Education

• Ph.D. in Applied Mathematics (Sept. 2007–Present)
  Northwestern University, Evanston, IL.
• M.S. in Applied Mathematics (Sept. 2007–June 2008)
  Northwestern University, Evanston, IL.
• M.S. in Mathematics (Aug. 2005–May 2007)
  Texas A&M University, College Station, TX.
• S.B. in Mathematics (Applied Option) (Sept. 2002–June 2005)
  Massachusetts Institute of Technology, Cambridge, MA.

Research Interests

• Complex and Nonlinear Systems: the study of the mechanics of natural phenomena using advanced mathematical techniques and state-of-the-art computational simulations; in particular: mixing and self-organization of granular matter, shock-formation in compressible flows, dynamics of coherent structures in nonlinear evolution equations, nonlinear Fourier analysis of physical data.
• Numerical Methods/Analysis: the development of high-performance reliable simulation techniques for real-world applications; in particular: Godunov-type schemes for conservation laws and Hamilton–Jacobi equations, finite-volume methods for reservoir simulation, wavelet-Galerkin methods for nonlinear partial differential equations, L¹-minimization finite element methods.

Work/Research Experience

• Northwestern University, McCormick School of Engineering and Applied Science (Sept. 2008–present) Used dynamical systems theory to elicit the physics of mixing and segregation in liquid and dry granular systems as a Graduate Research Assistant under the direction of Profs. J.M. Ottino and R.M. Lueptow.
• ExxonMobil Upstream Research Company (June 2008–Sept. 2008) Designed and implemented efficient higher-order finite volume methods for hyperbolic multiphase, multicomponent fluid flow equations on unstructured Voronoi meshes and applied these techniques to problems in reservoir simulation as a Summer Intern; supervised by Dr. Ilya D. Mishev.
• U.S. Naval Research Laboratory, Stennis Space Center (June 2007–Aug. 2007) Investigated the formation & propagation of acoustic, thermal and traffic shock waves, and applied nonlinear Fourier analysis to data of internal solitary waves in the ocean as a Summer Intern with the Acoustics Division; joint work with Drs. P.M. Jordan, S.A. Chin-Bing and A.C. Warn-Varnas funded by the Naval Research Enterprise Intern Program (NREIP).
• Texas A&M University, Department of Mathematics (Aug. 2006–May 2007) Designed and implemented a new nonoscillatory Godunov-type central scheme for solving hyperbolic systems of nonlinear conservation laws on unstructured triangulations as a Graduate Research Assistant; joint work with Prof. Bojan Popov funded, in part, by NSF grant DMS-0510650.
• U.S. Naval Research Laboratory, Stennis Space Center (June 2005–Aug. 2005) Investigated acoustic shock formation & propagation, and applied nonlinear Fourier analysis to data of internal solitary wave in the ocean as a Summer Intern with the Acoustics Division; joint work with Drs. P.M. Jordan and S.A. Chin-Bing funded by NRL's Student Summer Employment Program.
• Massachusetts Institute of Technology, Department of Mathematics (Sept. 2004–June 2005) Developed simulation tools for investigating the breaking of internal waves in two-dimensional stratified, rotating lakes under gravity; joint work with Prof. Roman Stocker funded by MIT’s Undergraduate Research Opportunities Program (UROP).
• Texas A&M University, Department of Mathematics (June 2004–Aug. 2004) Investigated the wavelet-Galerkin solution of the Korteweg–de Vries equation at the Research Experience for Undergraduates program on "Wavelets and Matrix Analysis"; supervised by Prof. D.R. Larson and funded through NSF grant DMS-0243822. A final report of my research is available in PDF.
• Massachusetts Institute of Technology, Department of Mathematics (Feb. 2004–June 2004) Investigated image anti-aliasing using a wavelet edge detection algorithm; supervised by Prof. Gilbert Strang and funded by MIT’s Undergraduate Research Opportunities Program (UROP). A preliminary report, including some results, can be found in Section 5 of the following PDF document.
• Texas A&M University, Department of Mathematics (June 2003–Aug. 2003) Investigated wavelet-Galerkin methods for partial differential equations at the Research Experience for Undergraduates program on "Wavelets and Matrix Analysis"; supervised by Prof. D.R. Larson and funded through NSF grant DMS-0243822. A final report of my research is available in PDF.
• Laser Interferometer Gravitational Wave Observatory, Livingston (June 2002–Aug. 2002) Investigated de-correlation of interferometer signals as a Summer Undergraduate Research Fellow; supervised by Prof. Rainer Weiss (MIT).
• McNair Science and Technology Program (Sept. 2002–June 2003) Mentored Boston public school students on science fair projects.

