Acoustics
- Multiple
scattering problems;
- Linear
and nonlinear waves in complex media with relaxation, dispersion, and
dissipation;
- Propagation
of pressure waves in bubbly liquids;
- Propagation
of pressure waves in particulate suspensions;
- Self-organization
processes in disperse systems under acoustic action;
- Dynamics
of single gas, vapor, and vapor-gas bubbles in acoustic fields;
- Dynamics
of single particles and droplets in acoustic fields;
- Acoustic
cavitation;
- Efficient
algorithms for multi-dimensional problems;
- Human
hearing.
Computational Methods
- Fast
multipole method;
- Boundary
element method;
- Spectral
and pseudospectral methods;
- Numerical-analytical
methods using asymptotic approaches;
- Optimization
strategies;
- Iterative
methods;
- Multidimensional
data structures.
Mathematical Methods
- Asymptotic
methods (particularly multi-scale methods for nonlinear systems);
- Spectral
methods for partial differential equations;
- Translation
theory (translation operators and fast transforms);
- Variational
methods;
- Qualitative
analysis of dynamic systems.
Inverse Problems
- Diffractional
tomography, including acoustic, seismic, electrical impedance, and other;
- Multidimensional
nonlinear optimization;
- Efficient
parametrization;
- Efficient
algorithms for computer vision;
- Genetic
algorithms;
- Artificial
intelligence.
Physichochemical Hydrodynamics
- Heat
and mass transfer near single bubbles;
- Heat
and mass transfer near single droplets;
- Kinetics
of single and multi-component liquid-gas phase transitions;
- Gas
hydrate formation/decomposition on liquid-gas interfaces;
- Diffusion
in gases including Soret and Dufour effects;
- Bubble
and droplet dynamics with chemical reactions;
- Computational
aspects.
Multiphase Flows
- Modeling
of multiphase flows;
- Models
of disperse systems (bubbly liquids, and particulate suspensions);
- Polydisperse
and multi-component systems;
- Pressure
waves in multiphase systems;
- Boiling;
- Dynamics
of single bubbles in bubbly liquids (collective effects);
- Dynamics
of single droplets and particles in particulate systems;
- Multiphase
filtration with chemical reactions and phase change;
- Modification
of medium properties under external action;
- Computational
models for multidimensional multiphase flows.
Classical Hydrodynamics and Aeromechanics
- Potential
flows;
- Unsteady
viscous flows at small Reynolds numbers;
- Viscous
boundary layer;
- Water
waves: linear, nonlinear, shallow water approximation;
- Vortex
ring dynamics;
- Shock
waves;
- Computational
fluid dynamics.
Electromagnetic Waves
- Multiple
scattering;
- Diffraction
of light;
- Photonic
materials;
- Computational
aspects.
Computer Vision
- Image
representation and interpolation;
- Unwarping
of images from surfaces;
- Applications
of the FMM (fast multipole methods) to multidimensional problems of
computer vision.