
NSF Org: |
DMS Division Of Mathematical Sciences |
Recipient: |
|
Initial Amendment Date: | February 7, 2011 |
Latest Amendment Date: | February 7, 2011 |
Award Number: | 1056471 |
Award Instrument: | Standard Grant |
Program Manager: |
Pedro Embid
DMS Division Of Mathematical Sciences MPS Directorate for Mathematical and Physical Sciences |
Start Date: | July 1, 2011 |
End Date: | June 30, 2016 (Estimated) |
Total Intended Award Amount: | $438,133.00 |
Total Awarded Amount to Date: | $438,133.00 |
Funds Obligated to Date: |
|
History of Investigator: |
|
Recipient Sponsored Research Office: |
845 N PARK AVE RM 538 TUCSON AZ US 85721 (520)626-6000 |
Sponsor Congressional District: |
|
Primary Place of Performance: |
845 N PARK AVE RM 538 TUCSON AZ US 85721 |
Primary Place of
Performance Congressional District: |
|
Unique Entity Identifier (UEI): |
|
Parent UEI: |
|
NSF Program(s): | APPLIED MATHEMATICS |
Primary Program Source: |
|
Program Reference Code(s): |
|
Program Element Code(s): |
|
Award Agency Code: | 4900 |
Fund Agency Code: | 4900 |
Assistance Listing Number(s): | 47.049 |
ABSTRACT
Fatkullin
DMS-1056471
The investigator addresses problems in liquid-crystalline and bacterial systems related to formation, evolution, and interaction of singularities and defects. Such singularities manifest themselves in mathematical equations when the underlying physical models lose validity on a given scale. To study such systems, one must connect often quite disparate physical models arising at different length and time scales. The investigator employs a combination of modern analytical and numerical methods introduced by him for the Onsager model of nematic liquid crystals and Keller-Segel model of bacterial chemotaxis. In particular, he investigates liquid-crystalline systems such as polydisperse and biaxial nematics, smectics, and elastomers; phenomenon of formation and interaction of particle aggregates in bacterial chemotaxis. He creates the Multiphysics Modeling Lab: a center for research and education in methods of mathematical modeling and computer simulations. This establishes a collaborative environment involving students at the University of Arizona as well as (utilizing the close connection of the investigator with the Tucson Math Circle) the local K-12 students in projects on modeling and simulation of complex systems.
The fundamental significance of the areas of this project has been widely recognized, e.g., by a Nobel Prize awarded in 1991 to P.-G. de Gennes for fundamental contributions to our understanding of order phenomena in complex systems, and by a Microsoft Award in 2006 to D. Bray for his work on chemotaxis on E. coli. The practical applications of the project range from liquid-crystalline display (LCD) technology to understanding the functioning of our immune system. Recently, the analytical and numerical methods employed in the investigations of such systems have matured enough to allow for new significant advances in these fields. Achieving this is the primary scientific goal of this project. Beyond that, the interdisciplinary nature of this program is perfect for illustrating the power of mathematics in describing diverse natural phenomena and is suitable for involving students of all levels. The Multiphysics Modeling Lab involves graduate and undergraduate students in active applied mathematics research and promotes mathematics and science among the K-12 students and educators via close integration with the system of math circles. Such activities are essential for improving the general level of scientific education in our society.
PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH
Note:
When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external
site maintained by the publisher. Some full text articles may not yet be available without a
charge during the embargo (administrative interval).
Some links on this page may take you to non-federal websites. Their policies may differ from
this site.
PROJECT OUTCOMES REPORT
Disclaimer
This Project Outcomes Report for the General Public is displayed verbatim as submitted by the Principal Investigator (PI) for this award. Any opinions, findings, and conclusions or recommendations expressed in this Report are those of the PI and do not necessarily reflect the views of the National Science Foundation; NSF has not approved or endorsed its content.
The PI addressed problems in liquid-crystalline and bacterial systems related to formation, evolution, and interaction of singularities, defects, and aggregates. In particular, the PI investigated the singular structures in liquid-crystalline films, and derived simple reduced equations governing their motion. The PI analyzed the internal structure of defect cores in nematic liquid crystals and classified the emerging hedgehog/biaxial torus type structures for a wide range of system parameters. Further on, the PI developed a complete theory describing distribution of cluster sizes in aggregation models relevant to the aforementioned systems, and related these models to limit shapes of Young diagrams and partitions of integers. The PI also supervised a PhD thesis of G. Zhelezov, who studied stochastic particle systems describing formation and interaction of particle aggregates in bacterial chemotaxis. These studies lead to a new class of numerical methods for solving partial differential equations exhibiting blow-ups via modeling coalescing stochastic particle systems.
The PI has been organizing educational activities involving postdocs, graduate, undergraduate, and K-12 students. Two graduate students, C. Xie, and G. Zhelezov have finished their theses with the support of the grant. Undergraduate students, V. Bhargava, D. Baldwin, and J. Abrams have been involved in research projects on modeling and analysis of neuronal systems, interacting particles, and traffic flows. Additionally, the PI is supervising the Tucson Math Circle bringing together students and postdocs from the University of Arizona and local K-12 students. The grant provided support to M. McCormick-Stone, who has been the Tucson Math Circle leader during 2012-2016 period. All in all, over the course of last five years, Tucson Math Circle has been a friendly and stimulating environment for discussing mathematics and science for several dozens of local students of all levels.
Last Modified: 09/28/2016
Modified by: Ibrahim Fatkullin
Please report errors in award information by writing to: awardsearch@nsf.gov.