Publications & Presentations
Publications | Conference Papers | Invited Seminars
A comprehensive listing of all publications and seminar talks can also be found in Dr. Ranjan’s resume.
Refereed Journal Publications [ * denotes graduate students advised/co-advised, ** denotes undergraduate students ]
- Akula, B.*, and Ranjan, D., “Dynamics of buoyancy driven flows at moderately high Atwood numbers”, Journal of Fluid Mechanics, Vol. 795, pp. 313-355 (2016)
- Sekhran, A., Morrison, G., and Ranjan, D., “An enquiry of the friction factor ‘jump’ phenomenon in hole-pattern seals,” Journal of Fluids Engineering, vol. 138, Issue 8, pp. 081102 (2016)
- [Edited Volume] Bonazza, R. and Ranjan D., “29th International Symposium on Shock Waves Vol. I and II” Springer International Publishing Switzerland, (2015) [DOI: Vol I- 10.1007/978-3-319-16835-7 and Vol II--10.1007/978-3-319-16838-78]
- Reilly, D.*, McFarland, J. A.*, Mohaghar, M.*, and Ranjan, D., “The effect of initial conditions and circulation deposition on the inclined-interface reshocked Richtmyer-Meshkov instability,” Experiments in Fluids, 56 (8), 1-16, (2015)
- McFarland, J. A.*, Reilly, D.*, Black, W., Greenough, J. A., and Ranjan, D., “Modal interactions between a large-wavelength inclined interface and small wave-length multimode perturbations in a Richtmyer-Meshkov Instability,” Physical Review E, Vol. 92, 013023 (2015)
- Pidaparti, S. R*, McFarland, J. A.*, Mikhaeil, M. M.*, Anderson, M.H., and Ranjan, D., “Investigation of buoyancy effects on heat transfer characteristics of Supercritical Carbon Dioxide in Heating Mode,” ASME Journal of Nuclear Engineering Radiation Science, 1(3): 031001-031001-10. (2015) doi:10.1115/1.4029592
- Pidaparti, S. R*, Moisseytsev, A., Sienicki, J. J., and Ranjan, D., “Counter flow induced draft cooling tower option for Supercritical Carbon Dioxide Brayton Cycle,” Nuclear Engineering and Design, Volume 295, Pages 549–558, (2015)
- Martin, M. A.*, Chen, C., Mukherjee, P. P., Pannala, S., Dietiker, J-F., Turner, J. A., and Ranjan, D., “Morphological Influence in Lithium-Ion Battery 3-D Electrode Architectures,” Journal of the Electrochemical Society, 2015, volume 162, issue 6, A991-A1002
- Thanapal, S.*, Annamalai, K., Ansley., J. and Ranjan, D., “Cofiring Carbon Dioxide torrefied woody biomass with coal on emission characteristics,” Biomass Conversion and Biorefinery, March 2016, Volume 6, Issue 1, pp 91-104
- Tang, Y.*, Guo, B., and Ranjan, D., “Numerical simulation of aerosol deposition from turbulent flows using three-dimensional RANS and LES turbulence models,” Engineering Applications of Computational Fluid Mechanics, Online First-Feb 25th, 2015 http://dx.doi.org/10.1080/19942060.2015.1004818
- [Book Chapter] Thanapal, S.*, Eseltine, D.*, Annamalai, K., and Ranjan, D., “Biomass Fuel Quality Enhancement and Respiratory Quotient (RQ) for Ranking Fossil and Biomass Fuels Based on CO2 Emissions,” Novel Combustion Concepts for Sustainable Energy Development, Springer India, 2014 pp 45-73
- McFarland, J. A.*, Reilly, D.*, Creel, S.*, McDonald, C.*, Finn, T.*, and Ranjan, D., “Experimental Investigation of Inclined Interface Richtmyer-Meshkov Instability Before and After Reshock,” Experiments in Fluids, Vol. 55, Issue 1, pp 1640 (2014)
- Siwatch, V., Lawrence, B., Kuchibhatla, S*., Annamalai, K., and Ranjan, D., “Excess air, Schmidt number and NOx formation in laminar jet flames,”Combustion Science and Technology, 186 (12), 1936-1953 (2014)
- McFarland, J. A.*, Greenough, J. A., and Ranjan, D., “Simulations and Analysis of the Reshocked Inclined Interface Richtmyer-Meshkov Instability for Linear and Non-linear Interface Perturbations,” Journal of Fluids Engineering, Vol. 136 (7), 071203, (2014).
