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The Sixth Meeting of the Illinois/Missouri Applied Harmonic Analysis Seminar, Saint Louis University, Missouri |
| Abstract: This one day meeting fosters research interactions among mathematicians, engineers and physicists who develop and apply techniques from harmonic analysis. Theoretical topics of interest include: Fourier analysis, wavelets, Gabor systems (time-frequency analysis), frames, Riesz bases, compressed sensing, approximation theory, X-ray type transforms.
Applications of interest include: all kinds of signal and image analysis, processing and reconstruction, both analogue and digital.
This conference is supported in part by the Institute for Mathematics and its Applications (IMA) through its Participating Institution (PI) Program. PI members may use IMA/PI funds to support travel of their personnel to this conference.
All interested researchers are welcome. There is no registration fee. Travel funding is available for participants based in the U.S.
For more information:
http://mathcs.slu.edu/~johnson/imaha/
|
| Nusret Balci (University of Minnesota) |
Turbulent times in flatland |
| Abstract: We will review the notion of turbulence, present a mathematical theory for it (in 2D), and then see how it can be twisted to have fun with a 3D system (Rayleigh-Benard heat convection problem). |
| Chi Hin Chan (University of Minnesota) |
The existence of smooth solutions to fractal Burgers equation with critical exponent |
| Abstract: In this talk, we present a piece of joint work of Chi Hin Chan and Magdalena Czubak, in which we establish the existence of smooth solutions to fractal Burgers equation with critical exponent by applying the parabolic De Giorgi's method as developed by Luis Caffarelli and Alexis Vasseur. In the talk, we will make a parallel comparison between our work on fractal Burgers' equation with critical exponent and the work by Caffarelli and Vasseur in their paper "Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation. |
| Bruno Eckhardt (Philipps-Universität Marburg) |
Turbulence transition in shear flows: what can we learn from pipe flow? |
| Abstract: According to textbook wisdom, flow down a pipe becomes turbulent near a Reynolds number of about 2000. This simple statement misses many subtleties of the transition: the absence of a linear stability of the laminar flow, the sensitive dependence on perturbations that sometimes succeed and sometimes fail to induce turbulence and the unexpected observation that the turbulent state, once achieved, is not persistent but can decay. All these observations are compatible with the formation of a strange saddle in the state space of the system. I will focus on three aspects: on the appearance of 3-d coherent states, on the information contained in lifetime statistics and on results on the boundary between laminar and turbulent regions. They suggest a generic structuring of state space in flows where turbulent and laminar flow coexist, such as plane Couette flow, Poiseuille flow and perhaps even boundary layers.
|
| Thomas C. Hagen (University of Memphis) |
On spider-man and film casting: the mathematics of free liquid fibers and films in elongation |
| Abstract: In this lecture we give an overview of the
mathematical theory of free liquid fibers and films of
highly viscous liquids in fiber spinning and film casting. The governing equations to be discussed arise as the slender body approximation of the Navier-Stokes equations with moving boundary as 1D or 2D nonlinear
coupled hyperbolic-elliptic systems of pdes. Topics
of interest in this presentation include existence and uniqueness results, failure of fiber breakup in the
purely viscous regime, and spectral determinacy/regularity of the linearized film equations. Some open questions will be
motivated. |
| Zhi (George) Lin (University of Minnesota) |
Mathematical models and measures of mixing |
| Abstract: Mixing by stirring can be measured in a variety of ways including tracer particle dispersion, the scalar flux-gradient relationship, or via suppression of scalar density variation in the presence of inhomogeneous sources and sinks. The mixing efficacy of a flow is often expressed in terms of enhanced diffusivity and quantified as an effective diffusion coefficient. In this work we compare and contrast these various notions of effective diffusivity. Via thorough examination of a simple shear flow mixing a scalar sustained by a steady source-sink distribution, we explore apparent inconsistencies and propose a conceptual approach that captures some compatible features of these different models and measures of mixing. |
| Kara Lee Maki (University of Minnesota) |
Experimental determination of the likelihood of catastrophic instability in Gaussian elimination |
| Abstract: The growth factor of a matrix quantifies the amount of potential error growth when a linear system is solved by Gaussian elimination with partial pivoting. While the growth factor has a maximum of 2n-1 for an n × n matrix, experience suggests the occurrence of matrices with exponentially large growth factors is extremely rare. To add computational evidence, we implemented a multicanonical Monte Carlo method to explore the tails of growth factor probability distributions for random matrices. |
| Michael Renardy (Virginia Polytechnic Institute and State University) |
Are viscoelastic flows under control or out of control? |
| Abstract: Controllability refers to the ability to steer a system from a
prescribed initial state to a desirable final state. The lecture
will give an overview of recent results on the controllability
of flows of viscoelastic fluids by means of a prescribed body
force or prescribed motion of the boundary. |
| Vladimir Sverak (University of Minnesota) |
Topics in the theory of the Navier-Stokes equations |
| Abstract: The course will cover certain selected
topics in the theory of the Navier-Stokes equations.
After a brief overview of the main issues of the
general theory we will focus on problems in the theory
of the steady-state solutions.
There are many open problems concerning the steady-state
solutions. These problems are presumably easier than
the main open questions about the time-dependent equations.
Nevertheless, some of them have remained unsolved
since their first explicit formulation in
the pioneering works of Jean Leray in the 1930s.
There is a certain indirect similarity (or "duality")
between the mathematical issues raised by these steady-state
problems and the issues which come up in connection with
the more well-known open problems about the time-dependent
equations. In the lectures I hope to cover some of the
important results about the steady-state solutions
and discuss some of the open problems.
