Victor Miroshnikov, Ph.D. - College of Mount Saint Vincent
Department of Mathematics

Victor Miroshnikov, Ph.D.

VictorMiroshnikovAssistant Professor of Mathematics
Ph.D., Moscow Institute of Physics and Technology
M.S., Moscow Institute of Physics and Technology
B.S., Moscow Institute of Physics and Technology

 


victor.miroshnikov@mountsaintvincent.edu

Areas of Interest

  • Computational mathematics education
  • Differential equations
  • General solutions of fluid dynamics
  • Invariant structures

Courses

  • MATH 100 Pre-Calculus
  • COMP 101 Computer Science I
  • COMP 102 Computer Science II
  • MATH 105 Linear Mathematical Analysis
  • MATH 106 Calculus for Business Decisions
  • MATH 107 Computational Mathematics with Spreadsheets
  • PHYS 107 Introduction to Physics I
  • PHYS 108 Introduction to Physics II
  • COMP 114 Computers and Their Uses
  • COMP 115 Intermediate Computer Applications
  • MATH 120 Computational Mathematics
  • MATH 121 Elementary Statistics
  • MATH 131 Calculus I
  • MATH 132 Calculus II
  • MATH 231 Calculus III
  • MATH 261 Symbolic Computing
  • MATH 262 Numeric Computing
  • MATH 255 Differential Equations
  • PHYS 360 Symbolic Methods
  • PHYS 370 Special Functions
  • MATH 431 Vector Calculus
  • MATH 455 Linear Partial Differential Equations
  • MATH 469 Independent Study: Elliptic Structures

Honors and Awards
Course Release Award, College of Mount Saint Vincent, 2012
European Communities, 1995
French Government, 1993
Latvian Scientific Council, 1991 and 1994
Summer Research Award, College of Mount Saint Vincent, 2006, 2007, and 2009

Professional Affiliations
American Mathematical Society
American Physical Society
Computational and Applied Mathematics
Sigma Xi
Society for Industrial and Applied Mathematics

Publications
Harmonic Wave Systems: Partial Differential Equations of the Helmholtz Decomposition by Victor A. Miroshnikov. Scientific Research Publishing, 2017, 448 pp. ISBN: 978-1-61896-413-7. View more information

“Conservative Interaction of N Internal Waves in Three Dimensions,” American Journal of Computational Mathematics, 4, No. 4, 329-356, 2014 Click to download

“Deterministic Chaos of N Stochastic Waves in Two Dimensions,” American Journal of Computational Mathematics, 4, No. 4, 289-303, 2014 Click to download

“New Exact Solution for Nonlinear Interaction of Two Pulsatory Waves of the Korteweg – de Vries Equation in an Invariant Zigzag Structure.” Final program and Abstracts of SIAM Conference on Nonlinear Waves and Coherent Structures, 65, 2014 Click to download

“Interaction of Two Pulsatory Waves of the Korteweg-de Vries Equation in a Zigzag Hyperbolic Structure,” American Journal of Computational Mathematics, 4, 254-270, 2014 Click to download

“Nonlinear Interaction of N Conservative Waves in Two Dimensions,American Journal of Computational Mathematics, 4, 127-142, 2014 Click to download

“Computing Nonlinear Waves of the Korteweg-de Vries and Korteweg-de Vries-Burgers Equations in Invariant Structures,” Final program and Abstracts of SIAM Annual Meeting, AN13, 110, 2013 Click to download

“Dual Perturbations of the Poiseuille Flow on Invariant Elliptic Structures,” Advances and Applications of Fluid Mechanics, 11, #1, 1-58, 2012 Click to download

“Existence of invariant elliptic structures and their application to conservative dynamical systems,” Abstracts of the XIX Annual HRUMC, Western New England University, Springfield, Mass., April 21, 2012

“Spatiotemporal cascades of the Poiseuille-Hagen flow in invariant elliptic structures,” Bulletin of APS, 56, #18, 268, 2011 Click to download

“Teaching fluid-dynamic cascades for undergraduates: analysis and simulation,” Far East Journal of Mathematical Education, 5, #1, 53-85, 2010 Click to download

“Transversal waves of dual perturbations of the Poiseuille flow,” Proceedings of SIAM Conference on Nonlinear Waves and Coherent Structures, 47, 2010 Click to download