- Thanapal, S.*, Chen, W., Annamalai, K., Carlin, N., Ansley., J. and Ranjan, D., “Carbon Dioxide torrefaction of woody biomass,” Energy and Fuels, 28 (2), 1147-1157 (2014)
- Matsuo, B.*, Anderson, M., and Ranjan, D., “Numerical Study of Compact Heat Exchanger design for GEN-IV Supercritical Carbon Dioxide Power Conversion Cycles,” Nuclear Science and Engineering, Vol 176, Issue 2, pp 138-153, (2014)
- Akula, B.*, Andrews, M. J., and Ranjan, D., “Effect of shear on Rayleigh-Taylor mixing at low Atwood number”, Physical Review E, Vol. 87, 033013 (2013)
- Stanic, M., McFarland, J. A.*, Stellingwerf, R. F., Cassibry, J. T., Ranjan, D., Bonazza, R., Greenough, J. A. and Abarzhi, Si. I., “Non-uniform volumetric structures in Richtmyer-Meshkov flows,” Physics of Fluids, 2013.
- Kuchibhatla, S.* and Ranjan, D., “Effect of initial conditions on Rayleigh-Taylor mixing: Modal interaction”, Physica Scripta, 2013.
- McFarland, J. A.*, Greenough, J. A., and Ranjan, D., “Investigation of the Initial Perturbation Amplitude for the Inclined Interface Richtmyer-Meshkov Instability,” Physica Scripta, 2013.
- Eseltine, D.*, Thanapal, S.*, Annamalai, K., and Ranjan, D., “Torrefaction of woody biomass (Juniper and Mesquite) using inert and non-inert gases”, Fuel, 2013.
- Haehn, N*, Ranjan, D., Weber, C., Oakley, J., Rothamer, D., and Bonazza, R., “Reacting Shock Bubble Interaction,” Combustion and Flame, Vol. 153, Issue 3, pp1339-1350 (2012).
- Bailie, C.**, McFarland, J. A.*, Greenough, J. A., and Ranjan, D., “Effect of incident shock wave strength on the decay of Richtmyer-Meshkov instability-introduced perturbations in the refracted shock wave,” Shock Waves, Vol. 22, Issue 6, pp 511-519, 2012 DOI: 10.1007/s00193-012-0382-y.
- Amini, N., Sekaran, A., Schwaenen, M., Vijaykumar, A., and Ranjan, D., “An experimental investigation of the free jet flow from a radially lobed nozzle using hot wire anemometry,” International Journal of Mechanical Engineering Education, 2012 [Educational Journal Publication].
- McFarland, J. A.*, Greenough, J. A., and Ranjan, D., “Computational parametric study of a Richtmyer-Meshkov instability for an inclined interface,” Physical Review E, Vol. 84, 026303 (2011).
- Ranjan, D., Oakley, J., and Bonazza, R., “Shock-Bubble Interactions,” Annual Rev. Fluid Mech., 43, pp117-140 (2011).
- Tillman, S. T., Kuchibhatla, S.*, Annamalai, K., Caton, J., and Ranjan, D., “Interactive Combustion in a Linear Array of 2D Laminar Isolated & Triple Burner Jets,” Journal of Combustion, Article ID 716050, 2012, DOI:10.1155/2012/716050.
- Kurizenga, A., Anderson, M., Fatima, R.*, Corradini, M., Towne, A., and Ranjan, D., “Heat Transfer of supercritical carbon-dioxide in printed circuit heat exchanger geometries,” Journal of Thermal Science and Engineering Application, Vol.3, September 2011.
- Haehn, N.*, Weber, C., Oakley, J., Anderson, M., Ranjan, D., and Bonazza, R., “Experimental investigation of of twice-shocked spherical inhomogeneity with Particle Image Velocimetry,” Shock Waves, Vol. 21, No. 3 (2011).
- Singh, O. P., Ranjan, D., Srinivasan, J., and Sreenivas, K. R., “ A study of basalt fingers using experiments and numerical simulations in double-diffusive systems,” Journal of Geography and Geology, 3, 1 (2011).
