4 AN09 Abstracts

101 Pages·2009·0.53 MB·English

4 AN09 Abstracts
IC1 and Engineering
Optimization Modeling: Recent Enhancements
The computer industry is going through an exciting, dis-
and Future Extensions
ruptivetransformationbyswitchingtomassiveparallelism
Modeling systems are an efficient way to develop the con- inprocessordesign. Today,morethan100millioncomput-
straints and objectives for optimization and equilibrium ersarerunningparallelizedapplications20-100timesfaster
problems. Weoutlineseveralrecentenhancementsofsuch than their sequential versions. By year 2016, parallelism
systems that facilitate grid solution techniques, comple- could provide over 1,000 times speedup. Such a dramatic
mentarity or equilibrium constraints within optimization increase in computation power has already enabled revo-
problems, model embedding, and explicit formulation of lutionary work, or time warp, in science and engineering
stochastic constraints and extended nonlinear program- disciplines. This talk aims to offer insight into the oppor-
ming problems. Further extensions of these systems to tunities that these inexpensive parallel computers offer to
ease the modeling burden in specific contexts will also be researchersandhowsomedisciplinesarealreadybenefiting
proposed, along with computational results in particular from the revolution.
application domains.
Wen-Mei Hwu
Michael C. Ferris Department of Electrical and Computer Engineering
University of Wisconsin University of Illinois at Urbana-Champaign
Department of Computer Science [email protected]
[email protected]
IC5
IC2 The Design and Analysis of Multithreaded Algo-
Multiscale Methods for Dilute Fluids and Plasmas rithms
Monte Carlo particle methods have been used with great This talk overviews multithreaded algorithmic design as
successforfluidandplasmaflowsinwhichcollisionaleffects supported by the Cilk++ concurrency platform. Cilk++
aresignificant. Applicationsrangefromflightintheupper allowsaprogrammertoanalyzealgorithmsintermsofthe
atmosphere to the lubrication of a hard disk and the edge theoreticallyelegantnotionsofworkandspan,whoseratio
region in a fusion plasma. In the near fluid regime, how- provides a quantitative measure of parallelism. The per-
ever,theparticlecollisionratebecomesverylarge,sothat formance of a Cilk++ program is mathematically guaran-
particlemethodscanbecomecomputationallyintractable. teed to scale up linearly with the number of processors,
Hybrid methods combining discrete and continuum (i.e., as long as the application exhibits sufficient parallelism
particle and fluid) descriptions are a promising alterna- and the computer architecture provides sufficient memory
tive that can retain the accuracy of a full particle method bandwidth. Exampleproblemsthatadmitefficientparallel
and the speed of a fluid dynamic solver. The formulation algorithms in both theory and practice include Strassen’s
andanalysisofthesemethodsdependssignificantlyonthe matrix-multiplicationalgorithm,sparsematrix-vectormul-
fluid dynamic limit for kinetic theory. This talk describes tiplication, sorting, and breadth-first search of a graph.
themathematicalbasisandcomputationalperformancefor
Charles E. Leiserson
several different hybrid methods.
MIT CSAIL & Cilk Arts
Russel Caflisch [email protected]
Department of Mathematics
University of California, Los Angeles
IC6
cafl[email protected]
Optimization: TheDifferenceBetweenTheoryand
Practice
IC3
Theres an old saying, In theory, theres no difference be-
Mathematical Neuroscience: From Neurons to
tweentheoryandpractice,butinpracticethereis.Today,
Networks
scientists are working on optimization problems arising in
The tools of dynamical systems theory are having an in- fields such as nanoscience, astrophysics, and the electric
creasingimpactonourunderstandingofpatternsofneural power grid. The resulting simulation-based optimization
activity. In this talk I will describe how to build tractable problemshavedifferentcharacteristicsthanclassicalprob-
tissue level models that maintain a strong link with bio- lemsandusuallyrequiredifferenttheoreticalassumptions.
physical reality. These models typically take the form of In this talk, I will discuss challenges one faces when solv-
nonlinear integro-differential equations. Their non-local ingtheseoptimizationproblemsandwhatrolestheoryand
nature has led to the development of a set of analytical practice play in developing new algorithms. I will present
and numerical tools for the study of waves, bumps and severaltechniquesforsimulation-basedoptimizationprob-
patterns, based around natural extensions of those used lems and some lessons learned in applying theory to prac-
for local differential equation models. Here I will present tical problems.
an overview of these techniques.
Juan C. Meza
Stephen Coombes Lawrence Berkeley National Laboratory
University of Nottingham [email protected]
[email protected]
IC7
IC4 Combinatorics Inspired by Biology
The Parallel Revolution in Computational Science
Mathematicshasplayedanimportantroleinbiology,both
as a useful language for modeling biological phenomena,
AN09 Abstracts 5
and in the tools it provides for data analysis. The flood software in the Towards Optimal Petascale Simulations
of data that is now emerging from the transformation of (TOPS)project,withemphasisonhowsuchsoftwarepro-
biology into a high-throughput science makes mathemat- vides robust, scalable, and extensible capabilities that are
ics particularly relevant for biologists at this time. In this increasingly important for multimodel and multiphysics
talk we will not emphasize the role of mathematics in bi- simulations on emerging high-performance architectures.
