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

On a Cintegrable equation for second sound propagation in heated dielectrics
Ivan C. Christov
submitted; eprint arXiv:1801.09857.
☞ Invited paper for the EECT special volume on Nonlinear Wave Phenomena in Continuum Physics: Some Recent Findings.

Acoustic shock and acceleration wave propagation in inhomogeneous fluids
R. S. Keiffer, P. M. Jordan* and I. C. Christov
Mechanics Research Communications, to appear, doi:10.1016/j.mechrescom.2017.11.003; eprint arXiv:1711.09451.
☞ Invited paper for the special issue in memoriam Gérard A. Maugin.
☞ Please be aware that due to the inability of Elsevier's contractors to produce proper typesetting from publicationready LaTeX source, the integrity of the "version of record" on ScicenceDirect is compromised. The arXiv preprint should be considered the authorative version of the manuscript, free of errors (as far as we know).

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Flow rate–pressure drop relation for deformable shallow microfluidic channels
Ivan C. Christov,* Vincent Cognet, Tanmay C. Shidhore and Howard A. Stone*
Journal of Fluid Mechanics, to appear; eprint arXiv:1712.02687.

On the numerical solution of a variablecoefficient Burgers equation arising in granular segregation
Ivan C. Christov
to appear in a special issue of Materials Physics and Mechanics; eprint arXiv:1707.00034.
In Refereed Journals:

Static response of deformable microchannels: a comparative modelling study
Tanmay C. Shidhore and Ivan C. Christov*
Journal of Physics: Condensed Matter 30 (2018) 054002, doi:10.1088/1361648X/aaa226; eprint arXiv:1709.03002.
☞ Invited paper for the special issue on Physics of Integrated Microfluidics.

Kink dynamics in a parametric φ^{6} system: a model with controllably many internal modes
A. Demirkaya, R. Decker, P. G. Kevrekidis, I. C. Christov and A. Saxena
Journal of High Energy Physics (JHEP) 2017 (2017) 71, doi:10.1007/JHEP12(2017)071; eprint arXiv:1706.01193.
☞ Open access (through DOI link above).

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On mechanical waves and Doppler shifts from moving boundaries
Ivan C. Christov* and C. I. Christov
Mathematical Methods in the Applied Sciences 40 (2017) 4481–4492, doi:10.1002/mma.4318; eprint arXiv:1612.09269.

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; eprint arXiv:1603.08277.
☞ Invited paper for the special issue on Mathematical Modeling and Physical Dynamics of Solitary Waves: From Continuum Mechanics to Field Theory.

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; eprint arXiv:1609.09542.
☞ Invited paper for the special issue Proceedings of a Workshop on the Nonlinear Dynamics of Many Body Systems.

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.

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; eprint arXiv:1601.06430.
☞ Invited paper for the special volume on Mathematics of nonlinear acoustics: New approaches in analysis and modeling.

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. ChinBing and A. WarnVarnas
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.

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; eprint arXiv:1512.09360.

Comment on "The velocity field due to an oscillating plate in an OldroydB 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/cjp20150374; eprint arXiv:1506.01470.

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; eprint 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.

Corrections to Morse and Ingard's variationalbased treatment of weaklynonlinear 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.

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.

Successive phase transitions and kink solutions in φ^{8}, φ^{10}, and φ^{12} field theories
Avinash Khare, Ivan C. Christov and Avadh Saxena
Physical Review E 90 (2014) 023208, doi:10.1103/PhysRevE.90.023208; eprint arXiv:1402.6766.

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Shear dispersion in dense granular flows
Ivan C. Christov* and Howard A. Stone
Granular Matter 16 (2014) 509–515, doi:10.1007/s1003501404980; eprint arXiv:1402.6765.
☞ Featured in the Princeton Carbon Mitigation Initiative's Fluids & Energy Group's Thirteenth Annual Report.

A Study in ThreeDimensional Chaotic Dynamics: Granular Flow and Transport in a BiAxial 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; eprint arXiv:1404.4660.

Influence of heterogeneity on secondkind selfsimilar 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.

On an instability exhibited by the ballisticdiffusive 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.

TwoPhase Fluid Displacement and Interfacial Instabilities Under Elastic Membranes
Talal T. AlHousseiny,* 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.

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On a difficulty in the formulation of initial and boundary conditions for eigenfunction expansion solutions for the startup of fluid flow
Ivan C. Christov
Mechanics Research Communications 51 (2013) 86–92, doi:10.1016/j.mechrescom.2013.05.005; eprint arXiv:1305.5999.