The course will be accessible to postdocs and to graduate
students with some knowledge of PDEs. For example,
an introductory graduate PDE course should be a sufficient
prerequisite.
|
| Vladimir Sverak (University of Minnesota) |
Topics in the theory of the Navier-Stokes equations |
| Abstract: The course will cover certain selected
topics in the theory of the Navier-Stokes equations.
After a brief overview of the main issues of the
general theory we will focus on problems in the theory
of the steady-state solutions.
There are many open problems concerning the steady-state
solutions. These problems are presumably easier than
the main open questions about the time-dependent equations.
Nevertheless, some of them have remained unsolved
since their first explicit formulation in
the pioneering works of Jean Leray in the 1930s.
There is a certain indirect similarity (or "duality")
between the mathematical issues raised by these steady-state
problems and the issues which come up in connection with
the more well-known open problems about the time-dependent
equations. In the lectures I hope to cover some of the
important results about the steady-state solutions
and discuss some of the open problems.
The course will be accessible to postdocs and to graduate
students with some knowledge of PDEs. For example,
an introductory graduate PDE course should be a sufficient
prerequisite.
|
| Vladimir Sverak (University of Minnesota) |
Topics in the theory of the Navier-Stokes equations |
| Abstract: The course will cover certain selected
topics in the theory of the Navier-Stokes equations.
After a brief overview of the main issues of the
general theory we will focus on problems in the theory
of the steady-state solutions.
There are many open problems concerning the steady-state
solutions. These problems are presumably easier than
the main open questions about the time-dependent equations.
Nevertheless, some of them have remained unsolved
since their first explicit formulation in
the pioneering works of Jean Leray in the 1930s.
There is a certain indirect similarity (or "duality")
between the mathematical issues raised by these steady-state
problems and the issues which come up in connection with
the more well-known open problems about the time-dependent
equations. In the lectures I hope to cover some of the
important results about the steady-state solutions
and discuss some of the open problems.
The course will be accessible to postdocs and to graduate
students with some knowledge of PDEs. For example,
an introductory graduate PDE course should be a sufficient
prerequisite.
|
| Vladimir Sverak (University of Minnesota) |
Topics in the theory of the Navier-Stokes equations |
| Abstract: The course will cover certain selected
topics in the theory of the Navier-Stokes equations.
After a brief overview of the main issues of the
general theory we will focus on problems in the theory
of the steady-state solutions.
There are many open problems concerning the steady-state
solutions. These problems are presumably easier than
the main open questions about the time-dependent equations.
Nevertheless, some of them have remained unsolved
since their first explicit formulation in
the pioneering works of Jean Leray in the 1930s.
There is a certain indirect similarity (or "duality")
between the mathematical issues raised by these steady-state
problems and the issues which come up in connection with
the more well-known open problems about the time-dependent
equations. In the lectures I hope to cover some of the
important results about the steady-state solutions
and discuss some of the open problems.
The course will be accessible to postdocs and to graduate
students with some knowledge of PDEs. For example,
an introductory graduate PDE course should be a sufficient
prerequisite.
|
| Vladimir Sverak (University of Minnesota) |
Topics in the theory of the Navier-Stokes equations |
| Abstract: The course will cover certain selected
topics in the theory of the Navier-Stokes equations.
After a brief overview of the main issues of the
general theory we will focus on problems in the theory
of the steady-state solutions.
There are many open problems concerning the steady-state
solutions. These problems are presumably easier than
the main open questions about the time-dependent equations.
Nevertheless, some of them have remained unsolved
since their first explicit formulation in
the pioneering works of Jean Leray in the 1930s.
There is a certain indirect similarity (or "duality")
between the mathematical issues raised by these steady-state
problems and the issues which come up in connection with
the more well-known open problems about the time-dependent
equations. In the lectures I hope to cover some of the
important results about the steady-state solutions
and discuss some of the open problems.
The course will be accessible to postdocs and to graduate
students with some knowledge of PDEs. For example,
an introductory graduate PDE course should be a sufficient
prerequisite.
|
| Vladimir Sverak (University of Minnesota) |
Topics in the theory of the Navier-Stokes equations |
| Abstract: The course will cover certain selected
topics in the theory of the Navier-Stokes equations.
After a brief overview of the main issues of the
general theory we will focus on problems in the theory
of the steady-state solutions.
There are many open problems concerning the steady-state
solutions. These problems are presumably easier than
the main open questions about the time-dependent equations.
Nevertheless, some of them have remained unsolved
since their first explicit formulation in
the pioneering works of Jean Leray in the 1930s.
There is a certain indirect similarity (or "duality")
between the mathematical issues raised by these steady-state
problems and the issues which come up in connection with
the more well-known open problems about the time-dependent
equations. In the lectures I hope to cover some of the
important results about the steady-state solutions
and discuss some of the open problems.
The course will be accessible to postdocs and to graduate
students with some knowledge of PDEs. For example,
an introductory graduate PDE course should be a sufficient
prerequisite.
|
| Jeffrey Weeks |
The shape of space |
| Abstract: When we look out on a clear night, the universe seems infinite. Yet this infinity might be an illusion. During the first half of the presentation, computer games will introduce the concept of a "multiconnected universe." Interactive 3D graphics will then take the viewer on a tour of several possible shapes for space. Finally, we'll see how recent satellite data provide tantalizing clues to the true shape of our universe. The only prerequisites for this talk are curiosity and imagination. For middle school and high school students, people interested in astronomy, and all members of the university and surrounding communities. |