“Hidden perturbations of the Couette flow,” Abstracts of the XVII Annual HRUMC, p. 17. Keene State College, Keene, N.H., April 17, 2010

“Spatiotemporal cascades of exposed and hidden perturbations of the Couette flow,” Advances and Applications of Fluid Mechanics, 6, #2, 141-165, 2009 Click to download

“General solutions for singular fluctuations, resonant disturbances, and hidden perturbations of the Couette flow,” Proceedings of SIAM Annual Meeting, 74, 2009 Click to download

“The general series solution of the one-dimensional fluid dynamics with a plane of symmetry,” Abstracts of the XVI Annual HRUMC, p. 39. Union College, Schenectady, N.Y., April 18, 2009

“General solutions of the Navier-Stokes Equations and the vorticity transport equations in the Lamb variables,” Proceedings of SIAM Annual Meeting, AN08, 41, 2008 Click to download

“General solutions of fluid dynamics,” Abstracts of the 6th International Congress on Industrial and Applied Mathematics, Zurich, Switzerland, July 16-20, 2007

“General solutions of the unsteady Navier-Stokes equations in one, two, and three dimensions,” Bulletin of APS, 51, #9, 146, 2006 Click to download

“General solutions of the Navier-Stokes equations in the class of the Boussinesq-Rayleigh series,” Proceedings of SIAM Annual Meeting, AN06, 187, 2006 Click to download

“The Boussinesq-Rayleigh series for two-dimensional flows away from boundaries,” Applied Mathematics Research eXpress, 5, 184-227, 2005 Click to download

“Multiscale three-dimensional vortex pairs of the Poiseuille flow,” Bulletin of APS, 50, #9, 253, 2005 Click to download

“Furcations of streamlines of the Poiseuille flow,” Proceedings of SIAM Annual Meeting, AN05, 212, 2005 Click to download

“The General Solution for the Two-Dimensional Poiseuille flow,” Final program and Abstracts of Frontiers in Applied and Computational Mathematics, Newark, New Jersey, May 13-15, 2005 Click to download

“Coherent structures of general solutions of the Navier-Stokes equations,” Proceedings of SIAM Conference on Nonlinear Waves and Coherent Structures, 73, 2004 Click to download

“Computing general solutions of the Navier-Stokes equations,” Proceedings of SIAM Annual Meeting, AN04, 233, 2004 Click to download

“General forced solution of the Navier-Stokes Equations,” Bulletin of APS, 48, #10, 140, 2003

“General unsteady solution for nonlinear interaction of coherent structures,” Proceedings of SIAM Annual Meeting, AN02, 138, 2002 Click to download

“The Boussinesq-Rayleigh approximation for the rotational solitary wave on shallow water with uniform vorticity,” Journal of Fluid Mechanics, 456, 1-32, 2002 Click to download

“Topographic waves with multi-eddy bifurcations formed by a stratified mixing layer,” Proceedings of the 6th SIAM Conference on Mathematical and Computational Issues in the Geosciences, 54, 2001

“Internal solitary waves with multiple eddy bifurcations in stratified flow,” Bulletin of APS, 45, #9, 111, 2000

“Flow separation in finite-amplitude solitary waves on shallow water with constant vorticity,” Bulletin of the APS, 44, #8, 90, 1999 Click to download

Book chapter: Coupled viscous solitary waves in quasi-two-dimensional magnetohydrodynamical and geophysical flows, Progress in Fluid Flow Research: Turbulence and Applied MHD, 182, 281-297, AIAA, Recton, 1998 Click to download

Book chapter: Non-slip electrolyte flow past a moving electromagnetic cylinder, Progress in Fluid Flow Research: Turbulence and Applied MHD, 182, 455-468, AIAA, Recton, 1998 Click to download

Miroshnikov, V. A., and Gelfgat, Y., “Classification of instabilities of metal bodies and liquid metal drops levitated electromagnetically,” Proceedings of the International Congress on Electromagnetic Processing of Materials, 2, 425-430, Paris, 1997

“The finite-amplitude solitary wave on a stream with linear vorticity,” European Journal of Mechanics B/Fluids, 15, #3, 395-411, 1996 Click to download

