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We study the motion of test particle in static axisymmetric vacuum spacetimes and discuss two criteria for strong chaos to occur: (1) a local instability measured by the Weyl curvature, and (2) a tangle of a homoclinic orbit, which is closely related to an unstable periodic orbit in general relativity. We analyze several static axisymmetric spacetimes and… (More)

We examine the effect of local matter on the chaotic behavior of a relativistic test particle in non-vacuum static axisymmetric spacetimes. We find that the sign of the sectional curvature in the geodesic deviation equation defined by the Riemann curvature does not always become a good tool to judge the occurrence of chaos in the non-vacuum case. However,… (More)

- Yasuhide Sota, Osamu Iguchi, Tohru Tashiro, Masahiro Morikawa
- Physical review. E, Statistical, nonlinear, and…
- 2008

We propose the self-organized relaxation process which drives a collisionless self-gravitating system to the equilibrium state satisfying local virial (LV) relation. During the violent relaxation process, particles can move widely within the time interval as short as a few free-fall times, because of the effective potential oscillations. Since such particle… (More)

- Y Sota, O Iguchi, M Morikawa, T Tatekawa, K Maeda Ki
- Physical review. E, Statistical, nonlinear, and…
- 2001

Fractal structures and non-Gaussian velocity distributions are characteristic properties commonly observed in virialized self-gravitating systems, such as galaxies and interstellar molecular clouds. We study the origin of these properties using a one-dimensional ring model that we propose in this paper. In this simple model, N particles are moving, on a… (More)

We apply the renormalization group (RG) method to examine the observable scaling properties in Newtonian cosmology. The original scaling properties of the equations of motion in our model are modified for averaged observables on constant time slices. In the RG flow diagram, we find three robust fixed points: Einstein-de Sitter, Milne and Quiescent fixed… (More)

- Osamu Iguchi, Yasuhide Sota, Akika Nakamichi, Masahiro Morikawa
- Physical review. E, Statistical, nonlinear, and…
- 2006

We demonstrate that the quasi-equilibrium state in a self-gravitating N-body system after cold collapse is uniquely characterized by the local virial relation using numerical simulations. Conversely, assuming the constant local virial ratio and Jeans equation for a spherically steady-state system, we investigate the full solution space of the problem under… (More)

- Osamu Iguchi, Yasuhide Sota, Takayuki Tatekawa, Akika Nakamichi, Masahiro Morikawa
- Physical review. E, Statistical, nonlinear, and…
- 2005

We study the velocity distribution in spherical collapses and cluster-pair collisions by use of N -body simulations. Reflecting the violent gravitational processes, the velocity distribution of the resultant quasistationary state generally becomes non-Gaussian. Through the strong mixing of the violent process, there appears a universal non-Gaussian velocity… (More)

- Y Sota, O Iguchi, M Morikawa, A Nakamichi
- 2008

We propose two hypotheses which characterize the collisionless quasi-equilibrium state that realizes after the cold collapse of self-gravitating systems. The first hypothesis is the linear temperature-mass (TM) relation, which yields a characteristic non-Gaussian velocity distribution. The second hypothesis is the local virial (LV) condition, which,… (More)

- Y Sota, O Iguchi, M Morikawa, A Nakamichi
- 2005

We propose two hypotheses which characterize the collisionless quasi-equilibrium state that realizes universally after the cold collapse of self-gravitating systems. The first hypothesis is the linear temperature-mass (TM) relation, which yields a characteristic non-Gaussian velocity distribution. The second is the local virial (LV) relation, which,… (More)

The collisionless quasi-equilibrium state realized after the cold collapse of self-gravitating systems has two remarkable characters. One of them is the linear temperature-mass (TM) relation, which yields a characteristic non-Gaussian velocity distribution. Another is the local virial (LV) relation, the virial relation which holds even locally in… (More)

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