Nikolay M. Bessonov

1. Bessonov N.M., Song D.J. Application of vector calculus to numerical simulation of continuum mechanics problems, Journal of Computational Physics, vol.167/1, 2001.
2. J. Pojman, N. Bessonov, R. Texier, V. Volpert, H. Wilke. Numerical simulations of transient interfacial phenomena in miscible fluids. Proceedings AIAA, January 2002, Reno, USA.
3. N. Bessonov, V. Volpert. On a problem of plant growth. "Patterns and Waves". A. Abramian, S. Vaculenko, V. Volpert, Eds. St Peterburg, 2003, pp 323-337.
4. N. Bessonov, J. Pojman, V. Volpert. Modelling of diffuse interfaces with temperature gradients. Journal of Engineering Mathematics, vol.49, no. 4, 2004 321-338. 76D45 (76R50)
5. J. Pojman, N. Bessonov, V. Volpert, S.S. Paley. Missible fluids in microgravity: a zero-upmass experiment on the International Space Station/ AIAA, 2004.
6. N. Bessonov, J. Pojman, V. Volpert. Miscible fluids in microgravity. AIAA-2004-962.
7. N. Bessonov, J. Pojman, V. Volpert. Munerical simulations of transient interfacial phenomena in miscible fluids. AIAA-2004-631.
8. N. Bessonov, J. Pojman, V. Volpert. Modelling of miscible liquids and microgravity experiments. Matamli No. 75(2004) 51-66. 76D45 (76E17 80A22)
9. S. Aristov, N. Bessonov, Yu. Gaponenko, V. Volpert. Interfacial waves in binary fluids. Problemes mathematiques de li mecanique, C.R. Acad. Sci. Paris, Serie I. 2004.
10. S. Golovashchenko, N. Bessonov, R. Davies. Numerical Simulation of Pulsed Electromagnetic Stamping Processes, Proceedings of 1st International Conference on High Speed Forming, Dortmund, Germany, 2004, p.83-91.
11. S.F. Golovashchenko, N.M. Bessonov, R.W. Davies. Pulsed electromagnetic Forming of Aluminum Body Panels, Proceedings of 6th Global Innovations Symposium: Trends in Materials and Manufacturing Technologies for Transportation Industries, TMS, 2005, p.71-76.
12. N. Bessonov, A. Ducrot, V. Volpert. Modelling of leukemia development in the bone marrow. Proc. of the Annual Symposium ''Mathematics applied in biology and biophysics'', Iasi, 2005, 79-88.
13. S. Golovashchenko N. Bessonov. Development of Sharp Flanging Technology for Aluminum Panels. Proceedings of the 6th International Conference on Numerical Simulation of 3D Sheet Forming Processes, NUMISHEET 2005, Detroit, MI, p.687-690.
14. N. Bessonov, P. Gordon, G. Sivashinsky, A Zinoviev. On metastable deflagration in porous medium combustion. Applied Mathematics Letters 18 (2005) p.897-903.
15. N. Bessonov, J. A. Pojman, V. A. Volpert, B.D. Zoltowski. Numerical simulations of convection induced by Korteweg stresses in miscible polymer-monomer systems. Microgravity sci. tech., 2005, XVII, 8-12.
16. N. Bessonov, V. Volpert. Dynamic models of plant growth. Editions Publibook. Paris, France, 2006, 67pp. ISBN: 2-7483-3165-6 92C80
17. N. Morozova, N. Bessonov, V. Volpert. Plant growth modelling. Conference on applied and industrila mathematics, Madrid, June 2006.
18. N. Bessonov, L. Pujo-Menjouet, V, Volpert. Nat. Phenom., Cell modelling of hematopoiesis. Math. Model. Nat. Phenom., 1, 2006, No. 2, 81-103.
19. N. Bessonov, N. Morozova, V. Volpert. Plant growth modelling. ECMI Newsletter, Mathematics and Industry, No. 41, 2007, pp. 27-28.
20. John A.Pojman and Nick Bessonov and Vitaly Volpert and Mark S. Paley, Miscible Fluids in Microgravity (MFMG): A Zero-Upmass Investigation on the International Space Station, Microgravity Science and Technology, Volume 19, Issue 1, Year 2007, Pages 33-41.
