Hiroto Kubotani

Wavelet analyses of velocities in laboratory isotropic turbulence

Orthonormal wavelet transformations are used to decompose velocity signals of grid turbulence into both space and scale. The transforms exhibit small-scale enhancements of (i) the spatial fluctuation, (ii) the correlation in space between the adjacent scales, and (iii) the correlation in space between the longitudinal and transverse components. The spatial fluctuation and the scale-scale correlation at small scales are more significant in the transverse component than in the longitudinal component. These features are the same for different families of wavelets. Turbulence contains tube-like structures of vorticity. We demonstrate that wavelet transforms of velocities are enhanced at the positions of the tubes, by using a direct numerical simulation. Thus our wavelet analyses have captured the effects of those coherent structures on velocities measured in the experiment, which would be difficult for traditional analysis techniques such as those with velocity increments

Wavelet identification of vortex tubes in a turbulence velocity field

Abstract This Letter proposes a new method to identify vortex tubes in one-dimensional velocity data of experimental turbulence. From the Taylor vortex, an ideal model for the tube, we construct a continuous wavelet transformation, and demonstrate its usefulness in studying properties of the tubes.

De Broglie-Bohm Interpretation for Analytic Solutions of the Wheeler-DeWitt Equation in Spherically Symmetric Space-Time

We discuss the implications of a wave function for quantum gravity that involves nothing but 3-dimensional geometries as arguments and is invariant under general coordinate transformations. We derive an analytic wave function from the Wheeler-DeWitt equation for spherically symmetric space-time with the coordinate system arbitrary. The de BroglieBohm interpretation of quantum mechanics is applied to the wave function. In this interpretation, deterministic dynamics can arise from a wave function in fully quantum regions as well as in semiclassical regions. By introducing a coordinate system, we obtain a cosmological black hole picture in compensation for the loss of general covariance.

Analytic solutions of the Wheeler-DeWitt equation in spherically symmetric space-time

We study the quantum theory of the Einstein-Maxwell action with a cosmological term in the spherically symmetric space-time, and explored quantum black hole solutions in Reissner-Nordstrom-de Sitter geometry. We succeeded to obtain analytic solutions to satisfy both the energy and momentum constraints.

Asymptotic analysis of singular values of rectangular complex matrices in the Laguerre and fixed-trace ensembles

We present for the first time the asymptotic expressions of the one-body distribution functions of singular values for the Laguerre ensemble and the fixed-trace ensemble in a systematic and unified way. These expressions can be utilized in a wide range of research fields such as data mining, time series analysis and quantum information where finite-size effects play a crucial role. The asymptotic analysis is performed based on our finding of systems of partial differential equations for the confluent Selberg–Kaneko integral and the simplex-type Selberg–Kaneko integral, both of which are introduced in Kubotani et al (2008 Phys. Rev. Lett. 100 240501) and Adachi et al (2009 Ann. Phys., NY 324 2278). Thus, we demonstrate that the systems provide us with new resources of special functions with multiple variables, which can be valuable for analytic studies in various areas.

Testing the Domain Wall Dominated Scenario for the Evolution of the Large Scale Structure of the Universe

A network of domain walls would accelerate the expansion of the universe, but it would also exert a repulsive force expected to help the formation of large-scale structures. We used three-dimensional (3D) N-body simulations of the dynamical evolution of the formation of the structure under the assumption of various configurations of the domain wall network and obtained some cosmological observables: the cosmic Mach number, the velocity distribution, and the two-point correlation. We conclude by comparing the simulation-derived values with values derived from observational data that an era of the domain wall dominated universe can exist. Recent observations of distant Type Ia supernovae 1) suggest that the expansion of the universe is accelerating.Some exotic form of the energy density is required for this accelerated expansion of the universe.More specifically, an equation of state for such energy density is α ≡ p/ρ < 0 with pressure p and energy density ρ, and this is not possible for ordinary matter.Candidates for such an exotic energy density are a non-Abelian cosmic string network, a domain wall network, and a cosmological constant.For example, if the cosmic string settles down to an equilibrium configuration, and if its energy density dominates the universe, an equation of state results with α = −1/3.Similarly, the equation of state for the domain wall dominated universe is α = −2/3, and that for the cosmological constant dominated universe is α = −1.Bucher and Spergel 2) derived an evolution equation for the cosmological perturbations in a flat universe with cold dark matter (CDM) and matter satisfying α< 0, and computed the resulting large-scale cosmic microwave background (CMB) anisotropy. In this paper, we report 3-dimensional (3D) numerical simulations testing the scenario of the domain wall dominated universe by investigating the possibility of the formation of large scale structure.The domain wall discussed here is a relic of the phase transition at late time and moves with only Hubble flow in the universe. According to the current understanding of particle physics, a high degree of symmetry among elementary fields is recovered at high energy scales.In the early universe, this symmetry is expected to be recovered also because of high temperature.The symmetry has been broken as the universe has cooled during its expansion.If the way in which the symmetry is broken is peculiar, topological defects, which are the

GRAVITATIONAL INSTANTONS IN ASHTEKAR’S FORMALISM

Gravitational instantons of Bianchi type IX space are constructed in Ashtekar’s canonical formalism. Instead of solving the self-duality condition, we fully solve the constraint on the “initial surface” and “Hamiltonian equations.” This formalism is applicable to the matter coupled system with cosmological constant.

DE BROGLIE–BOHM INTERPRETATION FOR WAVE FUNCTION OF REISSNER–NORDSTRÖM–DE SITTER BLACK HOLE

We study the canonical quantum theory of the spherically symmetric geometry with the cosmological constant and the electromagnetic field. We obtain a solution of the Wheeler–DeWitt equation for the geometrical variables and investigate the wave function from a viewpoint of the de Broglie–Bohm interpretation of the ordinary quantum mechanics. The de Broglie–Bohm interpretation introduces deterministic rigid trajectories on the minisuperspace without any outside observers nor the collapse of the wave function. It is shown that the wave function does not only correspond to the classical Reissner–Nordstrom–de Sitter black hole in the semiclassical region, but it also represents quantum geometrical fluctuations near the black hole horizon and the cosmological one. The result suggests that the semiclassical gravity on which the Hawking radiation is based is broken near the horizons.