Computational and Applied Mathematics Seminar

Spring 2008

4:10 PM 294 Carver unless otherwise stated

 

The CAM Seminar is organized in the ISU Mathematics Department. It brings speakers from inside and outside of  ISU,
raising issues and exchanging ideas on topics of current interest in the area of computational and applied mathematics.

Date

Speaker

Title

 

 

 

01/28

Paul Durbin
Aerospace Engineering
Iowa State University

Transition to Turbulent by Free-Stream Vortical Disturbances

02/04

Jangwoon (Leo) Lee,   Department of Math, ISU

On solving stochastic control problems constrained by stochastic partial differential equations

02/11
(4:10PM 268 Carver)

Mihaela Drignei, Department of Math, ISU

 Inverse Sturm-Liouville 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 Feynman-Vernon influence functional based on Fresnel integrals

03/17

Spring Break

 

03/24

 Xiaoliang Xie,  Department of Math, ISU

Implicit Smoothing methods for higher order time-dependent evolution equations

03/31

Shankar Subramaniam
Department of Mechanical Engineering, ISU

 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 Free-Stream Vortical Disturbances

Paul A. Durbin
Martin C. Jischke   Professor of Aerospace Engineering |
Iowa State University, Ames, IA

Recent work on transition with vortical free-stream disturbances will be reviewed.  Three cases are described: continuous mode transition, continuous-discrete mode interaction, and full blown simulation of transition in a compressor blade geometry.  The first two are fundamental studies, starting from Orr-Sommerfeld theory, proceeding to computer simulations of transition.

Orr-Sommerfeld 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 free-stream 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 free-stream turbulence; the features are quite similar to those seen in continuous mode transition. Indeed, free-stream 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 T-S 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 T-S 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 T-S--continuous 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 three-dimensionality 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 Sturm-Liouville problems by multiple spectra

Mihaela Drignei
Department of Math, ISU

The spectra of a Sturm-Liouville 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 Sturm-Liouville 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 2-dimensional cochlea model consists of a one-dimensional elastic structure (modeling the basilar membrane) surrounded by an incompressible 2-dimensional fluid within a 2-dimensional 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

An introduction

 

 

03/10

 

A representation of the Feynman-Vernon influence functional based on Fresnel integrals

 

Laura Cattaneo, 

Department of Math

 

A rigorous representation of the Feynman-Vernon 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 time-dependent evolution equations

Xiaoliang Xie
Department of Math, ISU
  

 When we do numerical computation for higher order time-dependent equations, the time step is often restricted by the CFL-type 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 Kuramoto-Sivashinsky 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

Shankar Subramaniam
Department of Mechanical Engineering, ISU

 

Abstract

 

04/07

 

Modeling of Coarsening Processes on Surfaces Ostwald vs Smoluchowski vs. Anomalous Ripening

James Evans,
Dept of Math & Ames Lab (USDOE)