Publications

machine learning fluid turbulence free surface flows fluid mixing excitable media feedback control spatiotemporal chaos field theory

Machine Learning

M. Golden, R. O. Grigoriev, J. Nambisan, A. Fernandez-Nieves, "Phyically-informed data-driven modeling of active nematics," Sci. Adv. 9, eabq6120 (2023)
L. Kageorge, R. O. Grigoriev, and M .F. Schatz, "Data-driven detection of drifting system parameters," arXiv 2111.12114 (2022)
D. R. Gurevich, P. A. K. Reinbold, and R. O. Grigoriev, "Learning fluid physics from highly turbulent data using sparse physics-informed discovery of empirical relations (SPIDER)," arXiv 2105.00048 (2021)
P. A. K. Reinbold, L. Kageorge, M. F. Schatz, and R. O. Grigoriev, "Robust learning from noisy, incomplete, high-dimensional experimental data via physically constrained symbolic regression," Nature Comm. 12, 3219 (2021)
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, "Data-driven discovery of partial differential equation models with latent variables," Phys. Rev. E 100, 022219 (2019)

Fluid Turbulence

M. Reynoso, D. Zhigunov, R. O. Grigoriev "Self-similarity and the direct (enstrophy) cascade in two-dimensional fluid turbulence," J. Fluid Mech. (under consideration), arXiv 2308:03007 (2023)
D. Zhigunov, R. O. Grigoriev "Exact coherent structures in fully developed two-dimensional turbulence," J. Fluid Mech. 970, A18 (2023)
C. J. Crowley, J. L. Pughe-Sanford, W. Toler, R. O. Grigoriev, M. F. Schatz, "Observing a Dynamical Skeleton of Turbulence in Taylor-Couette Flow Experiments," Phil. Trans. A 2243, 20220137 (2023)
C. J. Crowley, J. L. Pughe-Sanford, W. Toler, M. C. Krygier, R. O. Grigoriev and M. F. Schatz, "Turbulence tracks recurrent solutions," Proc. Natl. Acad. Sci. 119, e2120665119 (2022)
M. C. Krygier, J. L. Pughe-Sanford, and R. O. Grigoriev, "Exact coherent structures and shadowing in turbulent Taylor-Couette flow," J. Fluid Mech. 923, A7 (2021)
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. Borrero-Echeverry, R. O. Grigoriev, and M. F. Schatz, "A novel subcritical transition to turbulence in Taylor-Couette flow with counter-rotating 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 Kolmogorov-like flow," Phys. Rev. E 100, 013112 (2019).
B. Suri, J. Tithof, R. O. Grigoriev, M. F. Schatz, "Unstable equilibria and invariant manifolds in quasi-two-dimensional Kolmogorov-like flow," Phys. Rev. E 98, 023105 (2018)
J. Tithof, B. Suri, R. Pallantla, R. O. Grigoriev, M. F. Schatz, "Bifurcations in a quasi-two-dimensional Kolmogorov-like flow," J. Fluid Mech. 828, 837-866 (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 two-layer Kolmogorov-like flow," Phys. Fluids 26, 053601 (2014)
R. Mitchell and R. O. Grigoriev, "Instabilities and mixing in two-dimensional Kolmogorov flow," ArXiv (2012)

Free Surface Flows

T. Qin and R. O. Grigoriev, "The effect of gas-phase transport on Marangoni convection in volatile binary fluids," Int. J. Heat Mass Transfer 158, 119999 (2020)
T. Qin and R. O. Grigoriev, "Free-surface 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 high-aspect ratio geometry," Int. J. Heat Mass Transfer 133, 561 (2019)
T. Qin and R. O. Grigoriev, "A numerical study of buoyancy-Marangoni 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 buoyancy-thermocapillary convection of volatile fluids in confined geometries," Int. J. Heat Mass Transfer 90, 678 (2015)
T. Qin, Z. Tukovic, and R. O. Grigoriev, "Buoyancy-thermocapillary 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 buoyancy-thermocapillary convection in a volatile silicone oil," Phys. Fluids 26, 122112 (2014)
T. Qin, M. Yoda, and R. O. Grigoriev, "The effect of noncondensables on buoyancy-thermocapillary convection in confined volatile fluids," in Proc. ASME 2014 International Mechanical Engineering Congress and Exposition, IMECE2014-40124 (2014)
T. Qin and R. O. Grigoriev, "The effect of noncondensables on thermocapillary-buoyancy convection in volatile fluids," in Proc. 11th AIAA/ASME Joint Thermophysics and Heat Transfer Conference, AIAA14-1898558 (2014)
T. Qin, Z. Tukovic, and R. O. Grigoriev, "Buoyancy-thermocapillary 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 two-layer Kolmogorov-like 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, MNHMT12-75266 (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, AIAA-2004-756 (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. 1363-1374 (2003)
R. O. Grigoriev, "Control of evaporatively driven instabilities of thin liquid films," Phys. Fluids 14, 1895-1909 (2002)

