Annual Report 2008.pdf - SAMSI

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elastic structure is described on a Lagrangian coordinate system while the velocity and incompressibility of the fluid are described by the incompressible Navier-Stokes equations on the Eulerian coordinate system. There are different ways of charactering the visco-elastic body motion in the fluid. One approach is the immersed-boundary method (IB) developed by Peskin(1972) to simulate cardiac mechanics and associated blood flows. Another approach is the material point method (MPM) developed by Harlow(1957) and Sulsky(1996). Taking the advantage of an efficient framework of a public C++ software package IBAMR developed by Griffith(2007), I am able develop a new program of IB method to simulate complex fluid with linear-elastic structure in the domain with complex boundaries, multiple initial configurations, and the problem-specific spring force of the elastic structure. Alternatively, the parallel implementation of MPM is also accomplished in the framework of IBAMR with some modifications. By testing different models for various problems using efficient numerical packages, I intend to seek the optimal numerical methods for simulating complex fluids. Publications, Work in Preparation 1. Parallel implementation of material-point method for linear visco-elastic models, in preparation. Working Group II Interface problems Research Areas Numerical Approximations of generalized functions Collaborators & Mentor: Patrick Guidotti and Hongkai Zhao We study a general recipe for high-order approximation of generalized functions which is based on the use of L2-orthonormal bases consisting of C^inf-functions and the appropriate choice of a discrete quadrature rule. Although the local value of a function and its action as a linear function on test functions cannot be known at the same time with high accuracy in general, namely the “numerical uncertainty principle”, we can still obtain the high-order accurate point-wise approximations from a high accuracy distributional approximation. We apply this new family of high-order schemes for the 1D/2D elliptic interface problems to gain the high-order accuracy in the presence of discontinuities and singularities. Publications, Work in Preparation 2. High-order schemes for generalized functions in elliptic interface problems, in preparation. High-order Numerical Schemes for Hyperbolic-elliptic Mixed Systems Collaborator & Mentor: Zhilin Li I study a fluid mixture model of tissue deformations with a mixed system of nonlinear hyperbolic and elliptic PDEs. The tissues are considered to consist of an aqueous phase and a cell-fiber phase. Our research targets at simulating tissue deformations numerically for the 1D model by employing the high-order central WENO schemes for the hyperbolic equations and the standard central finite difference schemes for the elliptic equations. In the presence of the shock discontinuities that the hyperbolic equation may develop in the time evolution, the regular highorder central WENO schemes can only maintain first-order accuracy in the shock region, which makes it a challenging job to achieve high-order accuracy for this coupled elliptic-hyperbolic system. We employ the immersed-interface method to solve the elliptic equations to obtain the high-order accuracy near the interfaces. For the solutions of the hyperbolic equations, instead of the regular Riemann solver, we utilize the shock-capture mechanism near the shock discontinuities to maintain the high resolution of the shock profile, which guarantees high-order
accuracy of the solutions. Some preliminary results of the one-dimensional scalar problem discover the solutions with very high resolution in the shock regions. Publications, Work in Preparation 3. High-order numerical schemes for 1-D fluid mixture model of tissue deformations, in preparation. Other Research Papers from Ph.D. Research: Energy-preserving and stable approximations for two-dimensional shallow water equations. Submitted to the proceedings of the Abel Symposium 2006, Springer. Presentations: Entropy-stable approximations of 2-D Shallow Water Equations (Tentative)
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NSF Annual Report 2007-2008 Submitt
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Education and Outreach • 2-Day Wo
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C. Directorate’s Summary of Chall
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National Leadership and Involvement
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D. Synopsis of Developments in Rese
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the efficient treatment of complex
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c) RANDOM MEDIA Much of the work of
Page 15 and 16: 2. Human Resource Development SAMSI
Page 17 and 18: [it] from time to time.” (M. Rose
Page 19 and 20: Undergraduate Workshops 2007-08 Sum
Page 21 and 22: 3. Education The impact of SAMSI co
Page 23 and 24: The working group Climate and Weath
Page 25 and 26: oundary method as a means to impose
Page 27 and 28: assumed full responsibility for the
Page 29 and 30: I. Annual Progress Report The previ
Page 31 and 32: Kazi Ito NCSU Mathematics Ralph Smi
Page 33 and 34: 2007-08 Sensor Networks Transition
Page 35 and 36: Environmental Sensor Networks Progr
Page 37 and 38: Yang Yu Zhang Zhong Zhu Jun Bin Yi
Page 39 and 40: Mattingly McKinley Minion Mitran Ng
Page 41 and 42: Cheng Choi Clark Cooley Das Das Del
Page 43 and 44: Ren Resnick Rios Cuirong Sidney Jes
Page 45 and 46: Rosenblum Rotnitzky Scharfstein Sun
Page 47 and 48: B. Postdoctoral Fellows This sectio
Page 49 and 50: Administrative Mentor: Michael Mini
Page 51 and 52: We consider modeling multiple risk
Page 53 and 54: 1. Statistics Department Seminar, C
Page 55 and 56: Presentations: Change of Spatiotemp
Page 57 and 58: Presentations: “Some Thoughts on
Page 59 and 60: Theory for multiple change-point se
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Page 63 and 64: “Work on numerical large deviatio
Page 65: contributing team member, as often
Page 69 and 70: Continuing Collaborations: Helen Zh
Page 71 and 72: 7 th World Congress in Probability
