My M.Sc. degree in Physics and Ph.D. (Candidate of Science) degree in Physics & Mathematics are from Bashkir State University located in Ufa, a large city in southeastern European Russia and the capital of the Bashkortostan republic. Bashkir State University is among the top ten classical universities of Russia. It is especially strong in Organic Chemistry, Applied Mathematics, Philology, Information Technologies, Geophysics, and Petroleum Engineering. Many prominent applied mathematicians and physicists were among the faculty at Bashkir State University at different times, including Academicians Nikolay N. Bogolyubov, Alexei F. Leontiev, and Arlen M. Il'yn. In Ufa (from 1941 to 1943) Academician Bogolyubov developed his famous method of averaging. It is no wonder why the Department of Mathematics at Bashkir State University and the Ufa Institute of Mathematics with Computing Center are ones of the best Russian schools in Applied Mathematics, particularly, in the field of asymptotic and perturbation methods.

My M.Sc. thesis entitled "Microreological approach to chaotic motions of non-Newtonian media" was completed under the guidance of Profs. Iskander Sh. Akhatov and Mars M. Khasanov in 1994. In this work I constructed a mathematical model for oscillatory shearing motion of a non-Newtonian medium by incorporating the nonlinear kinetics of processes involving the association and dissociation of bonds between the structural elements of the medium. By numerical analysis of the proposed model the oscillatory motion of the medium was demonstrated to become chaotic for some values of parameters (via the Feigenbaum scenario).

After graduation from Bashkir State University I was hired as a Research Assistant (literal translation is Junior Researcher) in the Laboratory for Mechanics of Multiphase Systems, the Institute of Mechanics of the Ufa Branch of Russian Academy of Sciences (July 1994) and became a postgraduate (Ph.D.) student in the Continuum Mechanics Chair ("Kafedra Mekhaniki Sploshnykh Sred") of the Department of Mathematics, Bashkir State University (October 1994). My Ph.D. work was done under the guidance of and in the collaboration with Prof. Iskander Sh. Akhatov and Academician Robert I. Nigmatulin. Professor Akhatov is my Ph.D. advisor and Academician Nigmatulin is a Scientific Leader of the Laboratory for Mechanics of Multiphase Systems, Institute of Mechanics. (Note that the master's and graduate theses of Prof. Akhatov were completed under the guidance of Prof. Nigmatulin). Academician Robert I. Nigmatulin is a world-known expert in Multiphase Flows and Heat Transfer. He is the author of a two-volume text "Dynamics of Multiphase Media" whose English translation was published in 1991 by Hemisphere and which is a comprehensive reference on multiphase flows including bubbly liquids, gas suspensions, condensed and porous media. I am proud to belong to the russian scientific school on mechanics of multiphase media created by Academician Robert Iskanderovich Nigmatulin. The achievements made by Prof. Nigmatulin and his disciples in dynamics of bubbles and bubbly liquids, fundamental principles of multiphase flows, heat transfer, and other fiels of mechanics are enormous. It will suffice to mention that a group of scientists from Oak Ridge National Laboratory has recently achieved nuclear emissions from collapsing bubbles based on the basketball-dribbling regime of bubble supercompression proposed several years ago by Prof. Nigmatulin.

The objective of my Ph.D. thesis entitled "Mathematical modeling of resonant phenomena in dynamics of bubbly liquids" was to investigate long-wave/short-wave interaction in bubbly liquids and to model the effects of liquid compressibility on individual bubble pulsations. Using the method of multiple scales I constructed (and analyzed numerically) models for interaction between sound (long wave) and ultrasound (short wave) in a weakly compressible viscous liquid with gas bubbles. In the second part of the thesis I performed linear analysis of oscillatory solutions of the mathematical model proposed by Nigmatulin and his co-workers to describe the slow stage of variation of the gas bubble radius in experiments on single-bubble sonoluminescence. The details about my Ph.D. work can be found in the sections "Research Interests" and "Past Research". I was conferred Ph.D. degree in Physics & Mathematics (Application of mathematical modeling, mathematical methods and computer facilities in scientific research) on 13th October, 1998. My Ph.D. degree was approved by the Higher Attestation Committee of Russia on 19th March, 1999.

