My main research interests are:
- Statistical and predictive modeling
- Design of experiments
- Data mining: supervised feature extraction
- Machine learning: stochastic gradient descent, Hamiltonian Monte Carlo, Kernel methods
- Dynamical systems: chaotic advection, control
- Stability theory: stability of relative equilibria
- Fluid dynamics: vorticity evolution, point vortex evolution
- Geometric mechanics: Hamiltonian dynamical systems with symmetries, variational integrators
- Numerical methods based on moment expansions: hermitian expansion of 2D vorticity field
- Singular solutions of partial differential equations: justification of models of point vortices on a sphere
- Particle interaction problems: distributions of particles with logarithmic potential
My publications:
- P.K. Newton, V.V. Ostrovskyi, Energy-Momentum Stability of Icosahedral Configurations of Point Vortices on a Sphere, 2012, Journal of Nonlinear Science, Vol. 22, N4.
- P.K. Newton, V.V. Ostrovskyi, Stationary equilibrium singularity distributions in the plane, 2012, Nonlinearity, Vol.25.
- V.V. Meleshko, P.K. Newton, V.V. Ostrovskyi, Stability of the configurations of point vortices on a sphere, 2010, Journal of Mathematical Sciences, Vol.171.
- V.V. Ostrovskyi, Fluid motion in the field of vortex pair on a steady sphere, 2008, Bulletin of Kiev University, 1.(in Ukrainian)
- V.V. Ostrovskyi, A.F. Ulitko, Planar and axisymmetric problems for elastic layer on rigid substrate under Hertz pressure, 2006, Bulletin of Kiev University 1.(in Ukrainian)
In Fall 2010 I have successfully defended my first Ph.D. thesis. The work was written in Kiev university under the supervision of Prof. Vyacheslav Meleshko. In my dissertation, I've studied stability of configurations of 3 and 4 point vortices on a sphere. The main new result there is a condition for the stability of tetrahedral configuration on a sphere. The Ukrainian version of the thesis can be found here.
In Spring 2013 I have successfully defended my second Ph.D. thesis. The work was written in the University of Southern California under the supervision of Prof. Paul Newton. In the thesis, I've studied stability of symmetric configurations of point vortices on a sphere. Also, I've investigated stationary equilibria of point singularities in a plane and studied their stability. The thesis can be found at here.