Lefschetz Center for Dynamical Systems Seminar
PLEASE NOTE CHANGE OF ROOM AND LOCATION FOR TODAY ONLY! |
Abstract:
Tremendous advances have been made in cataloguing
the structures and motifs of genetic regulatory networks.
However, our understanding of the implications of these
structures on the dynamic response of the network is more
limited. I will discuss our efforts to build a simple scalable
model based on the Nitrogen Catabolite Repression (NCR)
circuit in Saccharomyces cerevisiae and provide a mathematical
analysis of its dynamics. In particular,I will touch on five
topics:
1) An introduction to the biology
2) Comments on mathematical results that allow one to make
statements about the dynamics of a system without detailed
knowledge of the nonlinear interactions of the system.
3) Our model and its comparison with experimental data.
4) Mathematical theorems about the asymptotic behavior of a
sub-circuit of the NCR circuit.
5) Some tantalizing numerical results.
==========
Brown University -
Joint Materials/Solid Mechanics Seminar Series
FAMU-FSU College of Engineering, Florida State University, Tallahassee, FL | |
Carbon Nanotube Reinforced Composites | |
Abstract: Interfaces can be defined as regions of separation between two different bodies. While these regions span a few microns in conventional composites, carbon nanotube (CNT) based composites exhibit interfaces at nanoscale. The basic issue raised here is, how the mechanics at nanoscale interface differs from that of the conventional micron scale interfaces. Surface modifications to CNTs are manifested as chemical attachments, and these alter the base CNT and composite properties. A number of CNT-matrix interfaces that differ from each other in terms of geometry and chemical bonds are studied under tension, compression and pull-out loading conditions. Some interesting observations unique to nanoscale interfaces are presented. We primarily use molecular dynamics based on Tersoff-Brenner bond order potential to simulate the problem.
Cognitive & Linguistic Sciences
Spring 2005 Colloquium and CG233 Speakers
Stochastic Systems Seminar
Cancelled and Rescheduled to Tuesday, February 22, 2005
Brown Analysis Seminar
Applied Mathematics Colloquium
Abstract: Smoluchowski's equation is used to describe the coagulation-fragmentation processes macroscopically. Microscopically clusters of various sizes coalesce to form larger clusters or fragment into smaller ones. I describe how from a stochastic model of interacting Brownian particles one can derive the Smoluchowski's equation in a scaling limit. I also formulate a conjecture regarding the nature of the fluctuations of the particle densities about the solutions to the Smoluchowski's equations.
Scientific Computing Seminar
Abstract: The dynamics of fibers immersed in a fluid are important to understanding many interesting problems arising in biology, engineering, and physics. In many applications, the fibers have large aspect ratios (length over radius), ranging from order 10 to a thousand for natural to synthetic fibers, and up to many thousands in biological settings.
The main challenge for a numerical method lies in its ability to include many fibers in the simulation, at a reasonable cost, while maintaining accuracy. This is difficult to achieve with grid based methods, partly due to the different scales in length and radius of the fibers.
In our formulation of the problem, we make explicit use both of the fact that we are considering Stokes flow, as well as of the slenderness of the fibers. The key points are that for Stokes flow, boundary integral methods can be employed to reduce the three-dimensional dynamics to the dynamics of the two-dimensional filament surfaces, and that using slender body asymptotics, this can be further reduced to the dynamics of the one-dimensional filament centerlines. The resulting integral equations include both the effect of the fibers on the flow field, as well as the interactions of fibers, as mediated by the flow.
We have developed a cost-effective numerical method based on this theory that allows for simulating highly flexible fibers in a three dimensional Stokes flow. Our numerical approach is based on second-order divided differences for spatial derivatives, combined with special product integration methods that reflect the nearly singular nature of the integral operators.
In the case of rigid fibers, the constraint in the motion of the fibers can be exploited in the development of the numerical method, even further enhancing the effectiveness of the method. The forces on the fibers are expanded on Legendre polynomials, in order to take advantage of a diagonalization result applicable to the modified Stokeslet operator present in the slender body equations.
We present illustrative numerical results for the dynamics of a single flexible fiber, for many interacting fibers, set within background shearing flows, and for rigid fibers sedimenting under the force of gravity.
Department of Mathematics Colloquium
<--- 2005 Index