# 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. "A velocity decomposition approach for solving the immersed interface problem with Dirichlet boundary conditions." *IMA Volume on Natural Locomotion in Fluids and on Surfaces: Swimming, Flying, and Sliding, in press* (2012): 263-270. (Academic Article)

Layton, AT, and Beale, JT. "A partially implicit hybrid method for computing interface motion in stokes flow." *Discrete and Continuous Dynamical Systems - Series B* 17.4 (2012): 1139-1153.
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Layton, A, Stockie, J, Li, Z, and Huang, H. "Preface: Special issue on fluid motion driven by immersed structures." *Communications in Computational Physics* 12.2 (2012): i-iii.

Layton, AT, and Wei, G. "Interface methods for biological and biomedical problems." *International Journal for Numerical Methods in Biomedical Engineering* 28.3 (2012): 289-290.
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Hou, G, Wang, J, and Layton, A. "Numerical methods for fluid-structure interaction - A review." *Communications in Computational Physics* 12.2 (2012): 337-377.
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Witelski, T, Ambrose, D, Bertozzi, A, Layton, A, Li, Z, and Minion, M. "Preface: Special issue on fluid dynamics, analysis and numerics." *Discrete and Continuous Dynamical Systems - Series B* 17.4 (2012): i-ii.
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Li, Y, and Layton, AT. "Accurate computation of Stokes flow driven by an open immersed interface." *Journal of Computational Physics* 231.15 (2012): 5195-5215.
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Layton, AT. "Modeling transport and flow regulatory mechanisms of the kidney." *ISRN Biomath* 2012 (2012): ID: 170594, 18 pages-. (Academic Article)

Sgouralis, I, and Layton, AT. "Autoregulation and conduction of vasomotor responses in a mathematical model of the rat afferent arteriole." *Am J Physiol Renal Physiol* 303.F229-F239 (2012). (Academic Article)

Layton, AT, and Layton, HE. "Countercurrent multiplication may not explain the axial osmolality gradient in the outer medulla of the rat kidney." *Am J Physiol Renal Physiol* 301.5 (November 2011): F1047-F1056.
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