)
Line 1: Line 1:
 
__NOTOC__
 
__NOTOC__
= GPS Applied Mathematics Seminar =
+
= Graduate Applied Math Seminar =
  
The GPS (Graduate Participation Seminar) is a weekly seminar by and for graduate students. If you're interested in presenting a topic or your own research, contact the organizers: Sarah Tumasz, Qin Li, Peter Mueller, and Bryan Crompton.
+
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 Jim Brunner (jdbrunner (at) math.wisc.edu).
  
All seminars are on Fridays from 9:55-10:45 am in room 901 VV.  Speakers should aim for their talk to last no longer than 45 minutes.
+
The seminar schedule can be found here. We meet in Van Vleck 901 from 1:00 to 2:00 on Fridays.
  
== Fall 2012 ==
+
==Spring 2016==
 +
 
 +
 
 +
{| cellpadding="5"
 +
!align="left" | date
 +
!align="left" | speaker
 +
!align="left" | title
 +
|-
 +
|February 12
 +
|Jim Brunner
 +
|"Chemical reaction networks"
 +
|-
 +
|February 19
 +
|Xiaoqian Xu
 +
|"Mixing: A brief introduction from the PDE aspect"
 +
|-
 +
|March 2
 +
|Fan Yang
 +
|"Berry phase in quantum mechanics"
 +
|-
 +
|April 1
 +
|Will Mitchell
 +
|"An exercise in asymptotics for finding stagnation points in a Stokes flow"
 +
|}
 +
 
 +
== Abstracts ==
 +
 
 +
Please add your abstracts here.
 +
 
 +
===Friday, Feb 12: Jim Brunner===
 +
"Chemical reaction networks"
 +
 
 +
Abstract: I will present an introduction to Mass Action Kinetic models of biochemical systems. Chemical reaction network theory draws on both the theory of dynamical systems as well as techniques from algebra, algebraic geometry and graph theory, so hopefully I will be able to convince even the more algebraically minded among us that dynamic models are interesting.
 +
 
 +
===Friday, Feb 19: Xiaoqian Xu===
 +
"Mixing: A brief introduction from the PDE aspect"
 +
 
 +
Abstract: I will discuss several definitions and examples of mixing, and introduce an interesting conjecture about mixing, and also talk about the way how we can use them for other complicated situations like social life of bacteria and reproducing of corals.
 +
 
 +
===Friday, April 1: Will Mitchell===
 +
"An exercise in asymptotics for finding stagnation points in a Stokes flow"
 +
 
 +
Abstract: In this two-part talk, I will describe the Stokes flow about a sphere which is held fixed in a background shear flow.  The flow and associated tractions are known exactly.  We wish to find where the tangential component of the traction vanishes.  This leads to some fourth-order polynomial equations which are hard to solve and provides a segue into the second part of the talk, wherein we attempt to solve them approximately using a small parameter argument.
 +
 
 +
== Spring 2014 ==
  
 
{| cellpadding="5"
 
{| cellpadding="5"
Line 13: Line 57:
 
!align="left" | title
 
!align="left" | title
 
|-
 
|-
|Sept. 21, '''B219'''
+
|February 3
|Saverio Spagnolie
+
|Jim Brunner
|''Fluid-body interactions: from fish to flagella''
+
|"Chemical reaction networks"
 
|-
 
|-
|Sept. 28
+
|February 17
| Zhennan Zhou
+
|Peter Mueller
|''Computing Schrodinger equation in the semi-classical regime and physical observables.''
+
|"Optimal swimming and evolution"
 
|-
 
|-
|Oct. 5
+
|March 3
|Leland Jefferis
+
|Zhennan Zhou
|''3D display technology using MATLAB and cardboard''
+
|-
 +
|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 3: Zhennan Zhou===
 +
"Efficient computation of the semi-classical limit of the Schrödinger equation"
 +
 
 +
Abstract: After looking at previous techniques, we will try using the Gaussian Wave Packet Transform on the semi-classical Schrödinger equation.
 +
 
 +
== Fall 2013 ==
 +
 
 +
{| cellpadding="5"
 +
!align="left" | date
 +
!align="left" | speaker
 +
!align="left" | 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 ==
 +
 
