Publications
machine learning
fluid turbulence
free surface flows
fluid mixing
cardiac dynamics
feedback control
spatiotemporal chaos
field theory
Machine Learning

P. A. K. Reinbold, L. Kageorge, M. F. Schatz, and R. O. Grigoriev,
"Robust learning from noisy, incomplete, highdimensional experimental data via physically constrained symbolic regression,"
Nature Comm. under review (2020)

P. A. K. Reinbold, D. R. Gurevich, and R. O. Grigoriev,
"Using Noisy or Incomplete Data to Discover
Models of Spatiotemporal Dynamics,"
Phys. Rev. E 101, 010203(R) (2020)

D. R. Gurevich, P. A. K. Reinbold, and R. O. Grigoriev,
"Robust and optimal sparse regression for nonlinear PDE models,"
Chaos 29, 103113 (2019)

P. A. K. Reinbold and R. O. Grigoriev,
"Datadriven discovery of partial differential equation models with latent variables,"
Phys. Rev. E, 100, 022219 (2019)
Fluid Turbulence

B. Suri, L. Kageorge, R. O. Grigoriev, M. F. Schatz,
"Capturing turbulent dynamics and statistics in experiments with unstable periodic orbits,"
Phys. Rev. Lett., 125, 064501 (2020)

C. J. Crowley, M. C. Krygier, D. BorreroEcheverry, R. O. Grigoriev, and M. F. Schatz,
"A novel subcritical transition to turbulence in TaylorCouette flow with counterrotating cylinders,"
J. Fluid Mech., 892, A12 (2020).

B. Suri, R. K. Pallantla, M. F. Schatz, and R. O. Grigoriev,
"Heteroclinic and homoclinic connections in a Kolmogorovlike flow,"
Phys. Rev. E 100, 013112 (2019).

B. Suri, J. Tithof, R. O. Grigoriev, M. F. Schatz,
"Unstable equilibria and invariant manifolds in quasitwodimensional Kolmogorovlike flow,"
Phys. Rev. E 98, 023105 (2018)

J. Tithof, B. Suri, R. Pallantla, R. O. Grigoriev, M. F. Schatz,
"Bifurcations in a quasitwodimensional Kolmogorovlike flow,"
J. Fluid Mech. 828, 837866 (2017)

J. Barnett, D. R. Gurevich, R. O. Grigoriev,
"Streamwise localization of traveling wave solutions in channel flow,"
Phys. Rev. E 95, 033124 (2017)

B. Suri, J. Tithof, R. O. Grigoriev, M. F. Schatz,
"Forecasting fluid flows using the geometry of turbulence,"
Phys. Rev. Lett. 118, 114501 (2017)

B. Suri, J. Tithof, R. Mitchell, Jr., R. O. Grigoriev, M. F. Schatz,
"Velocity profile in a twolayer Kolmogorovlike flow,"
Phys. Fluids 26, 053601 (2014)

R. Mitchell and R. O. Grigoriev, "Instabilities and mixing in
twodimensional Kolmogorov flow," ArXiv
(2012)
Free Surface Flows

T. Qin and R. O. Grigoriev,
"The effect of gasphase transport on Marangoni convection in volatile binary fluids,"
Int. J. Heat Mass Transfer 158, 119999 (2020)

T. Qin and R. O. Grigoriev,
"Freesurface flow of confined volatile simple fluids driven by a horizontal temperature gradient: From a comprehensive numerical model to a simplified analytical description,"
Int. J. Heat Mass Transfer 147, 118934 (2020)

J. Liu and R. O. Grigoriev,
"Analytical solution for filmwise condensation in confined highaspect ratio geometry,"
Int. J. Heat Mass Transfer 133, 561 (2019)

T. Qin and R. O. Grigoriev,
"A numerical study of buoyancyMarangoni convection of volatile binary fluids in confined geometry,"
Int. J. Heat Mass Transfer 127, 308 (2018)

R. O. Grigoriev and T. Qin,
"The effect of phase change on stability of convective flow in a layer of volatile liquid driven by a horizontal temperature gradient,"
J. Fluid. Mech. 838, 248 (2018)

T. Qin and R. O. Grigoriev,
"The effect of noncondensables on buoyancythermocapillary
convection of volatile fluids in confined geometries,"
Int. J. Heat Mass Transfer 90, 678 (2015)