“Coupled solitary waves in viscous MHD and geophysical flows,” Comptes Rendus Acad. Sci. Paris, 323, II b, 23-30, 1996 Click to download

“Coupled viscous solitary waves in quasi two-dimensional magnetohydrodynamic and geophysical flows,” Abstracts of the 7th Beer-Sheeva International Seminar on MHD Flows and Turbulence, 93, Jerusalem, 1996

Miroshnikov, V. A. and Shishko, A., “Non-slip electrolyte flow past a moving electromagnetic cylinder,” Abstracts of the 7th Beer-Sheeva International Seminar on MHD Flows and Turbulence, 92, Jerusalem, 1996

“MHD controlled formation of a single eddy on the solitary wave crest,” Abstracts of European Science Foundation/Free Boundary Problems Workshop: Free surface and electromagnetism, Riga, 1995

“The solitary wave on a Poiseuille stream in crossed electric and magnetic fields,” Abstracts of MAHYD 95, 33, Jurmala, 1995

“Nonlinear interaction of a parabolic sheared current with a free surface,” Abstracts of International Conference on Boundary Effects in Stratified and/or Rotating Fluids, 113-115, St. Petersburg, 1995

Miroshnikov, V. A., Izrar, B., and Lusseyran, F., “Two-level solitary waves as generalized solutions of the KdV equation,” Physics of Fluids, 7, 1056-1062, 1995 Click to download

“Solitary wave on the surface of a shear stream in crossed electric and magnetic fields: the formation of a single vortex,” Magnetohydrodynamics, 31, #1-2, 149-165, 1995 Click to download

Miroshnikov, V. A. and Kolesnikov, Yu. B., “Magnetohydrodynamic method of generating solitary waves,” Magnetohydrodynamics, 28, #1, 57-64, 1992

Yu. B. Kolesnikov and V. A. Miroshnikov, “Generation of solitary waves by the MHD method.” Magnetohydrodynamics, 28, No. 1, 57-64, 1992 Click to download

“Propagation theory of nonlinear solitary waves of the generalized KdV equation,” Abstracts of International Conference on Waves and Vortices in the Ocean and Their Laboratory Analogues, Vladivostok, 1991

Miroshnikov, V. A. and Kolesnikov, Yu. B., “Magnetohydrodynamic method of bore generation,” Abstracts of International Conference on Waves and Vortices in the Ocean and Their Laboratory Analogues, Vladivostok, 1991

Miroshnikov, V. A. and Kolesnikov, Yu. B., “The laboratory modeling of generalized KdV solitary waves using MHD method,” Abstracts of the First European Fluid Mechanics Conference, Cambridge, 1991

Miroshnikov, V. A. and Kolesnikov, Yu. B., “The completeness of the KdV bore system,” Abstracts of International Conference on Anisotropy of Fluid Flows in External Forces Fields: Geophysical: Technological, and Ecological Applications, Jurmala, 1990

Miroshnikov, V.A., Akishin, A. I., Aksenov, O. E., et al, “Radiative stability of electroinsulating materials for fusion reactors,” Abstracts of International Conference on Tests and Designs of Constructional Materials for the Thermonuclear Fusion (in Russian), Dubna, 1989

Miroshnikov, V. A., Aksenov, O. E., “Low-temperature installation for gamma irradiation and mechanical testing of electroinsulating materials applied in fusion reactors,” Proceedings of the First International Conference on Radiative Physics of Solid Bodies (in Russian), 12 pp., Sochi, 1989

Miroshnikov, V. A., Aluker, V. E., Aksenov, O. E., et al., “Influence of gamma irradiation at 9K on mechanical characteristics of composite electroinsulating materials,” Abstracts of International Conference on Experimental Methods for Physical Investigations (in Russian), Leningrad, 1989

Miroshnikov, V. A. and Gringoff, V. G., Installation for the Gamma Irradiation at Cryogenic Temperatures (in Russian), Riga, 1989

Miroshnikov, V. A., Aksenov, O. E., and Stepanov, A. N., et al., “Design and tests of electroinsulating materials and insulating systems for windings of the thermonuclear installation T-15,” Proceedings of the All-Union Conference on Constructional Materials for Thermonuclear Fusion Reactors (in Russian), 3 pp., Moscow, 1988

