My Publications

(* indicates corresponding author(s), if applicable; ► denotes a key publication; preprints available on arXiv.org or upon request by email.)

Forthcoming:

2. Kink Dynamics in a Parametric φ⁶ System: A Model With Controllably Many Internal Modes
   A. Demirkaya, R. Decker, P. G. Kevrekidis, I. C. Christov and A. Saxena
   submitted; e-print arXiv:1706.01193.
1. On mechanical waves and Doppler shifts from moving boundaries
   Ivan C. Christov and C. I. Christov
   Mathematical Methods in the Applied Sciences ?? (2017) to appear, doi:10.1002/mma.4318; e-print arXiv:1612.09269.

In Refereed Journals:

42. Nonlinear waves in electromigration dispersion in a capillary
    Ivan C. Christov
    Wave Motion 71 (2017) 42–52, doi:10.1016/j.wavemoti.2016.06.011; e-print arXiv:1603.08277.
    ☞ Invited paper for the special issue on Mathematical Modeling and Physical Dynamics of Solitary Waves: From Continuum Mechanics to Field Theory.
41. Peakompactons: Peaked compact nonlinear waves
    Ivan C. Christov,* Tyler Kress and Avadh Saxena
    International Journal of Modern Physics B 31 (2017) 1742008, doi:10.1142/S0217979217420085; e-print arXiv:1609.09542.
    ☞ Invited paper for the special issue Proceedings of a Workshop on the Nonlinear Dynamics of Many Body Systems.
40. Comment on "Locomotion of a microorganism in weakly viscoelastic liquids,"
    Ivan C. Christov* and P.M. Jordan
    Physical Review E 94 (2016) 057101, doi:10.1103/PhysRevE.94.057101.
39. Nonlinear acoustics and shock formation in lossless barotropic Green–Naghdi fluids
    Ivan C. Christov
    Evolution Equations and Control Theory 5 (2016) 349–365, doi:10.3934/eect.2016008; e-print arXiv:1601.06430.
    ☞ Invited paper for the special volume on Mathematics of nonlinear acoustics: New approaches in analysis and modeling.
38. Acoustic traveling waves in thermoviscous perfect gases: Kinks, acceleration waves, and shocks under the Taylor–Lighthill balance
    Ivan C. Christov, P.M. Jordan,* S.A. Chin-Bing and A. Warn-Varnas
    Mathematics and Computers in Simulation 127 (2016) 2–18, doi:10.1016/j.matcom.2013.03.011.
    ☞ Part of the special issue "Nonlinear Waves: Computation and Theory, WAVES 2011" comprised of a limited number of refereed papers from the 7^th IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory.
37. Stress retardation versus stress relaxation in linear viscoelasticity
    Ivan C. Christov* and C. I. Christov
    Mechanics Research Communications 72 (2016) 59–63, doi:10.1016/j.mechrescom.2016.01.005; e-print arXiv:1512.09360.
36. Comment on "The velocity field due to an oscillating plate in an Oldroyd-B fluid" by C.C. Hopkins and J.R. de Bruyn [Can. J. Phys. 92, 533 (2014)]"
    Ivan C. Christov
    Canadian Journal of Physics 93 (2015) 1651–1652, doi:10.1139/cjp-2015-0374; e-print arXiv:1506.01470.
35. On a hierarchy of nonlinearly dispersive generalized KdV equations
    Ivan C. Christov
    Proceedings of the Estonian Academy of Sciences 64 (2015) 212–218, doi:10.3176/proc.2015.3.02; e-print arXiv:1501.01044.
    ☞ Invited paper for the special issue "Complexity of Nonlinear Waves" comprised of refereed papers selected from those presented at the IUTAM Symposium on Complexity of Nonlinear Waves.
34. Corrections to Morse and Ingard's variational-based treatment of weakly-nonlinear acoustics in lossless gases
    Ivan C. Christov and P.M. Jordan*
    Journal of the Acoustical Society of America 138 (2015) 361–362, doi:10.1121/1.4922951.
