Chung-Sang Ng

(Home)	(Office)
P. O. Box 750224	Geophysical Institute
Fairbanks, AK 99775	University of Alaska Fairbanks
	PO Box 757320
	Fairbanks, AK 99775

E-mail: chung-sang.ng@gi.alaska.edu	Tel: (907) 474-7367

Download a pdf file of my latest CV: Ng-latest-cv.pdf

Work Experience

2008 -- present         Associate Professor, University of Alaska Fairbanks
2003 -- 2008         Research Assistant Professor, University of New Hampshire
2006 -- 2008         Adjunct Associate Professor, University of Maryland University College
2002 -- 2003            Associate Research Scientist, The University of Iowa

1996 -- 2002 Assistant Research Scientist, The University of Iowa

1994 -- 1996 Research Investigator, The University of Iowa

1989 -- 1994 Research/Teaching Assistant, Auburn University

1988 -- 1989 Full-time Teaching Assistant, The Chinese University of Hong Kong

1986 -- 1988 Graduate Teaching Assistant, The Chinese University of Hong Kong

Education

1994 Ph.D. Auburn University, Auburn, Alabama, USA

1988 M.Phil. The Chinese University of Hong Kong, Hong Kong

1986 B.S. The Chinese University of Hong Kong, Hong Kong

Research Interests

Main area: Theoretical/computational plasma physics, with applications in space and fusion plasmas. Topics (main results/publications -- see list below): MHD turbulence (show general existence of 3-wave interaction [11], derive scaling of weak turbulence [13,18,25], confirm IK spectrum and local anisotropy in 2D MHD simulations [29,30,37], show importance of background inhomogeneity in compressible turbulence [14,22], show consistency of IK energy cascade with solar wind heating observations [43]), heating of the solar corona (analytical and computational support of the Parker's theory [17], developing new computational scheme [40,41], show that heating rate is independent of dissipation mechanism with random footpoint motion [39,45,48], and relate to complex systems [ongoing work]) and heating of the solar wind [43,46], Landau damping (show a complete discrete spectrum which tends to Landau's roots in weak collision limit [21,31,35], support experimental work [24,28]), BGK modes (exact 3D Vlasov solutions [33], 2D Vlasov-Maxwell solutions [35,44], stability studies [50], and in dusty plasmas [in preparation]), magnetic reconnection (analytic support of simulations of solar corona [9], and lab plasmas [32,36], systems with multiple magnetic null points [42] or turbulence [47] ), dusty plasmas (simulations of void [34,38]), field-line resonances in ionosphere/magnetosphere (analysis [23] and simulations [ongoing work]), hydrodynamic singularities (possible Euler singularity in a model [10], and the highly-symmetric Kida flow [12,27]), free-electron laser (describe an oscillator by the Ginzburg-Landau model [19-20], study mode competition [15-16], and application in whistler waves in the magnetosphere [49]), mode conversion in fusion plasmas (new method in calculating scattering parameters [5,6], emission [7,8]), classical electrodynamics (new method of calculating radiation energy from a point charge [4], radiation from a moving source in media [2,3], axially enhanced radiation in plasmas [1] and biaxial media [26]).

Grants

Principal Investigator: National Science Foundation Award PHY-1004357, Nonlinear Studies of a Weakly Collisional Plasma: Landau Damping and 3D BGK Modes, $435,000, 09/01/2010 -- 08/31/2013.

Principal Investigator: National Science Foundation Award AGS-0962477, SHINE: Self-Consistent Turbulent Magnetic Reconnection in the Solar Corona, $383,718, 04/01/2010 -- 03/31/2013.

Principal Investigator: National Aeronautics and Space Administration Award NNX08BA71G, Heating and Acceleration of the Solar Wind and Corona by Anisotropic MHD and Hall MHD Turbulence, $370,909, 09/01/2008 -- 08/31/2011.

Principal Investigator: National Science Foundation Award AST-0434322, Spectral Element Method for the Study of Current Sheets in Astronomical Magnetic Fields, $449,789, 10/01/2004 -- 09/30/2008.

Principal Investigator: Grants of HPC resources from the Arctic Region Supercomputing Center and the DoD High Performance Computing Modernization Program, 480,000 total CPU hours of allocation since October, 2008 to present.

