Mikhail Stepanov
 Associate Professor, Mathematics
 Associate Professor, Applied Mathematics  GIDP
 Member of the Graduate Faculty
Contact
 (520) 6212685
 Environment and Natural Res. 2, Rm. N263
 Tucson, AZ 85719
 stepanov@arizona.edu
Degrees
 Ph.D. Physics: Optics
 Institute of Automation and Electrometry, Novosibirsk, Novosibirsk Oblast, Russia
 Strong field effects in nonlinear plasma spectroscopy
Interests
No activities entered.
Courses
202425 Courses

Intro to Linear Algebra
MATH 313 (Fall 2024)
202324 Courses

Intro to Linear Algebra
MATH 313 (Spring 2024) 
Calculus I
MATH 125 (Fall 2023) 
Intro to Linear Algebra
MATH 313 (Fall 2023)
202223 Courses

Algorithms of Applied Math II
MATH 589B (Spring 2023) 
Dissertation
MATH 920 (Spring 2023) 
Calculus II
MATH 129 (Fall 2022) 
Dissertation
MATH 920 (Fall 2022)
202122 Courses

Algorithms of Applied Math II
MATH 589B (Spring 2022) 
Dissertation
MATH 920 (Spring 2022) 
Algorithms of Applied Math I
APPL 589A (Fall 2021) 
Algorithms of Applied Math I
MATH 589A (Fall 2021) 
Dissertation
MATH 920 (Fall 2021) 
Intro to Linear Algebra
MATH 313 (Fall 2021)
202021 Courses

Dissertation
MATH 920 (Spring 2021) 
Numerical Analysis
CSC 575B (Spring 2021) 
Numerical Analysis
MATH 575B (Spring 2021) 
Dissertation
MATH 920 (Fall 2020) 
Intro to Linear Algebra
MATH 313 (Fall 2020) 
Numerical Analysis
MATH 575A (Fall 2020)
201920 Courses

Dissertation
MATH 920 (Spring 2020) 
Numerical Analysis
CSC 575B (Spring 2020) 
Numerical Analysis
MATH 575B (Spring 2020) 
Calculus II
MATH 129 (Fall 2019) 
Numerical Analysis
CSC 575A (Fall 2019) 
Numerical Analysis
MATH 575A (Fall 2019) 
Research
MATH 900 (Fall 2019)
201819 Courses

Prin+Method Applied Math
MATH 583B (Spring 2019) 
Research
MATH 900 (Spring 2019) 
Calculus I
MATH 125 (Fall 2018) 
Prin+Method Applied Math
MATH 583A (Fall 2018) 
Research
MATH 900 (Fall 2018)
201718 Courses

Appl Stochastic Process
MATH 468 (Spring 2018) 
Appl Stochastic Process
MATH 568 (Spring 2018) 
Independent Study
MATH 599 (Spring 2018) 
Independent Study
MATH 599 (Fall 2017) 
Intro to Linear Algebra
MATH 313 (Fall 2017) 
Math Analysis Engineers
MATH 322 (Fall 2017)
201617 Courses

Prin+Method Applied Math
MATH 583B (Spring 2017) 
Intro to Linear Algebra
MATH 313 (Fall 2016) 
Prin+Method Applied Math
MATH 583A (Fall 2016)
201516 Courses

Prin+Method Applied Math
MATH 583B (Spring 2016)
Scholarly Contributions
Journals/Publications
 Chertkov, M., Livescu, D., Hyett, C. M., Fryer, C., Stepanov, M., Woodward, M., & Tian, Y. (2023). Lagrangian Large Eddy Simulations via Physics Informed Machine Learning. PNAS.
 Tian, Y., Woodward, M., Stepanov, M., Fryer, C., Hyett, C. M., Livescu, D., & Chertkov, M. (2022). Lagrangian Large Eddy Simulations via Physics Informed Machine Learning. PNAS.
 Woodward, M., Tian, Y., Hyett, C. M., Fryer, C., Livescu, D., Stepanov, M., & Chertkov, M. (2022). Physicsinformed machine learning with smoothed particle hydrodynamics: Hierarchy of reduced Lagrangian models of turbulence. Physical Review Fluids, 8(5), 054602. doi:10.1103/PhysRevFluids.8.054602
 Woodward, M., Tian, Y., Hyett, C. M., Fryer, C., Livescu, D., Stepanov, M., & Chertkov, M. (2022). Physicsinformed machine learning with smoothed particle hydrodynamics: Hierarchy of reduced Lagrangian models of turbulence. Physical Review Fluids.
