CAM = seminar

Computational and Applied = Mathematics=20 Seminar

Spring 2008

4:10 PM 294 Carver unless = otherwise=20 stated

The CAM Seminar is organized in the ISU Mathematics Department. = It=20 brings speakers from inside and outside of ISU,
raising issues = and=20 exchanging ideas on topics of current interest in the area of = computational and=20 applied mathematics.

Date

Speaker

Title

01/28

Paul Durbin
Aerospace Engineering
Iowa State = University

Transition to Turbulent by Free-Stream Vortical Disturbances

02/04

<= SPAN=20 class=3DSpellE>Ja= ngwoon=20 (Leo) Lee,=EF=BF=BD=EF=BF=BD=20 Department=20 of Math, ISU

On solving stochastic control problems constrained by = stochastic=20 partial differential equations

02/11 =
(4:10PM=20 268 = Carver)

Mihaela=20 Drignei, Department of Math, = ISU

Inverse=20 Sturm-Liouville problems by multiple=20 spectra

02/18=20

Scott Hansen, =EF=BF=BD=20 Department=20 of Math,=EF=BF=BD=20 ISU

Modeling and=20 control of a cochlea

02/25

03/03=20

Ju Ming, Department=20 of Math, ISU

OPTIMAL=20 CONTROL OF STOCHASTIC BURGERS' EQUATION WITH RANDOM FORCING USING = WEINER=20 CHAOS EXPANSION

03/10=20

Laura Cattaneo,=EF=BF=BD = Department=20 of Math, ISU

A=20 representation of the Feynman-Vernon influence functional based on = Fresnel=20 integrals

03/17

Spring Break

03/24

Xiaoliang=20 Xie, Department=20 of Math, ISU

Implicit Smoothing methods for higher order time-dependent = evolution=20 equations

03/31

Shankar Subramaniam
Department of Mechanical Engineering, = ISU=20

Modeling=20 and Simulation of Nanoparticle = Aggregation in=20 Liquid=20 =EF=BF=BDSuspensions

04/07=20

James=20 Evans, Dept of Math & Ames Lab (USDOE)

Modeling=20 of Coarsening Processes on Surfaces Ostwald vs=20 Smoluchowski vs. Anomalous = Ripening

04/14=20

=20

For more information, please contact Hailiang Liu at hliu@iastate.edu

01/28

Transition to Turbulent by=20 Free-Stream Vortical Disturbances

Paul A. Durbin
Martin C. Jischke =EF=BF=BD Professor of Aerospace = Engineering |
Iowa=20 State University, Ames, IA

Recent work on transition with vortical free-stream disturbances will = be=20 reviewed. Three cases are described: continuous mode transition,=20 continuous-discrete mode interaction, and full blown simulation of = transition in=20 a compressor blade geometry. The first two are fundamental = studies,=20 starting from Orr-Sommerfeld theory, proceeding to computer simulations = of=20 transition.

Orr-Sommerfeld theory provides a basis for studying transition on = flat=20 walls. Initial disturbances are constructed from discrete and = continuous=20 modes. In the first of our three cases, the initial disturbance contains = only=20 continuous modes. They provide a basis for free-stream = disturbances. Then=20 mode interactions are studied by direct numerical simulation. = Continuous=20 modes produce streaks (or Klebanoff distortions) within the boundary = layer.=20 These amplify and interact with higher frequency disturbances to cause=20 transition through the spontaneous appearance of turbulent spots = (ref.1). =20 This case corresponds to bypass transition induced by free-stream = turbulence;=20 the features are quite similar to those seen in continuous mode = transition.=20 Indeed, free-stream turbulence can be synthesized as a random = superposition of=20 continuous modes. Hence, this is a commonly occurring transition = mechanism.

Another scenario is modeled by the combination of a discrete and a = continuous=20 mode. Again, the mode interactions are studied by direct numerical = simulation. However, now the process is a mixture of bypass and = stability=20 mode forms of transition. The continuous modes create Klebanoff = distortions,=20 again, but now they interacts with a T-S wave to cause transition via = lambda=20 vortices. The manner in which discrete and continuous modes = interact is=20 somewhat unclear. Floquet analysis of a base state consisting of a = boundary=20 layer with both streaks and T-S waves suggests that a secondary = instability=20 mechanism is at play.

Comparing simulations of transition in boundary layers and on a = compressor=20 blade show transition on the pressure side occurs via the continuous = mode=20 mechanism. The suction side shows marginal separation followed by=20 transition. That is not quite the same as the case of T-S--continuous = mode=20 interaction. However, it is an interaction between continuous modes and=20 instability waves, much as in the idealized mode interaction study. = Klebanoff=20 type of streaks are seen prior to separation, and some evidence exists = of their=20 role in the three-dimensionality which precedes transition.