ology, but rather we focus on the impact biology has had
on mathematics. Using a few key examples that are well Lois Curfman McInnes
knowntobiologists(butmaybenotasmuchtomathemati- Argonne National Laboratory
cians), we will highlight a few key ideas in combinatorics Mathematics and Computer Science Division
that were inspired by biologists. [email protected]
Lior Pachter
University of California, Berkeley IC11
Dept. of Mathematics Some Stochastic Control Problems in Mathemati-
[email protected] cal Finance
We formulate a class of stochastic control problems, col-
IC8 lectivelyknownundertherubricofportfoliooptimization,
Modeling Cancer-Immunology Dynamics that arise in the mathematics of finance. Ideas from con-
vex duality play a prominent role in their resolution; so
Immunotherapy, a treatment approach that enhances the do parabolic partial differential equations, under strong
body’snaturalabilitytofightcancers,isbecomingincreas- conditions on the financial market structure. Under less
ingly prevalent in many multi-stage treatment programs stringent conditions, stochastic analogues of the classical
thatalsoincludechemotherapy,radiationandsurgery. The Hamilton-Jacobi-Bellman equation emerge as particularly
critical importance of the immune system in combating relevant in this context, in connection with results from
cancerhasbeenverifiedbothclinicallyandthroughmath- backwards stochastic equations and the Ito-Wentzell for-
ematical models. In this talk, we will discuss the biologi- mula for random fields. Using such tools, feedback formu-
cal and mathematical sides of the question of how cancer lae become available for the investors optimal strategies,
grows, how the cancer interacts with the immune system, based on his current level of wealth. Recent progress on
and treatment approaches that harness the power of the theseissueswillbesurveyed,andsomeopenquestionswill
immune system. be mentioned.
L.G. de Pillis Ioannis Karatzas
Harvey Mudd College Columbia University
[email protected] [email protected]
IC9 IC12
Controlling Lagrangian Systems by Active Con- Parallel Network Analysis
straints
We consider methods for the parallel solution of graph-
The talk will survey past and recent work on the stabi- based and combinatorial problems arising in the design of
lization and control of mechanical systems, by imposing sensor networks or the analysis of social networks. While
a number of time-dependent, frictionless constraints. The some aspects of these applications have obvious partitions
basic mathematical description involves a Riemann man- with ”embarrassing” parallelism, the lack of locality when
ifold, together with a foliation describing the constraints. searching through graph neighborhoods has historically
Theequationsofmotionusuallyhaveanimpulsivecharac- made parallelization of graph algorithms difficult. A new
ter,containingthetimederivativesofthecontrolfunctions. generation of massively multithreaded parallel computers
Their analytical form is closely linked to the geometrical is well suited for algorithms with significant memory la-
structureofthefoliation. Weobservethatthissameframe- tency,providedthereissufficienttotalparallelism. Wewill
workcanalsobeusedtostudyswim-likemotionofoneor discuss algorithmic techniques for solving graph problems
more deformable bodies in a perfect fluid. on such architectures including a powerful primitive origi-
nallydevelopedfortheConnectionMachineCM-2andLa-
Alberto Bressan grangian techniques originally developed for low-memory
Pennsylvania State University PCs.
[email protected]
Cynthia Phillips
Sandia National Laboratories
IC10 [email protected]
Parallel Implicit Nonlinear Solvers in Large-Scale
Computational Science
IC13
Parallelimplicitsolutionstrategieshaveprovenrobustand Progress Toward a Stability Proof for Scott Rus-
efficient in resolving challenging nonlinearities in many sell’s Solitary Wave
large-scale PDE-based simulations. We discuss the use of
preconditioned Newton-Krylov methods for parallel appli- A classic story of nonlinear science started with the
cations in coupled core-edge plasma and multiphase reac- particle-like water wave that Russell famously chased on
tive flow, with emphasis on capabilities in the PETSc li- horseback in 1834. Nowadays the theory of solitons in
brary that enable users to leverage domain-specific legacy integrable PDE is highly developed and nonlinear pulses
code and to exploit library-provided functionality for compete for a prominent role in optical communications
sparse derivative computations and scalable precondition- technology. Yet the dynamics of many nonlinear waves
ers. Wehighlightcomplementarycapabilitiesofadditional remain rather ill-understood. I will recount progress re-
6 AN09 Abstracts
garding the robustness of solitary waves in nonintegrable IP0
model systems such as FPU lattices, and discuss a draft W. T. and Idalia Reid Prize in Mathematics Lec-
proof (with Shu-Ming Sun) of spectral stability of small ture: The Moment Problem for Positive Rational
solitary waves for the 2D Euler equations for water of fi- Measures: Convexity in the Spirit of Krein
nite depth without surface tension.
The moment problem as formulated by Krein and
Robert L. Pego Nudel’man is a beautiful generalization of several impor-
Carnegie Mellon University tantclassicalmomentproblems. However,theimportance
Department of Mathematical Sciences of rational functions in systems and control and other
[email protected] engineering applications imposes certain complexity con-
straints. In this talk we present a new formulation of the
moment problem which respects these constraints. While
IC14
this version of the problem is decidedly nonlinear, the ba-
OntheComplexityofGame,Market,andNetwork sic tools still rely on convexity. In particular, we present
Equilibria a solution in terms of a convex optimization problem that
generalizesthemaximumentropyapproachusedinseveral
As you may have already known, the notion of the Nash
classical special cases.