 Stepanov, M. (2022). Embedded (4, 5) pairs of explicit 7stage RungeKutta methods with FSAL property. Calcolo, 59(4), 41. doi:10.1007/s10092022004861
 Levashov, V. A., & Stepanov, M. G. (2015). Analysis of spatial correlations in a model twodimensional liquid through eigenvalues and eigenvectors of atomiclevel stress matrices. PHYSICAL REVIEW E, 93(1).
 Sturman, B., Podivilov, E., Stepanov, M., Tagantsev, A., & Setter, N. (2015). Quantum properties of charged ferroelectric domain walls. PHYSICAL REVIEW B, 92(21).
 Chertkov, M., & Stepanov, M. (2011). Polytope of correct (linear programming) decoding and lowweight pseudocodewords. IEEE International Symposium on Information Theory  Proceedings, 16481652.More infoAbstract: We analyze Linear Programming (LP) decoding of graphical binary codes operating over softoutput, symmetric and logconcave channels. We show that the errorsurface, separating domain of the correct decoding from domain of the erroneous decoding, is a polytope. We formulate the problem of finding the lowestweight pseudocodeword as a nonconvex optimization (maximization of a convex function) over a polytope, with the cost function defined by the channel and the polytope defined by the structure of the code. This formulation suggests new provably convergent heuristics for finding the lowest weight pseudocodewords improving in quality upon previously discussed. The algorithm performance is tested on the example of the Tanner [155,64,20] code over the Additive White Gaussian Noise (AWGN) channel. © 2011 IEEE.
 Chertkov, M., Pan, F., & Stepanov, M. G. (2011). Predicting failures in power grids: The case of static overloads. IEEE Transactions on Smart Grid, 2(1), 150160.More infoAbstract: Here we develop an approach to predict power grid weak points, and specifically to efficiently identify the most probable failure modes in static load distribution for a given power network. This approach is applied to two examples: Guam's power system and also the IEEE RTS96 system, both modeled within the static dc power flow model. Our algorithm is a power network adaption of the worst configuration heuristics, originally developed to study low probability events in physics and failures in errorcorrection. One finding is that, if the normal operational mode of the grid is sufficiently healthy, the failure modes, also called instantons, are sufficiently sparse, i.e., the failures are caused by load fluctuations at only a few buses. The technique is useful for discovering weak links which are saturated at the instantons. It can also identify generators working at the capacity and generators under capacity, thus providing predictive capability for improving the reliability of any power network. © 2010 IEEE.
 Chertkov, M., Stepanov, M., Pan, F., & Baldick, R. (2011). Exact and efficient algorithm to discover extreme stochastic events in wind generation over transmission Power Grids. Proceedings of the IEEE Conference on Decision and Control, 21742180.More infoAbstract: In this manuscript we continue the thread of [M. Chertkov, F. Pan, M. Stepanov, Predicting Failures in Power Grids: The Case of Static Overloads, IEEE Smart Grid 2011] and suggest a new algorithm discovering most probable extreme stochastic events in static power grids associated with intermittent generation of wind turbines. The algorithm becomes EXACT and EFFICIENT (polynomial) in the case of the proportional (or other low parametric) control of standard generation, and logconcave probability distribution of the renewable generation, assumed known from the wind forecast. We illustrate the algorithm's ability to discover problematic extreme events on the example of the IEEE RTS96 model of transmission with additions of 10%;20% and 30% of renewable generation. We observe that the probability of failure may grow but it may also decrease with increase in renewable penetration, if the latter is sufficiently diversified and distributed. © 2011 IEEE.
 Shkarayev, M., & Stepanov, M. G. (2009). New bisoliton solutions in dispersion managed systems. Physica D: Nonlinear Phenomena, 238(910), 840845.More infoAbstract: In this paper we propose a method which provides a full description of solitary wave solutions of the Schrödinger equation with periodically varying dispersion. This method is based on analysis and polynomial deformation of the spectrum of an iterative map. Using this method we discover a new family of antisymmetric bisoliton solutions. In addition to the fact that these solutions are of interest for nonlinear fiber optics and the theory of nonlinear Schrödinger equations with periodic coefficients, they have potential applications for increasing of bitrate in high speed optical fiber communications. © 2009 Elsevier B.V. All rights reserved.