Publications

Forthcoming:

5. Ivan C. Christov, Julio M. Ottino, Richard M. Lueptow, "Chaotic mixing via streamline jumping in quasi-two-dimensional tumbled granular flows," submitted.
4. Ivan C. Christov, "Hidden solitons in the Zabusky–Kruskal experiment: Analysis using the periodic, inverse scattering transform," submitted; e-print arXiv:0910.3345.
   * Winner of a Best Student Paper Award at the 6^th IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory.
3. Ivan C. Christov, P.M. Jordan, "On the Propagation of Second-Sound in Nonlinear Media: Shock, Acceleration and Traveling Wave Results," submitted.
2. Ivan C. Christov, Julio M. Ottino, Richard M. Lueptow, "Streamline Jumping: A New Mixing Mechanism," submitted.
1. Ivan Christov, C.I. Christov, "On the rotational inertia of spinning tops undergoing precession and nutation," submitted.

In Refereed Journals:

8. Ivan Christov, "Internal solitary waves in the ocean: Analysis using the periodic, inverse scattering transform," Mathematics and Computers in Simulation 80 (2009) 192–200, doi:10.1016/j.matcom.2009.06.005; e-print arXiv:0708.3421.
7. Ivan Christov, P.M. Jordan, "Shock and traveling wave phenomena on an externally damped, non-linear string," International Journal of Non-Linear Mechanics 44 (2009) 511–519, doi:10.1016/j.ijnonlinmec.2008.12.004.
   * Ranked 15^th out of the 25 most downloaded International Journal of Non-Linear Mechanics papers during April, May and June, 2009.
6. Ivan Christov, Bojan Popov, "New non-oscillatory central schemes on unstructured triangulations for hyperbolic systems of conservation laws," Journal of Computational Physics 227 (2008) 5736–5757, doi:10.1016/j.jcp.2008.02.007.
   * See also Other #5 below.
5. Ivan Christov, P.M. Jordan, "Shock bifurcation and emergence of diffusive solitons in a nonlinear wave equation with relaxation," New Journal of Physics 10 (2008) 043027, doi:10.1088/1367-2630/10/4/043027.
4. Ivan Christov, C.I. Christov, "Physical dynamics of quasi-particles in nonlinear wave equations," Physics Letters A 372 (2008) 841–848, doi:10.1016/j.physleta.2007.08.038; e-print arXiv:nlin/0612005.
3. Ivan Christov, C.I. Christov, P.M. Jordan, "Modeling weakly nonlinear acoustic wave propagation," The Quarterly Journal of Mechanics and Applied Mathematics 60 (2007) 473–495, doi:10.1093/qjmam/hbm017.
   * Ranked 5^th out of the 50 most downloaded QJMAM papers during September 2007 and 2^nd during October 2007.
2. Ivan Christov, C.I. Christov, P.M. Jordan, "Cumulative Nonlinear Effects in Acoustic Wave Propagation," CMES: Computer Modeling in Engineering & Sciences 17 (2007) 47–54.
1. Ivan Christov, P.M. Jordan, C.I. Christov, "Nonlinear acoustic propagation in homentropic perfect gases: A numerical study," Physics Letters A 353 (2006) 273–280, doi:10.1016/j.physleta.2005.12.101.
   * Ranked 11^th out of the 25 most downloaded Physics Letters A papers during April, May and June, 2006.

In Refereed Proceedings/Edited Volumes:

