Mathematicians develop new classes of stellar dynamics systems solutions

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The Vlasov-Poisson equations describe many vital bodily phenomena such because the distribution of gravitating particles within the interstellar area, high-temperature plasma kinetics, and the Landau damping impact. A joint group of scientists from the Mathematical Institute of RUDN University and the Mathematical Institute of the University of Munich instructed a new technique to acquire stationary solutions for a system of Vlasov-Poisson equations in a three-dimensional case. Credit: RUDN University

The Vlasov-Poisson equations describe many vital bodily phenomena such because the distribution of gravitating particles in interstellar area, high-temperature plasma kinetics, and the Landau damping impact. A joint group of scientists from the Mathematical Institute of RUDN University and the Mathematical Institute of the University of Munich instructed a new technique to acquire stationary solutions for a system of Vlasov-Poisson equations in a three-dimensional case. The obtained solutions describe the phenomena of stellar dynamics. The outcomes of the examine have been revealed within the Doklady Mathematics journal.

Modern-day physics distinguishes between 4 foremost varieties of interactions. Elementary particle physics covers sturdy and weak interactions, electromagnetism is studied by electrodynamics, and systems with gravitational interplay fall into the scope of a particular department of physics known as gravidynamics. On the area scale, gravitational fields play a key function. One area of examine inside gravidynamics is known as 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,” mentioned Alexander Skubachevskii, a D Sc in Physics and Mathematics, and the Head of the Nikolskii Mathematical Institute of RUDN University.

The motion and interplay of a number of particles in gravitational, electrical, and electromagnetic fields are described utilizing the equations that have been developed by the eminent Soviet physicist Anatoly Vlasov. They mannequin the dynamics and stationary distribution of a system of particles in view of the affect of a self-consistent subject. The Vlasov-Poisson equation for a system of gravitating particles consists of the Poisson equation masking the gravitational potential and the Vlasov equation masking the perform of density distribution in interconnected particles. Vlasov’s mannequin was initially supposed to explain electron gasoline dynamics. The mannequin views processes in plasma not as a collection of collisions between particular person particles however as a simplified system by which particles work together by a subject, and the sector, in flip, correlates with the particle density distribution perform. Therefore, the Vlasov equations are generally known as equations with a self-consistent subject. Together together with his German colleagues, the mathematician from RUDN University established the concept of expandability, i.e. demonstrated how the native density perform ought to appear like to ensure that it to be supplemented to a stationary spherically symmetric answer of the Vlasov-Poisson system.


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More data:
J. Batt et al, Stationary Spherically Symmetric Solutions of the Vlasov–Poisson System within the Three-Dimensional Case, Doklady Mathematics (2020). DOI: 10.1134/S1064562420040237

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RUDN University


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Mathematicians develop new classes of stellar dynamics systems solutions (2021, February 5)
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