 Chertkov, M., & Stepanov, M. G. (2008). An efficient pseudocodeword search algorithm for linear programming decoding of LDPC codes. IEEE Transactions on Information Theory, 54(4), 15141520.More infoAbstract: In linear programming (LP) decoding of a lowdensity paritycheck (LDPC) code one minimizes a linear functional, with coefficients related to loglikelihood ratios, over a relaxation of the polytope spanned by the codewords. In order to quantify LP decoding it is important to study vertexes of the relaxed polytope, socalled pseudocodewords. We propose a technique to heuristically create a list of pseudocodewords close to the zero codeword and their distances. Our pseudocodewordsearch algorithm starts by randomly choosing configuration of the noise. The configuration is modified through a discrete number of steps. Each step consists of two substeps: one applies an LP decoder to the noiseconfiguration deriving a pseudocodeword, and then finds configuration of the noise equidistant from the pseudocodeword and the zero codeword. The resulting noise configuration is used as an entry for the next step. The iterations converge rapidly to a pseudocodeword neighboring the zero codeword. Repeated many times, this procedure is characterized by the distribution function of the pseudocodeword effective distance. The efficiency of the procedure is demonstrated on examples of the Tanner code and Margulis codes operating over an additive white Gaussian noise (AWGN) channel. © 2008 IEEE.
 Chertkov, M., & Stepanov, M. (2007). Searching for low weight pseudocodewords. 2007 Information Theory and Applications Workshop, Conference Proceedings, ITA, 94100.More infoAbstract: Belief Propagation (BP) and Linear Programming (LP) decodings of Low Density Parity Check (LDPC) codes are discussed. We summarize results of instanton/pseudocodeword approach developed for analysis of the errorfloor domain of the codes. Instantons are special, code and decoding specific, configurations of the channel noise contributing most to the FrameErrorRate (FER). Instantons are decoded into pseudocodewords. Instanton/pseudocodeword with the lowest weight describes the largest SignaltoNoiseRatio (SNR) asymptotic of FER, while the whole spectra of the low weight instantons is descriptive of the FER vs SNR profile in the extended errorfloor domain. First, we describe a general optimization method that allows to find the instantons for any coding/decoding. Second, we introduce LPspecific pseudocodeword search algorithm that allows efficient calculations of the pseudocodeword spectra. Finally, we discuss results of combined BP/LP errorfloor exploration experiments for two model codes.
 Falkovich, G., Stepanov, M. G., & Vucelja, M. (2006). Rain initiation time in turbulent warm clouds. Journal of Applied Meteorology and Climatology, 45(4), 591599.More infoAbstract: A mean field model is presented that describes droplet growth resulting from condensation and collisions and droplet loss resulting from fallout. The model allows for an effective numerical simulation. The numerical scheme that is conservative in water mass and keeps accurate count of the number of droplets is applied, and the way in which the rain initiation time depends on different parameters is studied. In particular, it is shown that the rain initiation time depends nonmonotonically (has a minimum) on the number of cloud condensation nuclei. Also presented is a simple model that allows one to estimate the rain initiation time for turbulent clouds with an inhomogeneous concentration of cloud condensation nuclei. It is argued that by overseeding even a part of a cloud by small hygroscopic nuclei one can substantially delay the onset of precipitation. © 2006 American Meteorological Society.
 Stepanov, M., & Chertkov, M. (2006). Instanton analysis of lowdensity paritycheck codes in the errorfloor regime. IEEE International Symposium on Information Theory  Proceedings, 552556.More infoAbstract: In this paper we develop instanten method introduced in [1], [2], [3] to analyze quantitatively performance of LowDensity ParityCheck (LDPC) codes decoded iteratively in the socalled errorfloor regime. We discuss statistical properties of the numerical instantonamoeba scheme focusing on detailed analysis and comparison of two regular LDPC codes: Tanner's [155, 64, 20] and Margulis' [672, 336, 16] codes: In the regime of moderate values of the signaltonoise ratio we critically compare results of the instantonamoeba evaluations against the standard Monte Carlo calculations of the FrameErrorRate. © 2006 IEEE.