- Haehn, N*., Weber, C., Oakley, J., Anderson, M., Ranjan, D., and Bonazza, R., “Experimental study of shock-bubble interaction with reshock,” Shock Waves, Vol. 22, No. 1 (2011).
- Haehn, N.*, Ranjan, D., Weber, C., Oakley, J. G., Anderson, M. H., and Bonazza, R., “Experimental investigation of of twice-shocked spherical inhomogeneity,” Physica Scripta, T142 (2010).
- [Book Chapter] Ranjan, D., Niederhaus, J.H.J., Oakley, J.G., Anderson, M.H., and Bonazza, R., “Experimental investigation of shock-induced distortion of a light spherical gas inhomogeneity,” Shock Waves, Part XV111- Richtmyer-Meshkov, Springer Berlin Heidelberg, 2009. (DOI - 10.1007/978-3-540-85181-3_61).
- [Book Chapter] Niederhaus, J.H.J., Ranjan, D., Oakley, J.G., Anderson, M.H., ., Greenough, J. A., and Bonazza, R., “Computations in 3D for shock-induced distortion of a light spherical gas inhomogeneity,” Shock Waves Part XV111- Richtmyer-Meshkov, Springer Berlin Heidelberg, 2009. (DOI - 10.1007/978-3-540-85181-3_60).
- Motl, B., Oakley, J.G., Ranjan, D., Weber, C., Anderson, M.H., and Bonazza, R., “Experimental validation of a Richtmyer-Meshkov scaling law over large density ratio and shock strength ranges,” Physics of Fluids, 21, 126102 (2009).
- Ranjan, D., Niederhaus, J. H. J., Oakley, J., Anderson, M., Greenough, J. A, and Bonazza, R., “Experimental and numerical investigation of shock-induced distortion of a spherical gas inhomogeneity,” Physica Scripta, T132 (2008).
- Ranjan, D., Niederhaus, J., Oakley, J., Anderson, M., Bonazza, R., and Greenough, J., “Shock-bubble interactions: features of divergent refraction geometry observed in experiments and simulations,” Physics of Fluids, 20, 036101 (2008).
- Niederhaus, J. H. J., Greenough, J. A, Oakley, J., Ranjan, D., Anderson, M., and Bonazza, R., “A computational parameter study for the three-dimensional shock-bubble interaction,” Journal of Fluid Mechanics, 594, 85 (2008).
- Motl, B., Niederhaus, J., Ranjan, D., Oakley, J., Anderson, M., and Bonazza, R., “Experimental Study for ICF-Related Richtmyer-Meshkov Instabilities,” Fusion Science and Technology, 52, 4 (2007).
- Ranjan, D., Niederhaus, J., Motl, B., Anderson, M., Oakley, J., and Bonazza, R., “Experimental investigation of primary and secondary features in high Mach number shock-bubble interaction,” Physical Review Letters, 98, 024502 (2007).
- Niederhaus, J., Ranjan, D., Oakley, J., Anderson, M., and Bonazza, R., “Inertial-Fusion-Related Hydrodynamic Instabilities in a Spherical Gas Bubble Accelerated by a Planar Shock Wave,” Fusion Science and Technology, 47, 4 (2005), pp. 1160-1164.
- Ranjan, D., Anderson, M., Oakley, J., and Bonazza, R., “Experimental Investigation of a Strongly Shocked Gas bubble,” Physical Review Letters, 94, 184507 (2005).
Top of Refereed Journal Publications
Archival Peer Reviewed Conference Papers
- Jarrahbashi, D.*, Pidaparti, S.*, Kang, T.*, and Ranjan, D., “Nucleation of Supercritical CO2 Flow in a Converging-Diverging Nozzle,” Proceedings of The 5th International Symposium- Supercritical CO2 Power Cycles, March 28-31, 2016 San Antonio, Texas [won the best poster presentation award at the conference]
- Pidaparti, S.*, Hruska, P., Moisseytsev, A., Sienicki, J., and Ranjan, D., “Technical and economic feasibility of dry air cooling for the supercritical C02 Brayton Cycle using existing technology,” Proceedings of The 5th International Symposium- Supercritical CO2 Power Cycles, March 28-31, 2016 San Antonio, Texas
- Pidaparti, S.*, McFarland, J.*, Umrigar, E.*, Ranjan, D. and Anderson, M., “Effect of buoyancy on heat transfer characteristics of Supercritical Carbon Dioxide in the Heating Mode,” 11th AIAA/ASME joint Thermophysics and Heat Transfer Conference, AIAA 2014-3359.