33. Flow regimes for fluid injection into a confined porous medium
    Zhong Zheng, Bo Guo, Ivan C. Christov, Michael A. Celia and Howard A. Stone*
    Journal of Fluid Mechanics 767 (2015) 881–909, doi:10.1017/jfm.2015.68.
    ☞ Featured in the Princeton Carbon Mitigation Initiative's Fourteenth Annual Report.
    ☞ Dr. Zheng received the 2015 CMI Best Paper Award for Postdoctoral Fellows for this publication.
32. Successive phase transitions and kink solutions in φ⁸, φ¹⁰, and φ¹² field theories
    Avinash Khare, Ivan C. Christov and Avadh Saxena
    Physical Review E 90 (2014) 023208, doi:10.1103/PhysRevE.90.023208; e-print arXiv:1402.6766.
31. ► Shear dispersion in dense granular flows
    Ivan C. Christov* and Howard A. Stone
    Granular Matter 16 (2014) 509–515, doi:10.1007/s10035-014-0498-0; e-print arXiv:1402.6765.
    ☞ Featured in the Princeton Carbon Mitigation Initiative's Fluids & Energy Group's Thirteenth Annual Report.
30. A Study in Three-Dimensional Chaotic Dynamics: Granular Flow and Transport in a Bi-Axial Spherical Tumbler
    Ivan C. Christov, Richard M. Lueptow, Julio M. Ottino and Rob Sturman
    SIAM Journal on Applied Dynamical Systems 13 (2014) 901–943, doi:10.1137/130934076; e-print arXiv:1404.4660.
29. Influence of heterogeneity on second-kind self-similar solutions for viscous gravity currents
    Zhong Zheng, Ivan C. Christov and Howard A. Stone*
    Journal of Fluid Mechanics 747 (2014) 218–246, doi:10.1017/jfm.2014.148.
    ☞ Featured in the Princeton Carbon Mitigation Initiative's Fluids & Energy Group's Thirteenth Annual Report.
28. On an instability exhibited by the ballistic-diffusive heat conduction model of Xu and Hu
    Ivan C. Christov and P. M. Jordan*
    Proceedings of the Royal Society A 470 (2014) 20130557, doi:10.1098/rspa.2013.0557.
27. Two-Phase Fluid Displacement and Interfacial Instabilities Under Elastic Membranes
    Talal T. Al-Housseiny,* Ivan C. Christov and Howard A. Stone
    Physical Review Letters 111 (2013) 034502, doi:10.1103/PhysRevLett.111.034502.
    ☞ Featured in the Princeton Carbon Mitigation Initiative's Fluids & Energy Group's Twelfth Annual Report.
26. ► On a difficulty in the formulation of initial and boundary conditions for eigenfunction expansion solutions for the start-up of fluid flow
    Ivan C. Christov
    Mechanics Research Communications 51 (2013) 86–92, doi:10.1016/j.mechrescom.2013.05.005; e-print arXiv:1305.5999.
25. A mapping method for distributive mixing with diffusion: Interplay between chaos and diffusion in time-periodic sine flow
    Conor P. Schlick, Ivan C. Christov, Paul B. Umbanhowar, Julio M. Ottino and Richard M. Lueptow*
    Physics of Fluids 25 (2013) 052102, doi:10.1063/1.4803897.
    ☞ See a mapping-method simulation of the time-periodic sine flow in the background of McCormick's The Great Intersection.
24. Cutting and Shuffling a Line Segment: Mixing by Interval Exchange Transformations
    Marissa K. Krotter, Ivan C. Christov, Julio M. Ottino and Richard M. Lueptow*
    International Journal of Bifurcation and Chaos 22 (2012) 1230041, doi:10.1142/S0218127412300418; e-print arXiv:1208.2052.
    ☞ Cover article of December 2012 issue.
    ☞ One of twelve contributions on the 2012 Featured Articles list.