 Piryatinski, A., Stepanov, M., Tretiak, S., & Chernyak, V. (2005). Semiclassical scattering on conical intersections. Physical Review Letters, 95(22).More infoAbstract: We apply a semiclassical approach to the scattering problem of a vibrational wave packet in the vicinity of a conical intersection of electronic energy surfaces and derive analytical expressions for the scattering matrix. The latter are valid when the scattering length that scales as â., is small and a wave packet passes through the scattering region with a constant velocity. The analytical results are in excellent agreement with numerical simulations for a realistic set of parameters. © 2005 The American Physical Society.
 Babin, S. A., Stepanov, M. G., Churkin, D. V., & Shapiro, D. A. (2004). Coulomb broadening of the peak of electromagnetically induced transparency in plasma. Journal of Experimental and Theoretical Physics, 98(5), 953959.More infoAbstract: We have measured the shape of the AutlerTownes doublet and the peak of electromagnetically induced transparency (EIT) under plasma conditions. We compare the experimental results with the calculated spectrum of the probe field of a threelevel ArII Ascheme by taking into account Coulomb collisions. We show that the Coulomb broadening of the EIT peak is small (less than 40%), while the saturation resonance is broadened under the experimental conditions by a factor of 3. In contrast to the saturation resonance attributable to the Bennett dip in the velocity distribution of the population, the EIT peak is a coherent effect and is broadened mainly through Coulomb dephasing. © 2004 MAIK "Nauka/Interperiodica".
 Babin, S. A., Stepanov, M. G., Churkin, D. V., & Shapiro, D. A. (2004). Coulomb's broadening of peak of electromagnetically induced transparency in plasma. Zhurnal Eksperimental'noj i Teoreticheskoj Fiziki, 125(5), 10921100.
 Balk, A. M., Falkovich, G., & Stepanov, M. G. (2004). Growth of density inhomogeneities in a flow of wave turbulence. Physical Review Letters, 92(24), 2445041.More infoPMID: 15245088;Abstract: The growth of density inhomogeneities was investigated in a flow of wave turbulence. The conditions for a nonzero sum of the Lyapunov exponents was found which provides for an exponential growth of density inhomogeneities. The leading order contribution came from the pair of waves having coinciding frequencies but producing different stokes drifts. It was observed that nonzero Lyapunov exponents appear in two and three dimensions both for potential and solenoidal waves.
 Falkovich, G. E., Stepanov, M. G., & Turitsyn, S. K. (2002). Calculation of nonGaussian statistics and bit error rate degradation due to pulsetopulse interaction. Conference Proceedings  Lasers and ElectroOptics Society Annual MeetingLEOS, 1, 143144.More infoAbstract: In traditional optical soliton systems, arrival time jitter due the spontaneous emission noise and pulsetopulse interaction are two major factors limiting performance. As such, a theoretical method to calculate jitter statistics of interacting solitons is developed. Applying this approach, a nonGaussian probability density function and calculated biterror rate as a function of noise level, initial separation and phase difference between solitons is derived.
 Falkovich, G., & Stepanov, M. G. (2002). Role of interaction in causing errors in optical soliton transmission. Optics Letters, 27(1), 1315.More infoPMID: 18007700;Abstract: The role of interaction in causing errors in optical soliton transmission was studied. Two solitons propagating under a filtercontrol scheme was considered and the timing jitter caused by spontaneousemission noise and enhanced by attraction between solitons was described. Results showed the biterror rate as a function of system parameters, timing, initial distance and the phase difference between solitons.
 Falkovich, G., Fouxon, A., & Stepanov, M. G. (2002). Acceleration of rain initiation by cloud turbulence. Nature, 419(6903), 151154.More infoPMID: 12226661;Abstract: Vapour condensation in cloud cores produces small droplets that are close to one another in size. Droplets are believed to grow to raindrop size by coalescence due to collision1,2. Air turbulence is thought to be the main cause for collisions of similarsized droplets exceeding radii of a few micrometres, and therefore rain prediction requires a quantitative description of droplet collision in turbulence15. Turbulent vortices act as small centrifuges that spin heavy droplets out, creating concentration inhomogeneities614 and jets of droplets, both of which increase the mean collision rate. Here we derive a formula for the collision rate of small heavy particles in a turbulent flow, using a recently developed formalism for tracing random trajectories15,16. We describe an enhancement of inertial effects by turbulence intermittency and an interplay between turbulence and gravity that determines the collision rate. We present a new mechanism, the 'sling effect', for collisions due to jets of droplets that become detached from the air flow. We conclude that air turbulence can substantially accelerate the appearance of large droplets that trigger rain.