- Reilly, D.*, McFarland, J.*, Carter, J.*, and Ranjan, D., “Shock-Driven Variable-Density Turbulence: New Insight,” International Workshop on the Physics of Compressible Turbulent Mixing, San Francisco, CA, September 3, 2014.
- Chen, W., Thanapal, S.*, Annamalai, K., Ranjan, D., B. Lawrence, and Ansley., J. “Kinetics of Pyrolysis of Mesquite Fuel-Comparison of Different Methods,” Proceeding of ASME Turbo Expo 2014: Turbine Technical Conference and Exposition, paper no. GT2014-27349, doi:10.1115/GT2014-27349.
- McFarland, J. A.*, Creel, S.*, Finn, T., McDonald, C.*, Greenough, J., and Ranjan, D., “Simulations and experimental work on the inclined interface Richtmyer-Meshkov instability,” Proceedings of the 29th International symposium on Shock waves, Madison, Wisconsin, July 2013.
- McFarland, J. A.*, Creel, S.*, Finn, T., McDonald, C.*, Greenough, J., and Ranjan, D., “Inclined interface Richtmyer-Meshkov instability: Reshock study,” Proceedings of the 29th International symposium on Shock waves, Madison, Wisconsin, July 2013.
- Kuchibhatla, S*, and Ranjan, D., “Rayleigh-Taylor Experiments,” Paper # IMECE 2012-93087, Proceedings of 2012 IMECE meeting, Houston, Texas, Nov 2012.
- McFarland, J. A.*, Greenough, J. A., and Ranjan, D., “An investigation of the inclined interface Richtmyer-Meshkov instability: simulations and progress on students,” Proceedings of 13th International Workshop on Physics of Compressible and Turbulent Mixing, July 2012.
- Akula, B.* and Ranjan, D., “A study of combined KH and RT instabilities at low Atwood numbers,” Proceedings of 13th International Workshop on Physics of Compressible and Turbulent Mixing, July 2012.
- McFarland, J. A.*, Greenough, J. A., Ranjan, D. and B. Matsuo* “Simulations and analysis of shock accelerated inhomogenous flows with and without reshock,” Proceedings of 2012 ASME Fluids Engineering Division Summer Meeting, Puerto Rico, July 8th-12th, 2012.
- Matsuo, B.*, Anderson, M., and Ranjan, D. and “Numerical investigation of the geometric effects on the performance of printed circuit heat exchangers,” Proceedings of 2012 ASME Heat Transfer Summer Conference, Puerto Rico, July 8th-12th, 2012.
- Akula, B.*, McFarland, J.*, Kuchibhatla, S.*, and Ranjan, D., “Effect of shear on RT mixing at low Atwood numbers,” Proceedings of Turbulent Mixing and Beyond: 3rd International Conference, Trieste, Italy, August 21st -28th 2011.
- McFarland, J. A.*, Greenough, J. A., and Ranjan, D., “A computational parametric study of a Richtmyer-Meshkov instability for an inclined interface,” Proceedings of Turbulent Mixing and Beyond: 3rd International Conference, Trieste, Italy, August 21st -28th 2011.
- Kuchibhatla, S*, McFarland, J. A.*, Akula, B*, and Ranjan, D., “Effect of initial conditions on Rayleigh-Taylor mixing: wavelength interaction,” Proceedings of Turbulent Mixing and Beyond: 3rd International Conference, Trieste, Italy, August 21st -28th 2011.
- Fatima, R.*, Kurizenga, A., Anderson, M., and Ranjan, D., “Numerical Investigation of Thermal Hydraulic behavior of Supercritical Carbon-dioxide in Compact Heat exchanges,” Proceedings of 2011 Supercritical CO2 Power Cycle Symposium, 2011.
- Kuchibhatla, S.*, Koppenberger, P.**, Akula, B.*, McFarland, J.*, and Ranjan, D., “Rayleigh-Taylor experiments for low Atwood numbers with multimodal initial conditions,” Proceedings of 12th International Workshop on Physics of Compressible and Turbulent Mixing, July 2010.