    ☞ Marissa's contribution to this paper featured in Spring 2013 McCormick Magazine.
23. ► Resolving a paradox of anomalous scalings in the diffusion of granular materials
    Ivan C. Christov* and Howard A. Stone
    Proceedings of the National Academy of Sciences of the USA 109 (2012) 16012–16017, doi:10.1073/pnas.1211110109.
22. Parameters and scalings for dry and immersed granular flowing layers in rotating tumblers
    Florent Pignatel, Caroline Asselin, Lucas Krieger, Ivan C. Christov, Julio M. Ottino and Richard M. Lueptow*
    Physical Review E 86 (2012) 011304, doi:10.1103/PhysRevE.86.011304.
21. Hidden solitons in the Zabusky–Kruskal experiment: Analysis using the periodic, inverse scattering transform
    Ivan C. Christov
    Mathematics and Computers in Simulation 82 (2012) 1069–1078, doi:10.1016/j.matcom.2010.05.021; e-print arXiv:0910.3345.
    ☞ Part of the special issue "Nonlinear Waves: Computation and Theory IX" comprised of a limited number of refereed papers from the 6^th IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory.
    ☞ Winner of a Best Student Paper Award at the 6^th IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory.
20. Mixing by cutting and shuffling 3D granular flow in spherical tumblers
    Gabriel Juarez, Ivan C. Christov, Julio M. Ottino and Richard M. Lueptow*
    Chemical Engineering Science 73 (2012) 195–207, doi:10.1016/j.ces.2012.01.044.
    ☞ Featured on the Spanish-language science blog La Ciencia de la Mula Francis.
19. Comments on: "Starting solutions for some unsteady unidirectional flows of a second grade fluid," [Int. J. Eng. Sci. 43 (2005) 781]
    Ivan C. Christov* and P.M. Jordan
    International Journal of Engineering Science 51 (2012) 326–332, doi:10.1016/j.ijengsci.2011.10.012; e-print arXiv:1111.4464.
18. Dissipative acoustic solitons under a weakly-nonlinear, Lagrangian-averaged Euler-α model of single-phase lossless fluids
    Richard S. Keiffer, R. McNorton, P.M. Jordan and Ivan C. Christov*
    Wave Motion 48 (2011) 782–790, doi:10.1016/j.wavemoti.2011.04.013.
    ☞ Invited paper for the special issue "Nonlinear Waves in Action" dedicated to Professor Christo I. Christov on the occasion of his 60^th birthday.
    ☞ Winner of a Best Student Paper Award at the 7^th IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory.
17. ► From streamline jumping to strange eigenmodes: Bridging the Lagrangian and Eulerian pictures of the kinematics of mixing in granular flows
    Ivan C. Christov, Julio M. Ottino and Richard M. Lueptow*
    Physics of Fluids 23 (2011) 103302, doi:10.1063/1.3653280.
16. Comments on: "Energetic balance for the Rayleigh–Stokes problem of an Oldroyd-B fluid" [Nonlinear Anal. RWA 12 (2011) 1]
    Ivan C. Christov
    Nonlinear Analysis: Real World Applications 12 (2011) 3687–3690, doi:10.1016/j.nonrwa.2011.06.025; e-print arXiv:1107.2947.
    
15. Stretching and folding versus cutting and shuffling: An illustrated perspective on mixing and deformations of continua
    Ivan C. Christov, Richard M. Lueptow and Julio M. Ottino*
    American Journal of Physics 79 (2011) 359–367, doi:10.1119/1.3533213; e-print arXiv:1010.2256.
14. ► An improved formula for the frequency shift due to a variable phase speed
    Ivan C. Christov and C.I. Christov
    Journal of Physics A: Mathematical and Theoretical 44 (2011) 112001, doi:10.1088/1751-8113/44/11/112001.
    ☞ Open access (through DOI link above).
13. Stokes' first problem for some non-Newtonian fluids: Results and mistakes
    Ivan C. Christov
    Mechanics Research Communications 37 (2010) 717–723, doi:10.1016/j.mechrescom.2010.09.006; e-print arXiv:1009.4416.