 Babin, S. A., Kablukov, S. I., Khorev, S. V., Podivilov, E. V., Potapov, V. V., Shapiro, D. A., & Stepanov, M. G. (2001). Detuning characteristics of ionic antiStokes Raman laser. Proceedings of SPIE  The International Society for Optical Engineering, 4351, 4859.More infoAbstract: Continuouswave generation is demonstrated of the antiStokes Raman laser in new ∧ scheme ArII 3d′ 2G9/2 → 4p′ 2F7/2 → 4s′2 D5/2 with longlived start and final levels. Red pump radiation with wavelength λp = 611 nm from a dye laser that excites transition 3d′2G9/2 → 4p′ 2 F7/2 is converted into the blue radiation at λ = 461 nm (4p′ 2 F7/2 → 4s′ 2D5/2) with efficiency of about 30%. The tunability range spans more than ± 10 GHz around exact resonance, which is five times as wide as the Doppler contour. The output frequency ω is found to depend linearly on the frequency ωP of the pump field: ω ≃ ωP λP /λ. A sharp peak of output power is observed in the detuning curve at the exact resonance instead of wellknown twophoton dip. The model is proposed that includes ionic scattering in plasma and interaction of the running pump and standing output waves. The derived formula offers an interpretation of the observed peak.
 Babin, S. A., Kablukov, S. I., Khorev, S. V., Podivilov, E. V., Potapov, V. V., Shapiro, D. A., & Stepanov, M. G. (2001). Resonant peak in the output spectral profile of an ionic antiStokes Raman laser. Physical Review A. Atomic, Molecular, and Optical Physics, 63(6), 063804/1063804/8.More infoAbstract: A study was conducted to demonstrate that peculiarities of plasma as an active medium fundamentally modifies the spectral profile of the ion Raman laser with traveling pump wave and standing output wave. As distinct from the neutral gas, a comparatively broad peak with a width of 700 MHz was observed.
 Chernykh, A. I., & Stepanov, M. G. (2001). Large negative velocity gradients in Burgers turbulence. Physical Review E  Statistical, Nonlinear, and Soft Matter Physics, 64(2 II), 263061263069.More infoAbstract: The remote left tail of the velocity gradients probability density function (PDF) in Burgers forced turbulence was analyzed by saddle point approximation in the path integral describing the velocity statistics. The velocity field configuration realizing the maximum of probability was studied numerically. The analytical solution for the longtime part of the instanton was studied numerically. Direct solving of instanton equations by iterations were also demonstrated.
 Falkovich, G. E., Stepanov, M. G., & Turitsyn, S. K. (2001). Statistics of interacting optical solitons. Physical Review E  Statistical, Nonlinear, and Soft Matter Physics, 64(6 II), 067602/1067602/4.More infoAbstract: An original analytical method was developed to describe the nonGaussian tail of the probability distribution of the distance between interacting solitons. The whole distribution was numerically obtained. It was shown how soliton interaction enhances the effects of noise and increases the probability of two solitons to approach each other.
 Stepanov, M. G., & Levitov, L. S. (2001). Laplacian growth with separately controlled noise and anisotropy. Physical Review E  Statistical, Nonlinear, and Soft Matter Physics, 63(6 I), 061102/1061102/13.More infoAbstract: Growth models using conformal mappings have large flexibility allowing for independent control over noise and growth anisotropy. One such model is generalized by using flat particles to suppress noise. It is shown that favoring growth in certain directions can be used to simulate anisotropy of the growth rate.
 Babin, S. A., Kablukov, S. I., Khorev, S. V., Podivilov, E. V., Potapov, V. V., Stepanov, M. G., & Shapiro, D. A. (2000). Resonant peak in detuning curve of ionic antiStokes Raman laser. IQEC, International Quantum Electronics Conference Proceedings, 229.More infoAbstract: A continuous wave antiStokes Raman laser (ASRL) in ionic system provides for a highly efficient upconversion with a large frequency shift. The realization of ASRL in ArII system with longlived final level 4s′2 D5/2 was demonstrated. The pump radiation wavelength of 611 nm was converted into the output radiation of 461 nm with efficiency of more than 30% in a standing wave cavity formed for output radiation.