Teaching Experience

2011 PHYS 632 Electromagnetic Theory II

2010 PHYS 471C Space and Auroral Physics

2010 PHYS 631 Electromagnetic Theory I

2010 support and advise two graduate students on their research for master degrees

2009 PHYS 626 Fundamentals of Plasma Physics

2009 direct a research project for a graduate student during the summer

2009/2010 PHYS 301 Introduction To Mathematical Physics

2007-2008 Support and advise a graduate student on PhD research

2007 NSCI 100 Introduction to Physical Science (online course with UMUC)

2007 PHYS 407 General Physics I

2006 Took a course to learn the online teaching system at UMUC

2006 PHYS/EOS 940. Physics of Fluids

2005 PHYS 407 General Physics I

2005 PHYS/EOS 712/812 Introduction to Space Plasma Physics

2004 PHYS 401 Introduction to Physics I

2004 PHYS 407R General Physics I Recitation

1986-1994 Statistical Mechanics Recitation, Modern Physics Recitation, Quantum Mechanics Recitation, Nuclear Physics Lab, Modern Physics Lab, Optics Lab, Electronics Lab, E &M Lab, General Physics Labs

Partial List of Invited/Selected Talks in Conferences/Workshops

2011 Invited talk: Large-Scale High-Lundquist Number Reduced MHD Simulations of the Solar Corona using GPU Accelerated Machines, ASTRONUM-2011 - the 6th Annual International Conference on Numerical Modeling of Space Plasma Flows, Valencia, Spain, June 13-17.

2011 Invited talk: Electrostatic Structures in Space Plasmas: Properties of Two-dimensional Magnetic Bernstein-Greene-Kruskal Modes, 10th Annual International Astrophysics Conference: Physics of the Heliosphere: A 10-year Retrospective, Maui, Hawaii, March 13 - 18 (download movies here).

2010 Invited talk: High Lundquist Number Resistive MHD Simulations of Magnetic Reconnection: Searching for Secondary Island Formation, ASTRONUM-2010 - the 5th Annual International Conference on Numerical Modeling of Space Plasma Flows, San Diego, California, June 13-18.

2010 Invited talk: The Effect of Magnetic Turbulence Energy Spectra and Pickup Ions on The Heating of the Solar Wind, 9th Annual International Astrophysics Conference: Pickup Ions Throughout the Heliosphere and Beyond, Maui, Hawaii, March 14 - 19.

2009 Invited talk: Three Dimensional Simulations of the Parker's Model of Solar Coronal Heating: Lundquist Number Scaling due to Random Photospheric Footpoint Motion, ASTRONUM-2009 -- the 4th International Conference on Numerical Modeling of Space Plasma Flows, June 29th - July 3rd, 2009, Chamonix , France.

2008 I nvited talk: A Comparison of Spectral Element and Finite Difference Methods Using Statically Refined Nonconforming Grids for the MHD Island Coalescence Instability Problem, ASTRONUM-2008 -- the 3rd International Conference on Numerical Modeling of Space Plasma Flows at St. John, U.S. Virgin Islands

2007 Selected talk: The Effect of Magnetic Turbulence Energy Spectral Scaling on the Heating of the Solar Wind, Living With a Star Science Workshop 2007, Boulder, Colorado

2007 Invited talk: Anisotropic MHD Turbulence, Sixth IGPP Annual International Astrophysics Conference on "Turbulence and Nonlinear Processes in Astrophysical Plasmas" in Honolulu, Hawaii

2005 Invited talk: Weakly Collisional Landau Damping and 3D BGK Modes: New Results on Old Problems , 47th Annual Meeting, APS Division of Plasma Physics, Denver, Colorado

2003    Invited talk: Four-field model for dispersive field-line resonances, 7th Workshop on the Interrelationship between Plasma Experiment in Laboratory and Space (IPELS) in Whitefish, Montana

2002    Invited talk: Anisotropic MHD turbulence in the interstellar medium and the solar wind, 44th Annual Meeting, APS Division of Plasma Physics, Orlando, Florida

2002    Invited talk: Non-equilibrium and current sheet formation in line-tied magnetic fields, Mini-Conference on Singularities in Fluids and Plasmas, 44th Annual Meeting, APS Division of Plasma Physics, Orlando, Florida

1999    Invited talk: Anisotropic MHD turbulence spectra due to the weak interaction of shear-Alfven wave packets, Mini-Conference on Turbulence in the Interstellar Medium and Solar Wind, 41st Annual Meeting, APS Division of Plasma Physics, Seattle, Washington

1998    Selected talk: Interaction of shear-Alfven wave packets: implication for anisotropic MHD turbulence in the interstellar medium, Interstellar Turbulence, Guillermo Haro International Program, Puebla, Mexico.

