Math @ Duke
Anita T Layton, Associate Professor
- Contact Info:
Teaching (Fall 2013):
- MATH 161FS.01, MATHEMATICAL MODELS IN BIOLOGY
- Physics 205, TuTh 10:05 AM-11:20 AM
- FOCUS 195FS.26, SPECIAL TOPICS IN FOCUS
- SEE INSTRU, Th 06:00 PM-07:30 PM
|PhD||University of Toronto||2001|
|MS||University of Toronto||1996|
- Research Interests: Mathematical physiology; Multiscale numerical methods; Numerical methods for immersed boundary problems.
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
Multiscale numerical methods
- Curriculum Vitae
- Current Ph.D. Students
- Postdocs Mentored
- Rob Moss (October 1, 2012 - present)
- Aniel Nieves-Gonzales (January 1, 2011 - July 31, 2012)
- 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)
- Undergraduate Research Supervised
- Alex Wertheim (May 13, 2012 - June 30, 2012)
- Scott Cara (May 13, 2012 - December 31, 2012)
- Kara Karpman (May 13, 2012 - December 31, 2012)
- Recent Publications
- Karin Leiderman, Elizabeth L. Bouzarth, Ricardo Cortez, and Anita T. Layton, A regularization method for the numerical solution of periodic Stokes flow,
J Comput Phys, vol. 236 no. 187-202
- Hwayeon Ryu and Anita T. Layton, Tubular fluid flow and distal NaCl delivery mediated by tubuloglomerular feedback in the rat kidney,
J Math Biol, in press
- Aniel Nieves-Gonzalez, Chris Clausen, Anita .T. Layton, Harold E. Layton, and Leon C. Moore, Transport efficiency and workload distribution in a mathematical model of the thick ascending limb,
Am J Physiol Renal Physiol, vol. 304 no. F653-F664
- Aniel Nieves-Gonzalez, Chris Clausen, Mariano Marcano, Anita .T. Layton, Harold E. Layton, and Leon C. Moore, Fluid dilution and efficiency of Na+ transport in a mathematical model of a thick ascending limb cell,
Am J Physiol Renal Physiol, vol. 304 no. F634-F652
- Sarah D. Olson and Anita T. Layton, Simulating Fluid-Structure Interactions --- A Review,
AMS Contemporary Mathematics, Biological Fluid Dynamics: Modeling, Computations, and Applications, submitted
- 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.
Duke University, Box 90320
Durham, NC 27708-0320