# A convergent kinetic theory of collisional star clusters (i) a self-consistent 'truncated' mean-field potential.

The effects of 'discreteness

Publisher URL: http://arxiv.org/abs/1801.04903

DOI: arXiv:1801.04903v2

5 years ago# A convergent kinetic theory of collisional star clusters (i) a self-consistent 'truncated' mean-field potential.

$ of a collisional star cluster of $N$-point
stars may be conventionally understood as close two-body encounters,
statistical acceleration, and gravitational polarization. However, if the
system of concern is finite in size and density (not at the late stage of the
evolution) one must employ the fourth effect, self-consistent
$truncated
$
Newtonian mean field (m.f.) potential $\Phi^{\triangle}$ $(r,t)=$ $\int_{\|r-r'
\| > \triangle}
\phi\left(r-r'\right)f\left(r',p',t\right)\text{d}^{3}{r'}\text{d}^{3}{p'}$.
The lower limit $\triangle$ represents the smallest space scale that
statistical description is applicable, corresponding to the Landau distance.
The lower limit $\triangle$ represents the smallest spatial scale on which
statistical descriptions are applicable, corresponding to the Landau distance.
The truncated m.f. potential does not originate from the sparseness of stars in
phase space but is a necessary condition to separate the collision kinetic
description (close encounters) from the wave one (statistical acceleration).
The present paper studies a formulation of mathematically divergence-free
kinetic equations based on the truncated m.f. potential at three level. (i) No
stars can come closer each other than the Landau distance. (ii) Only test star
can come closer to one field star than the Landau distance at a time while the
other field stars can not. (iii) A convergent kinetic theory for levels (i) and
(ii) is formulated. Especially, the Kandrup's generalsied Landau equation was
extended by employing the Grad's truncated distribution function and
Klimontovich's theory of non-ideal systems. A correct relation is given between
the strong two-body encounter and m.f. potential.

Yuta Ito

The effects of 'discreteness

Publisher URL: http://arxiv.org/abs/1801.04903

DOI: arXiv:1801.04903v2

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5 years ago# A convergent kinetic theory of collisional star clusters (i) a self-consistent 'truncated' mean-field potential.

$ of a collisional star cluster of $N$-point
stars may be conventionally understood as close two-body encounters,
statistical acceleration, and gravitational polarization. However, if the
system of concern is finite in size and density (not at the late stage of the
evolution) one must employ the fourth effect, self-consistent
$truncated
$
Newtonian mean field (m.f.) potential $\Phi^{\triangle}$ $(r,t)=$ $\int_{\|r-r'
\| > \triangle}
\phi\left(r-r'\right)f\left(r',p',t\right)\text{d}^{3}{r'}\text{d}^{3}{p'}$.
The lower limit $\triangle$ represents the smallest space scale that
statistical description is applicable, corresponding to the Landau distance.
The lower limit $\triangle$ represents the smallest spatial scale on which
statistical descriptions are applicable, corresponding to the Landau distance.
The truncated m.f. potential does not originate from the sparseness of stars in
phase space but is a necessary condition to separate the collision kinetic
description (close encounters) from the wave one (statistical acceleration).
The present paper studies a formulation of mathematically divergence-free
kinetic equations based on the truncated m.f. potential at three level. (i) No
stars can come closer each other than the Landau distance. (ii) Only test star
can come closer to one field star than the Landau distance at a time while the
other field stars can not. (iii) A convergent kinetic theory for levels (i) and
(ii) is formulated. Especially, the Kandrup's generalsied Landau equation was
extended by employing the Grad's truncated distribution function and
Klimontovich's theory of non-ideal systems. A correct relation is given between
the strong two-body encounter and m.f. potential.

Yuta Ito

The effects of 'discreteness

Publisher URL: http://arxiv.org/abs/1801.04903

DOI: arXiv:1801.04903v2

You might also like

Discover & Discuss Important Research

Keeping up-to-date with research can feel impossible, with papers being published faster than you'll ever be able to read them. That's where Researcher comes in: we're simplifying discovery and making important discussions happen. With over 19,000 sources, including peer-reviewed journals, preprints, blogs, universities, podcasts and Live events across 10 research areas, you'll never miss what's important to you. It's like social media, but better. Oh, and we should mention - it's free.

Researcher displays publicly available abstracts and doesn’t host any full article content. If the content is open access, we will direct clicks from the abstracts to the publisher website and display the PDF copy on our platform. Clicks to view the full text will be directed to the publisher website, where only users with subscriptions or access through their institution are able to view the full article.

5 years ago# A convergent kinetic theory of collisional star clusters (i) a self-consistent 'truncated' mean-field potential.

$ of a collisional star cluster of $N$-point
stars may be conventionally understood as close two-body encounters,
statistical acceleration, and gravitational polarization. However, if the
system of concern is finite in size and density (not at the late stage of the
evolution) one must employ the fourth effect, self-consistent
$truncated
$
Newtonian mean field (m.f.) potential $\Phi^{\triangle}$ $(r,t)=$ $\int_{\|r-r'
\| > \triangle}
\phi\left(r-r'\right)f\left(r',p',t\right)\text{d}^{3}{r'}\text{d}^{3}{p'}$.
The lower limit $\triangle$ represents the smallest space scale that
statistical description is applicable, corresponding to the Landau distance.
The lower limit $\triangle$ represents the smallest spatial scale on which
statistical descriptions are applicable, corresponding to the Landau distance.
The truncated m.f. potential does not originate from the sparseness of stars in
phase space but is a necessary condition to separate the collision kinetic
description (close encounters) from the wave one (statistical acceleration).
The present paper studies a formulation of mathematically divergence-free
kinetic equations based on the truncated m.f. potential at three level. (i) No
stars can come closer each other than the Landau distance. (ii) Only test star
can come closer to one field star than the Landau distance at a time while the
other field stars can not. (iii) A convergent kinetic theory for levels (i) and
(ii) is formulated. Especially, the Kandrup's generalsied Landau equation was
extended by employing the Grad's truncated distribution function and
Klimontovich's theory of non-ideal systems. A correct relation is given between
the strong two-body encounter and m.f. potential.

Yuta Ito

The effects of 'discreteness

Publisher URL: http://arxiv.org/abs/1801.04903

DOI: arXiv:1801.04903v2

You might also like

Discover & Discuss Important Research

Keeping up-to-date with research can feel impossible, with papers being published faster than you'll ever be able to read them. That's where Researcher comes in: we're simplifying discovery and making important discussions happen. With over 19,000 sources, including peer-reviewed journals, preprints, blogs, universities, podcasts and Live events across 10 research areas, you'll never miss what's important to you. It's like social media, but better. Oh, and we should mention - it's free.

Researcher displays publicly available abstracts and doesn’t host any full article content. If the content is open access, we will direct clicks from the abstracts to the publisher website and display the PDF copy on our platform. Clicks to view the full text will be directed to the publisher website, where only users with subscriptions or access through their institution are able to view the full article.

Yuta Ito

The effects of 'discreteness

Publisher URL: http://arxiv.org/abs/1801.04903

DOI: arXiv:1801.04903v2

You might also like

Discover & Discuss Important Research