Publications

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Layton, A. T. . (2007). Role of UTB urea transporters in the urine concentrating mechanism of the rat kidney. Bulletin of mathematical biology, 69, 887–929. Springer-Verlag.
Layton, A. , & Minion, M. . (2007). Implications of the choice of predictors for semi-implicit Picard integral deferred correction methods. Communications in Applied Mathematics and Computational Science, 2, 1–34. Mathematical Sciences Publishers.
Layton, A. T. . (2006). Modeling water transport across elastic boundaries using an explicit jump method. SIAM Journal on Scientific Computing, 28, 2189–2207. Society for Industrial and Applied Mathematics.
Layton, A. T. , Moore, L. C. , & Layton, H. E. . (2006). Dynamics in coupled nephrons may contribute to irregular flow oscillations in spontaneously hypertensive rats. Federation of American Societies for Experimental Biology.
Layton, A. T. , Christara, C. C. , & Jackson, K. R. . (2006). Quadratic spline methods for the shallow water equations on the sphere: Collocation. Mathematics and Computers in Simulation, 71, 187–205. Elsevier.
Layton, A. T. , Christara, C. C. , & Jackson, K. R. . (2006). Quadratic spline methods for the shallow water equations on the sphere: Galerkin. Mathematics and Computers in Simulation, 71, 175–186. Elsevier.
Layton, A. T. . (2006). An explicit jump method for the two-fluid stokes equations with an immersed elastic boundary. Elsevier Science.
Layton, A. T. . (2006). Modeling water transport across elastic boundaries using an explicit jump method. SIAM Journal on Scientific Computing, 28, 2189–2207. SIAM.
Layton, A. T. , & Layton, H. E. . (2005). A mathematical model of the urine concentrating mechanism of the inner medulla of the chinchilla kidney. In FASEB JOURNAL (Vol. 19, pp. A149–A149). FEDERATION AMER SOC EXP BIOL 9650 ROCKVILLE PIKE, BETHESDA, MD 20814-3998 USA.
Layton, A. T. . (2005). A methodology for tracking solute distribution in a mathematical model of the kidney. Journal of Biological Systems, 13, 399–419. World Scientific.
Layton, A. T. , & Minion, M. L. . (2005). Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT, 45(2), 341–373.
Layton, A. T. . (2005). Role of structural organization in the urine concentrating mechanism of an avian kidney. Mathematical biosciences, 197, 211–230. Elsevier.
Layton, A. T. , Moore, L. C. , & Layton, H. E. . (2005). Multistability in tubuloglomerular feedback and spectral complexity in spontaneously hypertensive rats. American Journal of Physiology-Renal Physiology.
Layton, A. T. , & Layton, H. E. . (2005). A region-based mathematical model of the urine concentrating mechanism in the rat outer medulla. II. Parameter sensitivity and tubular inhomogeneity. American Journal of Physiology-Renal Physiology, 289, F1367–F1381. American Physiological Society.
Layton, A. T. , & Minion, M. L. . (2005). Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics, 45, 341–373. Springer-Verlag.
Layton, A. T. , & Layton, H. E. . (2005). A region-based mathematical model of the urine concentrating mechanism in the rat outer medulla. I. Formulation and base-case results. American Journal of Physiology-Renal Physiology, 289, F1346–F1366. American Physiological Society.
Layton, A. T. . (2004). Conservative multi-implicit integral deferred correction methods with adaptive mesh refinement.
Layton, A. T. , Pannabecker, T. L. , Dantzler, W. H. , & Layton, H. E. . (2004). Effects of structural organization on the urine concentrating mechanism of the rat kidney. In FASEB JOURNAL (Vol. 18, pp. A1021–A1021). FEDERATION AMER SOC EXP BIOL 9650 ROCKVILLE PIKE, BETHESDA, MD 20814-3998 USA.
Layton, A. T. , & Minion, M. L. . (2004). Conservative multi-implicit spectral deferred correction methods for reacting gas dynamics. Journal of Computational Physics, 194, 697–715. Elsevier.
Layton, A. T. , Pannabecker, T. L. , Dantzler, W. H. , & Layton, H. E. . (2004). Two modes for concentrating urine in rat inner medulla. American Journal of Physiology-Renal Physiology, 287, F816–F839. American Physiological Society.

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