1,105 research outputs found
An operator approach for Markov chain weak approximations with an application to infinite activity L\'{e}vy driven SDEs
Weak approximations have been developed to calculate the expectation value of
functionals of stochastic differential equations, and various numerical
discretization schemes (Euler, Milshtein) have been studied by many authors. We
present a general framework based on semigroup expansions for the construction
of higher-order discretization schemes and analyze its rate of convergence. We
also apply it to approximate general L\'{e}vy driven stochastic differential
equations.Comment: Published in at http://dx.doi.org/10.1214/08-AAP568 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Black Hole Perturbation
We present analytic calculations of gravitational waves from a particle
orbiting a black hole. We first review the Teukolsky formalism for dealing with
the gravitational perturbation of a black hole. Then we develop a systematic
method to calculate higher order post-Newtonian corrections to the
gravitational waves emitted by an orbiting particle. As applications of this
method, we consider orbits that are nearly circular, including exactly circular
ones, slightly eccentric ones and slightly inclined orbits off the equatorial
plane of a Kerr black hole and give the energy flux and angular momentum flux
formulas at infinity with higher order post-Newtonian corrections. Using a
different method that makes use of an analytic series representation of the
solution of the Teukolsky equation, we also give a post-Newtonian expanded
formula for the energy flux absorbed by a Kerr black hole for a circular orbit.Comment: 120 pages ptptex file. To appear in Progress of Theoretical Physics
Supplement No.128 (1997) `Perturbative and Numerical Approaches to
Gravitational Radiation
High-Speed Asymmetric Motion of Thermally Actuated Cilium
Microorganisms can generate net flows effectively even in a low Reynolds number regime by using asymmetric beating motion of hair-like cilia. Here, we demonstrate a high-speed novel artificial cilium driven by the heat engine using a self-propelled swing motion in a nucleate- to film-boiling regime. In particular, we report the asymmetrical motion of the thermal cilium with an asymmetric joint structure. We believe that our thermal cilium opens a new way to develop a microfluidic circuit.ArticleJOURNAL OF THE PHYSICAL SOCIETY OF JAPAN.89(11):114402(2020)journal articl
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