02/04

On solving stochastic control = problems=20 constrained by stochastic partial differential equations

<= SPAN=20 class=3DSpellE>Ja= ngwoon = (Leo)=20 Lee,=EF=BF=BD=EF=BF=BD =
Department=20 of Math, ISU

A = stochastic=20 optimal control problem associated with elliptic stochastic partial = differential=20 equations is considered. Existence of an optimal solution is proved and = a=20 stochastic optimality system of equations is derived. Discrete finite = element=20 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=20 spectra of a Sturm-Liouville=20 differential operator with a parameter function on appropriate domains = is=20 in a close relationship with the frequencies of oscillations of a = vibrating=20 string subject to various constraints. Knowledge of the frequencies of=20 oscillation of the string, and therefore of the spectra of the = differential=20 operator, give insight into the properties of the string (e.g. the = density). The=20 parameter function in the Sturm-Liouville = differential=20 operator is shown to encode such information about the string. Hence, = what is=20 intended to be found is the parameter function of the differential = operator from=20 information about the spectra of the same = operator.

02/18

Modeling=20 and Control of a Cochlea

Scott=20 Hansen
Department=20 of Math, ISU

The=20 standard 2-dimensional cochlea model consists of a one-dimensional = elastic=20 structure (modeling the basilar membrane) surrounded by an = incompressible=20 2-dimensional fluid within a 2-dimensional cochlear cavity. The dynamics = are=20 typically driven by a pressure differential across the basilar membrane=20 transmitted through the round and oval windows (a portion of the = boundary of the=20 cochlea). First we describe an idealized model in which the basilar = membrane is=20 modeled as an infinite array of oscillators and the fluid is described = by=20 Laplace's equation. In this idealized setting we show that the coupled = system is=20 approximately controllable with control acting on an arbitrary open set = of the=20 basilar membrane.=EF=BF=BD=EF=BF=BD = If the basilar=20 membrane has longitudinal membrane (string) elasticity, then exact=20 controllability can be proved.=EF=BF=BD=EF=BF=BD=EF=BF=BD=EF=BF=BD=EF=BF=BD=EF=BF=BD=EF=BF=BD=20

=EF=BF=BD

This=20 is joint work with my former student Isaac Chepkwony.

03/03

OPTIMAL=20 CONTROL OF STOCHASTIC BURGERS' EQUATION WITH RANDOM FORCING USING WEINER = CHAOS=20 EXPANSION

Ming=20 Ju

Department=20 of Math, ISU

An= =20 introduction

03/10

A=20 representation of the Feynman-Vernon influence functional based on = Fresnel=20 integrals

Laura=20 Cattaneo,=EF=BF=BD =

Department=20 of Math

A=20 rigorous representation of the Feynman-Vernon influence functional used = to=20 describe open quantum systems is given, based on the theory of infinite=20 dimensional oscillatory integrals. An application to the case of the = density=20 matrices describing the Caldeira- Leggett = model of two=20 quantum systems with a quadratic interaction is = presented.

03/24

Implicit = Smoothing=20 methods for higher order time-dependent evolution = equations

Xiaoliang=20 Xie
Department of Math, ISU

=EF=BF=BDWhen we do numerical=20 computation for higher order time-dependent equations, the time step is = often=20 restricted by the CFL-type condition. We propose a preconditioning = approximation=20 to a class of higher order PDEs so that stable numerical schemes are = constructed=20 for an arbitrary large time step, via a smoothing operator to regularize = the=20 solution at each step. While applying to linear equations, the operator = can be=20 identified based on a stability analysis. Nonlinear problems have to = rely on=20 certain intrinsic energy principles. We will present a stability = analysis=20 for different types of linear equations and discrete energy analysis for = some=20 nonlinear equations, including the KdV=20 equation, the Swift_Hohenberg equation = and the=20 Kuramoto-Sivashinsky equation.=EF=BF=BD Numerical examples together = with some error=20 comparison for both linear and nonlinear equations will be exhibited to = explain=20 the computational efficiency of the method.

03/31

Modeling and Simulation of Nanoparticle Aggregation in Liquid=20 =EF=BF=BDSuspensions

Shankar=20 Subramaniam
Department of Mechanical Engineering, ISU =

Abstract

04/07

Modeling of=20 Coarsening Processes on Surfaces Ostwald vs = Smoluchowski vs. Anomalous = Ripening

James Evans,
Dept of Math & Ames = Lab=20 (USDOE)

The CAM Seminar is organized in the ISU Mathematics Department. = It=20 brings speakers from inside and outside of ISU, raising issues = and=20 exchanging ideas on topics of current interest in the area of = computational and=20 applied mathematics.