 +
{| cellpadding="5"
 +
!align="left" | date
 +
!align="left" | speaker
 +
!align="left" | title
 
|-
 
|-
|Oct. 12
+
|February 1
|speaker
+
|Bryan Crompton
|''title''
+
|"The surprising math of cities and corporations"
 
|-
 
|-
|Oct. 19
+
|February 8
|speaker
+
|Peter Mueller
|''title''
+
|Mandelbrot's TED talk
|'
 
 
|-
 
|-
|Oct. 26
+
|February 15
|Matthew D. Johnston
+
|Jim Brunner
|''Stochastic Chemical Reaction Networks''
+
|"Logical Models, Polynomial Dynamical Systems, and Iron Metabolism"
 
|-
 
|-
|Nov. 2
+
|February 22
|Qin Li
+
|Leland Jefferis
|''From the Boltzmann to the Euler: the study of the Knudsen layer''
+
|Video lecture on intro quantum mechanics + The postulates of quantum mechanics + Spin 1/2 systems
 
|-
 
|-
|Nov. 9
+
|February 29
|
+
|Leland Jefferis
|
+
|Topics in quantum mechanics: Spin 1/2 systems + Uncertainty relations + Quantum harmonic oscillators + ...
 
|-
 
|-
|Nov. 16
+
|March 15
|Sarah Tumasz
+
|Will Mitchell
|''TBD''
+
|FEniCS, my favorite finite element software package
 
|-
 
|-
|Nov. 30
+
|March 22
 
|
 
|
 
|
 
|
 
|-
 
|-
|Dec. 7
+
|April 5
 
|Bryan Crompton
 
|Bryan Crompton
|''Mathematical Biology: Persistence in Chemical Reaction Networks''
+
|TBD
 
|-
 
|-
 +
|April 26
 +
|Peter Mueller
 +
|Stokeslets, flagella, and stresslet swimmers
 
|}
 
|}
  
 
== Abstracts ==
 
== 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, Sept 21: Prof. Saverio Spagnolie===
+
===Friday, Feb 15: Jim Brunner===
''Fluid-body interactions: from fish to flagella''
+
"Logical Models, Polynomial Dynamical Systems, and Iron Metabolism"
  
abstract:
+
Abstract: I will introduce logical models and polynomial dynamical systems in the context of a model of iron metabolism in an epithelial cell.
The length and velocity scales of swimming organisms on this
 
planet vary by many orders of magnitude. Some swimming strategies work for
 
small organisms but not for large ones, and vice versa, due to the
 
scale-dependent nature of the fluid dynamics governing such systems. In
 
this informal conversation, we will discuss some classical and recent
 
efforts to understand fluid-body interactions at scales relevant to fish
 
and birds, and separately to microorganisms. The methodology for their
 
study will range from classical tools of applied mathematics to highly
 
accurate numerical techniques. Questions to be addressed (briefly)
 
include: what is the optimal waveform of an undulating flagellum?; what is
 
the effect of boundaries on swimming microorganisms?; and what is the role
 
of flexibility in flapping fins and wings?
 
  
 +
===Friday, Feb 22 & Feb 29: Leland Jefferis===
 +
"Topics in Quantum Mechanics"
  
===Friday, Sept 28: Zhennan Zhou===
+
Abstract: I will introduce the key ideas of quantum mechanics and expose the fascinating mathematical framework behind the theory.
''Computing Schrodinger equation in the semi-classical regime and physical observables''
 
  
abstract
+
===Friday, Mar 15: Will Mitchell===
 +
"FEniCS, my favorite finite element software"
  
In this talk, we present a time splitting scheme for Schrodinger equation in the presence of electromagnetic field in the semi-classical regime, where wave function propagates O(\varepsilon) oscillation in both space and time. With operator splitting technique, the time evolution of the Schrodinger equation has been divided into three parts: the kinetic part, the convection part and the potential. With spectral approximation, the kinetic part and the potential part can be solved analytically. For the convection part, we proposed two numerical methods, a time explicit spectral method and a Lagrangian convection method. For the Lagrangian convection time splitting method, we prove the error estimate in L^{2} approximation of wave function, and by comparing with the semi-classical limit, we show this method can capture correct physical observable even if O(1) time step is taken. We implement this method in extensive numerical examples for both one dimensional and essentially two dimensional cases, and numerically verify that we achieve uniform time step error control in computing physical observables.
+
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, Oct 26: Matthew D. Johnston===
+
===Friday, Apr 6: Bryan Crompton===
''Stochastic Chemical Reaction Networks''
+
"Fractional Calculus and the Fractional Diffusion Wave Equation"
  
abstract
+
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.
  