- Akula, B.*, Andrews, M., and Ranjan, D., “Rayleigh-Taylor experiments for low Atwood numbers with multimodal initial conditions,” Proceedings of 12th International Workshop on Physics of Compressible and Turbulent Mixing, July 2010.
- Mukherjee, P. P., Ranjan, D., Mukundan, R., and Borup, R. L., “Heat and water transport in a polymer electrolyte fuel cell electrode, 14th International Heat Transfer Conference, Paper-22703, August 2010.
- Ranjan, D., Prestridge, K. P., Andrews, M., Gore, R., Marr-Lyon, M., and Merril, F., “ICF related Richtmyer-Meshkov instability: Mach 10 experiments,” Proceedings of 2nd International Conference and Advanced School “Turbulent Mixing and Beyond”, July-August 2009.
- Ranjan, D., Balakumar, B. J., Orlicz, G., Prestridge, K. P., and Tomkins, C. D., “Richtmyer-Meshkov Instability: Reshock Study,” 27th International Symposium on Shock Waves, Paper 30519, July 2009.
- Ranjan, D., Prestridge, K. P., Andrews, M., Gore, R., Marr-Lyon, M., and Merril, F., “Richtmyer-Meshkov Instability at a gas interface accelerated by a Mach 10 Shock wave,” 27th International Symposium on Shock Waves, Paper 30604, July 2009.
- Balakumar, B. J., Zoldi-Sood, C., Orlicz, G., Ranjan, D., Tomkins, C. D., and Prestridge, K. P., “Experimental and computational investigation of Richtmyer-Meshkov turbulence in fluid layers after reshock,” 27th International Symposium on Shock Waves, Paper 30672, July 2009.
- Ranjan, D., Balakumar, B. J., Orlicz, G., Tomkins, C. D., and Prestridge, K. P., “Experimental analysis of the physics of the reshock in the case of a shock-accelerated thin fluid layer,” 11th International Workshop on the Physics of Compressible Turbulent Mixing, Santa Fe, NM, July 14-18, 2008.
- Balakumar, B. J., Orlicz, G., Ranjan, D., Tomkins, C. D., and Prestridge, K. P., “Richtmyer-Meshkov instability induced by a Mach 1.2 shock in a varicose curtain,” 11th International Workshop on the Physics of Compressible Turbulent Mixing, Santa Fe, NM, July 14-18, 2008.
- Orlicz, G., Balakumar, B. J., Ranjan, D., Tomkins, C. D., and Prestridge, K. P., “Shock driven instabilities in a varicose, heavy-gas curtain: Mach number effects,” 11th International Workshop on the Physics of Compressible Turbulent Mixing, Santa Fe, NM, July 14-18, 2008.
- Ranjan, D., Niederhaus, J., Oakley, J., Anderson, M., and Bonazza, R., “Experimental investigation of shock-induced distortion of a light spherical gas inhomogeneity,” 26th International Symposium on Shock Waves, Paper 2960, Gottingen, Germany, July 15-20, 2007.
- Niederhaus, J., Ranjan, D., Oakley, J., Anderson, M., Greenough, J., and Bonazza, R., “Computations in 3D for shock-induced distortion of a light spherical gas inhomogeneity,” 26th International Symposium on Shock Waves, Paper 2961, Gottingen, Germany, July 15-20, 2007.
- Ranjan, D., Niederhaus, J., Anderson, M., Motl, B., Oakley, J., Bonazza, R., and Greenough, J., “Experimental Study of the Interaction of a Planar Shock with a Free-Rising Bubble,” 10th International Workshop on the Physics of Compressible Turbulent Mixing, Paris, France, July 17-21, 2006.
- Niederhaus, J., Greenough, J., Oakley, J., Ranjan, D., Anderson, M., and Bonazza, R., “A Computational Parameter Study for the Shock-Bubble Interaction in 3D, with and without Modeled Soap Film,” 10th International Workshop on the Physics of Compressible Turbulent Mixing, Paris, France, July 17-21, 2006.
- Motl, B., Niederhaus, J., Oakley, J., Ranjan, D., Anderson, M., Bonazza, R., and Greenough, J., “Shock Accelerated Two-Dimensional Interface,” 10th International Workshop on the Physics of Compressible Turbulent Mixing, Paris, France, July 17-21, 2006.