Refereed Publications (472 total citations according to ISI as of 9/27/10)

Five most cited papers: [11] -- 114 citations; [13] -- 54; [14] -- 50; [25] -- 38; [29] -- 33
Five most frequently cited: [11] -- 7.6/yr; [32] -- 4.83/yr; [29] -- 4.13/yr; [13] -- 3.86/yr; [25] -- 3.8/yr

[50] C. S. Ng, S. J. Soundararajan, and E. Yasin, Electrostatic Structures in Space Plasmas: Stability of Two-dimensional Magnetic Bernstein-Greene-Kruskal Modes, submitted to AIP Conf. Proc. [http://arxiv.org/abs/1106.4073] (2011).

[49] A. R. Soto Chavez, A. Bhattacharjee, and C. S. Ng, Whistler Amplification: A Free Electron Laser in the Earth's Magnetosphere, submitted to Phys. Rev. Lett. (2011).

[48] C. S. Ng, L. Lin, and A. Bhattacharjee, High-Lundquist Number Scaling in Three-Dimensional Simulations of the Parker's Model of Solar Coronal Heating due to Random Photospheric Footpoint Motion, submitted to Astrophys. J. [http://arxiv.org/abs/1106.0515] (2011).

[47] C. S. Ng, and S. Ragunathan, High-Lundquist Number Resistive MHD Simulations of Turbulent Magnetic Reconnection with Secondary Island Formation and Enhanced Reconnection Rate, ASP Conference Series, in press [http://arxiv.org/abs/1106.0521] (2011).

[46] C. S. Ng, A. Bhattacharjee, D. Munsi, P. A. Isenberg, and C. W. Smith, The Effect of Magnetic Turbulence Energy Spectra and Pickup Ions on the Heating of the Solar Wind, AIP Conf. Proc., 1302, 174 [http://arxiv.org/abs/1106.0528] (2010).

[45] C. S. Ng, L. Lin, and A. Bhattacharjee, Three-Dimensional Simulations of the Parker's Model of Solar Coronal Heating: Lundquist Number Scaling due to Random Photospheric Footpoint Motion, ASP Conference Series, 429, 201 (2010).

[44] C. S. Ng and A. Bhattacharjee, Response to "Comment on 'Weakly collisional Landau damping and three-dimensional Bernstein-Greene-Kruskal modes: New results on old problems'", Phys. Plasmas 17, 054701 (2010).

[43]    C. S. Ng, A. Bhattacharjee, D. Munsi, P. A. Isenberg, and C. W. Smith, Kolmogorov versus Iroshnikov-Kraichnan spectra: Consequences for ion heating in the solar wind, J. Geophys. Res., 115, A02101 (2010).

[42]    X. H. Deng, M. Zhou, S. Y. Li, W. Baumjohann, M. Andre, N. Cornilleau, O. Santolik, D. I. Pontin, H. Reme, E. Lucek, A. N. Fazakerley, P. Decreau, P. Daly, R. Nakamura, R. X. Tang, Y. H. Hu, Y. Pang, J. Buchner, H. Zhao, A. Vaivads, J. S. Pickett, C. S. Ng, X. Lin, S. Fu, Z. G. Yuan, Z. W. Su, and J. F. Wang, Dynamics and waves near multiple magnetic null points in reconnection diffusion region, J. Geophys. Res., 114, A07216, doi:10.1029/2008JA013197 (2009).

[41]    C. S. Ng, D. Rosenberg, K. Germaschewski, A. Pouquet, and A. Bhattacharjee, A Comparison of spectral element and finite difference methods using statically refined nonconforming grids for the MHD island coalescence instability problem, ASP Conference Series, 406, 255 (2009).

[40] C. S. Ng, D. Rosenberg, K. Germaschewski, A. Pouquet, and A. Bhattacharjee, A Comparison of Spectral Element and Finite Difference Methods Statically Refined Nonconforming Grids for the MHD Island Coalescence Instability Problem, Astrophys. J. Suppl., 177, 613 (2008).

