John A. Burns

 


Picture of
Myself

Email:

burns@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 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.

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