T. Qin, Z. Tukovic, and R. O. Grigoriev,
"Buoyancythermocapillary convection of volatile fluids under
their vapors,"
Int. J. Heat Mass Transfer 80, 38 (2015)

Y. Li, R. Grigoriev, and M. Yoda,
"Experimental study of the effect of noncondensables on
buoyancythermocapillary convection in a volatile silicone
oil,"
Phys. Fluids 26, 122112 (2014)

T. Qin, M. Yoda, and R. O. Grigoriev,
"The effect of noncondensables on buoyancythermocapillary
convection in confined volatile fluids,"
in Proc. ASME 2014 International Mechanical Engineering Congress and
Exposition, IMECE201440124 (2014)

T. Qin and R. O. Grigoriev, "The effect of noncondensables on
thermocapillarybuoyancy convection in volatile fluids,"
in Proc. 11th AIAA/ASME Joint Thermophysics and Heat Transfer
Conference, AIAA141898558 (2014)

T. Qin, Z. Tukovic, and R. O. Grigoriev,
"Buoyancythermocapillary convection of volatile fluids under
atmospheric conditions,"
Int. J. Heat Mass Transfer 75, 284 (2014)

B. Suri, J. Tithof, R. Mitchell, Jr., R. O. Grigoriev, M. F. Schatz,
"Velocity profile in a twolayer Kolmogorovlike flow,"
Phys. Fluids 26, 053601 (2014)

T. Qin and R. O. Grigoriev, "Convection, evaporation, and
condensation of simple and binary fluids in confined
geometries,"
in Proc. 3rd ASME Micro/Nanoscale Heat & Mass Transfer
International Conference, MNHMT1275266 (2012)

E. Greco and R. O. Grigoriev, "Thermocapillary migration of
interfacial droplets," Phys. Fluids 21, 042105
(2009)

R. O. Grigoriev, V. Sharma and M. F. Schatz, "Optically
controlled mixing in microdroplets," Lab Chip 6,
1369 (2006)

R. O. Grigoriev, "Transient growth in driven contact lines,"
Physica D 209, 105 (2005)

R. O. Grigoriev, "Chaotic mixing in spherical
microdroplets," Phys. Fluids 17, 033601 (2005)

R. O. Grigoriev and M. F. Schatz, "Optically controlled mixing in
microdroplets," Invited paper for Proc. 42nd AIAA Aerospace
Sciences Meeting, AIAA2004756 (2004)

N. Garnier, R. O. Grigoriev and M. F. Schatz, "Optical
manipulation of microscale fluid flow," Phys. Rev. Lett.
91, 054501 (2003)

R. O. Grigoriev, "Contact line instability and pattern selection
in thermally driven liquid films," Phys. Fluids 15,
pp. 13631374 (2003)

R. O. Grigoriev, "Control of evaporatively driven instabilities
of thin liquid films," Phys. Fluids 14,
18951909 (2002)
Fluid Mixing

R. Mitchell and R. O. Grigoriev, "Instabilities and mixing in
twodimensional Kolmogorov flow,"
(2012)

Transport and Mixing in Laminar Flows;
From Microfluidics to Oceanic Currents
(ed. R. Grigoriev, WileyVCH, 2011)

E. Greco and R. O. Grigoriev, "Thermocapillary migration of
interfacial droplets," Phys. Fluids 21, 042105
(2009)

D. L. Vainchtein, J. Widloski and R. O. Grigoriev, "Resonant
mixing in perturbed actionactionangle flow,"
Phys. Rev. E 78, 026302 (2008)

D. L. Vainchtein, J. Widloski and R. O. Grigoriev, "Resonant
chaotic mixing in a cellular flow," Phys. Rev. Lett.
99, 094501 (2007)

D. L. Vainchtein, J. Widloski and R. O. Grigoriev, "Mixing
properties of steady flow in thermocapillary driven droplets,"
Phys. Fluids 19, 067102 (2007)

R. O. Grigoriev, V. Sharma and M. F. Schatz, "Optically
controlled mixing in microdroplets," Lab Chip 6,
1369 (2006)

R. O. Grigoriev, "Chaotic mixing in spherical
microdroplets," Phys. Fluids 17, 033601 (2005)

R. O. Grigoriev and M. F. Schatz, "Optically controlled mixing in
microdroplets," Invited paper for Proc. 42nd AIAA Aerospace
Sciences Meeting, AIAA2004756 (2004)
Cardiac Tissue Dynamics