[39] C. S. Ng and A. Bhattacharjee, A Constrained Tectonics Model for Coronal Heating, Astrophys. J., 675, 899 (2008).

[38] C. S. Ng, A. Bhattacharjee, S. Hu, Z. W. Ma, and K. Avinash, Generalizations of a nonlinear fluid model for void formation in dusty plasmas, Plasma Phys. Control. Fusion, 49, 1583 (2007).

[37] C. S. Ng and A. Bhattacharjee, Anisotropic MHD Turbulence, AIP Conf. Proc., 932, 137 (2007).

[36] K. Germaschewski, A. Bhattacharjee, and C. S. Ng, The Magnetic Reconnection Code: an AMR-based fully implicit simulation suite, ASP Conf. Ser., 359, 151 (2006).

[35] C. S. Ng, A. Bhattacharjee, and F. Skiff, Weakly Collisional Landau Damping and Three-Dimensional Bernstein-Greene-Kruskal Modes: New Results on Old Problems, Phys. Plasmas, 13, 055903 (2006).

[34] A. Bhattacharjee, C. S. Ng, K. Avinash, S. Hu, and Z. W. Ma , Nonlinear Theory and Simulation of Void Formation in Dusty Plasmas, AIP Conf. Proc. 799 145 (2005).

[33] C. S. Ng and A. Bhattacharjee, Bernstein-Greene-Kruskal Modes in a Three-Dimensional Plasma, Phys. Rev. Lett., 95, 245004 (2005).

[32] A. Bhattacharjee, K. Germaschewski, and C. S. Ng, Current Singularities: Drivers of Impulsive Reconnection, Phys. Plasmas, 12, 042305 (2005).

[31] C. S. Ng, A. Bhattacharjee, and F. Skiff, Complete Spectrum of Kinetic Eigenmodes for Plasma Oscillations in a Weakly Collisional Plasma, Phys. Rev. Lett., 92, 065002 (2004).

[30] A. Bhattacharjee and C. S. Ng, Anisotropic MHD Turbulence in the Interstellar Medium and Solar Wind, AIP Conf. Proc., 679, 433 (2003).

[29] C. S. Ng, A. Bhattacharjee, K. Germaschewski, and S. Galtier, Anisotropic Fluid Turbulence in the Interstellar Medium and the Solar Wind, Phys. Plasmas, 10, 1954 (2003).

[28] F. Skiff, H. Gunell, A. Bhattacharjee, C. S. Ng, and W. A. Noonan, Electrostatic Degrees of Freedom in Non-Maxwellian Plasma, Phys. Plasmas, 9, 1931 (2002).

[27] C. S. Ng, and A. Bhattacharjee, Sufficient condition for finite-time singularity and tendency towards self-similarity in a high-symmetry flow, in "TUBES, SHEETS and SINGULARITIES in FLUID DYNAMICS", K. Bajer, and H. K. Moffatt (Eds.) (Kluwer, Dordrecht, 2002) pp. 317-328.

[26] H. M. Lai, B. Y. Xu, and C. S. Ng, Unusual 1/r-Dependent Radiation Intensity in any Biaxial Crystal, Phys. Rev. E, 64, 016606 (2001).

[25] A. Bhattacharjee, and C. S. Ng, Random Scattering and Anisotropic Turbulence of Shear-Alfven Wave Packets, Astrophys. J., 548, 318 (2001).

[24] F. Skiff, C. S. Ng, A. Bhattacharjee, W. A. Noonan, and A. Case, Wave-particle Interaction, Plasma Phys. Contr. Fusion, 42, B27 (2000).

[23] A. Bhattacharjee, C. A. Kletzing, Z. W. Ma, C. S. Ng, N. F. Otani, and X. Wang, Four-Field Model for Dispersive Field-Line Resonances: Effects of Coupling between Shear-Alfven and Slow Modes, Geophys. Res. Lett., 26, 3281 (1999).

[22] A. Bhattacharjee, C. S. Ng, S. Ghosh, and M. L. Goldstein, A Comparative Study of Four-Field and Fully Compressible Magnetohydrodynamic Turbulence in the Solar Wind, J. Geophys. Res., 104, 24835 (1999).

