research

Research interests:

Applied Mathematics, Scientific Computing, Mathematical Modeling, Dimension Reduction Method, Asymptotic Methods, Boundary Integral Methods, Vortex Methods, Pseudo-Spectral Methods, Fluid Dynamics, Interfacial Instability, Partial Differential Equations, Grid-Free Numerical Methods

Publications:

Panchenko A., Barannyk L.L., and Cooper K. Deconvolution closure for mesoscopic continuum models of particle systems. Submitted to SIAM MMS, arXiv:1109.5984. pdf

Panchenko A., Barannyk L.L., and Gilbert R. P. Closure method for spatially averaged dynamics of particle chains. Nonlinear Anal. Real World Appl., 12 (2011), 1681-1697. .pdf
Barannyk, L.L., Papageorgiou, D.T., and Petropoulos P.G., Suppression of Rayleigh-Taylor instability using electric fields, Mathematics and Computers in Simulation, accepted for publication. .pdf
Barannyk, L.L., Fully nonlinear interfacial waves in a bounded two-ﬂuid system, Ph.D. Dissertation, New Jersey Institute of Technology (2003), 158 p. .pdf
Barannyk, L.L., and Papageorgiou, D.T., Fully nonlinear gravity-capillary solitary waves in a two-ﬂuid system of ﬁnite depth, J. Engng. Math., 42 (2002), 321–339 .pdf
Barannyk, L.L. and Barannyk, L.F. On the classification of subalgebras of the Poincare algebra AP(2,n). Dopov. Nats. Akad. Nauk Ukrainy, 8 (1998) 17--20 (in Ukrainian).
Barannyk, L.L., Symmetry reduction of a generalized complex Euler equation for a vector ﬁeld. Proceed. of the 2nd Internat. Confer. ”Symmetry in Nonlinear Mathematical Physics”, July 7-13, Kyiv, 1997, Symmetry in Nonlin. Math. Phys., 2 (1997), 455–462. .pdf
Fushchych, W.I., and Barannyk, L.L., Symmetry reduction on subalgebras of the Poincare algebra of a nonlinear system of diﬀerential equations for a vector ﬁeld, Dopov. Nats. Akad. Nauk Ukrainy, 8 (1997), 50–57 (in Ukrainian). .pdf
Basarab-Horwath, P., Barannyk, L.L., and Fushchych, W.I., Some exact solutions of a conformally invariant nonlinear Schrodinger equation, Preprint Linkoping University, LiTH-MAT-R-97-11 (1997), 12 p. .pdf
Barannyk, L.L., Invariant solutions of a nonlinear system of diﬀerential equations for electromagnetic ﬁeld, J. Nonlin. Math. Phys., 4, 3–4 (1997), 482–491. .pdf
Barannyk, L.L., Symmetry reduction for a system of nonlinear evolution equations, J. Nonlin. Math. Phys., 3, 3–4 (1996), 447–452. .pdf
Fushchych W.I. and Barannyk L.L.. Symmetry reduction as a method for generating solutions of systems of linear differential equations. Dopov. Nats. Akad. Nauk Ukrainy, 12 (1996) 44--49 (in Ukrainian). .pdf
Barannyk L.L. On symmetry reduction and exact solutions of the linear one-dimensional Schrodinger equation. Dopov. Nats. Akad. Nauk Ukrainy, 9 (1996) 32--38 (in Ukrainian).