John A. Burns
John A. 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 and SIAM.
Research Interests: Distributed Parameter Control; Approximation, Control,
Identification and Optimization of Functional and Partial Differential
Equations; Aero-elastic Control Systems; Fluid/Structural and Thermal-Fluid
Control Systems; Smart Materials; Optimal Design; Sensitivity Analysis.
Vitae
Copies
of papers may be obtained by sending email to jaburns@vt.edu
citing the specific papers you wish to receive.
Links
Current Graduate Students
Past
Graduate Students
- P. D. Hirsch, Parameter Estimation in
Differential-Delay Models, M.S. Thesis, Department of Mathematics,
Virginia Tech, 1980.
- J. Amillo-Gil, Nonlinear
Neutral Functional Differential Equations in Product Spaces, Ph.D.
Thesis, Department of Mathematics, Virginia Tech, 1981.
- R. K. Powers, Chandrasekhar Algorithms for
Distributed Parameter Systems, Ph.D. Thesis, Department of
Mathematics, Virginia Tech, 1984.
- R. Fabiano, Approximations
of Integro-Partial Differential Equations of
Hyperbolic Type, Ph.D. Thesis, Department of Mathematics, Virginia
Tech, 1986.
- R. Miller, Approximation of the LQR
Control Problem for Systems Governed by Partial Functional Differential
Equations, Ph.D. Thesis, Department of Mathematics, Virginia Tech,
1988.
- Z. Liu, Approximation and Control of a Thermoviscoelastic System, Ph.D. Thesis,
Department of Mathematics, Virginia Tech, 1989.
- D. Hill, Finite Dimensional Approximations of
Distributed Parameter Control Systems, Ph.D. Thesis, Department of
Mathematics, Virginia Tech, 1989.
- S. Kang, A Control Problem for Burgers Equation,
Ph.D. Thesis, Department of Mathematics, Virginia Tech, 1990.
- K. L. Oates, A Study of Control System Radii for
Approximations of Infinite Dimensional Systems, M.S. Thesis,
Department of Mathematics, Virginia Tech, 1991.
- M. Tadi, An Optimal
Control Problem for a Timoshenko Beam, Ph.D. Thesis, Department of
Engineering Sciences and Mechanics, Virginia Tech, 1991.
- R. D. Spies, Mathematical Modeling, Finite
Dimensional Approximations and Sensitivity Analysis for Phase Transitions
in Shape Memory Alloys, Ph.D. Thesis, Department of Mathematics,
Virginia Tech, 1992.
- H. Marrekchi, Dynamic
Compensators for a Nonlinear Conservation Law, Ph.D. Thesis,
Department of Mathematics, Virginia Tech, 1993.
- W. Huang, Compensator Design for a System of Two
Connected Beams, Ph.D. Thesis, Department of Mathematics, Virginia
Tech, 1994.
- J. Borggaard, The
Sensitivity Equation Method for Optimal Design, Ph.D. Thesis,
Department of Mathematics, Virginia Tech, 1994.
- L. Zhang, Parameter Identification in Linear and
Nonlinear Parabolic Partial Differential Equations, Ph.D. Thesis,
Department of Mathematics, Virginia Tech, 1995.
- S. M. Pugh, Finite Element Approximations of
Burgers' Equation, M.S. Thesis, Department of Mathematics, Virginia
Tech, 1995.
- D. Rubio, Distributed Parameter Control of Thermal
Fluids, Ph.D. Thesis, Department of Mathematics, Virginia Tech, 1997.
- T. R. Bail, A Disturbance Rejection Problem for a 2D Airfoil, M.S. Thesis, Department of
Mathematics, Virginia Tech, 1997.
- S. D. Olds, Modeling and LQR
Control of a Two-Dimensional Airfoil, M.S. Thesis, Department of
Mathematics, Virginia Tech, 1997.
- L. C. Smith, Finite Element Approximations of
Burgers' Equation with Robin's Boundary Conditions, M.S. Thesis,
Department of Mathematics, Virginia Tech, 1997.
