- Ph.D. in Mathematical Sciences, New Jersey Institute of Technology and Rutgers the State University of New Jersey, 2003
- M.S. in Applied Mathematics, New Jersey Institute of Technology, 2000
- Applied Mathematics
- Scientific Computing
- Mathematical Modeling
- Asymptotic Method
- Boundary Integral Methods
- Vortex Methods
- Pseudo-Spectral Methods
- Fluid Dynamics
- Interfacial Instability
- Partial Differential Equations
- Grid-Free Numerical Methods
- L.L. Barannyk, D.T. Papageorgiou, and P.G. Petropoulos. Suppression of Rayleigh-Taylor instability using electric fields (2010) (submitted to Mathematics and Computers in Simulation)
- L.L. Barannyk and D.T. Papageorgiou. Fully nonlinear gravity-capillary solitary waves in a two-ﬂuid system of finite depth. J. Engrg. Math. 42 (2002) 321–339.
- L.L. Barannyk and L.F. Barannyk. On the classification of subalgebras of the Poincare algebra AP(2, n). (Ukrainian) Dopov. Nats. Akad. Nauk Ukrainy 8 (1998) 17–20.
- L.L. Barannyk. Invariant solutions of a nonlinear system of differential equations for electromagnetic field. J. Nonlin. Math. Phys. 4: 3–4 (1997) 482–491.
- W.I. Fushchych and L.L. Barannyk. Symmetry reduction on subalgebras of the Poincare algebra of a nonlinear system of differential equations of a vector field. (Ukrainian) Dopov. Nats. Akad. Nauk Ukrainy 8 (1997) 50–57.
- Nonlinear gravity-capillary waves in a channel in the presence of electric fields (joint with D.T. Papageorgiou, Imperial College London, and P.G. Petropoulos, New Jersey Institute of Technology)
- Evolution of solitary waves in a channel (joint with W. Choi, New Jersey Institute of Technology, and R. Krasny, University of Michigan)
- A fast method for simulating mesoscopic dynamics of large ODE systems (joint with A. Panchenko, Washington State University)
- SEED Grant, University of Idaho, Propagation of Solitary Waves in a Channel, 2008
- Rackham Faculty Research Fellowship, University of Michigan, Evolution of Vortex Sheets in a Channel, 2004