    ☞ Ranked 9^th out of the 25 most downloaded Mechanics Research Communications papers during October, November and December 2010.
    ☞ On the Most Cited Articles (since 2010) list for Mechanics Research Communications.
12. Comment on "On a class of exact solutions of the equations of motion of a second grade fluid" by C. Fetecău and J. Zierep (Acta Mech. 150, 135–138, 2001)
    Ivan C. Christov* and C.I. Christov
    Acta Mechanica 215 (2010) 25–28, doi:10.1007/s00707-010-0300-2; e-print arXiv:1003.2188.
11. On the Propagation of Second-Sound in Nonlinear Media: Shock, Acceleration and Traveling Wave Results
    Ivan C. Christov* and P.M. Jordan
    Journal of Thermal Stresses 33 (2010) 1109–1135, doi:10.1080/01495739.2010.517674.
10. Chaotic mixing via streamline jumping in quasi-two-dimensional tumbled granular flows
    Ivan C. Christov, Julio M. Ottino and Richard M. Lueptow*
    Chaos 20 (2010) 023102, doi:10.1063/1.3368695.
    ☞ Ranked 8^th out of the 20 most downloaded Chaos papers during June 2010, 18^th during July 2010 and 18^th during August 2010.
9. ► Streamline jumping: A mixing mechanism
   Ivan C. Christov, Julio M. Ottino and Richard M. Lueptow*
   Physical Review E 81 (2010) 046307, doi:10.1103/PhysRevE.81.046307.
8. Internal solitary waves in the ocean: Analysis using the periodic, inverse scattering transform
   Ivan Christov
   Mathematics and Computers in Simulation 80 (2009) 192–200, doi:10.1016/j.matcom.2009.06.005; e-print arXiv:0708.3421.
   ☞ Part of the special issue "Nonlinear Waves: Computation and Theory VII" comprised of a limited number of refereed papers from the 5^th IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory.
7. Shock and traveling wave phenomena on an externally damped, non-linear string
   Ivan Christov and P.M. Jordan*
   International Journal of Non-Linear Mechanics 44 (2009) 511–519, doi:10.1016/j.ijnonlinmec.2008.12.004.
   ☞ Invited paper for the special issue "Waves in Nonlinear Solid Mechanics" dedicated to Professor Philippe Boulanger on the occasion of his retirement from the Départment de Mathématiques at the Université Libre de Bruxelles.
   ☞ Ranked 15^th out of the 25 most downloaded International Journal of Non-Linear Mechanics papers during April, May and June 2009.
6. ► New non-oscillatory central schemes on unstructured triangulations for hyperbolic systems of conservation laws
   Ivan Christov and Bojan Popov*
   Journal of Computational Physics 227 (2008) 5736–5757, doi:10.1016/j.jcp.2008.02.007.
   ☞ See also Other #5 below.
5. Shock bifurcation and emergence of diffusive solitons in a nonlinear wave equation with relaxation
   Ivan Christov and P.M. Jordan*
   New Journal of Physics 10 (2008) 043027, doi:10.1088/1367-2630/10/4/043027.
   ☞ Open access (through DOI link above).
4. Physical dynamics of quasi-particles in nonlinear wave equations
   Ivan Christov* and C.I. Christov
   Physics Letters A 372 (2008) 841–848, doi:10.1016/j.physleta.2007.08.038; e-print arXiv:nlin/0612005.
3. ► Modeling weakly nonlinear acoustic wave propagation
   Ivan Christov, C.I. Christov and P.M. Jordan*
   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.
   • See also: Corrigendum and Addendum, ibid. 68 (2015) 231–233, doi:10.1093/qjmam/hbu023.
2. Cumulative Nonlinear Effects in Acoustic Wave Propagation
   Ivan Christov, C.I. Christov and P.M. Jordan*
   CMES: Computer Modeling in Engineering & Sciences 17 (2007) 47–54, doi:10.3970/cmes.2007.017.047.
