Tuesday, January 04, 2022

Oh so close ...

The 3 Body Problem, an example of chaos in action, is, for all intensive purposes, solved but like Heisenberg's Uncertainty Principle, a complete solution will never be at hand due to the vagaries of quantum and chaos. Really close but still a hedge as initial conditions rule as seen in Brownian  motion and the Random Walk because both relate to probability and the aforementioned 3 Body Problem.

Physicists have long tried to solve the three-body problem. Without success. This means that it is impossible to predict what will happen during close interactions between a binary star system and a third object — except through computer simulations.

They show that such an interaction takes place in two phases. The first phase is a chaotic phase, during which all three bodies are rapidly attracted to each other until one star is thrown away from the other two and settles into an elliptical orbit. It may both return to the close vicinity of the binary system and the whole process begins again. The second stage of the three-star interaction is the escape phase when one of the stars escapes into an outer orbit and becomes gravitationally independent of the binary system.

Professor Hagai Perets and his doctoral student Yonadav Barry Ginat of the Technion-Israel Institute of Technology solved the entire two-phase process statistically. Instead of predicting the actual outcome, they calculated the probability of each given outcome of each interaction in each stage of the three-body gravitational interactions. The entire series of motions of the three bodies can be modeled using the theory of random walks, commonly referred to as a “drunken walk.” This term was proposed by mathematicians considering how a drunk would walk, considering it as a random process. With each step, the drunk is unaware of where he is and what direction he is going.

The three-body system actually behaves in the same way. After each close interaction, one of the stars is randomly ejected from outside the system — this can be thought of as the drunken man walking.

The 3 Body Problem

This is a simulation of the Brownian motion of a big particle (dust particle) that collides with a large set of smaller particles (molecules of a gas) which move with different velocities in different random directions.

Random Walk/Brownian Motion

2-dimensional random walk of a silver adatom on an Ag(111) surface[1]

Oh so close ... indeed. :)

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