[21] C. S. Ng, A. Bhattacharjee, and F. Skiff, Kinetic Eigenmodes and Discrete Spectrum of Plasma Oscillations in a Weakly Collisional Plasma, Phys. Rev. Lett., 83, 1974 (1999).

[20] C. S. Ng, and A. Bhattacharjee, Ginzburg-Landau Model for a Long-Pulse Low-Gain Free-Electron Laser Oscillator, Nucl. Instrum. Methods Phys. Res. A, 429, 88, (1999).

[19] C. S. Ng, and A. Bhattacharjee, Ginzburg-Landau Model and Single-Mode Operation of a Free-Electron Laser Oscillator, Phys. Rev. Lett., 82, 2665 (1999).

[18] A. Bhattacharjee, and C. S. Ng, Reduced Models of Magnetohydrodynamic Turbulence in the Interstellar Medium and the Solar Wind, in "Nonlinear MHD waves and turbulence: proceedings of the workshop, held in Nice, France, 1-4 December 1998", T. Passot, P.-L. Sulem (eds.) (Springer, Berlin, 1999) pp. 182-197.

[17] C. S. Ng, and A. Bhattacharjee, Non-Equilibrium and Current Sheet Formation in Line-Tied magnetic Fields, Phys. Plasmas, 5, 4028 (1998).

[16] C. S. Ng, and A. Bhattacharjee, Ginzburg-Landau Model for Mode Competition and Single-Mode Operation of a Free-Electron Laser, Phys. Rev. E., 58, 3826 (1998).

[15] C. S. Ng, and A. Bhattacharjee, Ginzburg-Landau Model for a Free-Electron Laser: From Single Mode to Spikes, Nucl. Instrum. Methods Phys. Res. A., 407, 34 (1998).

[14] A. Bhattacharjee, C. S. Ng, and S. R. Spangler, Weakly Compressible Magnetohydrodynamic Turbulence in the Solar Wind and the Interstellar Medium, Astrophys. J., 494, 409 (1998).

[13] C. S. Ng, and A. Bhattacharjee, Scaling of Anisotropic Energy Spectra Due to the Weak Interaction of Shear-Alfven Wave Packets, Phys. Plasmas, 4, 605 (1997).

[12] C. S. Ng, and A. Bhattacharjee, Sufficient Condition for a Finite-Time Singularity in a High-Symmetry Euler Flow: Analysis and Statistics, Phys. Rev. E, 54, 1530 (1996).

[11] C. S. Ng, and A. Bhattacharjee, Interaction of Shear Alfven Wave Packets: Implication for Weak MHD Turbulence in Astrophysical Plasmas, Astrophys. J., 465, 845 (1996).

[10] A. Bhattacharjee, C. S. Ng and Xiaogang Wang, Finite-Time Vortex Singularity and Kolmogorov Spectrum in a Symmetric Three Dimensional Spiral Model, Phys. Rev. E, 52, 5110 (1995).

[9] Z. W. Ma, C. S. Ng, Xiaogang Wang, and A. Bhattacharjee, Dynamics of Current Sheet Formation and Reconnection in Two Dimensional Coronal Loops, Phys. Plasmas, 2, 3184 (1995).

[8] C. S. Ng, V. F. Shvets and D. G. Swanson, Inhomogeneous Cyclotron Emission Source for the Five Branch Mode Conversion Problem, Phys. Plasmas, 2, 1791 (1995).

[7] D. G. Swanson and C. S. Ng, Modification of Emission from the X-mode at the Third Electron Cyclotron Harmonic from Mode Conversion and Reflection, Phys. Plasmas, 2, 599 (1995).

[6] C. S. Ng and D. G. Swanson, Analytic Calculation of the Certain Scattering Parameters from a Mode Conversion Analysis of X-mode--O-mode Coupling, Phys. Plasmas, 1, 3751 (1994).

[5] C. S. Ng and D. G. Swanson, Analytic Calculation of the Nonzero Fast Wave Reflection Coefficient from the Tunneling Equation with Absorption, Phys. Plasmas, 1, 815 (1994).

[4] Chung-Sang Ng, Energy Conservation of a Uniformly Accelerated Point Charge, Phys. Rev. E, 47, 2038 (1993).

[3] H. M. Lai and C. S. Ng, Analytic Expressions for Far Fields and Radiation Fluxes Caused by a Moving Source in some Anisotropic Dispersive Media, Phys Fluids B, 2, 1968 (1990).