Fluid Mixing

R. Mitchell and R. O. Grigoriev, "Instabilities and mixing in two-dimensional Kolmogorov flow," (2012)
Transport and Mixing in Laminar Flows; From Microfluidics to Oceanic Currents (ed. R. Grigoriev, Wiley-VCH, 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 action-action-angle 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, "Chaotic mixing in microdroplets," Lab Chip 6, 1369 (2006)
R. O. Grigoriev, "Chaotic mixing in thermocapillary-driven 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, AIAA-2004-756 (2004)

Dynanimcs of Excitable Media

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 "Level-set method for robust analysis of optical mapping recordings of fibrillation," Computing in Cardiology 44, 197-427 (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 single-spiral 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, "Continuous-time 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, "Continuous-time 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, "Shock-induced termination of reentrant cardiac arrhythmias: Comparing monophasic and biphasic shock protocols," Chaos 23, 043119 (2013)
A. Garzon, R. O. Grigoriev and F. Fenton, "Model-based control of cardiac alternans in Purkinje fibers," Phys. Rev. E 84, 041927 (2011)
A. Garzon, R. O. Grigoriev and F. Fenton, "Model-based control of cardiac alternans on a ring," Phys. Rev. E 80, 021932 (2009)

Feedback Control

A. Garzon, R. O. Grigoriev and F. Fenton, "Continuous-time control of alternans in long Purkinje fibers," Chaos 24, 033124 (2014)
A. Garzon, R. O. Grigoriev, and F. H. Fenton, "Continuous-time 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, "Model-based control of cardiac alternans in Purkinje fibers," Phys. Rev. E 84, 041927 (2011)
A. Garzon, R. O. Grigoriev and F. Fenton, "Model-based 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, Wiley-VCH, 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, 171-193 (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, Wiley-VCH, 1998)
R. O. Grigoriev and M.C. Cross, "Controlling physical systems with symmetries," Phys. Rev. E 57, 1550-1554 (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, 2795-2798 (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 single-spiral 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 Rayleigh-Benard convection," Phys. Rev. Lett. 107, 064501 (2011)
R. O. Grigoriev and H.G. Schuster, "Solvable model for spatiotemporal chaos," Phys. Rev. E 57, 388-396 (1998)
R. O. Grigoriev and M.C. Cross, "Dynamics of coupled maps with a conservation law," Chaos 7, 311-330 (1997)

Field Theory

V. Bornyakov and R. Grygoryev, "3D SU(2) Pure gauge theory in the maximally abelian gauge," Nucl. Phys. B Supplement 30, 576-578 (1993)
R. O. Grigorev, "Quantization of systems in incomplete spaces and the problem of particle production by a gravitational field," Theor. Math. Phys. 89, 1348-1353 (1991)

Students' Ph.D. Theses

Michael Krygier, "Exact Coherent Structures in turbulent small-aspect-ratio Taylor-Couette flow" (2019)
Ravi Kumar Pallantla, "Exact coherent structures and dynamical connections in a quasi 2D Kolmogorov like flow" (2018)
Balachandra Suri, "Quasi-two-dimensional Kolmogorov flow: Bifurcations and exact coherent structures" (2017)
Christopher Marcotte, "Understanding sustained spiral chaos using non-chaotic solutions of a simple model of atrial excitation" (2016)
Tongran Qin, "Buoyancy-thermocapillary convection of volatile fluids in confined and sealed geometries" (2016)
Radford Mitchell, "Transition to turbulence and mixing in a quasi-two-dimensional Lorentz force-driven Kolmogorov flow" (2013)
Alejandro Garzon, "Model-based 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)