RUDN University mathematician first described the movement in a flat strip of plasma
The Zakharov-Kuznetsov equation is a one-function equation of two variables x and y. For physics, x is the direction of wave propagation, and the deformation of the medium occurs along the perpendicular direction y. For example, an oscillation of the guitar string looks like the wave runs down the string, while the oscillations occur perpendicular direction relative to the run of the wave.
There are a large number of results that describe solutions of the Zakharov-Kuznetsov equations in the case when there are no constraints on y. But the question of wave propagation in the strip — when y is limited — was almost not studied until recently. And this is although such a statement of the problem has a physical meaning, and therefore potential applications.
RUDN University mathematicians dealt with the Zakharov-Kuznetsov equation in the strip. They examined three main cases — when there are no oscillations on the boundary of the strip, when there is no current on the same boundary and when the boundary conditions are periodic in structure. The latter case corresponds to the propagation of waves in a medium whose structure is periodic in x.
In all these cases mathematicians managed to prove theorems of existence and uniqueness of solutions. For systems of partial differential equations, which include the Zakharov-Kuznetsov equation, such equations are very rare.
These results are the first for solutions of the equation with initial conditions in the strip. Flat plasma flows with boundary conditions, which were considered by RUDN University scientists, can occur in physics and astrophysics.
The Zakharov-Kuznetsov equations belong to a wider category of equations known as the Korteweg-de Vries equations. In the study of this category of equations for the first time, it was possible to describe solitons — waves whose shape does not change during movement. Physicists consider solitons as a tool for modern optical data transmission systems. The study of solitons, which can arise in the Zakharov-Kuznetsov equations, is one of the options for the development of the work done by RUDN University mathematicians.
RUDN University chemist proposed a new method to create catalysts on a porous silicon matrix with metal nanoparticles. Efficient catalysts for organic reactions are obtained, for example, for the synthesis of vanillin, which is in demand in the food and perfume industry.
When talking about COVID-19, television, newspapers, magazines, and social media turn to battle metaphors that make the fight against the pandemic feel like a war. Also, the coronavirus is often discussed in an excessively alarming and threatening tone. This problem is so acute that there is even the term for that — infodemia. It describes the panic in the media and social networks. A linguist of RUDN University studied how such a language affects the notions of people regarding COVID-19.
Ecologists of the RUDN University showed that one of the methods used to detect the soil organic matter turns out to be ineffective after precipitation. Studies have shown that the impact of rain on the surface of arable soils leads to a decrease in the accuracy of modelling of organic matter content by 70%. The ecologists also suggested the way to compensate for this negative phenomenon and increase the accuracy of calculations to 84%.