6. Ivan Christov, Ilya D. Mishev, Bojan Popov, "Finite volume methods on unstructured Voronoi meshes for hyperbolic conservation laws," in Hyperbolic Problems: Theory, Numerics and Applications, eds. E. Tadmor, J.-G. Liu, A.E. Tzavaras, Proceedings of Symposia in Applied Mathematics 67 (2009) 507–516.
   * Preprint available as Other #6 below.
5. I.C. Christov, C.I. Christov, "On the Inertial Force Experienced by a Solid Body Undergoing Rotation about Two Axes," in Proceedings of the 1^st International Conference on Applications of Mathematics in Technical and Natural Science (Sozopol, Bulgaria), eds. M.D. Todorov, C.I. Christov, AIP Conference Proceedings 1186 (2009) 226–230, doi:10.1063/1.3265333.
4. Ivan Christov, C.I. Christov, "The coarse-grain description of interacting sine-Gordon solitons with varying widths," in Dynamical Systems and Differential Equations: Proceedings of the 7^th AIMS International Conference (Arlington, TX, USA), eds. X. Hou, X. Lu, A. Miranville, J. Su, J. Zhu, Discrete and Continuous Dynamical Systems (DCDS) Supplement (2009) 171–180.
3. Ivan Christov, "Thermal shock waves under a Maxwell–Cattaneo model with temperature-dependent conductivity," Proceedings of the Eighth International Congress on Thermal Stresses (2009), eds. M. Ostoja-Starzewski, P. Marzocca, vol. II, 525–528. This article is available in PDF.
2. James A. Hawkins, Alex Warn-Varnas, Ivan Christov, "Fourier, Scattering, and Wavelet Transforms: Applications to Internal Gravity Waves with Comparisons to Linear Tidal Data," in Nonlinear Time Series Analysis in the Geosciences: Applications to Climatology, Geodynamics and Solar-Terrestrial Physics, eds. R.V. Donner, S.M. Barbosa, Springer Lecture Notes in Earth Sciences 112 (2008) 223–244, doi:10.1007/978-3-540-78938-3_10.
1. Stanley A. Chin-Bing, Alex C. Warn-Varnas, David B. King, Ivan Christov, "Using Ocean Acoustics to Improve Large Shallow-water Soliton Simulations," Proceedings of MTS/IEEE Oceans 2007 Conference (2007) 1754–1758, doi:10.1109/OCEANS.2007.4449377.

Other:

6. Ivan Christov, Ilya D. Mishev, Bojan Popov, "Finite Volume Methods on Unstructured Voronoi Meshes for Hyperbolic Conservation Laws," Preprint IAMCS-2008-30 (2008), Institute for Applied Mathematics and Computational Science, Texas A&M University.
5. Ivan Christov, Bojan Popov, "A Jiang–Tadmor Scheme on Unstructured Triangulations," Technical Report ISC-06-05-MATH (2006), Institute for Scientific Computation, Texas A&M University.
4. Jeff Baker, Ivan Christov, Simona Dediu, Elana Fertig, Wanda Strychalski, "Properties of a Gradient Descent Algorithm for Active Vibration Control," Proceedings of the Twelfth Industrial Mathematical and Statistical Modeling Workshop for Graduate Students, eds. Alina Chertock, Mansoor A. Haider, Mette S. Olufsen, Ralph C. Smith, Technical Report CRSC-TR06-23 (2006) 89–108, Center for Research in Scientific Computation, North Carolina State University.
3. Ivan Christov, "Shock Waves in a Tube," MIT Undergraduate Journal of Mathematics 7 (2005) 23–34. This article is available in PDF.
2. Ivan Christov, "Gyroscopic Systems as Alternative Propulsion Devices," FOLIO: Literary Journal of the Louisiana School for Math Science and the Arts (2002) 62–69.
1. Ivan Christov, "Integrating the Normal Curve," FOLIO: Literary Journal of the Louisiana School for Math Science and the Arts (2002) 5–8. This article is available in PDF.

Talks and Presentations

Invited Seminars and Colloquia:

• April 27, 2007 Co-author of an invited talk entitled "Nonoscillatory Central Schemes on Unstructured Meshes and Applications" by Ivan Christov, Bojan Popov and Peter Popov presented at the ExxonMobil Upstream Research Company, Houston, Texas.
• March 1, 2007 Presented a talk entitled "A Short Introduction to the Theory and Numerics of First-Order Hyperbolic PDEs" at the Graduate Student Seminar of the Department of Mathematics, Texas A&M University, College Station, Texas.
• November 2, 2006 Presented a talk entitled "Nonoscillatory Central Schemes on Unstructured Triangulations for Hyperbolic Systems of Conservation Laws" at the Department of Mathematics Colloquium, University of Louisiana at Lafayette. This talk is available in PDF.
• August 17, 2005 Presented a talk entitled "Solitary Internal Waves in the Ocean: The Scattering Transform Perspective" to the Acoustics Division (Code 7180) of the Naval Research Lab, Stennis Space Center, MS. This talk is available in PDF.
• August 5, 2005 Presented a talk entitled "Nonlinear Fourier Analysis: The Direct & Inverse Scattering Transforms for the Korteweg–de Vries Equation" to the Naval Research Laboratory (Stennis Space Center and Washington, DC contigents). This talk is available in PDF.

