# Anita T. Layton

- Robert R. & Katherine B. Penn Professor of Mathematics
- Professor in the Department of Mathematics
- Professor of Biomedical Engineering (Secondary)

**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. "Cubic spline collocation method for the shallow water equations on the sphere." *Journal of Computational Physics* 179.2 (2002): 578-592.
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Layton, AT, and Layton, HE. "A semi-Lagrangian semi-implicit numerical method for models of the urine concentrating mechanism." *SIAM J. Sci. Comput.* 23.5 (2002): 1528-1548. (Academic Article)

Layton, AT, and Panne, MVD. "A numerically efficient and stable algorithm for animating water waves." *Visual Computer* 18.1 (2002): 41-53.
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Layton, AT, and Layton, HE. "A numerical method for renal models that represent tubules with abrupt changes in membrane properties." *J. Math. Biol.* 45.5 (2002): 549-567. (Academic Article)

Layton, AT, and Layton, HE. "A numerical method for renal models that represent tubules with abrupt changes in membrane properties." *Journal of Mathematical Biology* 45.6 (2002): 549-567.
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Layton, AT, and Layton, HE. "A semi-lagrangian semi-implicit numerical method for models of the urine concentrating mechanism." *SIAM Journal on Scientific Computing* 23.5 (2002): 1526-1548.
Full Text