Day 2 :
Kazan Federal University, Russia
Time : 09:00-09:30
Vasily Yu Belashov received his PhD in Radiophysics and DSc in Physics and Mathematics. His main fields are theory and numerical simulation of the dynamics of
multidimensional nonlinear waves, solitons and vortex structures in plasmas and other dispersive media. Presently, he is Chief Scientist and Professor at the Kazan
Federal University. He was Coordinator of studies on the international program solar terminator during 1987-1992, and took part in the international programs WITS/
WAGS and STEP. He is the author of 320 publications including seven monographs. His main books are Solitary Waves in Dispersive Complex Media: Theory, Simulation,
Applications Springer-Verlag GmbH, 2005 and; Solitons: Theory, Simulation, Applications, Kazan Federal University, 2016.
Interaction of vortices is very complicated and diverse and depends on a lot of conditions, such as initial configuration of
a system, parity of the sizes, degree of symmetry and vorticity of vortical formations etc., as we have shown earlier in our
numerical modeling on a level with the quasi-recurrence phenomenon, at pair interaction of vortices nontrivial situations can be
observed when interaction can result to formation of complex forms of vorticity regions, such as the vorticity filaments and sheets
and can end to formation of complex turbulent field. Prediction of the result of interaction is an important problem in physics of
fluids and plasma including applications to dynamics of vortex structures in the atmosphere, hydrosphere and a plasma, namely:
evolution of the cyclonic type synoptic and ocean vortices which can be considered as a vorticity front and interactions in the
vortex dust particles system and also dynamics of charged filaments which represent streams of charged particles in a uniform
magnetic field. To study behavior of vortical system near critical point dividing the possible regimes of pair interaction of vortices,
we introduce the criterion of stability which represents a combination of critical parameters of the interaction. Using this criterion
we can give theoretical explanation of the result of pair interaction in the system of vortices including 2D and 3D vortical systems.
Our approach can be effective in studying of the atmospheric and plasma vortex dynamics and useful for the interpretation of
effects associated with turbulent processes in fluids and plasmas.
Institute of Mathematics of the Romanian Academy, Romania
Time : 10:00:10:30
Eliade Stefanescu completed his graduation from Faculty of Electronics, Section of Physicist Engineers in 1970. He is a Doctor in Theoretical Physics, Senior Scientist I at
Advanced Studies in Physics Center; Titular Member of Academy of Romanian Scientists and Member of American Chemical Society in the Division of Physical Chemistry
– Subdivision of Energy. His research interests include open quantum physics with applications in theoretical and condensed matter physics and nuclear physics. He is
known for a microscopic theory of open quantum systems; the invention and a detailed description of a system converting environmental heat into usable energy and a
unitary relativistic quantum theory.
In a previous paper, we showed that the Hamilton equations of motion of a quantum particle are obtained as group velocities of
the wave packet describing this particle only if the time dependent phase of a particle wave is proportional to the Lagrangian,
not to the Hamiltonian as in a solution of the conventional Schrödinger equation. When a Lagrangian of relativistic form is
considered, the wave packet of a quantum particle takes a physical form, with a finite spectrum of a cut off velocity (c). Based
on a relativistic quantum principle, asserting the invariance of the time dependent phase for an arbitrary change of coordinates,
we obtained the relativistic kinematics and dynamics, the electromagnetic field equations, the spin and the electromagnetic and
gravitational interactions. When the Lagrangian is considered as a function of the Hamiltonian, we obtain a Schrödinger type
equation with an additional term depending on the velocity and the momentum operator. Based on this equation, we investigate
the dynamics of a relativistic quantum particle. In this framework, such a particle is described as a continuous distribution of
conservative matter, according to the general theory of relativity. In an electromagnetic field, any time dependent phase variation
is modified with a term proportional to a vector potential conjugated to the spatial coordinates and a scalar potential conjugated
to time. In a gravitational field, the time space coordinates are deformed. In such a field, any plane wave remains perpendicular on
a geodesic, while an additional acceleration is possible in the wave plane.