Computational and Applied Mathematics Seminar
Spring 2008
4:10 PM 294 Carver unless otherwise stated
Date

Speaker

Title




01/28 
Paul Durbin

Transition to Turbulent by FreeStream Vortical
Disturbances

02/04 
Jangwoon (Leo)
Lee, Department of Math, ISU

On solving stochastic control problems constrained by stochastic partial
differential equations

02/11 
Mihaela Drignei, Department of Math, ISU

Inverse
SturmLiouville problems by multiple spectra

02/18 
Scott Hansen, Department of Math, ISU

Modeling and control
of a cochlea

02/25 

03/03 
Ju Ming, Department of Math, ISU 
OPTIMAL CONTROL OF STOCHASTIC BURGERS' EQUATION
WITH RANDOM FORCING USING WEINER CHAOS EXPANSION

03/10 
Laura Cattaneo, Department of Math, ISU

A
representation of the FeynmanVernon influence functional based on Fresnel
integrals

03/17 
Spring Break 

03/24 
Xiaoliang
Xie, Department of Math, ISU

Implicit Smoothing methods for higher order timedependent evolution
equations

03/31 
Shankar Subramaniam

Modeling
and Simulation of Nanoparticle Aggregation in Liquid
Suspensions

04/07 
James Evans, Dept of Math & Ames Lab (USDOE) 
Modeling
of Coarsening Processes on Surfaces Ostwald vs Smoluchowski vs. Anomalous Ripening

04/14



For more information, please contact Hailiang Liu at hliu@iastate.edu
01/28
Transition to Turbulent by FreeStream Vortical Disturbances
Paul A. Durbin
Martin C. Jischke Professor of Aerospace Engineering 
Iowa State University, Ames, IA
Recent work on transition with vortical freestream disturbances will be reviewed. Three cases are described: continuous mode transition, continuousdiscrete mode interaction, and full blown simulation of transition in a compressor blade geometry. The first two are fundamental studies, starting from OrrSommerfeld theory, proceeding to computer simulations of transition.
OrrSommerfeld theory provides a basis for studying transition on flat walls. Initial disturbances are constructed from discrete and continuous modes. In the first of our three cases, the initial disturbance contains only continuous modes. They provide a basis for freestream disturbances. Then mode interactions are studied by direct numerical simulation. Continuous modes produce streaks (or Klebanoff distortions) within the boundary layer. These amplify and interact with higher frequency disturbances to cause transition through the spontaneous appearance of turbulent spots (ref.1). This case corresponds to bypass transition induced by freestream turbulence; the features are quite similar to those seen in continuous mode transition. Indeed, freestream turbulence can be synthesized as a random superposition of continuous modes. Hence, this is a commonly occurring transition mechanism.
Another scenario is modeled by the combination of a discrete and a continuous mode. Again, the mode interactions are studied by direct numerical simulation. However, now the process is a mixture of bypass and stability mode forms of transition. The continuous modes create Klebanoff distortions, again, but now they interacts with a TS wave to cause transition via lambda vortices. The manner in which discrete and continuous modes interact is somewhat unclear. Floquet analysis of a base state consisting of a boundary layer with both streaks and TS waves suggests that a secondary instability mechanism is at play.
Comparing simulations of transition in boundary layers and on a compressor blade show transition on the pressure side occurs via the continuous mode mechanism. The suction side shows marginal separation followed by transition. That is not quite the same as the case of TScontinuous mode interaction. However, it is an interaction between continuous modes and instability waves, much as in the idealized mode interaction study. Klebanoff type of streaks are seen prior to separation, and some evidence exists of their role in the threedimensionality which precedes transition.
02/04
On solving stochastic control problems
constrained by stochastic partial differential equations
Jangwoon (Leo)
Lee,
Department of Math, ISU
A
stochastic optimal control problem associated with elliptic stochastic partial differential
equations is considered. Existence of an optimal solution is proved and a
stochastic optimality system of equations is derived. Discrete finite element
approximations of the stochastic optimality system are defined and error
estimates are obtained.
02/11
Inverse SturmLiouville
problems by multiple spectra
Mihaela Drignei
Department of Math, ISU
The spectra of a SturmLiouville differential operator with a parameter function
on appropriate domains is in a close relationship with the frequencies
of oscillations of a vibrating string subject to various constraints. Knowledge
of the frequencies of oscillation of the string, and therefore of the spectra
of the differential operator, give insight into the properties of the string
(e.g. the density). The parameter function in the SturmLiouville
differential operator is shown to encode such information about the string.
Hence, what is intended to be found is the parameter function of the
differential operator from information about the spectra of the same operator.
02/18
Modeling
and Control of a Cochlea
Scott Hansen
Department of Math, ISU
The standard 2dimensional cochlea model
consists of a onedimensional elastic structure (modeling the basilar membrane)
surrounded by an incompressible 2dimensional fluid within a 2dimensional
cochlear cavity. The dynamics are typically driven by a pressure differential
across the basilar membrane transmitted through the round and oval windows (a
portion of the boundary of the cochlea). First we describe an idealized model
in which the basilar membrane is modeled as an infinite array of oscillators
and the fluid is described by Laplace's equation. In this idealized setting we
show that the coupled system is approximately controllable with control acting
on an arbitrary open set of the basilar membrane. If the basilar membrane has longitudinal
membrane (string) elasticity, then exact controllability can be proved.
This is joint work with my former student
Isaac Chepkwony.
03/03
OPTIMAL CONTROL OF STOCHASTIC BURGERS' EQUATION WITH RANDOM FORCING
USING WEINER CHAOS EXPANSION
Ming Ju
Department of Math, ISU
03/10
A
representation of the FeynmanVernon influence functional based on Fresnel
integrals
Laura Cattaneo,
Department of Math
A rigorous representation of the
FeynmanVernon influence functional used to describe open quantum systems is
given, based on the theory of infinite dimensional oscillatory integrals. An
application to the case of the density matrices describing the Caldeira Leggett model of two quantum systems with a
quadratic interaction is presented.
03/24
Implicit Smoothing
methods for higher order timedependent evolution equations
Xiaoliang Xie
Department of Math, ISU
When we do numerical computation for higher order timedependent equations, the time step is often restricted by the CFLtype condition. We propose a preconditioning approximation to a class of higher order PDEs so that stable numerical schemes are constructed for an arbitrary large time step, via a smoothing operator to regularize the solution at each step. While applying to linear equations, the operator can be identified based on a stability analysis. Nonlinear problems have to rely on certain intrinsic energy principles. We will present a stability analysis for different types of linear equations and discrete energy analysis for some nonlinear equations, including the KdV equation, the Swift_Hohenberg equation and the KuramotoSivashinsky equation. Numerical examples together with some error comparison for both linear and nonlinear equations will be exhibited to explain the computational efficiency of the method.
03/31
Modeling and Simulation of Nanoparticle Aggregation in Liquid Suspensions
04/07
Modeling of
Coarsening Processes on Surfaces Ostwald vs Smoluchowski vs. Anomalous Ripening
James Evans,
Dept of Math & Ames Lab (USDOE)