Carl Gardner

Biography

Carl Gardner's research focuses on computational and theoretical fluid dynamics and the numerical solution of nonlinear partial differential equations. Differential equations constitute the basic language of how things change with time and/or with space -- Newton's second law of motion being the most well known example. His primary application areas are ion transport in biological cells (modeling ionic channels as well as synapses, with applications to the retina) and astrophysical flows like supersonic jets (modeling interactions of jets with their environments and star formation). These problems are governed by coupled systems of nonlinear partial differential equations, and exhibit complex fluid dynamical phenomena.

Education

Ph.D. Massachusetts Institute of Technology 1981

Publications

  • C. L. Gardner, J. R. Jones, S. M. Baer, and S. M. Crook. Drift-Diffusion Simulation of the Ephaptic Effect in the Triad Synapse of the Retina. Journal of Computational Neuroscience (2015).
  • C. L. Gardner, J. R. Jones, S. M. Baer, and S. Chang. Simulation of the Ephaptic Effect in the Cone-Horizontal Cell Synapse of the Retina. SIAM Journal on Applied Mathematics (2013).
  • C. L. Gardner. Numerical Simulation of Axion Quintessence. Advances in Mathematical Physics (2012).
  • R. K. Borchering, H. Liu, M. C. Steinhaus, C. L. Gardner, and Y. Kuang. A Simple Spatiotemporal Rabies Model for Skunk and Bat Interaction in Northeast Texas. Journal of Theoretical Biology (2012).
  • C. L. Gardner and J. R. Jones. Electrodiffusion Model Simulation of the Potassium Channel. Journal of Theoretical Biology (2011).
  • Carl Gardner, Steven Dwyer. Numerical Simulation of the XZ Tauri Supersonic Astrophysical Jet. Acta Mathematica Scientia (2009).
  • John Krist, Karl Stapelfeldt, Jeff Hester, Kevin Healy, Steven Dwyer, Carl Gardner. A Multi-Epoch HST Study of the Herbig-Haro Flow from XZ Tauri. Astronomical Journal (2008).
  • Youngsoo Ha, Carl Gardner. Positive Scheme Numerical Simulation of High Mach Number Astrophysical Jets. Journal of Scientific Computing (2008).
  • Carl Gardner. Braneworld Quintessential Inflation and Sum of Exponentials Potentials. published electronically as hep-th/0701036 at arXiv.org, unrefereed, but already has citations (2007).
  • Carl Gardner. Quintessence and the Transition to an Accelerating Universe. Nuclear Physics B (2005).
  • Carl Gardner, Y Ha, J Hester, J Krist, C Shu, K Stapelfeldt. Numerical Simulation of High Mach Number Astrophysical Jets. Analysis, Modeling and Computation of Hyperbolic PDE and Multiphase Flow (2005).
  • Y Ha, Carl Gardner, Anne Gelb, C Shu. Numerical Simulation of High Mach Number Astrophysical Jets with Radiative Cooling. Journal of Scientific Computing (2005).
  • Carl Gardner, G Klimeck, C Ringhofer. Smooth Quantum Hydrodynamic Model vs. NEMO Simulation of Resonant Tunneling Diodes. Journal of Computational Electronics (2004).
  • Carl Gardner, W Nonner, R Eisenberg. Electrodiffusion Model Simulation of Ionic Channels: 1D Simulations. Journal of Computational Electronics (2004).
  • Gardner, Carl, Ringhofer, C. Dispersive/Hyperbolic Hydrodynamic Models for Quantum Transport (in Semiconductor Devices). (2004).
  • C Ringhofer, Carl Gardner, D Vasileska. Effective Potentials and Quantum Fluid Models: A Thermodynamic Approach. International Journal of High Speed Electronics and Systems (2003).
  • Carl Gardner. Cosmological Variation of the Fine Structure Constant from an Ultra-Light Scalar Field: The Effects of Mass. Physical Review D (2003).
  • Carl Gardner. Semiconductor Device Simulation: The Hydrodynamic Model. IEEE Potentials (2003).
  • Carl Gardner. Primordial Inflation and Present-Day Cosmological Constant from Extra Dimensions. Physics Letters B (2002).
  • Carl Gardner, A Gelb, J Hernandez. A Comparison of Modern Hyperbolic Methods for Semiconductor Device Simulation: NTK Central Scheme vs. CLAWPACK. VLSI Design 15 (2002).
  • Carl Gardner, J Jerome, andR Eisenberg. Electrodiffusion Model Simulation of Rectangular Current Pulses in a Voltage Biased Biological Channel. Journal of Theoretical Biology (2002).
  • Carl Gardner, J Jerome, R Eisenberg. Electrodiffusion Model Simulation of Rectangular Current Pulses in a Biological Channel. Journal of Computational Electronics (2002).
  • N Ben Abdallah, O Pinaud, Carl Gardner, C Ringhofer. A Comparison of Resonant Tunneling Based on Schr¬®odinger's Equation and Quantum Hydrodynamics. VLSI Design 15 (2002).
  • . VLSI Design 15. (2002).
  • Carl Gardner, C Ringhofer. Numerical Simulation of the Smooth Quantum Hydrodynamic Model for Semiconductor Devices. Computer Methods in Applied Mechanics and Engineering (2000).
  • Carl Gardner, C Ringhofer. Resonant Tunneling in the Smooth Quantum Hydrodynamic Model for Semiconductor Devices. Transport Theory and Statistical Physics (2000).
  • Carl Gardner, C Ringhofer. The Chapman-Enskog Expansion and the Quantum Hydrodynamic Model for Semiconductor Devices. VLSI Design 10 (2000).
  • Carl Gardner, J Jerome, R Eisenberg. Electrodiffusion Model of Rectangular Current Pulses in Ionic Channels of Cellular Membranes. SIAM Journal on Applied Mathematics (2000).
  • . VLSI Design 10. (2000).

