The Center for Theoretical & Mathematical Sciences (CTMS) is pleased to invite applications from Duke Graduate students for a unique interdisciplinary fellowship in Applied Mathematics or Theoretical Science. Fellowships will provide support (stipend and tuition remission) for Spring and Summer 2010. Two fellowships will be awarded at this time. Applications for Summer/Fall 2010 and Spring/Summer 2011 will be announced in early 2010.

The purpose of these fellowships is to support graduate students whose research interests bridge those of faculty advisors in two different disciplines. Applicants may request support for a short term (e.g. one semester) project for which traditional support is not available, or for a more typical thesis-directed project. Applicants must be PhD students.

The critical requirement for the fellowship is that the project establish a link between advisors in different academic departments, one or more of whom will provide mathematical or theoretical expertise and training. It is generally expected that one of the involved supervisors is in a department in Arts & Sciences. Each application requires a cv, a description of the student’s project or research program, and letters of commitment of intellectual support for the specific research program from two faculty members under whose guidance the research and/or training will be performed. No other fellowship, RA-ship or TA support may be held concurrent with this award.

Deadline for applications is November 16, 2009 with award announcements on December 1, 2009 for fellowship support to begin on January 1, 2010. Please apply at Academic Jobs Online https://academicjobsonline.org/ajo/Duke/CTMS/245. Faculty members may upload letters of commitment directly to the site. For questions, please contact Jennifer Foreman, jennifer.foreman@duke.edu, (919) 684-8802.

Location: 2231 French Family Science Center

Time: 4:30pm

Abstract: Turbulence is sometimes call the “last unsolved problem of classical mechanics”. While it has long been understood that the details of turbulent flow are essentially unpredictable beyond a number of Lyapunov times due to the so-called “Butterfly effect”, hope remains for a comprehensive statistical description of turbulence. Two developments in dynamical systems theory over the past twenty years provide solid foundation for that hope. The first is the observation, placed on firm foundation in the 1980s, that Navier-Stokes flow has a finite-dimensional attracting set of states. The second is the development of the dynamical zeta function formalism by Ruelle, and its deployment by Cvitanovic, Pollicott, Eckhardt, Yorke and others, enabling statistical descriptions of chaotic dynamical systems, given knowledge of their unstable periodic orbits (UPOs). For this reason, the efficient numerical computation of UPOs has gained great importance over the past decade, in both the dynamical systems and turbulence literature. Periodic orbits for high-dimensional state spaces are devilishly difficult to calculate, requiring high-performance computing and placing new demands on algorithms, accuracy and hardware. This talk will discuss some of these computational challenges and demonstrate the successful computation of UPOs of driven Navier-Stokes turbulence in two spatial dimensions.

Date: Friday, November 13, 2009

Venue: Duke University

Organizers: Mauro Maggioni, Sayan Mukherjee

Location: Social Sciences 136 (morning session), Physics 128 (afternoon session)

For abstracts of the lectures, click here.

Please register for the workshop here.

Schedule

LOCATION: Social Sciences 136
08:30 Breakfast
08:50 - 09:00 Introduction
09:00 - 09:45 Anna Gilbert
09:50 - 10:35 Steve Marron
10:35 - 10:55 Break
10:55 - 11:30 Rachael Brady
11:30 - 12:15 Jack Silverstein

12:15 - 13:15 Lunch

LOCATION: Physics 128
13:15 - 14:00 Larry Carin
14:00 - 14:45 Andrea Montanari
14:45 - 15:10 Break
15:10 - 15:55 Michael Mahoney
15:55 - 16:40 Andrew Nobel
16:40 - 17:30 Discussion

Location: 4219 French Family Science Center

Time: 1:00 - 2:00 pm

Abstract: Studies of viral evolution have traditionally been both pathogen and host specific. Determining how a specific virus x evolves in a specific host population y is of course an important avenue of research. However, we are now at a point in time when we can synthesize across these research findings to identify general patterns of viral evolution and what processes shape them. An effective approach towards the identification of these general patterns and processes requires more than listing specific examples and qualitatively categorizing them - it requires a quantitative framework. Here, we detail the development of one possible framework, by deriving a dimensionless number to understand patterns of viral evolution and the processes driving them. We also describe an alternative to this dimensionless number approach. This is work in progress, so feedback on which approach is more effective and why would be very useful at this stage.

This work is in collaboration with Virginia Pasour (former Biology post-doc) and Jonathan Mattingly (Math).

Location: 4219 French Family Science Center

Time: 1:00 - 2:00 pm

Abstract: This talk will focus on the statistical, mathematical, and computational challenges in modeling complex phenotypes given high-dimensional data. The problem will be motivated based on practical problems in targeting cancer. Approaches to this problem will be discussed. A focus on stochastic aspects of geometric and probabilistic modeling will be emphasized.