equilibrium has captured the imagination of much of the
computer science theory community, both for its many Anders Lindquist
applications in the growing domain of online interactions Royal Institute of Technology
andforitsdeepandfundamentalmathematicalstructures. Dept Optimization & Syst Thry
As the scale of typical internet applications increases, the [email protected]
problemsofefficientlyanalyzingtheirgame-theoreticprop-
erties become more pointed. I will discuss some of our re-
cent results in settling several open questions about Nash IP0
equilibria of matrix games and Arrow-Debreu equilibria I.E. Block Community Lecture: “Kill All The
of exchange markets. I will also address the extensions Quants?”: Models vs. Mania In The Current Fi-
of these results to other equilibrium problems that arise nancial Crisis
in collaborative games and in the game-theoretic stud-
ies of the Internet BGP protocols. Joint work with Xi As the shockwaves of the financial crisis of 2008 propa-
Chen (Princeton), Xiaotie Deng (The City University of gate throughout the global economy, the “blame game”
HongKong);alsowithLi-ShaHuang(GoogleChina),Paul has begun in earnest, with some fingers pointing to the
Valiant(MIT),KyleBurke(BostonUniversity),ShivaKin- complexity of certain financial securities, and the mathe-
tali (Georgia Tech), Laura J. Poplawski (Northeastern), matical models used to manage them. In this talk, I will
RajmohanRajaraman(Northeastern),andRaviSundaram review the evidence for and against this view, and argue
(Northeastern). that a broader perspective will show a much different pic-
ture. Blaming quantitative analysis for the financial crisis
Shanghua Teng is akin to blaming E = MC2 for nuclear meltdowns. A
Boston University & Akamai Technologies moreproductivelineofinquirymightbetolookdeeperinto
[email protected] the underlying causes of financial crisis, which ultimately
leads to the conclusion that bubbles, crashes, and mar-
ketdislocationareunavoidableconsequencesofhardwired
IP0
human behavior coupled with free enterprise and modern
AWM-SIAMSoniaKovalevskyLecture: Swarming capitalism. However, even though crises cannot be legis-
by Nature and by Design latedaway,therearemanywaystoreducetheirdisruptive
effects, and I will conclude with a set of proposals for reg-
Thecohesivemovementofabiologicalpopulationisacom-
ulatory reform.
monly observed natural phenomenon. With the advent of
platforms of unmanned vehicles, such phenomena has at- Andrew Lo
tractedarenewedinterestfromtheengineeringcommunity. MIT
This talk will cover a survey of the speaker’s research and [email protected]
relatedworkinthisarearangingfromaggregationmodels
innonlinearPDEtocontrolalgorithmsandrobotictestbed
experiments. Weconcludewithadiscussionofsomeinter- IP0
esting problems for the applied mathematics community. Past Presidents Address: Parallelism and Puzzles
Every talk that Ive given at a SIAM meeting for the past
Andrea L. Bertozzi 30 years has included some material about parallel com-
UCLA Department of Mathematics puting. Thistalkwillbenoexception. Inaddition,Iwant
[email protected] to demonstrate some of our Experiments with MATLAB
project intended for younger students.
IP0 Cleve Moler
The John Von Neumann Lecture The MathWorks, Inc
[email protected]
To follow.
Franco Brezzi IP0
Universita Di Pavia
Theodore Von Karman Prize Lecture: Compu-
Italy
tational Environments for Coupling Multiphase
[email protected]
Flow, Transport, andGeomechanicsinPorousMe-
AN09 Abstracts 7
dia for Modeling Carbon Sequestration a theory which is based on Fourier and Laplace transform
which gives us the desired information about the solution
GeologicsequestrationbyinjectionofCO2intodeepbrine and apply it to the earlier mentioned equations.
aquifers and reservoirs represents one of the most promis-
ing approaches for reducing atmospheric CO2. A key goal Heinz-Otto Kreiss
of our work is to produce a prototypical computational Ehrensvardsgatan, 3
system to accurately predict the fate of injected CO2 in [email protected]
conditions governed by multiphase flow, rock mechanics,
multi-component transport, thermodynamic phase behav-
ior, chemical reactions within both the fluid and the rock, JP1
andthecouplingofallthesephenomenaovermultipletime Semi-smooth Newton Methods in Function Spaces
and spatial scales. We present a ”wish list” for simulator and Applications to Variational Problems in Opti-
capabilitiesanddescribealgorithmsandsoftwarebeingde- mal Control and Imaging
veloped at UT-Austin.
Non-differentiablevariationalproblemsariseindiversear-
Mary F. Wheeler eas of current interest, as for instance in optimal con-
Center for Subsurface Modeling trol governed by partial differential equations with con-
University of Texas at Austin straintsonthecontrolsorthestate,inmathematicalimag-
[email protected] ing with bounded variation (BV) type regularization or
sparsity constraints, in mathematical finance, and control
of variational inequalities. At first, second order New-
IP1 ton type methods appear to be out of scope, and there-
Computational Geosciences: A Perspective from fore (conjugate-) gradient methods are often used to solve
Geological Basin Modeling such problems in practice. Exploiting the special struc-
ture, however, frequently Newton-differentiability can still
The modeling of geological processes operating in a time- be ascertained. This guarantees super-linear convergence
scale of millions of years during the formation and evolu- of Newton-type methods. In case Newton-differentiability
tion of sedimentary basins is formidable challenge due to fails this is a phenomenon of the infinite dimensional set-
itsmutiphysics,multiscale,andcomputationalcharacteris- ting and can be remedied by a regularization process. For
tics. InthispresentationIwilldiscusstheissuesrelatedto the choice of the regularization parameter a model-based
mathematical modeling, simulation, data analysis, uncer- path-following strategy is proposed.
tainty,andhighperformanceparallelcomputing,fromthe
basinmodelingperspectivewithanhistoricalangle. Basin Karl Kunisch
modeling is an essential tool for the understating the for- Universitat Graz
mation of major mineral and hydrocarbon resources. Institut fuer Mathematik
[email protected]
Ulisses Mello
IBM Watson Research Center
[email protected] CP1
Possibly New Methods for Evaluating Bessel Inte-
grals and Series
IP2
InitialBoundaryValueProblemsforSecondOrder KnownresultsofintegralsandseriesinvolvingBesselfunc-
Systems of Partial Differential Equations tions currently avaliable in handbooks, but we found no
recourse in the well- known refferences to how they were
Problemsconcernedwithwavepropagationintwoorthree established. In the first part of this paper we introduce
spacedimensionsareoftenformulatedintermsofsystems a possibly new method for evaluating Bessel integrals by
ofwaveequationswhichwehavetosolvenumerically. Ex- identifying a certaint type of differential equations. In the
amplesareMaxwell’sequations,elasticwaveequationsand secondpartofthispaperwesuggestapossiblynewMethod
Einstein’s equation of general relativity. We want to solve for evaluating a class of schlomilch type series. The paper
the initial boundary value problems for t ≥ 0 in a finite concludes by indicating the wide range of results that can
domainΩinspacewithasmoothboundaryΓ.Att=0we be established.
