Mathematicians solve the year -old problem, explain how liquids move

During the 1900 International Math Congress, the theory of numbers, Ciros, Analysis, Analysis, Analysis, Analysis, Analysis, Analysis, Analysis, Analysis, Analysis, Analysis, Analysis, Analysis, Analysis, Analysis, Analysis and Mathematical Physics, David Hilbert, David Hilbert, presented a list of problems.

Known as “Hilbert’s 23 Problems”, These challenges tried to direct mathematical research in the 20th century, but some have not been solved to date. These include the complex sixth problem that requires a meticulous axiomatic formulation of physics laws, especially mechanical and probability theory.

Now, Zahr Hani of the University of Michigan, which is home to the Arxiv Preasers warehouse, claims to unite three physical theories explaining the movement of fluids in a recent study of the University of Michigan. This solution deals with the heart of the sixth problem, that is, from statistical mechanics to liquids from atoms to liquids.

Analysis levels in fluid dynamics

Although the distinction between mathematical vision and physics is sometimes scattered, the truth is that the liquids consist of individual particles with collisions and movements that can be monitored individually following the Newton’s laws. Already at the mesoscopic level, the equation of 1872 Boltzmann is dominant. It adopts a statistical approach considering the possible behavior of typical particles focusing on group trends.

In the macroscopic world, fluids are seen as continuous substances described by the Euler and Navier-Stokes equations combined without referring to individual particles in 1845. Connecting these three perspectives together was the “axiomatization ılan sought by Hilbert. With theories defining the macroscopic scales obtained from those who define behavior on smaller scales..

At least the problem that continues so far is that searching for a meticulous mathematical structure that shows how different physical models are logically connected is that it is a permanent difficulty in physics. Combining attempts have always been a species of special restrictions such as working on short or vacuum scales.

How did the researchers unite three fluid theories?

The combination of fluid dynamics develops in three parts: the mesoscopic macroscopic theory is the derivation and microscopic, and then integrates these derivatives into a single logical line. The first step was already well understood by Hilbert’s contributions, and the second represented a more complex mathematical difficulty because of the collective interactions between many particles.

In this way, Deng, Hani and Ma Newton examined the equations with endless particles and proved that it was convergent to the equation of Boltzmann. The difficulty was to protect this validity in comprehensive periods in which each collision added historical complexity. But they surpassed this, mathematically it The accumulated effects of previous interactions are controlled over time and remain limited.

The discovery shows that three liquid theories are part of a larger theory. This proves that scientists are right to use different mathematical models depending on the observed scale while looking at one individual particles, particle groups, or liquid as a whole. So, they all combine to describe the same physical reality. The result responds to a part of Hilbert’s sixth problem and opens new approaches.

What did you think about this problem to solve it 125 years? Comment on social networks and share this article with your friends who like unresolved logical difficulties. See how physicists discovered a new way to represent Pi