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
- Brian
Zazzara
- Veronica
Gheorgher
- Zachary
Grigorian
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