giveinitialconditionsandonΓboundaryconditionswhich
are either Diriclet conditions or relations between normal Ali A. Al-Jarrah
and tangential derivatives. The most desirable properties Dean of Information Technology and Computer Science
for these problems is that there is an energy estimate and Delmon University, Kingdom of Bahrain
that the problem is stable against lower order perturba- [email protected], [email protected]
tions. The usual way to prove the existence of an energy
estimateisbyintegrationbyparts. Thisisalwayspossible Saad Z. Darwish
fortheCauchyproblemandproblemswithDiricletbound- Vice President for academic Affairs
aryconditions. Inthesecasesthenumericalsolutionposes Delmon University
relatively few difficulties. Physical phenomena like glanc- saad [email protected]
ingorsurfacewavesleadtoderivativeboundaryconditions
which are not maximally dissipative. The energy estimate
doesnotgiveusadetailedunderstandingaboutthebehav- CP1
iorofthesolutionneartheboundarywhichisdesireableto Physical Modeling, Field Oriented Control Analy-
develop numerical techniques. By solving a Cauchy prob- sis of An Ac Machine
lem we can reduce the data such that only the boundary
conditionsareinhomogeneous. Also,therequiredstability ThisworkdealswiththestudyofMaxwell’sequationsaris-
estimates are such that we can reduce the discussion to ing by creation of electromagnetic fields in an electric ma-
halfspaceproblems. Forhalfspaceproblemswewilldiscuss chine which could be a transformer or an Induction ma-
8 AN09 Abstracts
chine. Thestructureofthesetwomachinescouldbesimilar CP1
thoughbehaviorinsomesensemaynotbesame. Forexam- Polygons and Circles in Computational Science
pleInductionmachinecanbeusedforadesignwhichsolely
requiresforheatingpurpose. Thetransformermaybeused The area between a unit circle and an inscribed n-sided
totransferlargeamountofpower,voltage. Inpresentcase regularpolygonisnothardtocompute. Whatisimportant
weconsiderthemachinewindingsforhomogeneousornon- is that this “change in area” gives the leading term in the
homogeneousmediumwithDirichletandMixedBoundary difference in the eigenvalues of the Laplacian for polygons
conditions. Westudytimeindependentequationsfirstand and circles. This leads to a practical suggestion for the
compare it with time dependent equations. Many cases eigenvalue problem (and for other problems too): Let the
of time dependent as well as time independent Rotor and polygongooutsidethecircleenoughtohavethesamearea.
Statorequationsforthreephasemachineshavebeenstud- Then the error from changing to a polygon and creating
ied before. A comparison of exact solutions to numerical a mesh and solving by finite elements is much reduced.
solutions is established for different layers of transformer (ThenexttermintheeigenvalueerrorwasfoundbyPavel
windingsunderdifferentstructure. Wefurtherlookforex- Grinfeld and it involves the Riemann zeta function...)
tra stator losses and eddy currents produced and the loss
of power. A Power-current or skin depth plot and that Gilbert Strang
Torque-skin depth plot will be done to find out how to Massachusetts Institute of Technology
control and minimize the power loss and increase amount [email protected]
of torque required to start the machine or stop the ma-
chine in no time by using transient analysis and classical
CP1
NYQuist and Bode plots. In other words we find torque
to be controlled b filed oriented control. An example is Four Bugs on a Rectangle
underconsiderationthatwilldepicthowequationsandso-
Four bugs start at t=0 at the vertices of a 2x1 rectangle.
lutionsbehavedifferentlyindifferentmedia/materialswith
Eachonechasesthebugtoitsleftwithspeed1. What’sthe
respecttopowerandtorquecontrol. Theanalysisisbeing
shapeoftheensuingspiral? Youmaythinkthissoundslike
donebyusingcombinationofsoftware. TheseareFemlab,
a problem made famous by Martin Gardner in Scientific
Mat-lab and Simulink and SCILAB.
American, but it is remarkably different because of the
Kumud S. Altmayer rectangular initial condition. This talk will describe the
Ashford University bugs’ extraordinary paths with the help of some unusual
Dept. of Math. Sc. asymptotic analysis, joint work with James Lottes and S.
[email protected]; kumud [email protected] J. Chapman. By the time the first circuit of the origin is
completed, the scale of the configuration has shrunk by a
factor of exp(exp(25))!
Kamran Iqbal
University of Arkansas
Lloyd N. Trefethen
Little Rock
Oxford University
[email protected]
Oxford University Compting Lab
[email protected]
CP1
Numerical Conformal Mappings onto the Linear CP2
Slit Domain
Modeling Framework for Fluid-Solid Mixtures Us-
ingDistinctPhasesandtheMaterialPointMethod
We propose a numerical method for the conformal map-
pingofunboundedmultiply-connecteddomainsexteriorto
Partiallyandfullysaturatedporousmediahavebeenare-
closed Jordan curves onto a canonical linear slit domain,
searchfocusforseveraldecades. Themostcommonsimula-
which is a generalization of the well-known parallel slit
tionapproachesarebasedonhomogenizationtechniquesto
domain. The method is based on the charge simulation
obtaincontinuum-likeformulationsenrichedby,e.g.,pres-
method (the fundamental solution method), and gives a
sure variables for embedded fluid phases. While proven
simple form of approximate mapping functions with high
very successful for solid dominated problems, such models
accuracy.