Beginning in Spring 1999 I started an appointment as Assistant Professor of Applied Mathematics at Bashkir State University. If you click here, you can see how I looked three years ago (second on the left). Note that the undergraduate program of the Department of Mathematics was divided into Pure Mathematics and Applied Mathematics Programs that year. The Continuum Mechanics Chair is one of four Chairs responsible for the Program in Applied Mathematics at Bashkir State University. During 1999 - 2000 I taught courses on "Higher Mathematics" for Freshmen and Sophomores of the Department of Engineering, "Mathematical Methods in Mechanics" for Juniors of the Department of Mathematics (specialized in Applied Mathematics), "Nonlinear Waves" and "Numerical Methods" for Seniors of the Department of Mathematics. It should be noted that as Graduate Teaching Assistant I taught "Computer Technologies" for Juniors of the Department of Mathematics and assisted Prof. Akhatov with lectures on "Nonlinear Waves" from Fall 1996 to Spring 1998. Details of my teaching experience can be found in the section "Teaching".

In 2000 I was awarded by the NSF-NATO Postdoctoral Fellowship, one of the most prestigious fellowships for foreign young scientists. The success rate for 2000 NSF-NATO fellowships was very small: only 12.9%. 11 out of 25 fellowships were given to specialists in Life Sciences. Physicists (including me) received 6 fellowships. 17 fellowships were for young scientists from NATO Partner Countries (only two were given to Russia), remaining 8 fellowships were for American scientists intended to visit NATO countries. As NSF-NATO Postdoctoral Fellow I have spent a year (from 1st August, 2000 to 31st July, 2001) in the Department of Aerospace and Mechanical Engineering, Boston University working on problems of nonlinear waves in multiphase fluids, shape oscillations of drops and radial oscillations of bubbles under the direction of Prof. Ali Nadim who is currently Professor of Mathematics at Claremont Graduate University and Professor of BioEngineering at Keck Graduate Institute (Claremont, California). Thanks to the NSF-NATO Postdoctoral Fellowship I have joined a well-established group with interests in acoustics of multiphase and non-Newtonian fluids as well as dynamics of bubbles, drops, and foams (Profs. Ali Nadim, Ronald A. Roy, and R. Glynn Holt). Professor Ali Nadim is well-known by his research in macrotransport phenomena, rheology of complex fluids, and dynamics of bubbles and drops. He received his Ph.D. in 1986 (being 24 years old !) from the Department of Chemical Engineering at the Massachussetts Institute of Technology. His Ph.D. advisor is Professor Howard Brenner, one of the pillars of physicochemical hydrodynamics. Professors Ronald Roy and Glynn Holt are well-known experimentalists in acoustic scattering by bubbles and acoustic levitation of droplets, respectively. The collaborative projects with Profs. Roy and Holt are in the stage of preparation (details are in the section "Research Projects"). I also collaborate with Prof. Robert Burridge in the field of acoustics of porous media. He is currently in the Earth Resources Laboratory of M.I.T. It should be noted that the Department of Aerospace and Mechanical Engineering of Boston University is one of the best U.S. institutions in Acoustics. It will suffice to say that Professors Alan D. Pierce (Editor-in-Chief of JASA), Ronald A. Roy (Executive Council of ASA), Robin O. Cleveland (Technical Council of ASA), Paul E. Barbone (R. Bruce Lindsay Award), William M. Carey and Michael S. Howe (Associate Editors of ASA) are among the faculty of this department. I have received excellent experience in Acoustics by working with these people and visiting departmental and "tea" seminars. The details of my research done at Boston University are in the sections "Research Interests", "Past Research", and "Current Research".

From 10th August 2001 to 31st July 2003 I have been a Research Assistant Professor in the Department of Mathematics of Virginia Tech. Virginia Tech (Virginia Polytechnic Institute and State University) is very strong by its Engineering school which ranks 23th in 2003 Best Graduate Schools Listing. The Department of Mathematics is 30th on the list of top Applied Mathematics schools. At Virginia Tech I was studying the effects of viscoelasticity, high viscosity ratio, and high inertia on the deformation and breakup of droplets in shear flow of an immiscible liquid as well as instabilities of two-layer flow of viscoelastic liquids. For this purpose, a novel parallelized algorithm for fully 3D transient simulation of shear flow of two immiscible viscoelastic liquids has been developed. It consists of the second order Volume-of-Fluid method for tracking the droplet interface, the projection method for solving the Navier-Stokes equation and the semi-implicit factorized scheme for solving the constitutive equation (Giesekus model). The description of the numerical algorithm and the current results on drop breakup and two-layer flow instabilities (including movies and pictures) can be found in the section "Current Research".