21. S. Genieys, N. Bessonov, V. Volpert. Mathematical model of evolutionary branching. Mathematical and computer modelling, 49, 2009, 2109-2115pp
22. Bessonov N., Morozova N., Volpert V., Modelling of branching patterns in plants. Bull. Math. Biol. 70 (2008), no. 3, 868--893.
23. S. Golovashchenko, N. Bessonov, R. Davies. Analysis of Blank-Die Contact Interaction in Pulsed Forming Processes, 3st International Conference on High Speed Forming, Germany, 2008.
24. S. Genieys, N. Bessonov, V. Volpert, Mathematical model of evolutionary branching, Special issue : Trends in Application of Mathematics to Medicine, France, 2008.
25. Nikolai Bessonov, Ivan Demin, Laurent Pujo-Menjouet, Vitaly Volpert, A mutli-agent model describing self-renewal of differentiation effects on the blood cell population, Special issue: Trends in Application of Mathematics to Medicine, France, 2008.
26. Sergey Golovashchenko, Nicholas Bessonov, Richard Davies, Modeling of Pulsed Electromagnetic Forming, Interiaken, Switzerland, September 1-5, 2008. (6pp)
27. N. Bessonov, J. Pojman, G. Viner, V. Volpert, B. Zoltowski Instabilities of diffuse interfaces. Math. Model. Nat. Phenom., 3 (2008), No. 1, 108-125.
28. John A. Pojman, Yuri Chekanov, Victor Wyatt, Nick Bessonov, Vitaly Volpert, Numerical Simulations of Convection Induced by Korteweg Stresses in a Miscible Polymer-Monomer System: Effects of Variable Transport Coefficients, Polymerization Rate and Volume Changes. Microgravity Sci. Technol DOI 10.1007/s12217-008-9071-y, Springer Science, Business Media B.V. 2009.
29. John Pojman, Nick Bessonov, Vitaly Volpert, Convection Caused by Gradients of Effective Interfacial Tension and Its Relevance to Polymer Processing in Space.64th Southwest Regional Meeting (SWRM) (October 1-4, 2008), USA, 2008.
30. N. M. Bessonov, S.F. Golovashchenko and V.A. Volpert Numerical modeling of contact elastic-plastic flows, Math. Model. Nat. Phenom. Vol. 4, N1, 2009, pp 44-87.
31. Morozova, N., Bessonov, N., Volpert, V. Plant growth modeling. Progress in industrial mathematics at ECMI 2006, 553-558, Math. Ind., 12, Springer, Berlin, 2008.
32. Nikolai Bessonov, Ivan Demin, Laurent Pujo-Menjouet, Vitaly Volpert, A mutli-agent model describing self-renewal of differentiation effects on the blood cell population, Mathematical and computer modelling, 2009.
33. V. Barelko, N. Bessonov, D. Kiryukhin, G. Kichigina, A. Pumir, V. Volpert. Travelling waves of fast cryo-chemical transformations in solids (non-Arrhenius chemistry of the cold Universe). Math. Model. Nat. Phenom., 3 (2008), No. 5, 50-72.
34. S.F. Golovashchenko, A.M. Ilinich, N.M. Bessonov and L.M.Smith, Analysis of Trimming Processes for Advanced High Strength Steels, SAE World Congress and Exhibition 2009, 7pp.
35. N. Bessonov, N. Morozova, V. Volpert. Modelling of plant growth. Third European Science Foundation Conference of Functional Dynamics, Cascais, Portugal, 2-5 March 2009, 98-197pp.
36. N. Bessonov, F. Crauste, I. Demin, V. Volpert. Dynamics of erythroid progenitors and erythroleukemia. Math.Model. Nat.Phenom., 4 (2009), No. 3, 210-232.