present tough challenges as the mixture undergoes a tran-
sition from solid-like to fluid-like behavior. The present
Dai Okano, Kaname Amano
paper proposes to model solid and fluid phases as distinct
Graduate School of Science and Engineering
matterusingspecializedparticlesforeachphasewithinthe
Ehime University
framework of the material point method (MPM). Mixture
[email protected], [email protected]
behaviorisobtainedbyintroducingdragtermsformomen-
tum transfer and a volume constraint to assess the effect
Hidenori Ogata
of confining pressure in fully saturated media. The paper
Graduate School of Electro-Communications
presents the basic ingredients which, in combination with
The University of Electro-Communications
the established MPM, will yield a generic framework for a
[email protected]
widevarietyofproblemsincorporatingfluid-solidmixtures.
Masa-Aki sugihara Peter Mackenzie-Helnwein
Graduate School of Information Science and Technology Department of Civil and Environmental Engineering
The University of Tokyo University of Washington
m [email protected] [email protected]
Pedro Arduino, Wookuen Shin, Gregory Miller
University of Washington
[email protected], [email protected],
AN09 Abstracts 9
[email protected] Department. of Mathematical Sciences
New Jersey Institute of Technology
[email protected]
CP2
Theory of Particle Heat Transfer in Gas-Solid Sys-
tems Applied to Discrete Element Methods (dem) CP2
Free Boundary Problem for a Supercavitating
There are various theories for calculating the heat trans- Wedge
fer in particles of gas-solid systems. A brief review of
these concepts along with the advantages and disadvan- Motion of a yawed supercavitating wedge under a free
tages surrounding their incorporation into a discrete ele- surface and in a jet of an ideal liquid is analyzed. The
ment method (DEM) model are presented. Tulin-Terent’ev cavity closure mechanism and the theory
of Riemann surfaces are used for the description of the
Jordan M. Musser, Mary Ann Drumright-Clarke flow around the cavity. A conformal map from a plane
Department of Mathematics with two cuts into the doubly connected flow domain is
West Virginia University constructed by solving two Riemann-Hilbert problems on
[email protected], [email protected] a genus-1 Riemann surface.
Anna Zemlyanova, Yuri A. Antipov
CP2 Louisiana State University
Fluid Structure Control Interactions For Coupled Department of Mathematics
Problems [email protected], [email protected]
The problem of efficient modeling and simulation of the
interaction of fluid with a solid undergoing nonlinear de- CP3
formation has remained a challenging problem in compu- Nonlinear Breathing Modes at a DNA Defect Site
tational science and engineering. The purpose of this talk
is to introduce a computational methodology using finite We develop a stochastic mesoscopic model of a DNA du-
elements that offers the flexibility and efficiency to study plex, with parameters fitted to AMBER data for different
coupledproblemsinvolvingfluid-structureinteraction. An twistangles(intherange30◦-40◦). Witha’rogue’difluoro-
Arbitrary Lagrangian-Eulerian (ALE) formulation is used toluenebaseatthedefectsite,breathingevents-thetem-
tomovethemeshateachtimestep. Thisapproachavoids porary breaking of bonds between complementary bases -
excessive deformation of the mesh near the fluid-structure occur more frequently, that is, on the nanosecond time-
interface that may occur due to transient dynamic loads. scale. We discuss fluctuation-dissipation relations, energy
Numerical computations will be presented to validate the barriers,thepotentialofmeanforceandpotentialenergies
performanceofthemethodforbenchmarkapplicationsin- in reduced models.
volving fluid-structure interaction. Theoretical and com-
putationalperformanceofsuchproblemsformulatedasop- Ciprian I. Duduiala
timal control problems will also be presented. Centre for Mathematical Medicine and Biology,
School of Mathematical Sciences, University of
Kumnit Nong Nottingham
George Mason University [email protected]
[email protected]
Jonathan Wattis
School of Mathematical Sciences
CP2
University of Nottingham
Efficient Numerical Computation of Fluid Inter- [email protected]
faces with Soluble Surfactant
Ian Dryden
Weaddressasignificantdifficultyinthenumericalcompu-
University of Nottingham
tationoffluidinterfaceswithsolublesurfactantthatoccurs
[email protected]
in the practically important limit of very large values of
bulk Peclet number Pe. At the high values of Pe in typi-
calfluid-surfactantsystems,thereisatransitionlayernear Charles Laughton
the interface in which the surfactant concentration varies School of Pharmacy
rapidly, and its gradient at the interface must be deter- University of Nottingham
mined accurately to find the drop’s dynamics. Accurately [email protected]
resolving the layer is a challenge for traditional numerical
methods. We present recent work that uses the slender-
CP3
ness of the layer to develop a fast and accurate ‘hybrid’
numerical method that incorporates a separate analytical A Dynamical Model of Exit From Mitosis in Bud-
reductionofthedynamicsinthetransitionlayerintoafull ding Yeast
numerical solution of the interfacial free boundary prob-
ExitfrommitosisrequiresactivationofCdc14,anessential
lem.