Page 73 and 74: N/A 9. Other Research while at SAMS
Page 75 and 76: Risk analysis (multivariate extreme
Page 77 and 78: Jesus Rios Plans for 2008-10 I will
Page 79 and 80: Communication: --a consistent, time
Page 81 and 82: C. Graduate Student Participation 1
Page 83 and 84: Elijah Gaioni (University of Connec
Page 85 and 86: Xiaoyan’s thesis work is on devel
Page 87 and 88: Jason Wilson (Duke) is involved in
Page 89 and 90: Ilka A. Reis (National Institute fo
Page 91 and 92: 4. Challenges in Dynamic Treatment
Page 93 and 94: 4.5 Program Activities The program
Page 95 and 96: which held morning and afternoon se
Page 97 and 98: • B. Carlin (Biostatistics, Unive
Page 99 and 100: Also following from the program, se
Page 101 and 102: 4.11 Summary of Exciting Research a
Page 103 and 104: interested students and faculty, an
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Page 107 and 108: Cherokee Investment Partners, Const
Page 109 and 110: G. Publications and Technical Repor
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• Krishnapur, M., Zeitouni, O., R
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• Hou, S., K. Huang, K. Solna, an
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• Das, S., “Analyzing Fatal Dri
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H. Diversity Efforts SAMSI puts con
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(University of Utah) and Natallia K
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2007-08 Random Media Opening Worksh
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2. Affiliate Involvement 2.1 Backgr
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J. Advisory Committees Committee Na
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Institute directors agree to inform
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analysis of DNA and protein sequenc
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University), Jeremy Gunawarden (Har
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Many problems and existing simulati
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Carolina), Gareth Peters (New South
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actually replace individual analyse
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effect parameter of interest prior
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with structures that are not tempor
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about confidence in results. Furthe
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2. Stochastic Dynamics 2.1 Overview
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Michael Reed (Mathematics, Duke), G
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These two approaches, through the u
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• Li Lexin (North Carolina State
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At NCAR, Boulder, Colorado and orga
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SAMSI working groups. Participation
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certain distances, be used to captu
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subject to the l 1 constraint. Zou
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3. Breiman, L. (1996): Heuristics o
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enabled high virtual attendance by
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(b) Estimation of large random matr
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We have already discussed problems
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Appendix C. Workshop Participant Li
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Sanso Bruno Male University of Cali
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Compmod New Methods and Case Studie
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El Karoui Nourredine Male UC Berkel
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Education and Outreach Program SAMS
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Sutton Karyn Female NCSU Mathematic
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Lin Rongheng Male U Mass Biostatist
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Geometry and Statistics of Shape Sp
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Heo Giseon Female Hirani Anil Male
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Pennec Xavier Male Pike Brian Male
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Yasamin Saeid Male Yezzi Anthony Ma
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Daum Keith Male Idaho National Labo
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Langstaff John Male Laurey Terri Fe
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Sedransk Nell Female NISS Statistic
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Risk PPP Workshop Workshop Particip
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Rezaei Mahmoud Male Clemson Mathema
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Lysenko Natalia Female ETH Zurich S
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Biondini Gino Male State U New York
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Khatri Shilpa Female Courant Instit
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Spiller Elaine Female SAMSI Mathema
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Interface Workshop Workshop Partici
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Cheney Margaret Female Rensselaer P
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Agarwal Ankit Male U Kansas Enginee
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Lahiri Soumendra Male Texas A & M U
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Last Name SAMSI/CRSC Industrial Mat
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Reale- Levis Jim Male NCSU Engineer
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Gray William Male U. North Carolina
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Serban Nicoleta Female Georgia Inst
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Brotherson Temitope Female NJ Scien
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Frink Kaiem Male Elizabeth City Sta