Research Activity

Courses

Spring 2018
Course Number Course Title
MAT 421 Applied Computational Methods
MAT 493 Honors Thesis
PHY 495 Project Research
MAT 495 Undergraduate Research
MAT 590 Reading and Conference
APM 792 Research
APM 799 Dissertation
Fall 2017
Course Number Course Title
MAT 267 Calculus for Engineers III
MAT 492 Honors Directed Study
MAT 495 Undergraduate Research
APM 522 Numerical Methods for Partial
MAT 590 Reading and Conference
MAT 792 Research
Summer 2017
Course Number Course Title
MAT 792 Research
APM 792 Research
Spring 2017
Course Number Course Title
MAT 421 Applied Computational Methods
MAT 493 Honors Thesis
PHY 495 Project Research
MAT 495 Undergraduate Research
MAT 590 Reading and Conference
APM 792 Research
APM 799 Dissertation
Fall 2016
Course Number Course Title
MAT 267 Calculus for Engineers III
MAT 492 Honors Directed Study
MAT 495 Undergraduate Research
APM 522 Numerical Methods for Partial
MAT 590 Reading and Conference
MAT 792 Research
Summer 2016
Course Number Course Title
MAT 792 Research
APM 792 Research
Spring 2016
Course Number Course Title
MAT 493 Honors Thesis
PHY 495 Project Research
MAT 495 Undergraduate Research
MAT 590 Reading and Conference
MAT 599 Thesis
APM 792 Research
APM 799 Dissertation
Fall 2015
Course Number Course Title
MAT 423 Numerical Analysis I
MAT 492 Honors Directed Study
MAT 495 Undergraduate Research
APM 522 Numerical Methods for Partial
MAT 590 Reading and Conference
MAT 792 Research
Summer 2015
Course Number Course Title
STP 595 Continuing Registration
MAT 784 Internship
STP 792 Research
MAT 792 Research
APM 792 Research
Spring 2015
Course Number Course Title
MAT 421 Applied Computational Methods
MAT 493 Honors Thesis
PHY 495 Project Research
MAT 590 Reading and Conference
MAT 599 Thesis
APM 790 Reading and Conference
APM 792 Research
APM 799 Dissertation
Fall 2014
Course Number Course Title
MAT 492 Honors Directed Study
MAT 494 Special Topics
MAT 499 Individualized Instruction
APM 522 Numerical Methods for Partial
MAT 590 Reading and Conference
MAT 591 Seminar
MAT 592 Research
MAT 599 Thesis
MAT 792 Research
APM 792 Research
MAT 795 Continuing Registration
APM 799 Dissertation
Summer 2014
Course Number Course Title
MAT 592 Research
MAT 595 Continuing Registration
APM 792 Research
APM 799 Dissertation
Spring 2014
Course Number Course Title
MAT 421 Applied Computational Methods
MAT 590 Reading and Conference
APM 790 Reading and Conference
APM 792 Research
MAT 795 Continuing Registration
APM 799 Dissertation
Fall 2013
Course Number Course Title
MAT 492 Honors Directed Study
APM 522 Numerical Methods for Partial
MAT 590 Reading and Conference
MAT 591 Seminar
MAT 592 Research
MAT 599 Thesis
MAT 792 Research
APM 799 Dissertation
Summer 2013
Course Number Course Title
APM 792 Research
APM 799 Dissertation