1. Nonlinear acoustic propagation in homentropic perfect gases: A numerical study
   Ivan Christov, P.M. Jordan* and C.I. Christov
   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:

9. Topological defects with power-law tails
   R. V. Radomskiy, E. V. Mrozovskaya, V. A. Gani,* I. C. Christov
   Proceedings of 2^nd International Conference on Particle Physics and Astrophysics (Moscow, Russian Federation), eds. M. Skorokhvatov and S. Rubin
   Journal of Physics: Conference Series 798 (2017) 012087, doi:10.1088/1742-6596/798/1/012087; e-print arXiv:1611.05634.
   ☞ Open access (through DOI link above).
8. A Parametric Study of Mixing in a Granular Flow a Biaxial Spherical Tumbler
   Ivan C. Christov,* Richard M. Lueptow, Julio M. Ottino and Rob Sturman
   Dynamical Systems: Modelling, ed. J. Awrejcewicz
   Springer Proceedings in Mathematics & Statistics 181 (2016) 143–154, doi:10.1007/978-3-319-42402-6_13; e-print arXiv:1510.01751.
7. Wave Solutions
   Ivan C. Christov
   Encyclopedia of Thermal Stresses (2014), ed. R.B. Hetnarski, Springer, 6495–6506, doi:10.1007/978-94-007-2739-7_33; e-print arXiv:1208.3622.
6. Finite volume methods on unstructured Voronoi meshes for hyperbolic conservation laws
   Ivan Christov, Ilya D. Mishev and Bojan Popov
   Hyperbolic Problems: Theory, Numerics and Applications, eds. E. Tadmor, J.-G. Liu and A.E. Tzavaras
   Proceedings of Symposia in Applied Mathematics 67 (2009) 507–516.
   ☞ Preprint available as Other #5 below.
5. On the Inertial Force Experienced by a Solid Body Undergoing Rotation about Two Axes
   I.C. Christov and C.I. Christov
   Proceedings of the 1^st International Conference on Applications of Mathematics in Technical and Natural Sciences (Sozopol, Bulgaria), eds. M.D. Todorov and C.I. Christov
   AIP Conference Proceedings 1186 (2009) 226–230, doi:10.1063/1.3265333.
4. The coarse-grain description of interacting sine-Gordon solitons with varying widths
   Ivan Christov and C.I. Christov
   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 and J. Zhu
   Discrete and Continuous Dynamical Systems (DCDS) Supplement (2009) 171–180, doi:10.3934/proc.2009.2009.171.
   ☞ Open access (through DOI link above).
3. Thermal shock waves under a Maxwell–Cattaneo model with temperature-dependent conductivity
   Ivan Christov
   Proceedings of the Eighth International Congress on Thermal Stresses (2009), eds. M. Ostoja-Starzewski and P. Marzocca, vol. II, 525–528, doi:10.13140/RG.2.1.4704.1047/1. [PDF]
2. Fourier, Scattering, and Wavelet Transforms: Applications to Internal Gravity Waves with Comparisons to Linear Tidal Data
   James A. Hawkins, Alex Warn-Varnas and Ivan Christov
   Nonlinear Time Series Analysis in the Geosciences: Applications to Climatology, Geodynamics and Solar-Terrestrial Physics, eds. R.V. Donner and S.M. Barbosa
   Springer Lecture Notes in Earth Sciences 112 (2008) 223–244, doi:10.1007/978-3-540-78938-3_10.
1. Using Ocean Acoustics to Improve Large Shallow-water Soliton Simulations
   Stanley A. Chin-Bing, Alex C. Warn-Varnas, David B. King and Ivan Christov
   Proceedings of MTS/IEEE Oceans 2007 Conference (2007) 1754–1758, doi:10.1109/OCEANS.2007.4449377.