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Jones Dana Female Bennett College f
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Munoz Breda Female RTI Internationa
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Smith Ralph Male NCSU Mathematics F
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Undergraduate Two-Day Workshop Part
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Schmidt Courtney Female Georgetown
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Schaeffer Amanda Female U Arizona M
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Presentation Chris Snyder, NCAR/MMM
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Chair of Afternoon Session Tom Sant
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1:00-2:15 Lunch Chair of Afternoon
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“Calibration of a Numerical Model
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model. The output is functional dat
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santner.1@osu.edu “Optimization o
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greatly from the active support of
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“Blind Kriging: a New Method for
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10:00-10:30 Break Characterizing th
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— hist_pie.m — hist_pie_exercis
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9:00 Presentations and Discussion
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11:25-11:55 From Population to Indi
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4:00 - 5:30 Shapes in Medical Imagi
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4:15 - 4:45 Discussion Panel Wednes
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dcremers@cs.uni-bonn.de “Shape In
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We will construct epsilon entropy e
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Department of Statistics flb@stat.w
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University of California Los Angele
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2:45 - 3:15 Break N. D. Shyamal Kum
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2:15 - 4:00 Working Group Formation
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and public health questions; little
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Howard Kunreuther University of Pen
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series. We propose a specific class
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Interface Tracking in Connection to
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Purdue University Center for Comput
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of the solution. Here we reveal a s
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of the grand challenges of science.
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numerical approach. Several example
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Biofilms are complicated, living co
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Knut Solna University of California
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This poster presents an analysis of
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X. Program on Risk Analysis, Extrem
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SPEAKER ABSTRACTS Chair: David Bank
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Thoughts on the Use of Decision Ana
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Bias Correction in Pharmaceutical R
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In the talk we will discuss some mo
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Stephen Sain, National Center for A
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Concha Gomez, University of Wiscons
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Iris Mack, Phat Math, Inc. and Flor
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8:15 - 8:45 Continental Breakfast a
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coordinate grids on the surface. To
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University of California, Irvine De
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overall a good agreement between im
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9:00-9:05 Alan Karr, National Insti
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3:30 - 4:00 Coffee Break Soumen Lah
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“Experiences in Developing an Eco
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Jennifer Hoeting Colorado State Uni
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kogle@uwyo.edu “Data-Model Integr
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“Compression and Analysis of Gold
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"A Cost-Efficient Approach to Wirel
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The main goal of a data collection
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Wednesday, January 23, 2008 Radisso
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“Robust Prediction Error Criterio
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one of the main sources of uncertai
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other. A core problem is how to inf
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"The Asymptotic Structure of Nearly
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SAMSI madar@post.tau.ac. “Bayesia
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11:30 - 12:00 Discussion Session 12
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garnier@math.jussieu.fr “Wave Pro
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has lagged. While it is quite clear
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Appendix E - Workshop Evaluations E
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E.2 Evaluation of Scientific Conten
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E.3 Evaluation of Staff Percent of
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E.5 Evaluation of Lodging Evaluatio
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