D. R. Gurevich and R. O. Grigoriev,
"Robust approach for rotor mapping in cardiac tissue,"
Chaos 29, 053101 (2019)

D. R. Gurevich, C. Herndon, I. Uzelac, F. Fenton, R. O. Grigoriev
"Levelset method for robust analysis of optical mapping recordings of fibrillation,"
Computing in Cardiology 44, 197427 (2017)

A. Garzon and R. O. Grigoriev
"Memory effects, transient growth, and wave breakup in a model of paced
atrium,"
Chaos 27, 093917 (2017)

C. D. Marcotte and R. O. Grigoriev
"Dynamical mechanism of atrial fibrillation: a topological approach,"
Chaos 27, 093936 (2017)

C. D. Marcotte and R. O. Grigoriev
"Adjoint eigenfunctions of temporally recurrent singlespiral solutions in a simple model of atrial fibrillation,"
Chaos 26, 093107 (2016)

C. D. Marcotte and R. O. Grigoriev
"Unstable spiral waves and local Euclidean symmetry in a model
of cardiac tissue,"
Chaos 25, 063116 (2015)

G. Byrne, C. D. Marcotte, and R. O. Grigoriev
"Exact coherent structures and chaotic dynamics in a model of
cardiac tissue,"
Chaos 25, 033108 (2015)

G. Byrne, C. Marcotte, and R. O. Grigoriev
"Exact coherent structures and dynamics of cardiac
tissue,"
in Proc. European Study Group on Cardiac Oscillations, Trento,
Italy 2014.

A. Garzon, R. O. Grigoriev and F. Fenton,
"Continuoustime control of alternans in long Purkinje
fibers,"
Chaos 24, 033124 (2014)

C. D. Marcotte and R. O. Grigoriev,
"Implementation of PDE models of cardiac dynamics on GPUs
using OpenCL," ArXiv (2013)

A. Garzon, R. O. Grigoriev, and F. H. Fenton,
"Continuoustime feedback control of alternans in a model of
Purkinje fibers," in Proc. IX Congress on Numerical Methods,
Cali, Colombia 2013.

J. Bragard, A. Simic, J. Elorza, R. O. Grigoriev, E. M. Cherry,
R. F. Gilmour Jr., N. F. Otani, and F. H. Fenton,
"Shockinduced termination of reentrant cardiac arrhythmias:
Comparing monophasic and biphasic shock protocols,"
Chaos 23, 043119 (2013)

A. Garzon, R. O. Grigoriev and F. Fenton,
"Modelbased control of cardiac alternans in Purkinje
fibers,"
Phys. Rev. E 84, 041927 (2011)

A. Garzon, R. O. Grigoriev and F. Fenton, "Modelbased control
of cardiac alternans on a ring," Phys. Rev. E 80,
021932 (2009)
Feedback Control

A. Garzon, R. O. Grigoriev and F. Fenton,
"Continuoustime control of alternans in long Purkinje
fibers,"
Chaos 24, 033124 (2014)

A. Garzon, R. O. Grigoriev, and F. H. Fenton,
"Continuoustime feedback control of alternans in a model of
Purkinje fibers," in Proc. IX Congress on Numerical Methods,
Cali, Colombia 2013.

A. Garzon, R. O. Grigoriev and F. Fenton,
"Modelbased control of cardiac alternans in Purkinje
fibers,"
Phys. Rev. E 84, 041927 (2011)

A. Garzon, R. O. Grigoriev and F. Fenton, "Modelbased control
of cardiac alternans on a ring," Phys. Rev. E 80,
021932 (2009)

R. O. Grigoriev, A. Handel "Localised Control of spatiotemporal
chaos," in Handbook of Chaos Control, 2nd Ed. (ed. E.
Schoell and H. G. Schuster, WileyVCH, 2007)

A. Handel and R. O. Grigoriev, "Transient dynamics and nonlinear
stability of spatially extended systems," Phys. Rev. E
74, 036302 (2006)

A. Handel and R. O. Grigoriev, "Pattern selection and control
via localized feedback," Phys. Rev. E 72, 066208
(2005)

R. O. Grigoriev and A. Handel, "Spectral theory for the failure
of linear control in a nonlinear stochastic system," Phys.
Rev. E 66, 065301(R) (2002)

R. O. Grigoriev and A. Handel, "Nonnormality and the localized
control of extended systems," Phys. Rev. E 66,
067201 (2002)