Conferences:

• June 3, 2009 Presented an invited talk entitled "Thermal shock waves under a Maxwell–Cattaneo model with temperature-dependent conductivity" at the Symposium on Second-Sound and Thermal Shock Phenomena, 8^th International Congress on Thermal Stresses, Urbana-Champaign, Illinois. This talk is available in PDF.
• March 25, 2009 Presented an invited talk entitled "Hidden solitons in the Zabusky–Kruskal experiment: Analysis using the periodic, inverse scattering transform" at the Special Session on Nonlinear Wave Phenomena in Discrete and Continuous Models, 6^th IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory, Athens, Georgia. This talk is available in PDF.
• May 18, 2008 Presented an invited talk entitled "The coarse-grain description of interacting sine-Gordon solitons with varying widths" at the Special Session on Nonlinear Waves and Solitons, 7^th AIMS International Conference on Dynamical Systems, Differential Equations and Applications, Arlington, Texas. This talk is available in PDF.
• April 18, 2007 Co-author of a contributed talk entitled "Analysis of internal gravity waves using the Fourier, scattering, and continuous wavelet transforms" by J. Hawkins, I. Christov and A. Warn-Varnas presented at the Session on Nonlinear Time Series Analysis in the Geosciences, EGU General Assembly 2007, Vienna, Austria.
• April 16, 2007 Co-author of an invited entitled "A feed-back algorithm using ocean acoustic modeling to improve shallow water soliton simulations" by S.A. Chin-Bing, A.C. Warn-Varnas, D.B. King, I. Christov presented at the Special Session on Nonlinear Wave Phenomena in the Physical Sciences: Some Recent Studies, 5^th IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory, Athens, Georgia.
• April 16, 2007 Presented an invited talk entitled "Internal solitary waves in the ocean: Analysis using the periodic, inverse scattering transform" at the Special Session on Nonlinear Wave Phenomena in the Physical Sciences: Some Recent Studies, 5^th IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory, Athens, Georgia. This talk is available in PDF.
• January 4, 2007 Presented a poster entitled "Dynamics of Quasi-Particles in Nonlinear Wave Equations" co-authored with C.I. Christov at Dynamics Days 2007: an International Conference on Chaos and Nonlinear Dynamics, Boston, Massachusetts. This poster is available in PDF.
• November 16, 2006 Presented a contributed talk entitled "Nonoscillatory Central Schemes on Unstructured Triangulations for Hyperbolic Systems of Conservation Laws" at the Minisymposium on Numerical Methods for First-Order PDEs, 8^th IMACS International Symposium on Iterative Methods in Scientific Computation, College Station, Texas. This talk is available in PDF.
• August 20, 2006 Presented a contributed talk entitled "On the Application of Godunov-type Schemes to Conservation Laws Arising from the Equations of Nonlinear Acoustics" at the special session on Numerical Methods for Hyperbolic Problems at the 6^th International Conference on Numerical Methods and Applications, Borovets, Bulgaria. This talk is available in PDF.
• July 12, 2006 Presented a contributed talk entitled "Nonoscillatory Central Schemes on Unstructured Triangular Grids for Hyperbolic Systems of Conservation Laws," co-authored with Bojan Popov and Peter Popov, at the 2006 SIAM Conference on Analysis of Partial Differential Equations, Boston, MA. This talk is available in PDF.

Undergraduate:

• January 5, 2005 Presented a poster entitled "On the Wavelet-Galerkin Solution to the KdV Equation" at the MAA Undergraduate Poster Session at the annual Joint Mathematics Meetings in Atlanta, Georgia. This poster is available in PDF.
• July 20, 2004 Presented a talk entitled "On the Wavelet-Galerkin Solution to the KdV Equation" at Texas A&M University's REU/VIGRE Student Mini-Conference. This talk is available in PDF.
• April 24, 2004 Presented a talk entitled "A Wavelet Method for Image Anti-Aliasing" at the Research by Undergraduates in Mathematics Boston University Symposium (RUMBUS). This talk is available in PDF.
• July 22, 2003 Presented a talk entitled "Wavelet-Galerkin Methods for Differential Equations" at Texas A&M University's REU/VIGRE Student Mini-Conference. This talk is available in PDF.

