Anita T Layton, Assistant Professor

Contact Info:

Office Location:	213 Physics
Office Phone:	(919) 660-6971
Email Address:
Web Page:	http://www.math.duke.edu/~alayton

Teaching (Fall 2012):

• MATH 476S.01, SEM MATHEMATICAL MODEL Synopsis

  Physics 205, TuTh 11:45 AM-01:00 PM

Education:

PhD	University of Toronto	2001
MS	University of Toronto	1996
BS	Duke University	1994
BA	Duke University	1994

Specialties:

Applied Math

Research Interests: Mathematical physiology; Multiscale numerical methods; Numerical methods for immersed boundary problems.

Mathematical physiology. My main research interest is the application of mathematics to biological systems, specifically, mathematical modeling of renal physiology. Current projects involve (1) the development of mathematical models of the mammalian kidney and the application of these models to investigate the mechanism by which some mammals (and birds) can produce a urine that has a much higher osmolality than that of blood plasma; (2) the study of the origin of the irregular oscillations exhibited by the tubuloglomerular feedback (TGF) system, which regulates fluid delivery into renal tubules, in hypertensive rats; (3) the investigation of the interactions of the TGF system and the urine concentrating mechanism; (4) the development of a dynamic epithelial transport model of the proximal tubule and the incorporation of that model into a TGF framework.

Multiscale numerical methods. I develop multiscale numerical methods---multi-implicit Picard integral deferred correction methods---for the integration of partial differential equations arising in physical systems with dynamics that involve two or more processes with widely-differing characteristic time scales (e.g., combustion, transport of air pollutants, etc.). These methods avoid the solution of nonlinear coupled equations, and allow processes to decoupled (like in operating-splitting methods) while generating arbitrarily high-order solutions.

Numerical methods for immersed boundary problems. I develop numerical methods to simulate fluid motion driven by forces singularly supported along a boundary immersed in an incompressible fluid.

Areas of Interest:

Mathematical physiology
Scientific computing
Multiscale numerical methods
Fluid-structure interactions

Curriculum Vitae

Current Ph.D. Students  

• Hwayeon Ryu  
• Ioannis Sgouralis  
• Yi Li  

Postdocs Mentored

• Aniel Nieves-Gonzales (January 1, 2011 - present)  
• Natasha Savage (October 18, 2010 - present)  
• Karin Leiderman (August 01, 2010 - present)  
• Jing Chen (March 1, 2009 - May 14, 2010)  
• Elizabeth L. Bouzarth (August 1, 2008 - July 31, 2011)  
• Amal El Moghraby (July 1, 2008 - May 31, 2009)  
• Milagros Loreto (August 01, 2007 - August 31, 2008)  

Recent Publications   (More Publications)

1. Gene Hou, Jin Wang, and Anita T. Layton, Numerical methods for fluid-structure interaction – a review, Comm Comput Phys, vol. 12 (2012), pp. 337-377
2. Anita T. Layton and J. Thomas Beale, A partially implicit hybrid method for computing interface motion in Stokes flow, Discrete and Continuous Dynamical Systems B, vol. 17 (2012), pp. 1139-1153
3. Anita T. Layton, John Stockie, Zhilin Li, and Huaxiong Huang (editors), Fluid Motion Driven by Immersed Structures, A special issue of Commun Comput Phys, vol. 2 (2012)
4. Anita T. Layton, Philip Pham, and Hwa-Yeon Ryu, Signal transduction in a compliant short loop of Henle, Int J Numer Methods Biomed Eng, vol. 28 no. 3 (2012), pp. 369-380
5. Natasha S. Savage, Anita T. Layton, and Daniel J. Lew, Mechanistic mathematical model of polarity in yeast, Mol Biol Cell, in press (Accepted, 2012)

Recent Grant Support

• Modeling Solute Transport and Urine Concentrating Mechanism in the Rat Kidney, National Institutes of Health, 2010/08-2015/07.      
• EMSW21-RTG: Enhanced Training and Recruitment in Mathematical Biology,, National Science Foundation, 2010/07-2015/07.      
• EMSW21-RTG: Enhanced Training and Recruitment in Mathematical Biology, National Science Foundation, DMS-0943760, 2010/09-2014/08.      
• Mathematical Model of Vascular and Tubular Transport in the Rat Outer Medulla, National Institutes of Health, 2009/07-2013/06.      
• Modeling Fluid Dynamics and Solute Transport in Modeling Fluid Dynamics and Solute Transport in the Kidney, National Science Foundation, 2007/08-2011/07.      
• Workshop on Fluid Motion Driven by Immersed Structures: Analysis, Computation, and Applications, National Science Foundation, 2010/08-2011/07.      
• FAN 2010: Conference on Fluid dynamics, Analysis and Numerics, National Science Foundation, 2010/04-2011/03.