It is common to model systems of simultaneously occurring chemical reactions using ordinary differential equations. In this setting, we imagine reactions as continuous state space, deterministic processes over the chemical concentrations. This is only justified, however, if the effect of each individual reaction---an inherently discrete state, stochastic event---is small enough compared to the net effect of all the reactions occurring that we can average them together. This is clearly not the case for many practical systems. Many cellular processes, for instance, typically involve only tens or hundreds of individual reacting molecules. We cannot average these reactions together without losing valuable information about the dynamics of the system.
+
===Friday, Apr 26: Peter Mueller===
 +
"Stokeslets, flagella, and stresslet swimmers"
  
In this talk, I will present an introductory-level overview of the state of stochastic modeling in chemical reaction networks theory under the assumption of mass-action kinetics. In particular, I will present two common tools---Gillespie's algorithm and the Chemical Master Equation---and explain the strengths and drawbacks of both approaches.
+
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.
  
 
== Archived semesters ==
 
== Archived semesters ==
 +
*[[Applied/GPS/Fall2012|Fall 2012]]
 
*[[Applied/GPS/Spring2012|Spring 2012]]
 
*[[Applied/GPS/Spring2012|Spring 2012]]
 
*[[Applied/GPS/Fall2011|Fall 2011]]
 
*[[Applied/GPS/Fall2011|Fall 2011]]

Latest revision as of 10:47, 30 March 2016

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 Jim Brunner (jdbrunner (at) math.wisc.edu).

The seminar schedule can be found here. We meet in Van Vleck 901 from 1:00 to 2:00 on Fridays.

Spring 2016

date speaker title
February 12 Jim Brunner "Chemical reaction networks"
February 19 Xiaoqian Xu "Mixing: A brief introduction from the PDE aspect"
March 2 Fan Yang "Berry phase in quantum mechanics"
April 1 Will Mitchell "An exercise in asymptotics for finding stagnation points in a Stokes flow"

Abstracts

Please add your abstracts here.

Friday, Feb 12: Jim Brunner

"Chemical reaction networks"

Abstract: I will present an introduction to Mass Action Kinetic models of biochemical systems. Chemical reaction network theory draws on both the theory of dynamical systems as well as techniques from algebra, algebraic geometry and graph theory, so hopefully I will be able to convince even the more algebraically minded among us that dynamic models are interesting.

Friday, Feb 19: Xiaoqian Xu

"Mixing: A brief introduction from the PDE aspect"

Abstract: I will discuss several definitions and examples of mixing, and introduce an interesting conjecture about mixing, and also talk about the way how we can use them for other complicated situations like social life of bacteria and reproducing of corals.

Friday, April 1: Will Mitchell

"An exercise in asymptotics for finding stagnation points in a Stokes flow"

Abstract: In this two-part talk, I will describe the Stokes flow about a sphere which is held fixed in a background shear flow. The flow and associated tractions are known exactly. We wish to find where the tangential component of the traction vanishes. This leads to some fourth-order polynomial equations which are hard to solve and provides a segue into the second part of the talk, wherein we attempt to solve them approximately using a small parameter argument.

Spring 2014

date speaker title
February 3 Jim Brunner "Chemical reaction networks"
February 17 Peter Mueller "Optimal swimming and evolution"
March 3 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 3: Zhennan Zhou

"Efficient computation of the semi-classical limit of the Schrödinger equation"

Abstract: After looking at previous techniques, we will try using the Gaussian Wave Packet Transform on the semi-classical Schrödinger equation.

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.

Archived semesters