37. John A. Pojman , Yuri Chekanov, Victor Wyatt, Nick Bessonov and Vitaly Volpert. Numerical Simulations of Convection Induced by Korteweg Stresses in a Miscible Polymer-Monomer System: Effects of Variable Transport Coefficients, Polymerization Rate and Volume Changes Microgravity Science and Technology: Volume 21, Issue 3 (2009), 225-237pp.
38. N. Bessonov, N. Morozova, V. Volpert. Modelling of plant growth. Third European Science Foundation Conference on Functional Dynamics, 2 - 5 March 2009, Lisbon, Portugal.
39. N. Bessonov, V. Volpert. Computational Algorithm for Some Problems with Variable Geometrical Structure. Transactions on Computational Issue of Transactions on Computational Science, Springer, (2010).
40. Sergey F. Golovashchenko, Nicholas M. Bessonov, Andrey M. Ilinich, "Two-step method of forming complex shapes from sheet metal", Journal of Materials Processing Technology. Online publication complete: 2-FEB-2010 DOI information: 10.1016/j.jmatprotec.2010.01.004.
41. Narcisa Apreutesei, Nikolai Bessonov, Vitaly Volpert and Vitali Vougalter, Spatial structures and generalized travelling waves for an integro-differential equation, in Discrete and Continuous Dynamical Systems Series B (DCDS-B), Volume 13, Number 3, May 2010.
42. N. Bessonov, P.Kurbatova, V. Volpert, Particle Dynamics Modelling of Cell Populations, Math. Model. Nat. Phenom. 5 7 (2010) 42-47
43. D.A. Indeitsev, A.K. Abramyan, N.M. Bessonov, L.V. Mirantsev. Mathematical model of fluid flow in nanochannels, International Journal of Nanomechanics. Science and Technology. 2010. V. 1. N 2. P.151-168
44. Polina Kurbatova, Samuel Bernard, Nikolai Bessonov, Fabien Crauste, Ivan Demin, Charles Dumontet, Stephan Fischer, and Vitaly Volpert, Hybrid Model of Erythropoiesis and Leukemia Treatment with Cytosine Arabinoside, SIAM J. on Applied Mathematics,Vol 71, (2011) Issue 6, pp. 2246-2268
45. Bessonov, N. ; Crauste, F. ; Fischer, S. ; Kurbatova, P. ; Volpert, V. Application of hybrid models to blood cell production in the bone marrow. Math. Model. Nat. Phenom. 6 (2011), no. 7, 2--12.
46. Bessonov, N. ; Crauste, F. ; Volpert, V. Modelling of plant growth with apical or basal meristem. Math. Model. Nat. Phenom. 6 (2011), no. 2, 107--132.
47. A. Tosenberger, V. Salnikov, N. Bessonov, E. Babushkina, V. Volpert. Particle Dynamics Methods of Blood Flow Simulations. Math. Model. Nat. Phenom. Vol. 6, No. 5 , 2011, 320-332
48. A. Tosenberger, F. Ataullakhanov, N. Bessonov, M. Panteleev, A. Tokarev, V. Volpert The role of platelets in blood coagulation during thrombus formation in flow. INRIA, hal-00729046, 2012, 22pp.
49. Kurbatova,P.(F-LYON-ICJ); Eymard, N.(F-LYON-ICJ); Tosenberger, A.(F-LYON-ICJ); Volpert, V.(F-LYON-ICJ); Bessonov, N.(RS-AOS2-ME) Application of hybrid discrete-continuous models in cell population dynamics. BIOMAT 2011, 1-10, World Sci. Publ., Hackensack, NJ, 2012.
50. Indeitsev, D. A. ; Abramyan, A. K. ; Bessonov, N. M. ; Mochalova, Yu. ./.A. ; Semenov, B. N. On the motion of the delamination boundary in the localization of wave processes.(Russian) Dokl. Akad. Nauk 443 (2012), no. 6, 682--685.
51. N. Bessonov, P. Kurbatova, V. Volpert. Pattern Formation in Hybrid Models of Cell Populations. In: Pattern formation in morphogenesis. Problems and Mathematical Issues Series: Springer Proceedings in Mathematics, 107--119, Springer Proc. Math., 15, Springer, Heidelberg, 2013, Capasso, V.; Gromov, M.; Harel-Bellan, A.; Morozova, N.; Pritchard, L. (Eds.) ISBN 978-3-642-20163-9, pp. 107-119.
