Ngoc Thanh Do

Research Interests:

• Analysis of PDEs, Wave propagation
• Inverse problems, Integral transforms of Radon type and their applications, Hybrid methods (TAT, PAT, MAET, etc)
• Spectral theory, Periodic Differential Operators, Nanomaterials

Publications and preprints:

Peer-reviewed papers:

• Do N., Kunyansky L., Theoretically exact photoacoustic reconstruction from spatially and temporally reduced data, Inverse Problems, Vol. 34, No. 9 (2018) arxiv
• Do N., Kuchment P., Ong B., On resonant spectral gap opening in quantum graph networks, Functional Analysis and Operator Theory for Quantum Physics, European Mathematical Society (2017) arxiv
• Do N., On the quantum graph spectra of graphyne nanotubes, Analysis and Mathematical Physics, Vol. 5.1, pp. 39-65, (2015) arxiv
• Do N., Kuchment P., Quantum graph spectra of a graphyne structure, Nanoscale Systems: Mathematical Modeling, Theory and Applications, Vol. 2, pp. 107-123 (2013) arxiv
• Do N.T., Levenshtam V.B., Asymptotic integration of a system of differential equations with high-frequency terms in the critical case, Differential Equations, Vol. 48, No. 8, pp. 1177-1179 (2012) pdf
• Do N.T., Levenshtam V.B., Asymptotic integration of system of differential equations with a large parameter in critical case, Computational Mathematics and Mathematical Physics, Vol. 51, No. 6, pp. 975-986 (2011) pdf
• Simonenko I.B., Do N.T., Asymptotics form of the lowest eigenvalues of truncated Toeplitz matrices with positive symbol, having power-logarithmic zero, Scientific educational and applied journal Izvestiya VUZov, Severo-Kavkazskii region, Natural sciences, Vol.3, pp.18-22, in Russian (2009) pdf

In preparation:

• Do N., Stability of inverse source problem for the wave equation with reduced data
• Do N., Kuchment P., Sottile F., On the generic structure of spectral edges for periodic difference operators

Other:

• Do N., PhD Thesis, 2016

Talks and Poster:

Invited Talks:

• Theoretically exact solution of the inverse source problem for the wave equation with spatially and temporally reduced data
• ---Special Session on Recent Advances in Inverse Problems and Imaging, JMM, Baltimore, 01/2019
• Inverse source problem for the wave equation with reduced data: an explicit solution
• ---Inverse Problems Seminar, Texas A&M University, 10/2018
• Quantum graph and some applications in nano-science and solid state
• --- Measure Theory Seminar, Kent State University, 10/2015
• On the genericity of non-degenerate spectral edges
• --- Gauge Theory and Mathematical Physics Seminar, Michigan State University, 03/2015
• Quantum graph model of a graphyne and graphyne nanotubes
• --- Spectral Theory section, AMS Sectional Meeting, University of New Mexico, 04/2014

Local Seminar Talks:

• Inverse source problem for the wave equation with reduced data: an explicit solution
• ---Modeling and Computation Seminar, University of Arizona, 02/2018
• Quantum graph and some applications in nano-science and solid state
• --- Mathematical Physics and Harmonic Analysis Seminar, Texas A&M University, 10/2014
• "E" vs. "y" or quantum graph model of graphyne structure
• --- Graduate Student Seminar, Texas A&M University, 10/2013
• --- Mathematical Physics and Harmonic Analysis Seminar, Texas A&M University, 02/2013

Contributed Talks:

• Theoretically exact solution of the inverse source problem for the wave equation with spatially and temporally reduced data
• --- Summer School Waves and Particles in Random Media: Theory and Applications, Colorado State University, 05/2018
• Quantum graph and some applications in nano-science and solid state
• --- Joint Mathematics Meetings, San Antonio, 01/2015
• --- Texas Analysis and Mathematical Physics Symposium, University of Texas at Austin, 11/2014
• Quantum graph model of a graphyne and graphyne nanotubes
• --- Joint Mathematics Meetings, Seattle, 01/2016
• --- Prairie Analysis Seminar, Kansas State University, 09/2015

Poster:

• Some graph models in nano-science and solid state
• --- AWM Poster Session, Joint Mathematics Meetings, Seattle, 01/2016
• --- Waves, Spectral Theory, and Applications, Princeton University, 09/2015
• --- Inverse problems and Spectral Theory, Texas A&M University, 10/2014