phosphatasepromotingmitoticexit. Wehavedevelopeda
Michael Siegel deterministic ODE model for the control of Cdc14 release
Department of Mathematical Sciences as the cells exit from mitosis. Our model provides a rigor-
New Jersey Institute of Technology ousaccountofthefactorsaffectingthedualexitpathways,
[email protected] called FEAR and MEN. The model captures the dynam-
icsofmitoticexitinwild-typeandmutantcells, including
many details of the physiology, biochemistry and genetics
Michael Booty
10 AN09 Abstracts
of the process. CP3
Mathematical Study of Islet Bursting and the De-
Baris Hancioglu
pendenceontheCytoarchetecturalOrganizationof
Virginia Polytechnic Institute & State University
Iset Cells
[email protected]
We report our mathematical development to study the
Kathy Chen spatial-temporal regulation of insulin release from pan-
VIRGINIA POLYTECHNIC INSTITUTE & STATE creatic islet beta cells. An islet can be mathematically
UNIVERSITY modeled as a networks of nonlinear oscillators (beta cells)
[email protected] coupled through gap junctions and various chemicals, and
the robust oscillatory insulin release is an emergent phe-
John J. Tyson nomenon. Using both ODE and PDE systems, we study
Virginia Poly Inst & St Univ the synchronization, pattern formation, wave front prop-
Department of Biology agation and noise-induced orders in the islet of coupled
[email protected] non-linear stochastic systems, and from the results derive
mathematical models of beta-cell function
CP3 Xujing Wang
University of Alabama at Birmingham
EmergentDynamicsGovernedbyRegulatoryCells
[email protected]
Produce a Robust Primary T Cell Response
Several theories exist concerning primary killer T cell re-
CP3
sponses,themostprevalentbeingthatTcellsfollowdevel-
opmentalprograms. Weproposethealternativehypothesis TheStochasticSimulationoftheFtsZRingAssem-
that the response is governed by a feedback loop between bly and Contraction
conventionalandregulatoryTcells. Bydevelopingamath-
In a previous research, a biochemical reaction network is
ematicalmodel,weshowthattheregulatedresponseisro-
developedtosimulatetheassemblyandcontractionofthe
bust to a wide variety of parameters and propose that T
FtsZ ring. We investigate its stochastic behavior since
cellresponsesmaybegovernedbyemergentgroupdynam-
numbersoflongopenpolymersandclosedringsaremostly
ics rather than by autonomous programs.
small(¡10). Amodifiednextreactionmethodisused. The
Peter S. Kim resultsarecomparedwiththoseobtainedwithdeterminis-
University of Utah tic model. For the assembly process, the two simulations
Department of Mathematics onlyshowsmalldifference. However,qualitativedifferences
[email protected] appear for the contraction process.
Zhigang Zhang
Peter Lee
Department of Mathematics
Stanford University
University of Houston
School of Medicine
[email protected]
[email protected]
Doron Levy CP4
University of Maryland A Differential Equation/agent-Based Hy-
[email protected] brid Model of Antibiotic-Resistant Infection in a
Hospital Ward
CP3 Whenmodelingthespreadofbacterialinfectionsinapopu-
Dynamic Bayesian Network Modeling of Gene Ex- lation, dynamics occur on two levels: Interaction between
pression Data the people in the ward, and the bacterial growth taking
placeinsideinfectedwardmembers. Weproposeamethod
We report our recently developments in network model- forcombiningbothintoasinglemodel,whereeachperson
ing of gene expression data using the dynamic Bayesian is treated as an agent in an agent-based system, with the
networkapproach. Thisincludesincorporatingexistingbi- agent-specific dynamic parameters driven by a differential
ological information (co-citation, GO similarity, positional equationssystemthatmodelsthewithin-hostbacterialdy-
and binding information, etc) as prior knowledge, fuzzy namics for that agent.
theory-based rules to the MCMC learning of DBYN, def-
inition of gene expression (phase) synchronization module Lester Caudill, Barry Lawson
and utilization of it it to assist initial network structure University of Richmond
construction,etc. Weshowthattheseleadtosignificantly [email protected], [email protected]
improvedperformance,throughapplicationtothemicroar-
ray study of pancreatic development.
CP4
Xujing Wang The Estimation of the Effective Reproductive
University of Alabama at Birmingham Number from Disease Outbreak Data
[email protected]
We consider a single outbreak susceptible-infected-
Shouguo Gao recovered (SIR) model and corresponding estimation pro-
Dept of Physics cedures for the effective reproductive number R((cid:3)). We
University of Alabama at Birmingham discuss the estimation of the underlying SIR parameters
[email protected] with a generalized least squares (GLS) estimation tech-
nique. We use asymptotic statistical theories to derive
AN09 Abstracts 11
the mean and variance of the limiting sampling distribu- Georgetown University
tion and to perform post statistical analysis of the inverse [email protected]
problems. We illustrate the ideas and pitfalls with both
synthetic and influenza incidence data sets.
CP4
Ariel Cintron-Arias Competition and Disease Dynamics in Multi-
North Carolina State University Species Interactions
Center for Research in Scientific Computation
[email protected] It has been shown that disease can modulate competition
between multiple host species and can be a major factor
Carlos Castillo-Chavez in invasion by exotic species. We model and analyze the
Arizona State University and dynamics of multi-host communities using Lotka-Volterra
Department of Mathematics full competition, which affects birth rates of species, and
[email protected] Susceptible-Infected disease dynamics, to understand how
the forces of inter-specific infection and competition com-
binetoallowinvasionbyexoticspecies. Forthecaseoftwo
Luis Bettencourt
speciesweanalyzethediseasefreeequilibriumforstability
Computer and Computational Science
andforthecaseofdiseasetransmissionviafrequencyinci-
Los Alamos National Laboratory
dence we consider the stability of the endemic coexistence
[email protected]
equilibrium. We also extend some threshold values to the
case of multiple species.