52. A. Tosenberger, F. Ataullakhanov, N. Bessonov, M. Panteleev, A. Tokarev, V. Volpert. Modelling of thrombus growth and growth stop in flow by the method of dissipative particle dynamics. Russian Journal of Numerical Analysis and Mathematical Modelling" 2012, Vol. 27, No.5, 507-522.
53. N. Bessonov, N. Eymard, P. Kurbatova, V. Volpert. Mathematical modelling of erythropoiesis in vivo with multiple erythroblastic islands. Applied Mathematics Letters, 25 (2012)1217-1221.
54. S. Fischer, P. Kurbatova, N. Bessonov, O. Gandrillon, V. Volpert, F. Crauste. Modelling erythroblastic islands: using a hybrid model to assess the function of central macrophage. Journal of Theoretical Biology, 298 (2012), 92-106.
55. Bessonov, N. ; Mironova, V. ; Volpert, V. Deformable cell model and its application to growth of plant meristem. Math. Model. Nat. Phenom. 8 (2013), no. 4, 62--79.
56. Evgenia Babushkina, Nicholas M. Bessonov, Alexander L. Korzhenevskii, Richard Bausch, Rudi Schmitz Oscillatory solidi_cation of dilute binary alloys at low growth velocities, Phys. Rev. E 87, 042402 (2013).
57. Le vivant entre discret et continu, edited by Nicolas Glade, Paris 2013 427pp. Chapter 3 "Modèle multi-échelle de la dynamique cellulaire", pp 90-110
58. A. Tosenberger, F. Ataullakhanov, N. Bessonov, M. Panteleev, A. Tokarev, V. Volpert Modelling of thrombus growth in flow with a DPD-PDE method. Journal of Theoretical Biology 337 (2013) 30-41
59. N. Bessonov, E. Babushkina, S.F. Golovashchenko, A. Tosenberger, F. Ataullakhanov, M. Panteleev, A. Tokarev, V. Volpert "Numerical Modelling of Cell Distribution in Blood Flow" Math. Model. Nat. Phenom. Vol. 9, No. 6, 2014, pp. 69-84
60. N. Bessonov, N. Reinberg, V.Volpert. Mathematics of Darwin's Diagram.Math. Model. Nat. Phenom., 9 (2014), no. 3, 5-25.
61. N. Eymard, N. Bessonov, O. Gandrillon, M. J. Koury, V. Volpert. The role of spatial organization of cells in erythropoiesis. Journal of Mathematical Biology, 2014.
62. Nikolai Bessonov,Michael Levin,Nadya Morozova,Natalia Reinberg,Alen Tosenberger,Vitaly Volpert "On a Model of Pattern Regeneration Based on Cell Memory", PLOS one, February 19, 2015, DOI: 10.1371/journal.pone.0118091
63. P.Kurbatova,N. Bessonov,V.Volpert, H.A.W.M.Tiddense, C.Cornu,P.Nony, D. Caudrie, "Model of mucociliary clearance in cystic fibrosis lungs", Volume 372, 7 May 2015, Pages 81-88 doi:10.1016/j.jtbi.2015.02.023
64. A. Tosenberger, N. Bessonov, M. Levin, N. Reinberg, V. Volpert, N. Morozova, A Conceptual Model of Morphogenesis and Regeneration, Acta Biotheoretica Vol 63, Volume 63, Issue 3 (2015), Page 283-294
65. A. Tosenberger, N. Bessonov, V. Volpert Influence of fibrinogen deficiency on clot formation in flow by hybrid model. Mathematical Modelling of Natural Phenomena 03/2015 10(1):36-47.
66. N. Bessonov, M. Levin, N. Morozova, N. Reinberg, A. Tosenberger, V. Volpert, Target morphology and cell memory: a model of regenerative pattern formation, Neural Regeneration Research, Vol 10, Issue 0, 2015. DOI:10.4103/1673-5374.165216
67. A.K.Abramyan, N.M.Bessonov, L.V.Mirantsev, N.A.Reinberg. Influence of liquid environment and bounding wall structure on fluid flow through carbon nanotubes. Physics Letters A 379 (2015) 1274-1282.
68. Evgenia S. Babushkina, Nikolay M. Bessonov, Fazoil I. Ataullakhanov, Mikhail A. Panteleev. Continuous Modeling of Arterial Platelet Thrombus Formation Using a Spatial Adsorption Equation. PLOS, Published: October 30, 2015 DOI: 10.1371/journal.pone.0141068.