 Belousov, Y., Podivilov, E. V., Stepanov, M. G., & Shapiro, D. A. (2000). Nonlinear Resonances Free of Field and Doppler Broadenings. Journal of Experimental and Theoretical Physics, 91(2), 287297.More infoAbstract: For the case where the Rabi frequencies of the guiding fields are much larger than the relaxation constants but much smaller than the Doppler broadening, it is shown that resonances which are neither field nor Doppler broadened can appear in the absorption (or gain) spectrum of the probe field. A classification of fourlevel systems according to the number of resonances is made for cases where two strong fields interact either with opposite or adjoining transitions. The conditions under which the number of resonances reaches eight, while for stationary atoms the maximum number is four, are found. A method is proposed for calculating the number of resonances in a multilevel system with several strong fields using analysis of the extremum points of the frequency branches in the velocityfrequency plane. © 2000 MAIK "Naiika/Interperiodica".
 Kolokolov, I., Lebedev, V., & Stepanov, M. (1999). Passive scalar in a largescale velocity field. Journal of Experimental and Theoretical Physics, 88(3), 506516.More infoAbstract: We consider advection of a passive scalar θ(t,r) by an incompressible largescale turbulent flow. In the framework of the Kraichnan model all PDF's (probability distribution functions) for the singlepoint statistics of θ and for the passive scalar difference θ(r1)  θ(r2) (for separations r1  r2 lying in the convective interval) are found. © 1999 American Institute of Physics.
 Kolokolov, I., Lebedev, V., & Stepanov, M. (1999). Passive scalar in a largescale velocity field. Zhurnal Eksperimental'noj i Teoreticheskoj Fiziki, 115(3), 920939.More infoAbstract: We consider advection of a passive scalar θ(t, r) by an incompressible largescale turbulent flow. In the framework of the Kraichnan model all PDF's (probability distribution functions) for the singlepoint statistics of θ and for the passive scalar difference θ(r2)  θ(r2) (for separations r1  r2 lying in the convective interval) are found.
 Stepanov, M. G. (1999). AutlerTownes doublet probed by strong field. Journal of Physics B: Atomic, Molecular and Optical Physics, 32(3), 649661.More infoAbstract: This paper deals with the AutlerTownes doublet structure. Applied driving and probing laser fields can have arbitrary intensities. An explanation is given of the broadening of doublet components with the growth of probing field intensity, which was observed in experiment. The effects of Doppler averaging are discussed.
 Shapiro, D. A., & Stepanov, M. G. (1998). Diffusionbroadened line shape near a turning point. JETP Letters, 68(1), 2935.More infoAbstract: The absorption spectrum of a gas with a large Doppler width and soft collisions between particles is studied. The particles are assumed to have a nonlinear dependence of the resonance frequency on velocity. The shape of the narrow peak in the spectrum resulting from an extremum of this dependence is calculated analytically for the first time. In the absence of collisions it has a characteristic asymmetric shape. Collisions are shown to broaden the line and change its shape. The profile of the probefield spectrum is obtained for a threelevel system with the strong field at an adjacent transition. The components of the AutlerTownes doublet are found to spread and repel each other because of collisions. © 1998 American Institute of Physics.
 Shapiro, D. A., & Stepanov, M. G. (1998). Power broadening of a diffusion resonance. Journal of Experimental and Theoretical Physics, 86(5), 888896.More infoAbstract: We derive an expression in terms of cylinder functions for the shape of a nonlinear resonance in a twolevel system with a rapidly decaying level. We show that when the natural linewidth is negligible, the square of the total width is the sum of squares of the power and diffusion widths. The traditional variational approximation yields a correct value for the full width at half maximum, but distorts the line profile. We derive a formula for the absorbed power as a function of the incident wave intensity for comparable power and diffusion broadening. The formula is found to be valid for a power width that is small or large compared to the diffusion width, and in a new intermediate domain where homogeneous saturation becomes inhomogeneous. © 1998 American Institute of Physics.
 Shapiro, D. A., & Stepanov, M. G. (1997). Diffusionbroadened lineshape under a strong field. Journal of Physics B: Atomic, Molecular and Optical Physics, 30(11), L377L381.More infoAbstract: The Bennett hole is analysed for a medium of twolevel particles with weak collisions beyond the scope of the perturbation theory. In the limit of small homogeneous width, the analytical expression for the hole shape is of the form of a Bessel function. The result is compared with data obtained by the variational approximation and numerical calculation. It is shown that the approximation gives the correct width, but an incorrect shape.
