# Jianfeng Lu

• Associate Professor of Mathematics
• Associate Professor of Chemistry (Secondary)
• Associate Professor of Physics (Secondary)
External address: 242 Physics Bldg, 120 Science Drive, Durham, NC 27708
Internal office address: Mathematics Department, Duke University, Box 90320, Durham, NC 27708
Phone: (919) 660-2875

### Research Areas and Keywords

##### Analysis
electronic structure models, calculus of variations, semiclassical analysis
##### Computational Mathematics
electronic structure models, multiscale modeling and simulations, numerical analysis, rare events simulation, computational physics, time-frequency analysis, fast algorithms, stochastic numerical methods, kinetic equations, nonlinear Schrodinger equations, quantum chemistry, computational statistical mechanics, optimization, high frequency wave propagation
##### Mathematical Physics
electronic structure models, quantum chemistry, kinetic theory, quantum information
##### PDE & Dynamical Systems
multiscale modeling and simulations, numerical analysis, calculus of variations, kinetic equations, Schroedinger equations
##### Physical Modeling
electronic structure models, multiscale modeling and simulations, rare events simulation, computational physics, kinetic equations, nonlinear Schroedinger equations, quantum chemistry, computational statistical mechanics
##### Probability
rare events simulation, computational statistical mechanics, stochastic numerical methods
##### Signals, Images & Data
time-frequency analysis, fast algorithms, optimization, applied harmonic analysis

Jianfeng Lu is an applied mathematician interested in mathematical analysis and algorithm development for problems from computational physics, theoretical chemistry, materials science and other related fields.

More specifically, his current research focuses include:
Electronic structure and many body problems; quantum molecular dynamics; multiscale modeling and analysis; rare events and sampling techniques.

##### Education & Training
• Ph.D., Princeton University 2009

Li, C, Lu, J, and Yang, W. "Gentlest ascent dynamics for calculating first excited state and exploring energy landscape of Kohn-Sham density functionals." The Journal of chemical physics 143.22 (December 2015): 224110-. Full Text

Yang, H, Lu, J, Brown, WP, Daubechies, I, and Ying, L. "Quantitative Canvas Weave Analysis Using 2-D Synchrosqueezed Transforms: Application of time-frequency analysis to art investigation." IEEE Signal Processing Magazine 32.4 (July 2015): 55-63. Full Text Open Access Copy

Lu, J, and Mendl, CB. "Numerical scheme for a spatially inhomogeneous matrix-valued quantum Boltzmann equation." Journal of Computational Physics 291 (June 2015): 303-316. Full Text Open Access Copy

Lu, J, Liu, JG, and Margetis, D. "Emergence of step flow from an atomistic scheme of epitaxial growth in 1+1 dimensions." Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 91.3 (March 4, 2015). Full Text Open Access Copy

Lu, J, and Nolen, J. "Reactive trajectories and the transition path process." Probability Theory and Related Fields 161.1-2 (February 2015): 195-244. Full Text Open Access Copy

Liu, J, Lu, J, and Zhou, X. "Efficient Rare Event Simulation for Failure Problems in Random Media." SIAM Journal on Scientific Computing 37.2 (January 2015): A609-A624. Full Text Open Access Copy

Yang, H, Lu, J, and Ying, L. "Crystal Image Analysis Using 2D Synchrosqueezed Transforms." Multiscale Modeling & Simulation 13.4 (January 2015): 1542-1572. Full Text Open Access Copy

Lu, J, and Marzuola, JL. "Strang splitting methods for a quasilinear Schrödinger equation: convergence, instability, and dynamics." Communications in Mathematical Sciences 13.5 (2015): 1051-1074. Full Text Open Access Copy

Lai, R, Lu, J, and Osher, S. "Density matrix minimization with ${\ell}_1$ regularization." Communications in Mathematical Sciences 13.8 (2015): 2097-2117. Full Text Open Access Copy