Carl Gardner's research focuses on computational and theoretical fluid dynamics and the numerical solution of nonlinear partial differential equations. His primary application areas are electron propagation in quantum semiconductor devices, ion transport in biological cells (modeling ionic channels as well as synapses), and supersonic flows in astrophysical 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 involving nonlinear wave interactions.
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
Carlson,Marilyn P*, Boggess,Albert, Gardner,Carl L, Jackiewicz,Zdzislaw, Milner,Fabio Augusto, Roh,Kyeong Hah, Saldanha,Luis, Thompson,Patrick W, Van De Sande,Carla. Pathways to Preparing Future Mathematics Faculty to Transform Undergraduate Mathematics Teaching and Learning. NSF-EHR-DUE(9/1/2013 - 8/31/2018).
Kostelich,Eric John*, Armbruster,Hans Dieter, Crook,Sharon Marie, Crook,Sharon Marie, Gardner,Carl L, Gelb,Anne, Jackiewicz,Zdzislaw, Jones,Donald, Lopez,Juan Manuel, Mahalov,Alex, Renaut,Rosemary Anne, Ringhofer,Christian, Welfert,Bruno Denis. CSUMS: Undergraduate research Experiences for Computational Math Science Majors at ASU. NSF-MPS-DMS(9/15/2007 - 8/31/2014).
Baer,Steven M*, Crook,Sharon Marie, Gardner,Carl L, Ringhofer,Christian. Multiscale Modeling of the Neural Subcircuits in the Outer-Plexiform Layer of the Retina. NSF-MPS-DMS(9/1/2007 - 8/31/2011).
Gardner,Carl L*. EVOLUTION OF YOUNG STELLAR OUTFLOWS: XZ TAURI AND HH 30. SPACE TELESCOPE SCIENCE INST(1/1/2004 - 12/31/2005).
Gardner,Carl L*. MODELING OF BIOLOGICAL CHANNELS. RUSH-PRESBYTERIAN-ST. LUKE'S(8/15/2003 - 6/30/2004).
Gardner,Carl L*. NUMERICAL SIMULATION OF QUANTUM TRANSPORT IN SEMICONDUCTOR DEVICES. NSF-MPS(8/1/1997 - 7/31/2001).
Gardner,Carl L*. THE QUANTUM HYDRODYNAMIC MODEL FOR SEMICONDUCTOR DEVICES: TH. DOD-ARMY(3/1/1995 - 2/28/1998).
Gardner,Carl L*. HYDRODYNAMIC MODEL FOR SEMICONDUCTOR. NSF-MPS(9/1/1994 - 10/31/1996).
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)