 Podivilov, E. V., Shapiro, D. A., & Stepanov, M. G. (1996). Narrowing of saturation resonance in collisional plasma. Proceedings of SPIE  The International Society for Optical Engineering, 2797, 226231.More infoAbstract: The profile of nonlinear resonance in the probefield ionic spectrum is shown to narrow down with the saturating field detuning. Physical cause of the effect is the falling velocity dependence of Coulomb collision frequency.
 Podivilov, E. V., Shapiro, D. A., & Stepanov, M. G. (1995). Narrowing of the Bennett hole in collisional plasma. Physical Review Letters, 74(20), 39793982.More infoAbstract: The profile of a Bennett hole, induced by a laser field, in the ionic distribution of a collisional plasma is calculated. The influence of Chandrasekhar's dependence of the coefficients of velocity space transport on the profile is included in the calculation for the first time. It is found that the hole narrows down as the fielddetuning frequency increases. The physical cause for this effect is the falling dependence of the Coulomb collision frequency on the ionic velocity. Estimations show that the effect is quite observable under conditions of a highcurrent gasdischarge plasma.
Presentations
 Stepanov, M. (2023, February 9). Eightstage pseudosymplectic RungeKutta methods of order (4, 8). Modeling, Computation, Nonlinearity, Randomness and Waves Seminar. University of Arizona, MATH 402.
 Stepanov, M. (2022, February 10). Two continuous (4, 5) pairs of explicit 9stage RungeKutta methods. Modeling, Computation, Nonlinearity, Randomness and Waves Seminar. University of Arizona, MATH 402.
 Tian, Y., Woodward, M., Stepanov, M., Fryer, C., Hyett, C. M., Chertkov, M., & Livescu, D. (2022, March). Physicsinformed Machine Learning for Reducedorder Modeling of Lagrangian Turbulence. APS March Meeting 2022.
 Hyett, C. M., Chertkov, M., Tian, Y., Livescu, D., & Stepanov, M. (2021, November). Machine Learning Statistical Evolution of the CoarseGrained Velocity Gradient Tensor. 74th Annual Meeting of the APS Division of Fluid Dynamics.
 Woodward, M., Chertkov, M., Tian, Y., Stepanov, M., Livescu, D., Hyett, C. M., & Fryer, C. (2021, November). Physics Informed Machine Learning of Smooth Particle Hydrodynamics: Solving Inverse Problems using a mixed mode approach. 74th Annual Meeting of the APS Division of Fluid Dynamics.
 Woodward, M., Tian, Y., Chertkov, M., Stepanov, M., Livescu, D., & Fryer, C. (2021, January). Learning reduced Lagrangian models of turbulence. LANL program review. online: LANL.
 Woodward, M., Tian, Y., Chertkov, M., Stepanov, M., Livescu, D., Hyett, C. M., & Fryer, C. (2021, November). Physics Informed Machine Learning of Smooth Particle Hydrodynamics: Validation of the Lagrangian Turbulence Approach. 74th Annual Meeting of the APS Division of Fluid Dynamics.
 Woodward, M., Tian, Y., Chertkov, M., Stepanov, M., Livescu, D., & Fryer, C. (2020, November). Machine Learning of Reduced Lagrangian Models of Turbulence. 73rd Annual Meeting of the APS Division of Fluid Dynamics. Virtual, CT (Chicago time): APS.
 Johnson, G., Stepanov, M., Zeng, X., & Guo, B. (2019, October 24). A numerical scheme for saturated flows based on convex optimization. Department of Hydrology and Atmospheric Sciences weekly Colloquium. University of Arizona.More infoA talk (by Misha Stepanov) at local (UofA) seminar, namely Colloquium at HAS. Presented the current state of the joint project on new numerical scheme for soil moisture evolution.
 Stepanov, M., & Chertkov, M. (2019, November). Towards (Machine) Learning of Large Eddy Lagrangian Models (of Turbulence). 72nd Annual Meeting of the APS Division of Fluid Dynamics. Seattle, WA, USA.More infoPresentation (by Michael Chertkov) of our joint work at APS meeting.
 Stepanov, M. (2016, July 48). Instantons causing iterative decoding to cycle. Nonequilibrium Statistical Physics: from molecular materials to theoretical engineering. Honoring Professor Valdimir Chernyak 60th Birthday. Telluride, CO, USA.