Applied Mathematics

Vladimir Dobrushkin

Visiting Professor of Applied Mathematics
Room 206, 170 Hope Street
Office Hours: MWF 9 - 11
Research Interests Partial Differential Equations, Numerical Methods, Mathematical Modelling

Biography

   Extensive experience in applied mathematics, solid, and fluid mechanics. Combination of strong theoretical background and mathematical simulation skills. Fields of activity include mathematical modeling of physical phenomena in solid mechanics, dynamic fracture mechanics, and two phase flow of incompressible fluid. Intensive applications of boundary element methods, finite element methods, and finite difference methods. Regularization and numerical calculation of singular and hypersingular integrals. Solid background in statistics. Good computer programming skills (Fortran, C/C++, PowerBuilder, and Matlab), UNIX experience (on SUN and SGI platform), and proficient in Windows applications (Word, Excel, Excess) and Software tools (HTML, Minitab, SAS, R, LaTeX, CASs).

Publications

48. (with R.A. Beauregard) Powers of a Class of Generating Functions. Mathematics Magazine, 89/5, 359 -- 363 (2016).

47. (with R.A. Beauregard) Multisection of series. The Mathematical Gazette, 100/549, 460 -- 470 (2016).

46. (with R.A. Beauregard) A discrete view of Faa di Bruno. The Rocky Mountain Journal of Mathematics , 46, No. 1, 73 -- 83 (2016).

45. (with R.A. Beauregard) Differential equations vs power series. The Mathematical Gazette, 99/546, 499 -- 503 (2015).

44. (with R.A. Beauregard) Finite sums of the Alcuin Numbers. Mathematics Magazine, 86/4, 280 -- 287 (2013).

43. (with V.A. Tsurko and G.M. Zayats) On convergence of difference schemes for two-dimensional second-order hyperbolic equations with discontinuous coefficients. Matematychni Studii, 31/1, 91 -- 101 (2009).

42. (with M.R. Maxey) An improved boundary element formulation for the motion of spherical bubbles. Differential Equations, 44/9, 1305 -- 1312 (2008).

41. (with F.F. Komarov, O.I. Velichko, and A.M. Mironov) Mechanisms of arsenic clustering in silicon. Physical Review B, 74, July, 035205-1 -- 035205-10 (2006).

40. (with O. I. Velichko and L. Pakula) A Model of Clustering of Phosphorus Atoms in Silicon. Materials Science and Engineering: B, 123/2, 176 -- 180 (2005).

39. (with I. I. Abramov, V.A. Tsurko, and V.A. Zhuk) Numerical ''Renaissance'' Procedure of Device and Process Parameters in Integrated Circuits. Nonlinear Phenomena in Complex Systems, 78/3, 296 -- 301 (2005)

38. (with A.K. Fedotov and O. I. Velichko) A set of equations for stress-mediated evolution of the nonequilibrium dopant-defect system in semiconductor crystals, Journal of Alloys and Compounds, 382, Issue 1-2, pp. 283-287 (2004).

37. (with O. I. Velichko, A. N. Muchynski, V. A. Tsurko, and V. A. Zhuk) Simulation of Coupled Diffusion of Impurity Atoms and Point Defects under Nonequilibrium Conditions in Local Domain. Journal of Computational Physics, 178, 1 - 14 (2002).

36. (with O. I. Velichko, A. K. Fedotov, V. A. Tsurko) Segregation of Mg Implanted into InAs: Influence of the Internal Elastic Stresses, Diffusion and Defect Data, Part B: Solid State Phenomena, 2002, Vols.82-84. pp.569 - 574.

35. (1994). On solvability of mixed problem in a domain with an angle for wave equation. Sib. J. Diff. Equations, 1994, 3, No. 2, 3 - 10.

34. (with Nitrebych, Z.N.) (1993). Initial and boundary value problems for hyperbolic partial differential operators with constant coefficient. Sib. J. Diff. Equations, 1993, 2, No. 2, 39 - 46.

