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 2009):

• MATH 107.01, LINEAR ALGEBRA & DIFF EQUATION Synopsis

  Old Chem 116, TuTh 10:05 AM-11:20 AM

• MATH 107.02, LINEAR ALGEBRA & DIFF EQUATION Synopsis

  Old Chem 116, TuTh 11:40 AM-12:55 PM

• MATH 388.03, RESEARCH IN DIFF EQUATIONS

  Physics 227, MW 10:05 AM-11:20 AM

Office Hours:

Tue 9:00-10:00am; Thur 1:00-2:00pm

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 global atmospheric models

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 global atmospheric models. I have also been involved in the development and analysis of high-order numerical methods for weather prediction and climate modeling problems. I have developed numerical methods based on high-order splines and on double Fourier series in space, and combined these methods with a semi-Lagrangian semi-implicit time-stepping method. These methods were successfully tested using the shallow water equations, which have been used for decades by the atmospheric community as a testbed for promising numerical methods. I plan to apply the deferred correction approach to equations arising in global atmospheric models.

Areas of Interest:

Mathematical physiology
Scientific computing
Multiscale numerical methods
Global atmospheric models

Curriculum Vitae

Current Ph.D. Students  

• Yi Li  

Postdocs Mentored

• Jing Chen (March 01, 2009 - present)  
• Elizabeth L. Bouzarth (August 01, 2008 - present)  
• Amal El Moghraby (July 01, 2008 - present)  
• Milagros Loreto (August 01, 2007 - August 31, 2008)  

Undergraduate Researches Supervised

• M. Hallen (May 01, 2008 - April 01, 2009)
  Thesis: Expanding the scope of quantitative FRAP analysis 

Recent Publications   (More Publications)

1. Jing Chen, Aurelie Edwards, and Anita T. Layton, Effects of pH and medullary blood flow on oxygen transport and sodium reabsorption in the rat outer medulla, Am J Physiol Renal Physiol, submitted (Submitted, 2009)
2. Milargros Loreto and Anita T. Layton, An optimization study of a mathematical model of the urine concentrating mechanism of the rat kidney, Math. Biosci., in press (Accepted, 2009)
3. Anita T. Layton, Yusuke Toyama, Guo-Qiang Yang, Glenn S. Edwards, Daniel P. Kiehart, and Stephanos Venakides, Drosophila morphogenesis: tissue force laws and the modeling of dorsal closure, HFSP, in press (Accepted, 2009)
4. Anita T. Layton, Using integral equations and the immersed interface method to solve immersed boundary problems with stiff forces, Comput. Fluids., vol. 38 (2009), pp. 266-272
5. J. Thomas Beale and Anita T. Layton, A velocity decomposition approach for moving interfaces in viscous fluids, J. Comput. Phys., vol. 228 (2009), pp. 3358-3367

Recent Grant Support

• 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, 2007/08-2010/07.      
• Mathematical Model of Vascular and Tubular Transport in the Rat Outer Medulla, National Institutes of Health, 2008/07-2009/06.      
• A Conference on Applications of Analysis to Mathematical Biology, National Science Foundation, 2007/05-2008/04.      
• Conferece on Applications of Analysis to Mathematical Biology, Arts and Sciences Committee on Faculty Research, 2006/11-2007/07.      
• NSF Graduate Support Supplement, National Science Foundation, DMS-0539136, 2006/06-2007/06.      
• NSF ADVANCE Fellows Award: Mathematical modeling of renal physiology, National Science Foundation, 2004/04-2007/06.