Presentations

  • Carl Gardner. Numerical Simulation of High Mach Number Astrophysical Jets with Radiative Cooling. U of A Mathematics Dept Colloquium (Oct 2014).
  • Carl Gardner. Simulation of the Ephaptic Effect in the Cone-Horizontal Cell Synapse of the Retina. Society for Mathematical Biology Meeting, Minisymposium (Jun 2013).
  • Carl Gardner. Simulation of the Ephaptic Effect in the Cone-Horizontal Cell Synapse of the Retina. Applied Mathematics Modeling and Computation Seminar, University of Arizona (Oct 2012).
  • Carl Gardner. Modeling Ionic Flow in the Retina. ICIAM Meeting, Minisymposium (Jul 2011).
  • Carl Gardner. Modeling Ionic Flow in the Retina. Informal seminar to Prof Peskin's group at Courant Institute, NYU (Oct 2010).
  • Carl gardner. Numerical Simulation of High Mach Number Astrophysical Jets with Radiative Cooling. ASU HPC Seminar (Sep 2010).
  • Carl Gardner. Modeling Ionic Flow in Biological Cells. Applied Mathematics Seminar, Northwestern University (Feb 2010).
  • Carl Gardner. Axion Quintessence Revisited. ASU Cosmology Seminar (Dec 2009).
  • Carl Gardner. Electro-Diffusion Modeling and the Retina. SIAM Annual Meeting, Minisymposium (Jul 2009).
  • Carl Gardner. Numerical Methods for Electro-Reaction-Diffusion Modeling of Biological Cells. SIAM Annual Meeting, Minisymposium (Jul 2008).
  • Gardner, Carl. Electrodiffusion Model Simulation of Ionic Channels. Institute Seminar, Mathematics Department, Indiana University (Oct 2006).
  • Gardner, Carl, Ringhofer, Christian. Applications of Maximum Entropy Closures to Device Simulation. SEMIC 2006, Recent Advances in Modeling and Simulation of Semiconductor Devices (Feb 2006).
  • Chi-Wang, Shu, Gardner, Carl. High Order Weighted Essentially Non-Oscillatory (WENO) Schemes and Their Application in Cosmological Simulations. IPAM Workshop I: Astrophysical Fluid Dynamics (Apr 2005).
  • Gardner, Carl. Numerical Simulation of High Mach Number Astrophysical Jets. Conference on Analysis, Modeling and Computation of Hyperbolic PDE and Multiphase Flow (Aug 2004).