33. (1993). Approximate calculation of a class of integro-differential expressions that describe the propagation of elastic waves. Prikladn. Mat. i Mech., No. 2, 164 -167. (in Russian; English transl. J. Appl. Math. Mechs. 1993, 57, 393 - 397).

32. (with Kolesnikov, A.N., Podkopaev, P.A., & Shestokov, V.N.) (1993). Algorithm for calculation of strain-stress state of elastic semi-plane. Vesty Akad Nauk Belarus, ser. fiz.-mat. nauk, 1993, No. 2, 219.

31. (1992). Regularization in Marchaud form and approximate calculation of a class of integro- differential expressions. Izvestiya vuzov. Matematika, 1992, 36, No. 9, 38 - 41 (in Russian; English transl. in Russian Mathematics. Izvest. VUZMatematika, 1992, No. 9, 34 - 37).

30. (with Djum, T.R.) (1992). On the solution of the Cauchy problem for the Lame operator and its regularization. Differ. Uravn., 1992, 28, No. 10, 1830 - 1833.(in Russian; English summary).

29. (1990). Regularization and approximate calculation of the Marchaud's derivative of a two-dimensional integral with sliding singularities. In: Some applications of functional analysis to the problems of mathematical physics. Novosibirsk: Mathematical institute of Siberian branch of the Academy of Science of the USSR, 1990, 81 - 91 (in Russian).

28. (1989). Approximate calculation of the Marchaud's derivative of a two-dimensional integral with singularities. Dokl. Akad. Nauk BSSR, 1989, 33, 101 - 103 (in Russian; English summary).

27. (with Podkopaev, P.A.) (1988). On the solution of the first boundary value problem of elastodynamics for the plane with cracks. Minsk, 1988. 38 pp. (Preprint /Mathematical Institute, Byelorussian Academy of Science, No. 9 (319)) (in Russian).

26. (with Podkopaev,P.A.) (1986). Mathematical investigation of the first boundary value problem of elasticity for the plane with two semi-infinite cracks. Minsk, 1986. 28 pp. (Preprint /Mathematical Institute, Byelorussian Academy of Science; No. 20 (256)) (in Russian).

25. (with Podkopaev, P.A.) (1986). Mathematical investigation of the first boundary value problem of elasticity for the plane with semi-infinite crack. Minsk, 1986. 32 pp. (Preprint /Mathematical Institute, Byelorussian Academy of Science; No. 19 (255)) (in Russian).

24. (1986). Solution of the second boundary value problem of elasticity theory for a semiband. Differ. Uravn., 1986, 22, No. 6, 987 -993 (in Russian; English transl. in Differential Equations, 1986, 22, 697 - 702).

23. (1985). Analytical solution of a static boundary value problem of the plane theory of elasticity. DifferUravn., 1985, 21, No. 4, 717 - 720 (in Russian; English summary).

22. (1985). Solution of the second boundary value problem of the theory of elasticity elasto for a wedge. Izvest. Akad. Nauk BSSR, ser. fiz.-mat. nauk, 1985. No. 4, 8 - 13 (in Russian; English summary).

21. (1984). About certain problems of ordering of noncommutative operators and continual integration. Minsk, 1984, 18 pp. (Preprint /Mathematical Institute, Byelorussian Academy of Science; No. 14 (199)) (in Russian; English summary).

20. (1984). The second boundary value problem of the plane theory of elasticity for a wedge. Dokl. Akad. Nauk SSSR, 1984, 279, No. 11 77 -79 (in Russian; English transl. in Soviet Phys. Dokl. 1984, 29, No. 11, 905 - 907).

19. (1984). Solution of the first boundary value problem of the theory of elasticity for a quadrant. Dokl. Akad. Nauk BSSR, 1984, 28, No. 2, 115 - 118 (in Russian; English summary).

18. (1983). A general boundary value problem for an abstract operator-differential equation. Dokl. Akad. Nauk BSSR, 1983, 27, No. 9, 776 - 779 (in Russian; English summary).