I am a Senior Research Scientist in the Department of Biomedical Engineering of Duke University starting from 1st August 2003. Duke University is one of the best schools in the United States. In 2003 U.S. News rating, it ranked 5th together with Stanford University, University of Pensilvania, and California Institute of Technology. Moreover, the Department of Biomedical Engineering is on the 2nd place. Duke is famous by its Medical School. Under the supervision of Professor George Truskey, I am working on 3-D numerical modeling of cell-surface adhesion, micropipette aspiration of cells, and other problems relevant to atherosclerosis. I also collaborate with other faculty of Duke and several other universities on the problems of contrast-enhanced ultrasound imaging and drug delivery. My current results on cell adhesion can be found in the section "Current Research".

At Virginia Tech I taught MATH 2214 ("Introduction to Differential Equations"), MATH 2224 ("Multivariable Calculus") for students (mostly Sophomores) of the College of Engineering and MATH 4574 ("Vector/Complex Analysis for Engineers") for Seniors. If you click here, you can find the course contract and a list of online lectures for MATH 2214 that I taught in Spring 2002 and Summer 2003. The information about MATH 4574 (I taught it in Summer 2002) is on this page. The course contract for MATH 2224 (Spring 2003) can be found here.

Robert Iskanderovich Nigmatulin is a Full Member (Academician) of Russian Academy of Sciences (Division of Mathematics and Mechanics). He holds the positions of President of Ufa Branch of Russian Academy of Sciences, Professor of Mechanics at Lomonosov Moscow State University, Visiting Professor of Environmental and Energy Engineering in the Center for Multiphase Research, Rensselaer Polytechnic Institute (USA), Scientific Leader of the Laboratory for Mechanics of Multiphase Systems, Institute of Mechanics, Ufa Branch of Russian Academy of Sciences. He is a founder and first Scientific Chief of Tyumen Institute of Mechanics and Multiphase Systems (now Tyumen Institute of Theoretical and Applied Mechanics), He was a Professor of Sorbonna at the Universite Pierre et Marie Curie (France).

Academician Nigmatulin graduated from two of Russia's most prestigious universities: Bauman Moscow State Technical University in 1963 and Lomonosov Moscow State University in 1965. He received his Ph.D. and D.Sc. degrees from Lomonosov Moscow State University in 1967 and 1971, respectively. He received Lenin Comsomol Prize, USSR State Prize, Gold Medal of USSR Economical Achievement Exibition, First Prize of Siberian Branch of USSR Academy of Sciences, and Makeev Gold Medal of Russian Federation of Cosmonautics.

Academician Nigmatulin is a founder of Russian scientific school on mechanics of multiphase media. His research interests span the area of applied mathematics, mechanics, and thermophysics. Particularly, he deals with:

The results of Prof. Nigmatulin and his disciples prior to 1990 can be found in the two-volume text "Dinamika Mnogofaznykh Sred" whose English translation ("Dynamics of Multiphase Media") was published in 1991 by Hemisphere. One of his recent results is the elaboration of a new "basketball-dribbling" method of bubble supercompression by which a group of scientists from Oak Ridge National Laboratory has recently achieved nuclear emissions from collapsing bubbles. He was an invited (and keynote) speaker at many International Conferences on Acoustics, Multiphase Flows, and Heat Transfer. He is in the Editorial Board of International Journal of Multiphase Flow, International Journal of Heat and Mass Transfer, Experimental Thermal and Fluid Science and several other international and Russian journals. Professor Nigmatulin's selected publications (total number of his publications exceeds 300) are

Bashkortostan: The Republic of Bashkortostan is located at western slopes of the southern Ural Mountains and the adjoining plains. It occupies the territory of 143,600 square kilometers with a population of over four million people. Ufa, the capital of Bashkortostan, is located 1519 kilometers from Moscow and 800 kilometers from Yekaterinburg.