# Anita T. Layton

- Professor in the Department of Mathematics
- Professor of Biomedical Engineering (Secondary)
- Professor in Medicine (Secondary)
- Bass Fellow

**External address:**213 Physics Bldg, Durham, NC 27708

**Internal office address:**Box 90320, Durham, NC 27708-0320

**Phone:**(919) 660-6971

### Research Areas and Keywords

##### Biological Modeling

##### Computational Mathematics

##### PDE & Dynamical Systems

**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.

Layton, AT. "Role of structural organization in the urine concentrating mechanism of an avian kidney." *Math Biosci* 197.2 (October 2005): 211-230.
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Layton, AT, and Minion, ML. "Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations." *Bit Numerical Mathematics* 45.2 (June 1, 2005): 341-373.
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Layton, AT. "A methodology for tracking solute distribution in mathematical models of the kidney." *J. Biol. Sys.* 13.4 (2005): 1-21. (Academic Article)

Layton, AT, and Minion, ML. "Implications of the choice of quadrature nodes for Picard Integral deferred correction methods." *BIT* 45.2 (2005): 341-373. (Academic Article)

Layton, AT, Pannabecker, TL, Dantzler, WH, and Layton, HE. "Two modes for concentrating urine in rat inner medulla." *American Journal of Physiology. Renal Physiology* 287.4 (October 2004): F816-F839.
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Layton, AT, and Minion, ML. "Conservative multi-implicit spectral deferred correction methods for reacting gas dynamics." *Journal of Computational Physics* 194.2 (March 1, 2004): 697-715.
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Layton, AT, and Spotz, WF. "A semi-Lagrangian double Fourier method for the shallow water equations on the sphere." *Journal of Computational Physics* 189.1 (July 20, 2003): 180-196.
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Layton, AT. "A semi-Lagrangian collocation method for the shallow water equations on the sphere." *Siam Journal on Scientific Computing* 24.4 (January 1, 2003): 1433-1449.
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Layton, AT, and Layton, HE. "An efficient numerical method for distributed-loop models of the urine concentrating mechanism." *Mathematical Biosciences* 181.2 (2003): 111-132.
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Layton, AT, and Layton, HE. "A region-based model framework for the rat urine concentrating mechanism." *Bull. Math. Biol.* 65.6 (2003): 859-901. (Academic Article)