Anita Layton, Assistant Professor

Anita Layton
Office Location:  213 Physics Bldg
Office Phone:  (919) 660-6971
Email Address: send me a message
Web Page:  http://www.math.duke.edu/~alayton

Teaching (Fall 2008):

Education:

PhDUniversity of Toronto2001
MSUniversity of Toronto1996
BSDuke University1994
BADuke University1994
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

Recent Publications

  1. Jin Wang and Anita T. Layton, Numerical simulations of fiber sedimentation in Navier-Stokes flows, Comm. Comput. Phys., in press (Accepted, 2008)
  2. Mariano Marcano, Anita T. Layton, and Harold E. Layton, Maximum urine concentrating capability for transport parameters and urine flow within prescribed ranges, Bull. Math. Biol., submitted (Submitted, 2008)
  3. Anita T. Layton, On the choice of correctors for semi-implicit Picard deferred correction methods, Appl. Numer. Math., vol. 58 no. 6 (2008), pp. 845-858
  4. Thomas L. Pannabecker, William H. Dantzler, Harold E. Layton, and Anita T. Layton, Role of three-dimensional architecture in the urine concentrating mechanism of the rat renal inner medulla, Am. J. Physiol. Renal Physiol., submitted (Submitted, 2008)
  5. Anita T. Layton, On the efficiency of spectral deferred correction methods for time-dependent partial differential equations, Appl. Numer. Math., submitted (Submitted, 2007)
Recent Grant Support