A new study uses flux-based statistical theory to successfully ** the chaotic behavior of non-hierarchical three-body systems, which is expected to bring more accurate and efficient analysis methods to astrophysics, molecular dynamics and other fields.
The study was published in the journal Celestial Mechanics and Dynamics Astronomy. A research team led by Professor Barak Kol at the Institute of Physics at the Hebrew University has validated a new approach to understanding the dynamics of nonhierarchical three-body systems. This flux-based statistical theory demonstrates astonishing accuracy in terms of chaotic behavior, paving the way for simplified computations and a deeper understanding of complex systems.
This study aims to test a theory about the behavior of a three-body system, i.e., chaotic behavior can be achieved by a formula involving a chaotic emission function and an asymptotic flux (known function). To measure the chaotic emission function, the researchers conducted simulations that tracked millions of scattering events to distinguish between regular scattering and chaotic scattering.
This process produces a ternary absorption function, which provides a basis for testing the theory for chaotic behavior. The results are closely related to the actual distribution, which confirms the validity of the theory and proposes a more efficient method to calculate the distribution of chaotic behavior in these systems.
Traditionally, the chaotic behavior of three-body systems has been a major problem for physicists to analyze and analyze. However, flux-based statistical theory offers a novel approach to simplify this complex problem.
The core of the theory is that the distribution of chaotic behavior can be expressed by multiplying the chaotic emission function by the asymptotic flux (a known function). This innovative concept opens the door to more efficient calculations and a clearer understanding of chaotic dynamics.
To test the theory, the research team conducted extensive simulations to carefully measure the chaotic emission function (or absorption function) over millions of scattering events. By focusing on events until they could distinguish between regular and chaotic scattering, they were able to derive a ternary absorption function.
Using these newly discovered data, the research team successfully calculated a flux-based distribution of chaotic behavior that covers binary binding energy and angular momentum. Surprisingly, the results show a high degree of agreement with the measured distribution, confirming in detail the accuracy and validity of the flux-based theory.
"The three-body problem is one of the oldest and most intractable problems in physics," said Professor Kol. In 2021, I wrote an article proposing a new theory that aims to provide a statistical solution. This approach challenged the basic assumptions of previous theories, introduced the concept of fluxes in phase space, and earned the title of flux-based statistical theory. ”
In this collaborative study, we critically scrutinize and question flux-based statistical theories through a series of extensive computer simulations. The validation process showed an impressive 6% accuracy across the entire 2D variable space. This exhaustive study shows that flux-based theory is the most precise statistical framework for unraveling this complex system. In fact, it marks an important step forward in our understanding of the three-body problem. ”
The most recently published article is the culmination of five articles. Among other things, the previous article proposed new variables to reduce the formulation of the problem. Of these variables, nine variables describing the positions of three objects are replaced with one three-dimensional space in the shape of three pipe joints. This space describes the geometry of a triangle defined by three objects and is therefore called geometric space.
It should be complemented by the rotational motion of the instantaneous position defined by the three objects. Motion in geometric space is described by an electrical-like force, which describes Newton's gravitational force, and a magnetic-like force that describes the Coriolis force in a rotating frame.
Taken together, the foundational knowledge gained from this type of research can have a wide impact on a wide range of fields involving complex dynamic systems, from astronomy to materials science.