Alun Lloyd
North Carolina State University Carrie A. Manore, Vrushali Bokil
alun [email protected] Oregon State University
[email protected],
H.T. Banks [email protected]
North Carolina State University
CRSC
[email protected] CP5
A Uniqueness Question Relating to Thermo-
Acoustic Tomography and Reconstruction in the
CP4 Radially Symmetric Case
Spatial Propagation of Alleles in a Human Popula-
tion Anewresultpertainingtoamostlyunexploreduniqueness
question in thermo-acoustic tomography is presented. We
Weseektomodelthespatialpropagationofallelesthrough demonstrate a partial answer to the question, If u1(x,t)
apopulationusingmodifiedFisher-KolmogorovEquations and u2(x,t) satisfy
inoneandtwodimensions. Wewillpresentpreliminaryre-
sultsofourinvestigationintotheanalysisandsimulationof ∂t2u1−c21(x)Δu1 =0 in Rn×R+
solutions to our model. We will also discuss our investiga- ∂t2u2−c22(x)Δu2 =0 in Rn×R+
tionintotheinverseproblemofidentifyingthepropagation
speed as well as geographic barriers to migration. We ap- u1(x,0),u2(x,0)∈C0∞(D),
n
ply our mathematical model to study allele distributions ∂tu1(x,0)=0=∂tu2(x,0) in R
in human populations. u1(x,t)=u2(x,t) on ∂D×R+
Jason F. Hammond, David M. Bortz thenisc1(x)=c2(x)inD? Weusetherelationofthewave
University of Colorado equationtotheHelmholtzequationanddecayestimatesfor
Department of Applied Mathematics the wave equation to show that uniqueness of the sound
[email protected], [email protected] speed is connected to the interior transmission problem.
Techniques for the reconstruction of the sound speed and
Noah Rosenberg initial impulse in thermo-acoustic tomography are shown
University of Michigan for a radial symmetric problem.
Dept. of Human Genetics
[email protected] Kyle S. Hickmann
Oregon State University
[email protected]
CP4
A Coalescent Analysis of Genetic Statistics Used
CP5
in Population Subdivision Inference
Conditional Well-Posedness for An Elliptic Inverse
Populations are often divided into subpopulations. Biol- Problem
ogists use various statistics formed from genetic data to
infer migration rates between subpopulations. In this talk The inverse elliptic equation −∇·(p(x)∇v)+λq(x)v =
we consider such statistics under a certain class of evolu- f, x ∈ Ω ⊂ Rn, is important in groundwater modeling.
tionary models. We use coalescent theory to derive the The problem of determining when one or more of the co-
distribution of a certain subset of such statistics. We then efficientfunctionsp,q,andf dependscontinuouslyonthe
useourresultstocommentonanimportantquestion: Can solution functions v = vp,q,f,λ is considered. We establish
the shape of a subdivided population be determined from conditions required for weak-L2(Ω) continuity of q and f
genetic data? and ∇v-weak L2(Ω) continuity of p, given H1(Ω) continu-
ity of v.
Sivan Leviyang
Mary A. Larussa, Ian Knowles
12 AN09 Abstracts
University of Alabama at Birmingham CP6
[email protected], [email protected] Capillary Gravity Surface Waves by a Positive
Forcing
CP5 Weconsiderforcedsurfacewavesonanincompressible,in-
Multilevel Domain Decomposition Algorithms for viscid fluid in a two-dimensional channel with a small ob-
Inverse Elliptic Problems structiononahorizontalrigidflatbottomarestudiedwhen
surfacetensionisconsidered. Thewavemotiononthefree
We investigate scalable multilevel domain decomposition surface is determined by a nondimensional wave speed F,
algorithms for solving inverse elliptic problems formulated called Froude number, and F=1 is a critical value of F. If
as optimization problems constrained by partial differen- F=1 + lambda with lambda ¿0 a small parameter, then
tial equations. To solve these optimization problems, we a time-dependent forced Korteweg de Vries (FKdV) equa-
employ a fully coupled Lagrange-Newton-Krylov-Schwarz tion can be derived to model the wave motion on the free
algorithm. One of the key steps in the algorithm is the surface. Here, the case F ¿ 1, called supercritical case, is
Jacobian preconditioning, for which we study and com- considered. The solutions of KdV equation with positive
pare four types of two-level domain decomposition meth- forcingarestudiedtheoriticallyandnumericallywithzero
ods. Our numerical results show that the algorithms work or nonzero initial conditions .
well for different types of observations in terms of the ac-
curacy of the solution, and some of the algorithms scale Jeongwhan Choi
better than the others when the number of processors is Korea University
large. We also study and report the sensitivity of the al- Dept of Mathematics
gorithms with respect to the jumps of the coefficients, the [email protected]
level of noise in the observed data, the size of the compu-
tational domain, the size of the mesh, and the number of Sungim Whang
processors. NIMS
[email protected]
Si Liu
Department of Applied Mathematics
University of Colorado, Boulder 80309-0526 CP6
[email protected]
An All-Speed Asymptotic-Preserving Method for
the Isentropic Euler Equations
CP5
In low-Mach number flows, compressible solvers require
Recovering Doping Profiles in Semiconductor De- high resolution in space and time due to the presence of
vices with the Boltzmann-Poisson Model fast acoustic waves. We propose a semi-implicit splitting
of the isentropic Euler equations that formulates the fast
In inverse problem of semiconductor devices, one intends
termsasanimplicitlinearsystem,whichcanbecomputed
to identify device doping profile from measurement of the
with a Poisson solver, and computes the slow terms ex-
device characteristics. The problem has been extensively
plicitly. This method is stable for any Mach number, and
studied in the past decade. We present in this talk some
captures the correct incompressible limit at the discrete
analytical and numerical studies of the doping profile re-
level.