69. M. Benmir, N. Bessonov, S. Boujena, V. Volpert Travelling Waves of Cell Differentiation, Acta Biotheor (2015) 63:381-395 DOI 10.1007/s10441-015-9264-x
70. N. Bessonov, N. Reinberg, V. Volpert. How morphology of artificial organisms influences their evolution. Ecological Complexity 24 (2015) 57-68.
71. Maya Emmons-Bell, Fallon Durant, Jennifer Hammelman, Nicholas Bessonov, Vitaly Volpert, Junji Morokuma, Kaylinnette Pinet, Dany S. Adams, Alexis Pietak, Daniel Lobo and Michael Levin.Gap Junctional Blockade Stochastically Induces Different Species-Specific Head Anatomies in Genetically Wild-Type Girardia dorotocephala Flatworms, International Journal of Molecular Sciences 2015, 16(11), 27865-27896; doi:10.3390/ijms161126065
72. N.Morozova, G.Pinna, N. Bessonov, V.Capasso, A.Harel-Bellan Mathematical modeling of Cancer Stem Cells population dynamics, 1-er Congres du reseau SUNRiSE, 18 et 19 novembre 2015, Marseille, France
73. Babushkina E., Bessonov N., Reinberg N. NUMERICAL SIMULATION OF CELL BEHAVIOR IN NARROW CHANNEL, APM-2015, The International Conference "Advanced Problems in Mechanics", St. Petersburg, Russia, June 22-27, 2015
74. Bessonov N.M., Reinberg N.A. ON THE NATURE OF BOUNDARY CONDITIONS FOR FLUID FLOW IN TUBES, APM-2015 The International Conference "Advanced Problems in Mechanics", St. Petersburg, Russia, June 22-27, 2015
75. Andrei Abramian, Nikolas Bessonov and Dmitry Indeitsev. Fluid effect on ice induced vibrations. N. 254, Track MS08 - Fluid-Structures Interaction, EURODYN 2016.
76. Gennady Bocharov, Andreas Meyerhans, Nikolas Bessonov, Sergei Trofimchuk, Vitaly Volpert. Spatiotemporal Dynamics of Virus Infection Spreading in Tissues, 2016.
77. G. Bocharov, A. Meyerhans, Nikolas Bessonov, S. Trofimchuk, V. Volpert.Modelling the dynamics of virus infection and immune response in space and time, International Journal of Parallel, Emergent and Distributed Systems, Published online: 29 Aug 2017.
78. Nikolas Bessonov, Vitaly Volpert. Deformable Cell Model of Tissue Growth. MDPI Computation 2017 5 45, published 30 October, 2017 pp.1-18
79. N. Bessonov, N. Morozova. Geometry of Morphogenesis, First International conference From Molecules and Cells to Human Health: Ideas and Concepts, 5-9 March 2018, Paris, France.
80. Nikolas Bessonov, Natalia Reinberg, Malay Banerjee, Vitaly Volpert. The Origin of Species by Means of Mathematical Modelling Acta Biotheoretica (2018).
81. A.K.Abramyan,Nikolas Bessonov, L. V. Mirantsev, A. A. Chevrychkina. Equilibrium structures and flows of polar and nonpolar liquids in different carbon nanotubes. // The European Physical Journal B, 2018, 91(3), pp. 48.
82. N. Bessonov, A. Beuter, S. Trofmchuk, V. Volpert, Estimate of the travelling wave speed for an integro-differential equation Applied Mathematics Letters , (2018).
83. Dmitry Grebennikov, Anass Bouchnita, Vitaly Volpert, Nickolay Bessonov. Andreas Meyerhans, Gennady Bocharov. Physics-based Modelling of Spatial Lymphocyte Dynamics in Multicellular Environment of Lymph Nodes, Cell Systems journal (accepted).
84. G. Bocharov, A. Meyerhans, N. Bessonov, S. Tromchuk, V. Volpert. Interplay between reaction and diusion processes in governing the dynamics of virus infections, Journal of Theoretical Biology (2018) accepted.

