- The Quantum Faedo-Galerkin Equation: Evolution Operator and Time Discretization
- Time Dependent Closed Quantum Systems: Nonlinear Kohn-Sham Potential Operators and Weak Solutions
- Nonlinear Conformation Response in the Finite Channel: Existence of a Unique Solution for the Dynamic PNP Model
- Ascertaining the Limitations of Low Mobility on Organic Solar Cell Performance (with B.M. Savoie, S. Tan, C.-W. Shu, M.A. Ratner, and T.J. Marks)
- Discretization of Time Dependent Quantum Systems: Real-time Propagation of the Evolution Operator (with Eric Polizzi)
- The Steady Boundary Value Problem for Charged Incompressible Fluids: PNP/Navier Stokes Systems
- Simulation of the Buxton-Clarke Model for Organic Photovoltaic Cells (with Mark Ratner, Jon Servaites, Chi-Wang Shu, and Sirui Tan)
- Charge Transport in an Incompressible Fluid: New Devices in Computational Electronics
- Conservative and Monotone Mixed-Hybridized Finite Element Approximation of Transport Problems in Heterogeneous Domains (with Marco Brera, Yoichiro Mori, and Riccardo Sacco)
- Mathematical Advances and Horizons for Classical and Quantum-Perturbed Drift-Diffusion Systems: Solid State Devices and Beyond
- Steady Euler Poisson Systems: A Differential/Integral Equation Formulation with General Constitutive Relations
- Global Weak Solutions for an Incompressible Charged Fluid with Multi-Scale Couplings: Initial-Boundary Value Problem (with Riccardo Sacco)
- Quantum Corrected Drift--Diffusion Models: Solution Fixed Point Map and Finite Element Approximation (with Carlo de Falco and Riccardo Sacco)
- A Trapping Principle and Convergence Result for Finite Element Approximate Solutions of Steady Reaction/Diffusion Systems
- Local Properties of an Isothermal Charged Fluid: Initial-Boundary Value Problem
- Efficient Approximation of Implicitly Defined Functions: General Theorems and Classical Benchmark Studies (with Anders Linner)
- Convergence of Density Functional Iterative Procedures with a Newton-Raphson Algorithm (with Paul Sievert, Linhui Ye, In Gee Kim, and Arthur Freeman)
- A Unique Graph of Minimal Elastic Energy (with Anders Linner)
- A Three-Dimensional Model of Cellular Electrical Activity (with Yoichiro Mori and Charles Peskin)
- Mixed-Hybrid Discretization Methods for the Linear Boltzmann Transport Equation (with Serge Van Criekingen, Robert Beauwens, and Elmer Lewis)
- Functional Analytic Methods for Evolution Systems: Local Smooth Theory Stable Under Singular Limits
- The Thermodynamic Characterization of Spontaneous Electrochemical Reactions
- Drift-Diffusion in Electrochemistry: Thresholds for Boundary Flux and Discontinuous Optical Generation (with Siegfried Carl)
- Trapping Regions for Discontinuously Coupled Systems of Evolution Variational Inequalities and Application (with Siegfried Carl and Seppo Heikkila)
- The Cauchy Problem for Compressible Hydrodynamic-Maxwell Systems: A Local Theory for Smooth Solutions
- Trapping Regions for Elliptic Systems with Discontinuously Coupled Vector Fields (with Siegfried Carl)
- An Analytical Study of Smooth Solutions of the Blotekjaer Hydrodynamic Model of Electron Transport
- Trapping Region for Discontinuous Quasilinear Elliptic Systems of Mixed Monotone Type (with Siegfried Carl)
- Analytical Approaches to Charge Transport in a Moving Medium
- A Trapping Principle for Discontinuous Elliptic Systems of Mixed Monotone Type
- Newton Iteration for Partial Differential Equations and the Approximation of the Identity (with Gregory E. Fasshauer and Eugene C. Gartland, Jr. )
- Electrodiffusion Model of Rectangular Current Pulses in Ionic Channels of Cellular Membranes (with Carl Gardner and Robert Eisenberg)
- Analytical and Computational Advances for Hydrodynamic Models of Classical and Quantum Charge Transport
- Algorithms Defined by Nash Iteration: Some Implementations via Multilevel Collocation and Smoothing (with Gregory E. Fasshauer and Eugene C. Gartland, Jr. )
- A Domain Decomposition Method for Silicon Devices (with Carlo Cercignani, Irene Gamba, and Chi-Wang Shu)
- Compressible Euler-Maxwell Equations (with Gui-Qiang Chen and Dehua Wang)
- The Utility of Modeling and Simulation in Determining Transport Performance Properties of Semiconductors (with Bernardo Cockburn and Chi-Wang Shu)
- Device Benchmark Comparisons via Kinetic, Hydrodynamic, and High-Field Models (with Carlo Cercignani, Irene Gamba, and Chi-Wang Shu)
- Multistep Approximation Algorithms: Improved Convergence Rates through Postconditioning with Smoothing Kernels (with Gregory E. Fasshauer)
- A Domain Decomposition Method: A Simulation Study (with Carlo Cercignani, Irene Gamba, and Chi-Wang Shu)
- Applicability of the High Field Model: An Analytical Study via Asymptotic Parameters Defining Domain Decomposition (with Carlo Cercignani, Irene Gamba, and Chi-Wang Shu)
- Applicability of the High Field Model: A Preliminary Numerical Study (with Carlo Cercignani, Irene Gamba, and Chi-Wang Shu)
- Two Carrier Semiconductor Device Models with Geometric Structure and Symmetry Properties (with Gui-Qiang Chen, Chi-Wang Shu, and Dehua Wang)
- Existence and the Singular Relaxation Limit for the Inviscid Hydrodynamic Energy Model (with Gui-Qiang Chen and Bo Zhang)
- Particle Hydrodynamic Moment Models in Biology and Microelectronics: Singular Relaxation Limits (with Gui-Qiang Chen and Bo Zhang)
- Qualitative Properties of Steady-State Poisson-Nernst-Planck Systems: Mathematical Study (with J.-H. Park)
- Qualitative Properties of Steady-State Poisson-Nernst-Planck Systems: Perturbation and Simulation Study (with V. Barcilon, D.-P. Chen, and R.S. Eisenberg)
- On a Steady-State Quantum Hydrodynamic Model for Semiconductors (with Bo Zhang)
- Energy Transport Systems for Semiconductors: Analysis and Simulation (with Chi-Wang Shu)
- The Approximation Problem for Drift-Diffusion Systems
- A Hydrodynamic Model of Temperature Change in the Open Ionic Channel (with D.-P. Chen, R.S. Eisenberg, and C.-W. Shu)
- An Asymptotically Linear Fixed Point Extension of the Inf-Sup Theory of Galerkin Approximation
- Quantum Hydrodynamic Simulation of Hysteresis in the Resonant Tunneling Diode (with Z. Chen, B. Cockburn, and Carl Gardner)
- Transport Effects and Characteristic Modes in the Modeling and Simulation of Submicron Devices (with Chi-Wang Shu)
- The Mathematical Study and Approximation of Semiconductor Models
- A Finite Element Approximation Theory for the Drift-Diffusion Semiconductor Model (with Thomas Kerkhoven)
- Drift-Diffusion Systems:Variational Principles and Fixed Point Maps for Steady-State Semiconductor Models
- Numerical Approximation of PDE System Fixed-Point Maps via Newton's Method
- Modular Algorithms for Transient Semiconductor Device Simulation (with W.E. Coughran)