- Ranjan, D., Niederhaus, J., Anderson, M., Oakley, J., and Bonazza, R., “Shock-induced instabilities on a spherical gas bubble,” 25th International Symposium on Shock Waves, Paper 1197-2, Bangalore, India, July 17-22, 2005.
- Ranjan, D., Sreenivas, R. K., Singh, P. O., and Srinivasan, J., “Laboratory Study of Scale Transitions in Oceanic Double-x Diffusive Finger,” International Conference on Environmental Fluid Mechanics, pp. 178-182, Guwahati, India, 2005.
- Ranjan, D., Niederhaus, J., Anderson, M., Oakley, J., and Bonazza, R., “Measurements of mixing induced at a gas interface by the Richtmyer-Meshkov Instability,” Paper 2691, Z.L. Jiang (Ed.), Shock Waves, Proceeding, 24th International Symposium on Shock Waves Beijing, China, July 2004.
- Ranjan, D., Niederhaus, J., Bauer, T., Oakley, J., Anderson, M., Smith, L., Greenough, J., and Bonazza, R., “Experimental and Computational Investigations of Shock-Accelerated Gas Bubbles,” 9th International Workshop on the Physics of Compressible Turbulent Mixing, Cambridge, UK, July 19-23, 2004.
Top of Archival Peer Reviewed Conference Papers
Invited Seminars
- “Techno-Economic Development for Supercritical CO2 Advanced Energy Conversion,” at Mechanical Engineering Seminar, Carnegie Mellon University, on Nov. 6th, 2015.
- Plenary Speaker at 14th International Workshop on Physics of Compressible Turbulent Mixing (IWPCTM) Meeting at San Francisco, 2014, titled “Progress with Experiments on Understanding the Rayleigh-Taylor and Richtmyer-Meshkov Driven Flows for Complex Environments”
- “Understanding the dynamics of shock-and buoyancy-driven flows at Extreme Conditions,” Environmental Fluid Mechanics and Water Resources Seminar, Georgia Tech, on Nov. 14th 2014.
- “Experimental measurements of velocity and density statistics in turbulent Rayleigh-Taylor mixing layers with and without shear”, at 17th USNCTAM Meeting, June 18th, 2014.
- “Fluid instabilities and mixing in variable density flows at extreme conditions” at Fluid Days (Special conference in honor of the 80th birthday of Prof. Roddam Narasimha) at IISC Bangalore, Bangalore, India, July 19th 2013.
- “Velocity, density and mixing growth measurements in turbulent Rayleigh-Taylor mixing layers with and without shear” at Stewardship Science Academic Alliance (SSAA) Symposium, Albuquerque, June 28th, 2013.
- “Fluid instabilities and mixing in variable density flows at extreme conditions” at George W. Woodruff school of Mechanical Engineering, Georgia Institute of Technology, May 1st, 2013.
- “Mechanical Engineering perspective on energy research: From turbulence mixing to nuclear fusion” at SYNERGY 2013, Mechanical Engineering, National Institute of Technology-Trichy, March 17th, 2013.
- “Detailed measurements of Turbulent Rayleigh-Taylor mixing at Large and Small Atwood numbers” at Stewardship Science Academic Alliance (SSAA) Symposium, Washington DC, Feb. 23rd, 2012.
- “Putting design into Turbulence,” at REU Site: Energy and Combustion-College Station, June 8th, 2012.
- “Fluid instabilities and mixing at Extreme Conditions,” at Graduate Seminar, Department of Mechanical Engineering, Texas A&M Univ., April 18th, 2012.
- “Transition, Turbulence and Mixing in Shock and Buoyancy-Accelerated Variable Density Flows at Extreme Conditions,” at CRASH center, Department of Atmospheric, Oceanic and Space Sciences, University of Michigan, August 29, 2011.
- “Experimental Investigation of Shock-Induced Interfacial Instability, Mixing, and Turbulence,” at Mechanical Engineering Department, IIT-Bombay, June 19, 2009.
- “Experimental Investigation of Shock-Induced Distortion of a Spherical Gas Inhomogeneity” at Mechanical Engineering Department, Caltech, May 29, 2007.
- “Experimental Investigation of Richtmyer-Meshkov Instability for a three-dimensional interface” at Los Alamos National Laboratory, May 15, 2007.
- “Richtmyer-Meshkov Instability” at Jawaharlal Nehru Center for Advanced Scientific Research (JNCASR), July, 2004.