Institute of Problems in Mechanical Engineering RAS (1987-current time)

Research and development work in theoretical and computation biology, fluid and solid mechanics, heat transfer, electrodynamics, lubrication. The generalization of the classical theory of viscous liquids to liquids with microstructure. Development of a theory of micropolar liquid which describes various capillary phenomena. Development of a micropolar lubrication theory in submicron channels based on with anomalies near solid surfaces. Application of the theory to analysis of filtration, lubrication, flow of suspensions and for similar problems. Mathematical modeling of the behavior of deformable bodies of complex structure.

Cooperation with group on theoretical biology in Institut des Hautes études Scientifiques (IHES) France 2015-2016

Project 1. Mathematical modelling of morphogenesis and regeneration (N.Morozova, R. Penner, C. Soule, A. Tosenberger). The main goal of this project is creating a model which provides a proof of concept for a patterning towards an encoded target morphology and helps to formulate the assumptions necessary for regeneration of cellular structures.
Project 2. Mathematical modelling of cancer stem cells population dynamics (M. Gromov, N. Morozova, C. Soule) Cancer stem cells (CSC) are present at a low percentage in many tumors and are thought to be responsible for tumor relapses following conventional cancer therapies. Most intriguingly, the proportion of CSCs returns to its original level after (almost) any perturbation of proportion of cell populations, as shown in vitro by many experimental teams. This phenomenon still remains to be explained. We suggest a mathematical model of cancer cell population dynamics, based on the main parameters of cell population growth, such as the proliferation rates, the rates of cell death and the proportions of the possible scenarios of cell divisions (symmetric or asymmetric) in stem and non-stem cancer cells. Analysis of this model helps to elucidate some important rules, underlying cancer stem and non-stem populations' behavior. As a practical application, the results of the modeling may provide a mean to evaluate the success of a treatment based on the properties and dynamics of cancer stem cell population in a particular type of cancer.

Cooperation with University of Lyon 1, France (2000- 2005, 2007-2010, 2012-2015)

Development of the model of regeneration of biological organisms. Biological cell structures are considered as ensemble of mathematical points on the plane. Each cell produces a signal which propagates in space. It is received by other cells. Total signal received by each cell forms a signal distribution defined on the cell structure. This distribution characterizes the geometry of the cell structure. If a part of this structure is removed, then remaining cells have two signals. They keep the value of the signal which they had before the amputation (memory), and they receive a new signal produced after the amputation. Regeneration of the cell structure is stimulated by the difference between the old and the new signals. It is stopped when the two signals coincide. The algorithm of regeneration contains certain rules which are essential for its functioning, being the first quantitative model of cellular memory that implements regeneration of complex patterns to a specific target morphology. Correct regeneration depends on the form and on the size of the cell structure and on parameters of regeneration.
Modeling of tissue growth with a deformable cell model. Each cell represents a polygon with particles located at its vertices. Stretching, bending and pressure forces act on particles and determine their displacement. Pressure dependent cell proliferation was considered. Various patterns of growing tissue are observed.