- K. L. Massa, Control of Burgers' Equation with
Mixed Boundary Conditions, M.S. Thesis, Department of Mathematics,
Virginia Tech, 1998.
- D. L. Stewart, Numerical Methods for Accurate
Computation of Design Sensitivities, Ph.D. Thesis, Department of
Mathematics, Virginia Tech, 1998.
- R. C. Camphouse, Approximations
and Object-Oriented Implementation for a Parabolic Partial Differential
Equation, M.S. Thesis, Department of Mathematics, Virginia Tech,
1999.
- D. T. Herdman, Approximations
for Singular Integral Equations, M.S. Thesis, Department of
Mathematics, Virginia Tech, 1999.
- L. G. Stanley, Computational Methods for
Sensitivity Analysis with Applications to Elliptic Boundary Value Problems,
Ph.D. Thesis, Department of Mathematics, Virginia Tech, 1999.
- K. P. Hulsing, Methods
for Computing Functional Gains for LQR Control
of Partial Differential Equations, Ph.D. Thesis, Department of
Mathematics, Virginia Tech, 1999.
- V. Q. Nguyen, A Numerical Study of Burgers'
Equation with Robin Boundary Conditions, M.S. Thesis, Department of
Mathematics, Virginia Tech, 2001.
- R. C. Camphouse, Modeling
and Numerical Approximations of Optical Activity in the Chemical
Oxygen-Iodine Laser, Ph.D. Thesis, Department of Mathematics,
Virginia Tech, 2001.
- E. D. Vugrin, On
Approximation and Optimal Control of Non-normal Distributed Parameter
Systems, Ph.D. Thesis, Department of Mathematics, Virginia Tech,
2004.
- J. Singler, Sensitivity
Analysis of Partial Differential Equations With Applications to Fluid Flow,
Ph.D. Thesis, Department of Mathematics, Virginia Tech, 2005.
- G. Newbury, A Numerical Study of a Delay
Differential Equation Model for Breast Cancer, M.S. Thesis,
Department of Mathematics, Virginia Tech, August, 2007 .
- A. Childers, Parameter Identification and the
Design of Experiments for Continuous Non-Linear Dynamical Systems,
Ph.D. Thesis, Department of Mathematics, Virginia Tech, 2009.
- C. N. Rautenberg, A
Distributed Parameter Approach to Optimal Filtering and Estimation with
Mobile Sensor Networks, Ph.D. Thesis, Department of Mathematics,
Virginia Tech, 2010.
- B. Kraemer, Model Reduction of the Coupled Burgers
Equation in Conservation Form, M.S. Thesis, Department of
Mathematics, Virginia Tech, August, 2011.
- B. K. McBee, Computational
Approaches to Improving Room Heating and Cooling for Energy Efficiency in
Buildings, Ph.D. Thesis, Department of Mathematics, Virginia Tech,
August, 2011.
- C. Jarvis, Reduced Order Model Study of Burgers'
Equation using Proper Orthogonal Decomposition, M.S. Thesis, Department
of Mathematics, Virginia Tech, February, 2012.
- W. W. Hu, Approximation and Control of the Boussinesq Equations with Application to Control of
Energy Efficient Building Systems, Ph.D. Thesis, Department of
Mathematics, Virginia Tech, May, 2012.
- A. Grimm, Taming
of Complex Dynamical Systems, M.S. Thesis, Department of Mathematics,
Virginia Polytechnic Institute and State University, December, 2013.
- C. Jarvis, Parameter
Dependent Model Reduction for Complex Fluid Flows, Ph.D. Thesis,
Department of Mathematics, Virginia Polytechnic Institute and State
University, March, 2014
- B. Kramer, Model and Data Reduction for Control, Identification and Compressed Sensing, Ph.D. Thesis,
Department of Mathematics, Virginia Polytechnic Institute and State
University, July, 2015