A mapping method for distributive mixing with diffusion: Interplay between chaos and diffusion in timeperiodic 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 mappingmethod simulation of the timeperiodic sine flow in the background of McCormick's The Great Intersection.

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; eprint 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.

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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.

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.

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; eprint 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.

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 Spanishlanguage science blog La Ciencia de la Mula Francis.

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; eprint arXiv:1111.4464.

Dissipative acoustic solitons under a weaklynonlinear, Lagrangianaveraged Eulerα model of singlephase 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.

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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.

Comments on: "Energetic balance for the Rayleigh–Stokes problem of an OldroydB 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; eprint arXiv:1107.2947.

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; eprint arXiv:1010.2256.

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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:10.1088/17518113/44/11/112001.
☞ Open access (through DOI link above).

Stokes' first problem for some nonNewtonian fluids: Results and mistakes
Ivan C. Christov
Mechanics Research Communications 37 (2010) 717–723, doi:10.1016/j.mechrescom.2010.09.006; eprint 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.

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/s0070701003002; eprint arXiv:1003.2188.

On the Propagation of SecondSound 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.

Chaotic mixing via streamline jumping in quasitwodimensional 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.

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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.

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; eprint 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.

Shock and traveling wave phenomena on an externally damped, nonlinear string
Ivan Christov and P.M. Jordan*
International Journal of NonLinear 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 NonLinear Mechanics papers during April, May and June 2009.

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New nonoscillatory 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.

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:10.1088/13672630/10/4/043027.
☞ Open access (through DOI link above).

Physical dynamics of quasiparticles 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; eprint arXiv:nlin/0612005.

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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.

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.

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:

Topological defects with powerlaw 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:10.1088/17426596/798/1/012087; eprint arXiv:1611.05634.
☞ Open access (through DOI link above).

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:10.1007/9783319424026_13; eprint arXiv:1510.01751.

Wave Solutions
Ivan C. Christov
Encyclopedia of Thermal Stresses (2014), ed. R.B. Hetnarski, Springer, 6495–6506, doi:10.1007/9789400727397_33; eprint arXiv:1208.3622.

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.

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.

The coarsegrain description of interacting sineGordon 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).

Thermal shock waves under a Maxwell–Cattaneo model with temperaturedependent conductivity
Ivan Christov
Proceedings of the Eighth International Congress on Thermal Stresses (2009), eds. M. OstojaStarzewski and P. Marzocca, vol. II, 525–528, doi:10.13140/RG.2.1.4704.1047/1.
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Fourier, Scattering, and Wavelet Transforms: Applications to Internal Gravity Waves with Comparisons to Linear Tidal Data
James A. Hawkins, Alex WarnVarnas and Ivan Christov
Nonlinear Time Series Analysis in the Geosciences: Applications to Climatology, Geodynamics and SolarTerrestrial Physics, eds. R.V. Donner and S.M. Barbosa
Springer Lecture Notes in Earth Sciences 112 (2008) 223–244, doi:10.1007/9783540789383_10.

Using Ocean Acoustics to Improve Large Shallowwater Soliton Simulations
Stanley A. ChinBing, Alex C. WarnVarnas, David B. King and Ivan Christov
Proceedings of MTS/IEEE Oceans 2007 Conference (2007) 1754–1758, doi:10.1109/OCEANS.2007.4449377.
Other:

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 coedited 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.

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 coedited 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.

Maxwell's "other" equations
Ivan Christov and Pedro Jordan
The Royal Society Publishing Blog (September 22, 2015), blogs.royalsociety.org/publishing/maxwellsotherequations.

Kinematic Waves
Ivan Christov
LinkedIn Pulse (August 11, 2015), www.linkedin.com/pulse/kinematicwavesivanchristov.

From Streamline Jumping to Strange Eigenmodes and ThreeDimensional 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

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.

Finite Volume Methods on Unstructured Voronoi Meshes for Hyperbolic Conservation Laws
Ivan Christov, Ilya D. Mishev and Bojan Popov
Preprint IAMCS200830 (2008), Institute for Applied Mathematics and Computational Science, Texas A&M University.

A Jiang–Tadmor Scheme on Unstructured Triangulations," Technical Report
Ivan Christov and Bojan Popov
Technical Report ISC0605MATH (2006), Institute for Scientific Computation, Texas A&M University.

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 CRSCTR0623 (2006) 89–108, Center for Research in Scientific Computation, North Carolina State University.

Multiscale Image Edge Detection
Ivan Christov
1.130/18.327, Spring 2004, Final Project (2004), doi:10.13140/RG.2.1.2213.7363.

Shock Waves in a Tube
Ivan Christov
MIT Undergraduate Journal of Mathematics 7 (2005) 23–34. [PDF]

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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