John A. Burns

$Picture of Myself$

Office hours: 1:00 PM - 2:00 PM W

Email:	jaburns@math.vt.edu
Telephone:	(540) 231-7667
Fax:	(540) 231-7079
Office:	ICAM, West Campus Drive

Interdisciplinary Center for Applied Mathematics
Virginia Tech
ICAM, West Campus Drive, Blacksburg, VA 24061, USA

John Burns is the Hatcher Professor of Mathematics in the Virginia Tech Department of Mathematics and a member of the Interdisciplinary Center for Applied Mathematics. He is a Fellow of the IEEE.

$*$ Research Interests: Distributed Parameter Control; Approximation, Control, Identification and Optimization of Functional and Partial Differential Equations; Aero-elastic Control Systems; Fluid/Structural Control Systems; Smart Materials; Optimal Design; Sensitivity Analysis.

Conference on Mathematics in the Life and Biological Sciences

Vitae

Recent Publications

John A. Burns and Lizette Zietsman, "Upwind Approximations and Mesh Independence for LQR Control of Convection Diffusion Equations", submitted.

J. A. Burns, D. Rubio and M. I. Troparevsky, "Sensitivity Computation for Elliptic Equations with Interfaces", submitted.

J. A. Burns, E. M. Cliff, T. Herdman, Z. Liu and R. D. Spies, "Results on Transversal and Axial Motions of a System of Two Beams Coupled to a Joint Through Two Legs", submitted.

J. A. Burns, E.M. Clif, Z. Liu and R. D. Spies, "Polynomial Stability of a Joint-Leg-Beam System with Local Damping", J. Mathematical and Computer Modeling, to appear.

J. A. Burns, E. M. Cliff, and S. E. Doughty, "Sensitivity analysis and parameter estimation for a model of Chlamydia Trachomatis infection", J. Inv. Ill-Posed Problems 15(2007), to appear.

J. A. Burns and Gunther H. Peichl, "Control System Radii and Robustness Under Approximation", in Robust Optimization-Directed Design, A. Kurdila, P. Pardalos and M. Zabarankin, Eds., Springer-Verlag, 2005, 25 - 62.

Copies of other papers may be obtained by sending email to burns@math.vt.edu citing the specific papers you wish to receive.

Links

Department of Mathematics

Interdisciplinary Center for Applied Mathematics

Society for Industrial and Applied Mathematics

Current Graduate Students

Adam Childers

Golnar Newbury

Betty Paredez-Alvarez

Carlos Rautenberg

Daniel Sutton

Past Graduate Students

P. D. Hirsch, Parameter Estimation in Differential-Delay Models, M.S. Thesis, Virginia Tech, 1980.

J. Amillo-Gil, Nonlinear Neutral Functional Differential Equations in Product Spaces, Ph.D. Thesis, Virginia Tech, 1981.

R. K. Powers, Chandrasekhar Algorithms for Distributed Parameter Systems, Ph.D. Thesis, Virginia Tech, 1984.

R. Fabiano, Approximations of Integro-Partial Differential Equations of Hyperbolic Type, Ph.D. Thesis, Virginia Tech, 1986.

R. Miller, Approximation of the LQR Control Problem for Systems Governed by Partial Functional Differential Equations, Ph.D. Thesis, Virginia Tech, 1988.

Z. Liu, Approximation and Control of a Thermoviscoelastic System, Ph.D. Thesis, Virginia Tech, 1989.

D. Hill, Finite Dimensional Approximations of Distributed Parameter Control Systems, Ph.D. Thesis, Virginia Tech, 1989.

S. Kang, A Control Problem for Burgers Equation, Ph.D. Thesis, Virginia Tech, 1990.

K. L. Oates, A Study of Control System Radii for Approximations of Infinite Dimensional Systems, M.S. Thesis, Virginia Tech, 1991.

M. Tadi, An Optimal Control Problem for a Timoshenko Beam, Ph.D. Thesis, Virginia Tech, 1991.

R. D. Spies, Mathematical Modeling, Finite Dimensional Approximations and Sensitivity Analysis for Phase Transitions in Shape Memory Alloys, Ph.D. Thesis, Virginia Tech, 1992.

H. Marrekchi, Dynamic Compensators for a Nonlinear Conservation Law, Ph.D. Thesis, Virginia Tech, 1993.

W. Huang, Compensator Design for a System of Two Connected Beams, Ph.D. Thesis, Virginia Tech, 1994.

J. Borggaard, The Sensitivity Equation Method for Optimal Design, Ph.D. Thesis, Virginia Tech, 1994.

L. Zhang, Parameter Identification in Linear and Nonlinear Parabolic Partial Differential Equations, Ph.D. Thesis, Virginia Tech, 1995.

S. M. Pugh, Finite Element Approximations of Burgers' Equation, M.S. Thesis, Virginia Tech, 1995.

D. Rubio, Distributed Parameter Control of Thermal Fluids, Ph.D. Thesis, Virginia Tech, 1997.

T. R. Bail, A Disturbance Rejection Problem for a 2D Airfoil, M.S. Thesis, Virginia Tech, 1997.

S. D. Olds, Modeling and LQR Control of a Two-Dimensional Airfoil, M.S. Thesis, Virginia Tech, 1997.

L. C. Smith, Finite Element Approximations of Burgers' Equation with Robin's Boundary Conditions, M.S. Thesis, Virginia Tech, 1997.

K. L. Massa, Control of Burgers' Equation with Mixed Boundary Conditions, M.S. Thesis, Virginia Tech, 1998.

D. L. Stewart, Numerical Methods for Accurate Computation of Design Sensitivities, Ph.D. Thesis, Virginia Tech, 1998.

R. C. Camphouse, Approximations and Object-Oriented Implementation for a Parabolic Partial Differential Equation, M.S. Thesis, Virginia Tech, 1999.

D. T. Herdman, Approximations for Singular Integral Equations, M.S. Thesis, Virginia Tech, 1999.

L. G. Stanley, Computational Methods for Sensitivity Analysis with Applications to Elliptic Boundary Value Problems, Ph.D. Thesis, Virginia Tech, 1999.

K. P. Hulsing, Methods for Computing Functional Gains for LQR Control of Partial Differential Equations, Ph.D. Thesis, Virginia Tech, 1999.

V. Q. Nguyen, A Numerical Study of Burgers' Equation with Robin Boundary Conditions, M.S. Thesis, Virginia Tech, 2001.

R. C. Camphouse, Modeling and Numerical Approximations of Optical Activity in the Chemical Oxygen-Iodine Laser, Ph.D. Thesis, Virginia Tech, 2001.

E. D. Vugrin, On Approximation and Optimal Control of Non-normal Distributed Parameter Systems, Ph.D. Thesis, Virginia Tech, 2004.

J. Singler, Sensitivity Analysis of Partial Differential Equations With Applications to Fluid Flow, Ph.D. Thesis, Virginia Tech, 2005.