covering problem based on the Boltzmann-Poisson model
forelectrontransportinsemiconductors. Wewillmakede- Jeffrey R. Haack
tailednumericalcomparisonbetweenreconstructionsbased Department of Mathematics
theBoltzmann-Poissonmodelandthosebasedonthedrift- Univsersity of Wisconsin-Madison
diffusion model. [email protected]
Kui Ren
Shi Jin
University of Texas
Department of Mathematics
[email protected]
University of Wisconsin-Madison
[email protected]
CP5
Numerical Recovery of a Boundary Condition in Jian-Guo Liu
An Inverse Sturm-Liouville Problem University of Maryland
USA
It is well known that spectral data consisting of an eigen- [email protected]
valuesequenceandassociatednormingconstantsuniquely
determines a potential in a Sturm-Liouville problem, to-
gether with one of the boundary conditions in the direct CP6
problem. However numerical approaches to the inverse Large-Eddy Simulation of Turbulent Combustion
Sturm-Liouville problem which have been developed tend
to regard all boundary conditions as known. In this talk I In recent years, large-eddy simulation (LES) has been in-
willdiscussmodificationofaparticularnumericalapproach creasingly and successfully applied to both premixed and
to allow for an unknown boundary condition. An applica- non-premixed reacting flows . The present research con-
tion to the inverse Sturm-Liouville problem for a singular cerns the numerical prediction of turbulent swirling react-
potential will be given. ingflows,usingthelarge-eddysimulation(LES)approach.
ThestudyshowsthatLEStogetherwithalaminarflamelet
Paul E. Sacks model provides a good prediction of the structure of tur-
Iowa State University bulent swirling flames, involving vortex breakdown, flow
[email protected]
AN09 Abstracts 13
instability, and the occurrence of localized extinction. inmanyengineeringapplications,particularlyinoptimiza-
tion. The algorithm augments the Krylov subspace with
Marcel Ilie a proper orthogonal decomposition subspace that approx-
University of California San Diego imately minimizes the orthogonal projection error of the
Department of Mechanical and Aerospace Engineering solution, thereby accelerating convergence.
[email protected]
Kevin T. Carlberg, Charbel Farhat
Stanford University
CP6 [email protected], [email protected]
A High Order Compact Navier-Stokes Solver on
Non-Rectangular Domains
CP7
In the present paper, we develop a fourth order compact EffectsofBoundaryConditionsonPreconditioning
finite difference method for solving the biharmonic formu- Strategies for the Navier-Stokes Equations
lationoftheNavier-Stokes(N-S)equations. Thisformula-
tion, which makes use of conformal mappings can be used Block preconditioners for the linearized Navier-Stokes
on geometries beyond rectangular. It is tested on three equations have shown great potential as the basis of ef-
different problems, namely, (i) fluid flow in a constricted ficient iterative solution algorithms. In the derivation of
channel, (ii) driven polar cavity and (iii) flow past an im- these techniques, boundary conditions have not played a
pulsively started circular cylinder. The scheme is seen to prominentrole. Weshowthatboundaryconditionscanbe
captureveryefficientlythesteady-statesolutionsoftheN- used to construct improved preconditioners by improving
S equations with Dirichlet as well as Neumann boundary the quality of certain commutators used in the derivation.
conditions. We present our numerical results and validate A new, Robin, condition for preconditioners for problems
thembycomparingwithestablishednumericalandexperi- with velocities satisfying inflow boundary conditions leads
mentalresultsavailableinliterature. Excellentcomparison to dramatically improved performance.
is obtained in all the cases.
Howard C. Elman
Jiten C. Kalita University of Maryland, College Park
Indian Institute of Technology Guwahati [email protected]
Guwahati INDIA
[email protected] Ray S. Tuminaro
Sandia National Laboratories
Shuvam Sen Computational Mathematics and Algorithms
Tezpur University [email protected]
INDIA
[email protected]
CP7
Parallel Algorithms for Sparse Matrix Inverse and
CP6 Sparse Linear Systems
Mass Flow and Thermal Transfer in a Wide Chan-
nel: a Variational Approach to Solve a a Free Computingsparsematrixinverseiscriticalinmanyappli-
Boundary Problem cations including quantum transport in nano-devices. We
proposetwoparallelalgorithmsforsuchapplicationsbased
Atacertainlocationofachannel,waterispumpedoutcon- onideasfromcyclicreduction,dynamicprogramming,and
tinuously (sink, as coolant. The heated water is dumped nested dissection. They are the first parallel algorithms
backtothechanelatafurtherlocationalongtheflowdirec- withsignificantspeedupfor2Ddevicesandalsofasterthan
tion (source). The minimum distance between source and other parallel algorithms for 1D devices. A similar paral-
sinkthatinsureswatertempraturesteadiness,inthesense lel algorithm for sparse linear systems with repeated right
thattempratureatthesinkdoesnotrise,isfoundbysolv- hand sides with significant speedup was also developed.
ingafreeboundaryproblem,usingvariationaltechniques.
Validityoftheresultsischeckedbyfinitedifferencesmeth- Song Li
ods. Institute for Computational and Mathematical
Engineering
Sadia M. Makky Stanford University
Owens Community College [email protected]
sadia [email protected]
Eric F. Darve
Ali Ghalib Stanford University
Post Buck Schuh and Jernigan Inc. Mechanical Engineering Department
amghalib@pbs&j.com [email protected]
CP7 CP7
A Proper Orthogonal Decomposition-Based Aug- A Novel Sparse Linear System Solver
mented Conjugate Gradient Algorithm for Nearby
Problems Weproposeahybridsparsesystemsolverforhandlinglin-
earsystemsusingdomaindecomposition-basedtechniques.
A novel augmented conjugate gradient algorithm is pre- The scheme implicitly imposes an overlapped block diag-
sented for the fast solution of consecutive linear systems onal structure on the matrix. Using a modified iterative
of equation of the form Aixi = bi, where Ai are nearby method a balance system is solved and an adjustment of
symmetric positive definite matrices. Such systems arise theright-hand-sideisfoundsuchthatthesolutionofadja-