Teaching Experience

• Prepared and taught a 4 hour seminar entitled "Chaos in Simple Systems" at the annual MIT Splash weekend. (Nov. 23, 2003)
• Prepared and taught a 5 hour seminar entitled "Chaos: An Introduction to Dynamical Systems" at the annual MIT Splash weekend. (Nov. 23–24, 2002)

Awards and Honors

• Travel Grant from The Graduate School at Northwestern University to attend the 62^nd Annual Meeting of the Division of Fluid Dynamics of the American Physical Society.
• Best Student Paper Award, 6^th IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory. Certificate is available in PDF.
• Student Travel Award to attend the 6^th IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory funded through NSF grant DMS-0840362.
• Travel Grant from The Graduate School at Northwestern University to attend the 61^st Annual Meeting of the Division of Fluid Dynamics of the American Physical Society.
• Travel Award to attend the 7^th AIMS International Conference on Dynamical Systems and and Differential Equations funded through NSF grant DMS-0738356.
• Walter P. Murphy Fellowship for graduate study at Northwestern University (2007–present).
• Student Travel Award to attend the 5^th IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory funded through NSF grant DMS-0631857.
• Travel Grant to attend Dynamics Days 2007: an International Conference on Chaos and Nonlinear Dynamics.
• SIAM Student Travel Award to attend the 2006 SIAM Conference on Analysis of Partial Equations and Annual Meeting.
• Regents Fellowship for graduate study at Texas A&M University (2005–2006 academic year).

Workshop Participation

• 12^th Industrial Mathematical & Statistical Modeling Workshop for Graduate Students at the North Carolina State University; received funding from the NCSU/CRSC/SAMSI. (July 24–Aug. 1, 2006)
• Louisiana State University Workshop on Harmonic Analysis and Fractal Geometry; received funding from NSF Grant DMS-0139783. (Feb. 24–26, 2006)
• Institute for Mathematics and its Applications Workshop on New Mathematics and Algorithms for 3-D Image Analysis; received funding from the IMA. (Jan. 9–12, 2006)

Service

• Refereed manuscripts for:

  AIAA Journal	New Journal of Physics
  AIP Conference Proceedings	Nonlinear Analysis A: Theory, Methods & Applications
  International Journal of Computer Mathematics	Nonlinear Analysis C: Hybrid Systems
  Journal of Physics A: Mathematical and Theoretical	Philosophical Transactions of the Royal Society A
  Lecture Notes in Earth Sciences	Physica Scripta
  Mathematical Biosciences and Engineering	Physics of Fluids
  Mechanics Research Communications

• Elected Student Representative of the American Physical Society's Prairie Section (2010 calendar year).
• Webmaster for the Texas A&M Department of Mathematics’ Numerical Analysis group, 2006–2007 academic year.

Computer Experience

Advanced knowledge of

• Microsoft Windows 95/98/NT/2000/XP (daily usage and system administration),
• Linux, in particular Gentoo and Ubuntu distribution (daily usage and system administration),
• Mac OS X 10.3.x/10.4.x/10.5.x (daily usage and system administration),
• the C and C++ programming languages,
• the L^AT_EX typesetting language (including various add-on packages, e.g., Beamer),
• Mathworks MATLAB 6.x/7.x (R13/R14/R2006x/R2007x/R2008x) (including programming in the MATLAB environment),
• Wolfram Mathematica 4.x/5.x/6.x/7.x,
• deal.II finite element library.

Intermediate knowledge of

• FORTRAN 77,
• Java,
• HTML 4.01, JavaScript and Cascading Style Sheets Level 1,
• Microsoft Office 95/97/2000/XP/2003/2007.

Some experience with

• OpenOffice.Org 1.x/2.x/3.x,
• Microsoft Visual Basic 5/6,
• Waterloo Maple 6/7/8/9/10/11.

Professional Memberships

• American Physical Society, Society for Industrial and Applied Mathematics

Scientometrics

• h-index: 3 (source: Web of Science^®).
• Citations: 27 (source: Web of Science^®) or 44 (source: personal count excluding self-citations).
• ResearcherID: B-9418-2008.
• Mathematical Reviews (MR) Author ID: 805473.
• Erdős number: 4 (source: MathSciNet).

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