# Mathematics developed new classes of stellar dynamics systems solutions

February 05, 2021The Vlasov-Poisson equations describe many important physical phenomena such as the distribution of gravitating particles in the interstellar space, high-temperature plasma kinetics, and the Landau damping effect. A joint team of scientists from the Mathematical Institute of RUDN University and the Mathematical Institute of the University of Munich suggested a new method to obtain stationary solutions for a system of Vlasov-Poisson equations in a three-dimensional case. The obtained solutions describe the phenomena of stellar dynamics. The results of the study were published in the

*Doklady Mathematics*journal.

Modern-day physics distinguishes between four main types of interactions. Elementary particle physics covers strong and weak interactions, electromagnetism is studied by electrodynamics, and systems with gravitational interaction fall into the scope of a special branch of physics called gravidynamics. On the space scale, gravitational fields play a key role. One domain of study within gravidynamics is called stellar dynamics.

"We have considered a three-dimensional stationary system of the Vlasov-Poisson equations concerning the distribution function of gravitating matter, local density, and Newtonian potential, and developed a new method for obtaining spherically symmetric stationary solutions. This was the result of our fruitful collaboration with renowned German scientists J. Batt and E. Joern," said Alexander Skubachevskii, a D Sc in Physics and Mathematics, and the Head of the Nikolskii Mathematical Institute of RUDN University.

The movement and interaction of multiple particles in gravitational, electric, and electromagnetic fields are described using the equations that were developed by the eminent Soviet physicist Anatoly Vlasov. They model the dynamics and stationary distribution of a system of particles in view of the influence of a self-consistent field. The Vlasov-Poisson equation for a system of gravitating particles consists of the Poisson equation covering the gravitational potential and the Vlasov equation covering the function of density distribution in interconnected particles. Vlasov's model was initially supposed to describe electron gas dynamics. The model views processes in plasma not as a series of collisions between individual particles but as a simplified system in which particles interact through a field, and the field, in turn, correlates with the particle density distribution function. Therefore, the Vlasov equations are sometimes called equations with a self-consistent field. Together with his German colleagues, the mathematician from RUDN University established the theorem of expandability, i.e. demonstrated how the local density function should look like in order for it to be supplemented to a stationary spherically symmetric solution of the Vlasov-Poisson system.

-end-

RUDN University

## Related Plasma Articles from Brightsurf:

Plasma treatments quickly kill coronavirus on surfaces

Researchers from UCLA believe using plasma could promise a significant breakthrough in the fight against the spread of COVID-19.

Fighting pandemics with plasma

Scientists have long known that ionized gases can kill pathogenic bacteria, viruses, and some fungi.

Topological waves may help in understanding plasma systems

A research team has predicted the presence of 'topologically protected' electromagnetic waves that propagate on the surface of plasmas, which may help in designing new plasma systems like fusion reactors.

Plasma electrons can be used to produce metallic films

Computers, mobile phones and all other electronic devices contain thousands of transistors, linked together by thin films of metal.

Plasma-driven biocatalysis

Compared with traditional chemical methods, enzyme catalysis has numerous advantages.

How bacteria protect themselves from plasma treatment

Considering the ever-growing percentage of bacteria that are resistant to antibiotics, interest in medical use of plasma is increasing.

A breakthrough in the study of laser/plasma interactions

Researchers from Lawrence Berkeley National Laboratory and CEA Saclay have developed a particle-in-cell simulation tool that is enabling cutting-edge simulations of laser/plasma coupling mechanisms.

Researchers turn liquid metal into a plasma

For the first time, researchers at the University of Rochester's Laboratory for Laser Energetics (LLE) have found a way to turn a liquid metal into a plasma and to observe the temperature where a liquid under high-density conditions crosses over to a plasma state.

How black holes power plasma jets

Cosmic robbery powers the jets streaming from a black hole, new simulations reveal.

Give it the plasma treatment: strong adhesion without adhesives

A Japanese research team at Osaka University used plasma treatment to make fluoropolymers and silicone resin adhere without any adhesives.

Read More: Plasma News and Plasma Current Events

Researchers from UCLA believe using plasma could promise a significant breakthrough in the fight against the spread of COVID-19.

Fighting pandemics with plasma

Scientists have long known that ionized gases can kill pathogenic bacteria, viruses, and some fungi.

Topological waves may help in understanding plasma systems

A research team has predicted the presence of 'topologically protected' electromagnetic waves that propagate on the surface of plasmas, which may help in designing new plasma systems like fusion reactors.

Plasma electrons can be used to produce metallic films

Computers, mobile phones and all other electronic devices contain thousands of transistors, linked together by thin films of metal.

Plasma-driven biocatalysis

Compared with traditional chemical methods, enzyme catalysis has numerous advantages.

How bacteria protect themselves from plasma treatment

Considering the ever-growing percentage of bacteria that are resistant to antibiotics, interest in medical use of plasma is increasing.

A breakthrough in the study of laser/plasma interactions

Researchers from Lawrence Berkeley National Laboratory and CEA Saclay have developed a particle-in-cell simulation tool that is enabling cutting-edge simulations of laser/plasma coupling mechanisms.

Researchers turn liquid metal into a plasma

For the first time, researchers at the University of Rochester's Laboratory for Laser Energetics (LLE) have found a way to turn a liquid metal into a plasma and to observe the temperature where a liquid under high-density conditions crosses over to a plasma state.

How black holes power plasma jets

Cosmic robbery powers the jets streaming from a black hole, new simulations reveal.

Give it the plasma treatment: strong adhesion without adhesives

A Japanese research team at Osaka University used plasma treatment to make fluoropolymers and silicone resin adhere without any adhesives.

Read More: Plasma News and Plasma Current Events

Brightsurf.com is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for sites to earn advertising fees by advertising and linking to Amazon.com.