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Recently I've encountered work by prof. B.V. Alekseev, in which he claims that some physical problems can be easily solved if we consider non-local interactions in kinetic theory (interactions of neighbouring volumes in medium).

This concept seems rather logical, but is it consistent with the reality? Does it violate anything important?

Particularly, I want to know if publication http://arxiv.org/abs/1012.5286 (which deals with antimatter) and http://arxiv.org/abs/1007.2800 (which deals with dark matter) has anything to do with the physical world we live in. It seems that author claims that dark matter phenomenon is just an anomaly of oversimplified theories.

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Nonlocal in kinetic theory means you substitute local variables like the heat flux: q(r,t)=ec(r,t)*v by a non local variable wich usually involves an integral kernel. One needs to do so if the particle distribution function has a long tail in the high energy domain. Particles traveling at hight velocity do have a non negligible effect on the heat flux, even if they are few. But their hight velocity means that between t a t+dt they have travelled a substantial distance. So to take them into account you need to widden the local operator to a non local one. Electron transport in the divertor plasma ans scrape off layer in Tokamaks are typically non local.

I haven't read both papers you've linked, but in the first one: "Solution of the Dark Matter Problem in the Frame of the Non-Local Physics" Pr Alexeev first generalizes the Boltzmann's equation by introducing a term that takes into account the finite size of the kinetic cell (small enough to be considered a point when looked from a macroscopic point of view, but large enough to contain a sufficient number of particles to introduce a continuous distribution function). This extra term is non local in the sense that it adds an integral operator to the collision Boltzmann's operator. Then The author takes the hydrodynamical limit to derive fluid equations. When ones uses these new set of equations to cosmological problems, one can deduce the observed effects that are up to now attributed to dark matter. But the extra non local term avoid to introduce exotic matter. This term is not due to a new physics but to a better treatement of the kinetic equation: one just drops the point size hypothesis of the kinetic cell.

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Maybe I described the idea wrong. He adds new additional (dissipative?) term to Boltzmann equation to account non-local interactions. I don't know exactly. That is why I asked here if his ideas on antimatter, dark matter and kinetic theory are consistent. If they are, I will study them. –  Mixo123 Sep 20 '12 at 6:56
So, it tends to be good thing that is worth studying? And by the way: the paper states that dark matter is just an anomaly of oversimplification in physical models? –  Mixo123 Sep 20 '12 at 7:28
It is indeed a very interesting possible explanation. But if you are new to the field of kinetic theory, I suggest you first read: Generalized Boltzmann Physical Kinetics [Hardcover] by Alexeev, Boris V. –  Shaktyai Sep 20 '12 at 8:03

There is, in the Alekseev paper a rather strange description of the dark matter. In introduction he writes: 'It was postulated that the source of antigravitation is “dark matter” which inferred to exist from gravitational effects on visible matter'.

The search for the dark matter was triggered by the observations showing the conventional gravitational effect of unknown source. Therefore the claim of antigraviational effect of the dark matter requires large separate invisible pools of matter and antimatter, something as speculatif as dark energy and dark matter itself.

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