101 research outputs found
On the Nonlinear Stability of Asymptotically Anti-de Sitter Solutions
Despite the recent evidence that anti-de Sitter spacetime is nonlinearly
unstable, we argue that many asymptotically anti-de Sitter solutions are
nonlinearly stable. This includes geons, boson stars, and black holes. As part
of our argument, we calculate the frequencies of long-lived gravitational
quasinormal modes of AdS black holes in various dimensions. We also discuss a
new class of asymptotically anti-de Sitter solutions describing noncoalescing
black hole binaries.Comment: 26 pages. 5 figure
Effective numerical simulation of the KleinâGordonâZakharov system in the Zakharov limit
Solving the Klein-Gordon-Zakharov (KGZ) system in the high-plasma frequency regime is numerically severely challenging due to the highly oscillatory nature or the problem. To allow reliable approximations classical numerical schemes require severe step size restrictions depending on the small parameter . This leads to large errors and huge computational costs. In the singular limit the Zakharov system appears as the regular limit system for the KGZ system. It is the purpose of this paper to use this approximation in the construction of an effective numerical scheme for the KGZ system posed on the torus in the highly oscillatory regime . The idea is to filter out the highly oscillatory phases explicitly in the solution. This allows us to play back the numerical task to solving the non-oscillatory Zakharov limit system. The latter can be solved very efficiently without any step size restrictions. The numerical approximation error is then estimated by showing that solutions of the KGZ system in this singular limit can be approximated via the solutions of the Zakharov system and by proving error estimates for the numerical approximation of the Zakharov system. We close the paper with numerical experiments which show that this method is more effective than other methods in the high-plasma frequency regime
Non-ergodicity of Nose-Hoover dynamics
The numerical integration of the Nose-Hoover dynamics gives a deterministic
method that is used to sample the canonical Gibbs measure. The Nose-Hoover
dynamics extends the physical Hamiltonian dynamics by the addition of a
"thermostat" variable, that is coupled nonlinearly with the physical variables.
The accuracy of the method depends on the dynamics being ergodic. Numerical
experiments have been published earlier that are consistent with non-ergodicity
of the dynamics for some model problems. The authors recently proved the
non-ergodicity of the Nose-Hoover dynamics for the one-dimensional harmonic
oscillator.
In this paper, this result is extended to non-harmonic one-dimensional
systems. It is also shown for some multidimensional systems that the averaged
dynamics for the limit of infinite thermostat "mass" have many invariants, thus
giving theoretical support for either non-ergodicity or slow ergodization.
Numerical experiments for a two-dimensional central force problem and the
one-dimensional pendulum problem give evidence for non-ergodicity
The prevalence of hepatitis B virus markers in a cohort of students in Bangui, Central African Republic
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