[2] H. M. Lai and C. S. Ng, Relation Between Emitted and Received Powers from a Moving Radiating Source in a Medium, Astro. Lett. and Communications, 28, 27 (1990).

[1] H. M. Lai, C. S. Ng, and S. S. Tong, Axially Enhanced Far Field and Radiation Flux in a Magnetoplasma, Phys. Rev. A, 40, 959 (1989).

Some Recent Presentations

2011 UAF-Journal Club: Electrostatic Structures in Space Plasmas

2010 UAF-Journal Club: Random Walk on the Surface of the Sun

2010 UAF-Journal Club: What do I get from giving a Journal Club talk? How about publishing a paper on it!

2008 UAF-Journal Club: Bernstein-Greene-Kruskal Mode in Two or Three Dimensions

2007 CMSO general meeting: Solar Wind Heating by MHD Turbulence

2006 APS/DPP meeting: Three-dimensional Bernstein-Greene-Kruskal modes in a multi-species plasma: Void solutions in a dusty plasma?

2006 APS/DPP meeting: Spectral-element adaptive refinement magnetohydrodynamic simulations of the island coalescence instability

2005 AGU Fall meeting: Turbulent Magnetic Reconnection Near a 3D Magnetic Null

2005 APS/DPP meeting: Theory and Simulation of a Nonlinear Fluid Model for Void Formation in Dusty Plasmas

2005 UNH-Space Science Center Seminar: Bernstein-Greene-Kruskal (BGK) Modes in a Three Dimensional Unmagnetized Plasma

2005 UAH- Physics Colloquium: Non-Equilibrium and Current Sheet Formation in Line-Tied Magnetic Fields: Heating of the Solar Corona

2004 APS/DPP meeting: Theory and Simulation of a Nonlinear Fluid Model for Void Formation in Dusty Plasmas

2003 APS/DPP meeting: Complete Spectrum of Kinetic Eigenmodes for Plasma Oscillations in a Weakly Collisional Plasma

Partial List of Conference Presentations (115)

Services

2011 -- present: Senator of the Faculty Senate representing CNSM of UAF.

2009 -- present: help coordinating Physics Journal Club.

2009 -- 2011: Senator Alternate representing CNSM of UAF.

2009 -- present: member of the Publication Committee of the American Physical Society/Division of Plasma Physics.

2009 -- present: member of graduate committees for five graduate students at UAF.

2009: member of the search committee for a new faculty position at Physics/GI at UAF.

2008 -- present: external member of a graduate committee for a graduate student at UNH.

2008 -- 2009: chair of a search committee for a Postdoctoral Research Fellow at UAF.

2007 -- 2008: direct an undergraduate research project for a summer exchange student from India at UNH for two summers

2004 -- 2006: coordinator of the Graduate Student Journal Club at UNH.

2004: participate in the Project SMART (Science and Mathematics Achievement through Research Training) at UNH.

2004: scientific proof-reader of the textbook: Introduction to Plasma Physics: With Space and Laboratory Applications, by D. A. Gurnett and A. Bhattacharjee, Cambridge University Press, 2005.

Regularly served as Referee/Reviewer/Panelist: National Aeronautics and Space Administration, National Science Foundation, Physics of Plasmas, Physical Review, Journal of Geophysical Research, New Journal of Physics, etc; as well as judges for local science fairs/competitions.

Dissertations

1994 Ph.D. dissertation, Auburn University: Analytic Calculations of Certain Scattering Parameters from Mode Conversion Equations

(advisor: D. G. Swanson)

1988 M. Phil. thesis, The Chinese University of Hong Kong: Characteristics of Far Field and Energy Flow Due to a Moving Radiation Source in Various Media

(advisor: H. M. Lai) (In memory of late Professor Tom Stix: see his Examiner's report, and the citations of our works in his classic book, Waves in Plasmas)

Computing Skills

Machines: Supercomputers, Vax, Workstations, PC, Macintosh

Languages: MPI, Fortran, Pascal, Mathematica, Macsyma, Unix Shell

Libraries: NAG, TV80, NCAR Graphics, IDL, SAS

Experience: MHD simulations, Integral Equation, ODE Solvers, 3D Ray Tracing, Minimization, Finite Difference, Finite Elements, Symbolic Calculation

Typesetting: TeX, LaTeX, REVTeX

Honors