R. O. Grigoriev, "Symmetry and control: spatially extended
chaotic systems," Physica D 140, 171193 (2000)

R. O. Grigoriev, "Identification and control of symmetric
systems,"
(1998)

R. O. Grigoriev, "Symmetry and localized control of extended
chaotic systems," Ph.D. Thesis, 1998

R. O. Grigoriev, "Control of spatially extended chaotic
systems," in Handbook of Chaos Control (ed. H. G.
Schuster, WileyVCH, 1998)

R. O. Grigoriev and M.C. Cross, "Controlling physical systems
with symmetries," Phys. Rev. E 57, 15501554
(1998)

R. O. Grigoriev, S.G. Lall and G.E. Dullerud, "Localized optimal
control of spatiotemporal chaos," in Proc. of International
Symposium on Nonlinear Theory and its Applications, 1997.

R. O. Grigoriev, "Optimal control of spatiotemporal chaos in
coupled map lattices," in Proc. of IUTAM Symposium on New
Applications of Nonlinear and Chaotic Dynamics in Mechanics, 1997
(Kluwer Academic, 1998)

R. O. Grigoriev, M.C. Cross and H.G. Schuster, "Pinning control
of spatiotemporal chaos," Phys. Rev. Lett. 79,
27952798 (1997)
Spatiotemporal Chaos

D. R. Gurevich and R. O. Grigoriev,
"Robust approach for rotor mapping in cardiac tissue,"
Chaos 29, 053101 (2019)

C. D. Marcotte, and R. O. Grigoriev
"Adjoint eigenfunctions of temporally recurrent singlespiral solutions in a simple model of atrial fibrillation,"
Chaos 26, 093107 (2016)

C. D. Marcotte, and R. O. Grigoriev
"Unstable spiral waves and local Euclidean symmetry in a model
of cardiac tissue,"
Chaos 25, 063116 (2015)

G. Byrne, C. D. Marcotte, and R. O. Grigoriev
"Exact coherent structures and chaotic dynamics in a model of
cardiac tissue,"
Chaos 25, 033108 (2015)

G. Byrne, C. Marcotte, and R. O. Grigoriev
"Exact coherent structures and dynamics of cardiac
tissue,"
in Proc. European Study Group on Cardiac Oscillations, Trento,
Italy 2014.

A. C. Perkins, R. O. Grigoriev, and M. F. Schatz, "Modal
spectra extracted from nonequilibrium fluid patterns in laboratory
experiments in RayleighBenard convection,"
Phys. Rev. Lett. 107, 064501 (2011)

R. O. Grigoriev and H.G. Schuster, "Solvable model for
spatiotemporal chaos," Phys. Rev. E 57, 388396
(1998)

R. O. Grigoriev and M.C. Cross, "Dynamics of coupled maps with a
conservation law," Chaos 7, 311330 (1997)
Field Theory

V. Bornyakov and R. Grygoryev, "3D SU(2) Pure gauge theory in
the maximally abelian gauge," Nucl. Phys. B Supplement
30, 576578 (1993)

R. O. Grigorev, "Quantization of systems in incomplete spaces
and the problem of particle production by a gravitational
field," Theor. Math. Phys. 89, 13481353 (1991)
Students' Ph.D. Theses
 Michael Krygier, "Exact Coherent Structures in turbulent smallaspectratio TaylorCouette flow" (2019)
 Ravi Kumar Pallantla, "Exact coherent structures and dynamical connections in a quasi 2D Kolmogorov like flow" (2018)
 Balachandra Suri, "Quasitwodimensional Kolmogorov flow: Bifurcations and exact coherent structures" (2017)
 Christopher Marcotte, "Understanding sustained spiral chaos using nonchaotic solutions of a simple model of atrial excitation" (2016)
 Tongran Qin, "Buoyancythermocapillary convection of volatile fluids in confined and sealed geometries" (2016)
 Radford Mitchell, "Transition to turbulence and mixing in a quasitwodimensional Lorentz forcedriven Kolmogorov flow" (2013)
 Alejandro Garzon, "Modelbased control of cardiac alternans on one dimensional tissue" (2010)
 Edwin Greco, "Thermal and hydrodynamic interactions between a liquid droplet and a fluid interface" (2008)
 Andreas Handel, "Limits of localized control in extended nonlinear systems" (2004)