October 23, 2009 — 8:30am - 5:00pm

Location: Duke University, Thomas Center, Glaxo Classroom

For (preliminary) program details, please visit the Retreat page.

Location: 4219 French Family Science Center

Time: 1:00 - 2:00 pm

Abstract: Fermions are naturally described in terms of statistical mechanics of loops with the caveat that the Boltzmann weight is not necessarily positive definite. This strange type of statistical mechanics is at the heart of quantum mechanics and has hindered the application of the Monte Carlo method to the physics of fermions. In this talk I will argue that in fact taking quantum interference seriously suggests a more natural approach to the problem and leads to new Monte Carlo algorithms for fermions which are more natural than what is currently available.

Location: 4219 French Family Science Center

Time: 1:00 - 2:00 pm

Abstract: Networks of binary elements interacting through Boolean rules can exhibit complex dynamics and may provide useful models for biological and physical systems (gene regulation and high-speed electronic circuits). In developing such models, a crucial issue is the update scheme used to implement the Boolean logic. In autonomous Boolean networks (ABNs), the timing of updates is determined by time delays assigned to each link. I will discuss some general features of ABNs and describe two applications of current interest here at Duke.

Location: 4219 French Family Science Center

Time: 1:00 - 2:00 pm

Abstract: We discuss current research in the characterization and role of cell dynamics in tissue in the fruit fly embryo. During the fruit fly embryo’s development, two flanking tissues in the shape of an eye are brought together via a third force-producing tissue (amnioserosa) in a process called Dorsal Closure. From confocal images we can follow cell shapes, more specifically, cross-sectional areas of the cells that comprise the amnioserosa. Dorsal Closure occurs over a couple of hours, during which these cells are gradually removed from the tissue as these cells are programmed to undergo a cell death (apoptosis). In addition to their transient existence, these cells exhibit faster time scale oscillations (on the order of minutes) in what is well accepted as a Low Reynolds environment. This is strongly suggestive of the existence of an active biological process. How these fast, cell level oscillations effects the larger scale tissue dynamics is an open research question and requires a physical and mathematical approach to solve. The talk will cover a brief explanation of the biological framework and the segmentation of confocal images to lead into our efforts to characterize the dynamics of the cells in tissue. The talk will end with a discussion of future research which will include a mapping of the force fields of the tissue and an attempt to approximate parameters of the inverse problem.

Workshop on

Theory and Applications of Multi-Scale Modeling

Friday, September 11, 2009

Saturday, September 12, 2009

Organizing Committee: Harold Baranger (Physics), Robert Behringer (Physics), Patrick Charbonneau (Chemistry), Katia Koelle (Biology), Jonathan Mattingly (Mathematics), James Nolen (Mathematics), Tom Witelski (Mathematics)

For abstracts of the lectures, click here.

Schedule:

FRIDAY, SEPTEMBER 11

LOCATION: Von Canon A room, lower level of the Bryan University Center

9:15 - 9:30

Welcome, Introduction, Coffee.

9:30 - 10:15

Effective field theories and multiple scales in quantum physics
Thomas Mehen (Duke University, Physics)

10:15 - 10:30

Break

10:30 - 12:00

Modeling the dynamics of immune responses and infections
Rustom Antia (Emory University, Biology)

12:00 - 1:00

Lunch and discussion

1:00 - 1:30

Combining the molecular with the ecological: modeling the dynamics of rapidly-evolving viruses
Katia Koelle (Duke University, Biology)

1:40 - 2:10

Soft dynamical systems and gene expression
Thomas Kepler (Duke University, Biostatics and Bio-informatics)

2:10 - 2:40

Break

2:40 - 4:10

Multiscale simulations of solvated biomolecules
Jerzy Bernholc (North Carolina State University, Physics)

4:10 - 5:00

Discussion

SATURDAY, SEPTEMBER 12

LOCATION: 130 Physics Building

9:00 - 10:30

“Consistency” between atomistic and coarse-grained models
William Noid (Pennsylvania State University, Chemistry)

10:30 - 10:50

Break

10:50 - 11:20

Multiscale modeling of catalysis in chemistry and biology
Weitao Yang (Duke University, Chemistry)

11:30 - 12:00

Controlling numerical dissipation and time stepping in some multi-scale fluid simulations
Jian-Guo Liu (Duke University, Physics and Math)

12:00 - 1:00

Lunch and discussion

1:00 - 2:30

Coarsening in cellular systems
David Kinderlehrer (Carnegie Mellon University, Mathematical Sciences)

2:30 - 2:50

Break

2:50 - 3:20

A molecular renormalization group approach to connecting simulations at different length scales
Garegin Papoian (University of North Carolina at Chapel Hill, Chemistry)

3:30 - 4:00

Design and modeling of nucleic acids nanomaterials
Yaroslava Yingling (North Carolina State University, Materials Science)

4:00 - 4:30

Discussion