Miroshnikov, V. A., Rumyancev, C. A., Aksenov, O. E., et al., “Conduct of electroinsulating materials on the basis of filamentary polyimides in irradiation conditions,” Abstracts of the Fourth All-Union Conference on Physics of Dielectric Materials (in Russian), Tomsk, 1988

“Thermophysical characteristics of electroinsulating materials,” Report for Meeting of the Electrotechnical Department of USSR (in Russian), Riga, 1986

Miroshnikov, V. A., Gringoff, V. G., and Temkin, A. G., “Determination of the radiative sources intensity in polymer insulating materials induced by the gamma irradiation,” Proceedings of the Conference on New Designs in the Field of Electroinsulating Materials (in Russian), 8 pp., Riga, 1985

Miroshnikov, V. A., Stepanov, A. N., Aksenov, O. E., et al., “Design and investigation of electroinsulating materials for the T-15 windings,” Proceedings of the Third All-Union Conference on Investigation and Design of Materials for Thermonuclear Fusion Reactors (in Russian), 8 pp., Leningrad, 1984

Miroshnikov,  V. A., Gringoff, V. G., and Yagolkovskiy, A. G., “Heat discharge induced by the gamma irradiation of the electroinsulating system of T-15,” Proceedings of the Third All-Union Conference on Investigation and Design of Materials for Thermonuclear Fusion Reactors (in Russian), 4 pp., Leningrad, 1984

Miroshnikov, V. A., Temkin, A. G., and Gringoff, V. G., “Non-uniform heat discharge in electro-insulating materials,” Proceedings of the Conference on Heat Conductivity and Diffusion (in Russian), 7 pp., Riga, 1984

Miroshnikov, V. A., Gringoff, V. G., Stepanov, A. N., and Aksenov, O. E., “Heat-discharge field generated by the gamma radiation absorption in compounds used in the electroinsulating system of the installation T-15,” Proceedings of the Third All-Union Conference on Engineering Problems of Thermonuclear Fusion Reactors (in Russian), 6 pp., Moscow, 1984

Miroshnikov V. A. and Gringoff, V. G., “Heat discharge induced by the gamma irradiation in electroinsulating materials,” Proceedings of the All-Union Conference of Junior Scientists on Electroinsulating and Foiled Dielectric Materials (in Russian), 9 pp., Moscow, 1983

Miroshnikov V. A. and Gringoff, V. G., “Determination of the heat-discharge field and the gamma radiation absorption in electroinsulating materials,” Proceedings of the Scientific-Technical Conference of Riga Polytechnic Institute (in Russian), 8 pp. Riga, 1982

Miroshnikov, V. A. and Ozols, R. Ya., “High-gradient magnetic separation,” Magnetohydrodynamics, 18, #4, 5-17, 1982 Click to download

Processes of the Phoresis in Magnetic and Electric Fields (in Russian), Dolgoprudniy, 1981

“Magnetohydrodynamic sedimentation in a cylindrical current-carrying tube,” Magnetohydrodynamics, 17, #2, 131-133, 1981

“Thermophoresis of a ferromagnetic sphere,” Magnetohydrodynamics, 17, #2, 16-21, 1981

Miroshnikov, V. A., Blums, E., and Ozols, R., “Thermomagnetophoretic separation,” Proceedings of the 10th Riga MHD Conference (in Russian), 217-218, Salaspils, 1981 Click to download

Miroshnikov, V. A. and Ozols, R., “Non-stationary magnetophoresis in a gradient flow,” Proceedings of the 10th Riga MHD Conference (in Russian), 215-216, Salaspils, 1981

“Motion of a sphere in crossed electric and magnetic fields at small Reynolds numbers,” Magnetohydrodynamics, 17, #1, 63-71, 1981 Click to download

“Magnetohydrodynamic flow around a stationary sphere,” Magnetohydrodynamics, 16, #3, 262-267, 1980 Click to download

“Thermophoresis of ferrosuspensions in a magnetic field,” Proceedings of the All-Union Conference on Hydrodynamics and Heat Physics of Magnetic Fluids (in Russian), 177-182, Salaspils, 1980

“Non-stationary convective magnetic sedimentation in the field of a straight conductor,” Magnetohydrodynamics, 15, #4, 10-16, 1979 Click to download