Other:

12. Editorial: Special issue of Wave Motion — "Mathematical modeling and physical dynamics of solitary waves: From continuum mechanics to field theory"
    Ivan C. Christov, Michail D. Todorov and Sanichiro Yoshida
    Wave Motion 71 (2017) 1–4, doi:10.1016/j.wavemoti.2016.09.007.
    ☞ Introduction to the special issue on "Mathematical modeling and physical dynamics of solitary waves: From continuum mechanics to field theory," guest co-edited by Ivan C. Christov, Michail D. Todorov and Sanichiro Yoshida, comprised of a limited number of refereed papers arising from presentations made at the special session on "Mathematical Modeling and Physical Dynamics of Solitary Waves: From Continuum Mechanics to Field Theory" of the 9^th IMACS International Conference on Nonlinear Waves and Phenomena in Athens, Georgia, USA, as well at the 7^th AMiTaNS conference in Albena, Bulgaria.
11. Introduction: energy and the subsurface
    Ivan C. Christov* and Hari S. Viswanathan
    Philosophical Transactions of the Royal Society A 374 (2016) 20150430, doi:10.1098/rsta.2015.0430.
    ☞ Introduction to the theme issue on "Energy and the subsurface," guest co-edited by Ivan C. Christov and Hari S. Viswanathan, comprised of a limited number of refereed papers from the 2015 Center for Nonlinear Studies workshop on Grand Challenges in Geological Fluid Mechanics.
10. Maxwell's "other" equations
    Ivan Christov and Pedro Jordan
    The Royal Society Publishing Blog (September 22, 2015), blogs.royalsociety.org/publishing/maxwells-other-equations.
9. Kinematic Waves
   Ivan Christov
   LinkedIn Pulse (August 11, 2015), www.linkedin.com/pulse/kinematic-waves-ivan-christov.
8. From Streamline Jumping to Strange Eigenmodes and Three-Dimensional Chaos: A Tour of the Mathematical Aspects of Granular Mixing in Rotating Tumblers
   Ivan C. Christov
   Ph.D. Thesis (2011), Northwestern University, Evanston, Illinois. UMI:3456537
7. DynSyst_Special_Topics: A Dynamical Systems Approach to Mixing and Segregation of Granular Matter
   Julio M. Ottino, Richard M. Lueptow and Ivan C. Christov
   Proceedings of the 2011 NSF Engineering Research and Innovation Conference, Atlanta, Georgia.
6. Finite Volume Methods on Unstructured Voronoi Meshes for Hyperbolic Conservation Laws
   Ivan Christov, Ilya D. Mishev and Bojan Popov
   Preprint IAMCS-2008-30 (2008), Institute for Applied Mathematics and Computational Science, Texas A&M University.
5. A Jiang–Tadmor Scheme on Unstructured Triangulations," Technical Report
   Ivan Christov and Bojan Popov
   Technical Report ISC-06-05-MATH (2006), Institute for Scientific Computation, Texas A&M University.
4. Properties of a Gradient Descent Algorithm for Active Vibration Control
   Jeff Baker, Ivan Christov, Simona Dediu, Elana Fertig and Wanda Strychalski
   Proceedings of the Twelfth Industrial Mathematical and Statistical Modeling Workshop for Graduate Students, eds. Alina Chertock, Mansoor A. Haider, Mette S. Olufsen and Ralph C. Smith
   Technical Report CRSC-TR06-23 (2006) 89–108, Center for Research in Scientific Computation, North Carolina State University.
3. Multiscale Image Edge Detection
   Ivan Christov
   1.130/18.327, Spring 2004, Final Project (2004), doi:10.13140/RG.2.1.2213.7363.
2. Shock Waves in a Tube
   Ivan Christov
   MIT Undergraduate Journal of Mathematics 7 (2005) 23–34. [PDF]
1. Integrating the Normal Curve
   Ivan Christov
   FOLIO: Literary Journal of the Louisiana School for Math Science and the Arts (2002) 5–8, doi:10.13140/RG.2.1.4441.9609. [PDF]

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