On the dynamics of a one-dimensional self-gravitating medium

Roytvarf, Alexander A.

doi:10.1016/0167-2789(94)90156-2

Cited by 6 publications

(6 citation statements)

References 5 publications

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“…For smooth initial data, the support of f remains smooth even after particle crossing (see Ref. [39] for the onedimensional case). In one dimension, it is easy to show that, near a point x * where the tangent to the graph of the support is parallel to the v-axis (such as points x ± on Fig.…”

Section: Discussionmentioning

confidence: 99%

Singularities and the distribution of density in the Burgers/adhesion model

Frisch

Bec

Villone

2001

Physica D: Nonlinear Phenomena

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Physica D in pressWe are interested in the tail behavior of the pdf of mass density within the one and d-dimensional Burgers/adhesion model used, e.g., to model the formation of large-scale structures in the Universe after baryon-photon decoupling. We show that large densities are localized near "kurtoparabolic" singularities residing on space-time manifolds of codimension two (d ≤ 2) or higher (d ≥ 3). For smooth initial conditions, such singularities are obtained from the convex hull of the Lagrangian potential (the initial velocity potential minus a parabolic term). The singularities contribute universal power-law tails to the density pdf when the initial conditions are random. In one dimension the singularities are preshocks (nascent shocks), whereas in two and three dimensions they persist in time and correspond to boundaries of shocks; in all cases the corresponding density pdf has the exponent −7/2, originally proposed by E, Sinai (1997 Phys. Rev. Lett. 78, 1904) for the pdf of velocity gradients in one-dimensional forced Burgers turbulence. We also briefly consider models permitting particle crossings and thus multi-stream solutions, such as the Zel'dovich approximation and the (Jeans)-Vlasov-Poisson equation with single-stream initial data: they have singularities of codimension one, yielding power-law tails with exponent −3.su quell' immenso baratro di stelle sopra quei gruppi, sopra quegli ammassi, quel seminío, quel balenío di stelle Giovanni Pascoli, from La Vertigine [1]

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Section: Discussionmentioning

confidence: 99%

Singularities and the distribution of density in the Burgers/adhesion model

Frisch

Bec

Villone

2001

Physica D: Nonlinear Phenomena

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“…After caustic formation, velocity is a multi-valued function of position and in that region, a Zeldovich pancake, or blini, carries an increasing fraction of the mass. single-stream, the dynamics of a self-gravitating system can nevertheless be proven to stay close to the Zeldovich approximation for short enough times [14]. Fig.…”

Section: Free Motionmentioning

confidence: 69%

“…single-stream, the dynamics of a self-gravitating system can nevertheless be proven to stay close to the Zeldovich approximation for short enough times [14].…”

Section: Free Motionmentioning

confidence: 89%

A heap-based algorithm for the study of one-dimensional particle systems

Noullez

Fanelli²,

Aurell

2003

Journal of Computational Physics

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“…The first and most common caustic has a density with an inverse square root singularity (as occurs in the Zel'dovich approximation). This singularity has been rigorously proven to be robust in the case of a one‐dimensional Vlasov–Poisson system (Roytvarf 1994), and is the only singularity that is of relevance to the present work. The other generic singularities can lie on one‐dimensional manifolds (lines) or be isolated points.…”

Section: Introductionmentioning

confidence: 86%

Gravitational cooling and density profile near caustics in collisionless dark matter haloes

Mohayaee

Shandarin

2006

Monthly Notices of the Royal Astronomical Society

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Cold dark matter haloes are populated by high‐density structures with sharply peaked profiles known as caustics, which have not yet been resolved by three‐dimensional numerical simulations. Here, we derive semi‐analytic expressions for the density profiles near caustics in haloes that form by self‐similar accretions of dark matter with infinitesimal velocity dispersion. A simple rescaling shows that, similarly to the case of absolutely cold medium, these profiles are universal: they are valid for all caustics irrespective of the physical parameters of the halo. We derive the maximum density of the caustics and show that it depends on the velocity dispersion and the caustic location. We show that both the absolute and relative thickness of the caustic decrease monotonically towards the centre of the halo while the maximum density grows. This indicates that the radial component of the thermal velocities decreases in the inner streams, i.e. the collisionless medium cools down in the radial direction descending to the centre of the halo. Finally, we demonstrate that there can be a significant contribution to the emission measure from dark matter particle annihilation in the caustics.

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On the dynamics of a one-dimensional self-gravitating medium

Cited by 6 publications

References 5 publications

Singularities and the distribution of density in the Burgers/adhesion model

Singularities and the distribution of density in the Burgers/adhesion model

A heap-based algorithm for the study of one-dimensional particle systems

Gravitational cooling and density profile near caustics in collisionless dark matter haloes

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