Yasushi Mino

Gravitational Radiation Reaction to a Particle Motion

A small mass particle traveling in a curved spacetime is known to trace a background geodesic in the lowest order approximation with respect to the particle mass. In this paper, we discuss the leading order correction to the equation of motion of the particle, which presumably describes the effect of gravitational radiation reaction. We derive the equation of motion in two different ways. The first one is an extension of the well-known formalism by DeWitt and Brehme developed for deriving the equation of motion of an electrically charged particle. Constructing the conserved rank two symmetric tensor, and integrating it over the interior of the world tube surrounding the orbit, we derive the equation of motion. Although the calculation in this approach is straightforward, it contains less rigorous points. In contrast to the electromagnetic case, in which there are two different charges, i.e., the electric charge and the mass, the gravitational counterpart has only one charge. This fact prevents us from using the same renormalization scheme that was used in the electromagnetic case. In order to overcome this difficulty, we put an ansatz in evaluating the integral ofthe conserved tensor on a three spatial volume which defines the momentum of the small particle. To make clear the subtlety in the first approach, we then consider the asymptotic matching of two different schemes, i.e., the internal scheme in which the small particle is represented by a spherically symmetric black hole with tidal perturbations and the external scheme in which the metric is given by small perturbations on the given background geometry. The equation of motion is obtained from the consistency condition of the matching. We find that in both ways the same equation of motion is obtained. The resulting equation of motion is analogous to that derived in the electromagnetic case. We discuss implications of this equation of motion. PACS number(s): 04.30.Db, 04.25.-g

Chapter 1 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.

Fabrication of Colloidal Grid Network by Two-Step Convective Self-Assembly

We explored a template-free approach to arranging colloidal particles into a network pattern by a convective self-assembly technique. In this approach, which we call two-step convective self-assembly, a stripe pattern of colloidal particles is first prepared on a substrate by immersing it in a suspension. The substrate with the stripes is then rotated by 90° and again immersed in the suspension to produce stripes perpendicular to the first ones, resulting in a grid-pattern network of colloidal arrays. The width of the colloidal grid lines can be controlled by changing the particle concentration while maintaining an almost constant spacing between the lines. On the basis of these results, we propose a mechanism for grid pattern formation. Our method is applicable to various types of particles. In addition, the wide applicability of this method was employed to create a hybrid grid pattern.

Spontaneous Formation of Cluster Array of Gold Particles by Convective Self-Assembly

Cluster arrays composed of metal nanoparticles are promising for application in sensing devices because of their interesting surface plasmon characteristics. Herein, we report the spontaneous formation of cluster arrays of gold colloids on flat substrates by vertical-deposition convective self-assembly. In this technique, under controlled temperature, a hydrophilic substrate is vertically immersed in a colloid suspension. Cluster arrays form when the particle concentration is extremely low (in the order of 10(-6)-10(-8) v/v). These arrays are arranged in a hierarchically ordered structure, where the particles form clusters that are deposited at a certain separation distance from each other, to form dotted lines that are in turn aligned with a constant spacing. The size of the cluster can be controlled by varying the particle concentration and temperature while an equal separation distance is maintained between the lines formed by the clusters. Our technique thus demonstrates a one-step, template-free fabrication method for cluster arrays. In addition, through the direct observation of the assembly process, the spacing between the dotted lines is found to result from the stick-and-slip behavior of the meniscus tip, which is entirely different from the formation processes observed for the striped patterns, which we reported previously at higher particle concentrations. The difference in the meniscus behavior possibly comes from the difference in colloidal morphology at the meniscus tip. These results demonstrate the self-regulating characteristics of the convective self-assembly process to produce colloidal patterns, whose structure depends on particle concentration and temperature.

Gravitational waves from a spinning particle in circular orbits around a rotating black hole

Using the Teukolsky and Sasaki-Nakamura formalisms for the perturbations around a Kerr black hole, we calculate the energy flux of gravitational waves induced by a spinning particle of mass m and spin S moving in circular orbits near the equatorial plain of a rotating black hole of mass M(@m) and spin Ma . The calculations are performed by using the recently developed post-Newtonian expansion technique of the Teukolsky equation. To evaluate the source terms of perturbations caused by a spinning particle, we use the equations of motion of a spinning particle derived by Papapetrou and the energy-momentum tensor of a spinning particle derived by Dixon. We present the post-Newtonian formula of the gravitational wave luminosity up to the order (v/c) 5 beyond the quadrupole formula including the linear order of particle spin. The results obtained in this paper will be an important guideline to the post-Newtonian calculation of the inspiral of two spinning compact objects. @S0556-2821~96!02016-4#

In Situ Observation of Meniscus Shape Deformation with Colloidal Stripe Pattern Formation in Convective Self-Assembly

Vertical convective self-assembly is capable of fabricating stripe-patterned structures of colloidal particles with well-ordered periodicity. To unveil the mechanism of the stripe pattern formation, in the present study, we focus on the meniscus shape and conduct in situ observations of shape deformation associated with particulate line evolution. The results reveal that the meniscus is elongated downward in a concave fashion toward the substrate in accordance with solvent evaporation, while the concave deformation is accelerated by solvent flow, resulting in the rupture of the liquid film at the thinnest point of the meniscus. The meniscus rupture triggers the meniscus to slide off from the particulate line, followed by the propagation of the sliding motion of the three-phase contact line, resulting in the formation of stripe spacing.

Chapter 7. Gravitational Radiation Reaction

We consider the radiation reaction to the motion of a point-like particle of mass

Formation of regular stripes of chemically converted graphene on hydrophilic substrates.

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Gravitational waves induced by a spinning particle falling into a rotating black hole

and specific spin

Controlling self-assembled structure of Au nanoparticles by convective self-assembly with liquid-level manipulation

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