Model of elastic cells for simulation of root growth was developed. The model consists of three cell types and takes into account dynamics of initials which provide for development of vascular cylinder. This model can be regarded as a first approximation for simulation of root meristem development. The model allows to make some hypothesis on the rules of cell divisions. Among them the relative rates and angles of divisions for different initials, the necessity. The model was tested to simulate auxin distribution under the mechanism of the reflected flow.

Development of a new multi-agent model is used to describe blood cell population dynamics in the bone marrow. The model takes into account cell proliferation, differentiation and apoptosis, as well as their motion due to the mechanical interaction and cell communication. Some possible explanations of the mechanism for recovery of the system under important blood loss or diseases such as anemia or leukemia are given. Leukemia development in the bone marrow taking into account intro-cellular and extra-cellular regulation for normal and malignant cells was studied.

Simulation of blood flow in capillaries using dissipative particles dynamics method. Model of erythrocytes and platelets bases on equations of elastic shell with large deformation. Interaction between erythrocytes and platelets described by soft contact algorithm. Particularly, the separation of erythrocytes and platelets (thrombocytes) in blood flow is obtained.

Development of a mathematical model and the computational algorithm for a problem of plant growth.The plant is represented as a system of connected intervals corresponding to branches. The main physiological factors of plant growth and development are taken into consideration.

New physiologically based mathematical model of mucus flow mechanism for human airways was proposed. The results of the model simulations stress the potential relevance of the location of the drug deposition in the central or peripheral airways.

Cooperation with University of Oakland, USA (2012, 2010, 2007), University of Dearborn, USA (2005, 2006), University of Michigan, USA (1997, 1998) (Supported by Ford Motor Co).

Modeling of bubbles migration in viscous fluid. Mathematical model of the gas phase motion in viscous fluid under the action of vibration, numerical method and computer code were developed.

Research and Development work in theoretical and computation electrodynamics. Development of a model and numerical methods for simulations of high velocity elastics-plastics flows: complex rheological neo-Hooke's constitutive relations, Maxwell equations, new elastics predictor plastics corrector procedure which based on correction of initial configuration of solid and allows to describe Bauschinger effect also, explicit and implicit numerical schemes, universal contact algorithm, based on "mild" contact idea. Development of a sharp flanging technology for aluminum panels.

Development of a computational technique for steady and unsteady 3D deformations of elastomers as applied to seals in hydroelastic lubrication applications using the general rheological model. A robust algorithm has been added for solid-solid contact with a lubricant layer. Development of the numerical procedures for analysis of elastoplastic and viscoelastic deformation with application to sheet metal forming and shearing simulation (contact interaction with complex shape moving rigid bodies, taking into account material fracture) and numerical analysis of elastomers with application to rubber seals.

Cooperation with University of Southern Mississippi, USA (2000-2005) (Supported by NASA).

Development of model of a binary miscible liquids. The model is based on the Navier-Stokes equations with the Korteweg stress. In particular, there exists a miscible analogue to the Marangoni convection where the temperature gradient is applied along the transition zone between two fluids. Convection also appears if instead of the temperature gradient the case where the width of the transition zone varies in space was considered. Development of a numerical method and programming code for simulation of interaction in binary miscible liquids. The basic conclusion of the numerical simulations is that transient capillary phenomena in miscible liquids exist and can produce convective flows sufficiently strong to be observed experimentally. Several configurations corresponding to the microgravity experiments planned for the International Space Station.