17. (with Podkopaev, P.A.) (1983). Representation of the solutions of boundary value problems for the heat equation in the form of a continual integral with respect to. a Wiener measure. Izvest. Akad. Nauk BSSR, ser. fiz.-mat. nauk, 1983, No. 6, 9 - 14 (in Russian; English summary)

16. (with Lihoded, N.A.) (1982). On approximate evaluation of continual integrals with respect to measures corresponding to a Markov process of telegraph type. Dokl. Akad. Nauk BSSR, 1982, 26, No. 11. 965 - 968 (in Russian; English summary).

15. (with Lihoded, N.A.) (1982). On approximate calculation of continual integral with respect to a Cauchy's measure with weight in the Hilbert space. Izvest. Akad. Nauk BSSR, ser. fiz.-mat. nauk, 1982, No. 1, 104 - 106 (in Russian; English summary).

14. (1981). Evaluation of continual integrals with respect to Cauchy's, Abel's and Gauss's measures in the product of Hilbert spaces. Minsk, 1981, 40 pp. (Preprint /Mathematical Institute, Byelorussian Academy of Science; No. 2 (103)) (in Russian).

13. (1981). The Kolmogorov-Khinchin criterion for certain measures in the space W. Izvest. AkadNauk BSSR, ser. fiz.-mat. nauk, 1981, No. 6, 120 - 123 (in Russian; English summary).

12. (1981). Generalized summation of continual integrals. Izvest. Akad. Nauk BSSR, ser. fiz.-mat. nauk, 1981, No. 5. 5 - 10 (in Russian; English summary

11. (1980). Investigation of the problem on simultaneous thermal and mechanical shocks onto a composite finite rod. Izvest. Akad. Nauk BSSR, ser. fiz.-mat. nauk, 1980, No. 4, 20 - 27 (in Russian; English summary).

10. (1979). Cezaro's summation of certain series and integrals. - Minsk, 1979. 16 pp. (Preprint /Mathematical Institute, Byelorussian Academy of Science; No. 1(57)) (in Russian).

9. (with Gaiduk, S.I.). (1979). Solution of a problem in the theory of thermoelasticity related to mechanical and thermal shocks. Differ. Uravn., 1979, 15, No. 9, 1632 - 1645 (in Russian; English transl. in Differential equations, 1979, 15, No. 9, 1165 - 1174).

8. (1978). Investigation of several initial boundary value problems about the impact onto the semi-infinite beams. Minsk, 1978, 29pp. (Preprint /Mathematical Institute, Byelorussian Academy of Science; No. 6 (38))(in Russian).

7. (1978). A dynamic problem of shock theory for an elastic plate. Dokl. AkadNauk BSSR, 1978, 22, No. 3, 197 - 199 (in Russian; English summary ).

6. (1978). The solution of a problem of a shock on elastic semi-infinite plate. Izvest. Akad. Nauk BSSR, ser. fiz.-mat. nauk, 1978, No. 1, 134 (in Russian; English summary).

5. (1977). Solution of a problem of a longitudinal shock along an inhomogeneous viscoelastically relaxing rod. Differ. Uravn., 1977, 13, No. 9, 1658 - 1666 (in Russian; English transl. in Differential Equations, 1977, 13, No. 9, 1155 - 1160).

4. (1977). The uniqueness of the generalized solution of a certain problem in shock theory. DifferUravn., 1977, 13, No. 8, 1521-1523. English transl. in Differential Equations13, 1061 - 1063.

3. (1976). A problem in the theory of longitudinal vibrations of an elastic-viscous-relaxing rod. Izvest. Akad. Nauk BSSR, ser. fiz.-mat. nauk, 1976, No. 5, 53 - 60 (in Russian; English summary).

2. (with Gaiduk S.I.). (1975). Solution of a problem of longitudinal shock along a viscoelastically relaxing rod. Izvest. Akad. Nauk BSSR, ser. fiz.-mat. nauk, 1975. No. 6, 30 - 41 (in Russian; English summary).

1. (with Antonevich, A.B.). (1973). A general boundary value problem for an elliptic system with deviating argument. Dokl. Akad. Nauk BSSR, 1973. 17, 491 - 493 (in Russian).