arXiv Astrophysics
arXiv Astrophysics
5 years ago

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

Yuta Ito

The effects of 'discreteness

$ 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.

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

DOI: arXiv:1801.04903v2

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$ of a collisional star cluster of $N$-point\nstars may be conventionally understood as close two-body encounters,\nstatistical acceleration, and gravitational polarization. However, if the\nsystem of concern is finite in size and density (not at the late stage of the\nevolution) one must employ the fourth effect, self-consistent ; window.__REDUX_STATE__ = {"feed":{"scrollPos":0,"openAccess":false,"performRefetch":{}},"history":{"historyChanges":0},"onboarding":{"stepsList":[{"stepId":"type","stepName":"What kind of researcher are you?","stepDesc":"","options":[]},{"stepId":"Role","stepName":"What role describes you the best?","stepDesc":"","options":[]},{"stepId":"Org","stepName":"Where do you work or study?","stepDesc":""},{"stepId":"ra","stepName":"Research Areas","stepDesc":"Select the research areas you are interested in","options":[]},{"stepId":"topics","stepName":"Topics","stepDesc":"Select the topics you are interested in","options":[]},{"stepId":"publications","stepName":"Publications","stepDesc":"We have selected some popular publications for you to follow","options":[]},{"stepId":"feeds","stepName":"Feeds","stepDesc":"We have created this feed based on your interests, you can edit and add more from the side menu","options":[]}],"step":1,"loading":false,"loadingText":"Loading...","selections":[{"name":"type","selection":null,"type":"single","mandatory":true},{"name":"role","selection":null,"type":"single","mandatory":true},{"name":"work_study","selection":null,"type":"single","mandatory":false},{"name":"ra","selection":[],"type":"multiple","mandatory":true},{"name":"topics","selection":[],"type":"multiple","mandatory":true},{"name":"publications","selection":[],"type":"multiple","mandatory":false},{"name":"feeds","selection":[],"type":"multiple","mandatory":false}],"topicsNextCursor":null,"topicsFetchingNext":false},"feedManager":{"isManageFeedsFlow":false,"manageFeedType":0,"createEditStep":0,"isSubmitBtnDisable":true,"isPrimaryBtnDisable":true,"activeFeed":{"id":null,"name":"","isOnlyOpenAccess":false,"isOnlyFollowedPublications":false,"inclusions":[],"exclusions":{"keywordsTopics":[],"subjects":[],"publications":[],"articleTypes":[],"authors":[]}},"feedsListCursor":0,"filters":[],"articleTypes":[],"subjects":[],"journals":[]},"common":{"researchAreasAndSubjects":null,"userFilters":[]}};
arXiv Astrophysics
arXiv Astrophysics
5 years ago

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

Yuta Ito

The effects of 'discreteness

$ 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.

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

DOI: arXiv:1801.04903v2

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$truncated; window.__REDUX_STATE__ = {"feed":{"scrollPos":0,"openAccess":false,"performRefetch":{}},"history":{"historyChanges":0},"onboarding":{"stepsList":[{"stepId":"type","stepName":"What kind of researcher are you?","stepDesc":"","options":[]},{"stepId":"Role","stepName":"What role describes you the best?","stepDesc":"","options":[]},{"stepId":"Org","stepName":"Where do you work or study?","stepDesc":""},{"stepId":"ra","stepName":"Research Areas","stepDesc":"Select the research areas you are interested in","options":[]},{"stepId":"topics","stepName":"Topics","stepDesc":"Select the topics you are interested in","options":[]},{"stepId":"publications","stepName":"Publications","stepDesc":"We have selected some popular publications for you to follow","options":[]},{"stepId":"feeds","stepName":"Feeds","stepDesc":"We have created this feed based on your interests, you can edit and add more from the side menu","options":[]}],"step":1,"loading":false,"loadingText":"Loading...","selections":[{"name":"type","selection":null,"type":"single","mandatory":true},{"name":"role","selection":null,"type":"single","mandatory":true},{"name":"work_study","selection":null,"type":"single","mandatory":false},{"name":"ra","selection":[],"type":"multiple","mandatory":true},{"name":"topics","selection":[],"type":"multiple","mandatory":true},{"name":"publications","selection":[],"type":"multiple","mandatory":false},{"name":"feeds","selection":[],"type":"multiple","mandatory":false}],"topicsNextCursor":null,"topicsFetchingNext":false},"feedManager":{"isManageFeedsFlow":false,"manageFeedType":0,"createEditStep":0,"isSubmitBtnDisable":true,"isPrimaryBtnDisable":true,"activeFeed":{"id":null,"name":"","isOnlyOpenAccess":false,"isOnlyFollowedPublications":false,"inclusions":[],"exclusions":{"keywordsTopics":[],"subjects":[],"publications":[],"articleTypes":[],"authors":[]}},"feedsListCursor":0,"filters":[],"articleTypes":[],"subjects":[],"journals":[]},"common":{"researchAreasAndSubjects":null,"userFilters":[]}};
arXiv Astrophysics
arXiv Astrophysics
5 years ago

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

Yuta Ito

The effects of 'discreteness

$ 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.

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

DOI: arXiv:1801.04903v2

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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.

$\nNewtonian mean field (m.f.) potential $\\Phi^{\\triangle}$ $(r,t)=$ $\\int_{\\|r-r'\n\\| > \\triangle}\n\\phi\\left(r-r'\\right)f\\left(r',p',t\\right)\\text{d}^{3}{r'}\\text{d}^{3}{p'}$.\nThe lower limit $\\triangle$ represents the smallest space scale that\nstatistical description is applicable, corresponding to the Landau distance.\nThe lower limit $\\triangle$ represents the smallest spatial scale on which\nstatistical descriptions are applicable, corresponding to the Landau distance.\nThe truncated m.f. potential does not originate from the sparseness of stars in\nphase space but is a necessary condition to separate the collision kinetic\ndescription (close encounters) from the wave one (statistical acceleration).\nThe present paper studies a formulation of mathematically divergence-free\nkinetic equations based on the truncated m.f. potential at three level. (i) No\nstars can come closer each other than the Landau distance. (ii) Only test star\ncan come closer to one field star than the Landau distance at a time while the\nother field stars can not. (iii) A convergent kinetic theory for levels (i) and\n(ii) is formulated. Especially, the Kandrup's generalsied Landau equation was\nextended by employing the Grad's truncated distribution function and\nKlimontovich's theory of non-ideal systems. A correct relation is given between\nthe strong two-body encounter and m.f. potential.\n

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arXiv Astrophysics
arXiv Astrophysics
5 years ago

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

Yuta Ito

The effects of 'discreteness

$ 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.

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

DOI: arXiv:1801.04903v2

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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.