Service

  • Chair, Comprehensive Exam Committee for APM 522 and APM 526, Chair (2015 - 2015)
  • Computer Committee, Member (2015 - 2015)
  • Referee: Applied Numerical Mathematics 1 article, SISC 1 article, Referee (2015 - 2015)
  • CLAS Special Committee for Graduate Programs, member (2015 - 2015)
  • Graduate Committee, Chair (2015 - 2015)
  • SoMSS, Associate Director for Graduate Programs (2015 - 2015)
  • SIAM Computational Science & Engineering Conference, Organizer (2015 - 2015)
  • CLAS Special Committee for Graduate Programs, member (2014 - 2014)
  • Chair, Comprehensive Exam Committee for APM 522 and APM 526, Chair (2014 - 2014)
  • Computer Committee, Member (2014 - 2014)
  • Graduate Committee, Chair (2014 - 2014)
  • Referee Applied Numerical Mathematics: 1 article, Journal of Biological Dynamics: 1 article, referee (2014 - 2014)
  • SoMSS, Associate Director for Graduate Programs (2014 - 2014)
  • SoMSS Web Pages, Help redesign Graduate Program web pages (2014 - 2014)
  • Field of Dreams Conference, Represented SoMSS graduate programs 11/8/2014 (2014 - 2014)
  • SIAM Computational Science & Engineering Conference, Organizer (2014 - 2014)
  • Computer Committee, Member (2011 - 2014)
  • CLAS Special Committee for Graduate Programs, member (2013 - 2014)
  • Graduate Committee, Chair (2013 - 2014)
  • SoMSS, Associate Director for Graduate Programs (2013 - 2014)
  • SoMSS Web Pages, Help redesign Graduate Program web pages (2013 - 2014)
  • Chair, Comprehensive Exam Committee for APM 522 (3 students), Chair (2013 - 2013)
  • Referee for Journal of Scientific Computing: 1, Applied Numerical Mathematics: 1, Physica D: 1, referee (2013 - 2013)
  • Field of Dreams Conference, Represented SoMSS graduate programs 11/1 through 11/3 (2013 - 2013)
  • Applied Math Coordinator, Coordinator (2011 - 2013)
  • Computer Committee, Member (2011 - 2013)
  • Graduate Committee, Member (2011 - 2013)
  • Society for Mathematical Biology Annual Meeting, Organizer (2013 - 2013)
  • National Science Foundation, Proposal Reviewer (2012 - 2012)
  • Referee for J Scientific Comp, Applied Numerical Math, J Comp Electronics, & Math Biosci (4 total), referee (2012 - 2012)
  • Chair, Comprehensive Exam Committee for APM 522 (3 students), Chair (2012 - 2012)
  • Applied Math Coordinator, Coordinator (2011 - 2012)
  • Computer Committee, Member (2011 - 2012)
  • Graduate Committee, Member (2011 - 2012)
  • Referee for J of Computational Physics, Applied Numerical Math, J of Math Physics (3 total), referee (2011 - 2011)
  • Chair, Comprehensive Exam Committee for APM 522 (2 students), Chair (2011 - 2011)
  • ICIAM Meeting, Organizer (2011 - 2011)
  • ICIAM Meeting, Organizer (2010 - 2011)
  • Awards Committee, Member (2011 - 2011)
  • Personnel and Budget Committee, Member (2009 - 2011)
  • MATH COMP ENVIRON Search Committee, Chair (2010 - 2011)
  • National Science Foundation, Proposal Reviewer (2010 - 2010)
  • Referee for Physics of Plasmas, Applied Numerical Mathematics, SISC (one each), referee (2010 - 2010)
  • Comprehensive Exam Committee for APM 522, Chair (2010 - 2010)
  • Personnel and Budget Committee, Member (2008 - 2010)
  • Newsletter Committee, Chair (2008 - 2010)
  • Personnel and Budget Committee, Member (2008 - 2009)
  • Newsletter Committee, Chair (2008 - 2009)
  • Statistics Search Committee, Chair (2008 - 2009)
  • Comprehensive Exam Committee for MAT 533, Chair (2009 - 2009)
  • Communications in Mathematical Sciences, Referee -- two articles (2008 - 2008)
  • SIAM Annual Meeting, Organizer (2008 - 2008)
  • Undergraduate Committee, Member (2005 - 2008)
  • Communications in Mathematical Sciences, Referee -- one article (2007)
  • SIAM Journal on Applied Mathematics, Referee -- one article (2007)
  • Universit√© Paul Sabatier, Toulouse, France, External reviewer for Samy Gallego's PhD Thesis (2007)
  • Comprehensive Exam Committee for MAT 533-534, Member (2007)
  • Comprehensive Exam Committee for MAT 520-535, Member (2006)
  • Comprehensive Exam Committees for MAT 533 & 534 (final exams May & December), Chair (2006)
  • SIAM Multiscale Modeling & Simulation, Referee -- one article (2006)
  • Comprehensive Exam Committee for MAT 503-533, Member (2006)
  • Comprehensive Exam Committee for MAT 520-533, Chair (2006)
  • Comprehensive Exam Committee for MAT 533-534, Chair (2006)
  • Comprehensive Exam Committee for MAT 534-535, Chair (2006)
  • Safety Committee, Member (2006)
  • Numerical Analysis Qualifier Committee, Chair (2004 - 2005)
  • SIAM Journal on Numerical Analysis, Referee -- one article (2005)
  • Transport Theory and Statistical Physics, Referee -- one article (2005)
  • Computer Committee, Member (2004 - 2005)
  • Journal of Applied Numerical Mathematics, Referee -- one article (2004)
  • Computer Committee, Fall 2003, Member (2003)
  • Numerical Analysis Qualifier Committee, Member (2003)
  • SIAM, Organizer (2003)
  • Undergraduate Committee, Spring 2003, Member (2003)
  • Workshop at CSCAMM, University of Maryland, Organizer (2003)