Bounds for triple zeta-functions

AbstractIn the present paper we consider the problem of the order of magnitude for the triple zeta-functions of Euler-Zagier type in the region 0≤ ℜsj < 1 (j = 1,2,3). We apply the Euler-Maclaurin summation formula and van der Corput's method of multiple exponential sums to the triple zeta-functions

Evaluation of Trapped Magnetic Field Properties in Superconducting MgB2_2 Bulk Magnets of Various Shapes by Finite Element Method

The trapped magnetic field properties of superconducting MgB2 bulk magnets with various shapes such as a triangular, a quadrangular, a hexangular bulk were calculated by the Finite Elements Method (FEM). The effect for the combination of several numbers of bulks was also investigated for several kinds of shapes to obtain large area of bulk surface in spite of one large bulk. In this calculation, the simple magnetization process replaced by the field-cool magnetization was used to obtain the equivalent distribution of the magnetic field, and the thermal equation in FEM was omitted. The trapped magnetic field for the triangular bulk by FEM was compared with the experimental result. It was found that the calculated results agreed well with the experimental result. The maximum trapped magnetic field was obtained in the cylindrical shape among several kinds of shapes. The trapped magnetic field was increased by the combination of multi-bulks. It was confirmed that the trapped magnetic field of the multi-bulks was larger than that of the single bulk. The trapped magnetic field increases with increasing the number of the bulks.28th International Symposium on Superconductivity(ISS 2015), November 16-18, 2015, Tokyo, Japa

Development of hydrogen masers for K-3 VLBI system

Two field operable hydrogen masers were developed for the VLBI joint experiment conducted by the cooperation between RRL and NASA. They are now playing an important role as the time and frequency standard of the K-3 VLBI system, which has also been developed by RRL

Inhomogeneous distribution of flux pinning strength and its effecton irreversibility line and vortex glass-liquid transition line in Bi-2212 tapes

The irreversibility line and the vortex glass-liquid transition line under a magnetic field parallel to the c-axis are investigated for silver-sheathed and dip-coated Bi-2212 tape wires. It is found that the two characteristic lines for silver-sheathed tape is well explained by the flux creep-flow model assuming the distribution of pinning strength with a single peak. On the other hand, general agreements are obtained for these characteristic lines and the critical current density between experiments and theory only when two peaks are assumed in the distribution of flux pinning strength for the dip-coated tape. The causative structure in the dip-coated tape for the peak at small strength in the distribution is discusse

Evaluation of Magnetic Cutting and Polishing with Superconducting Bulks

In this paper, magnetic levitation tool with superconducting bulks is introduced as a new hollow machining technology. Magnetic levitation tool is the machine that magnet levitates above superconducting bulks and driving force of rotating magnet shaves the object. This tool is expected to use for a grinding machine and machining device because of hollow machining and micromachining by strong fixing. For using magnetic levitation tool, the attractive force, the repulsive force and rotating torque are important for grinding machine, machining outer surface and both, respectively. These forces are calculated by FEM, and compared with experimental results. The experimental results are agreed well with calculated results. However, the attractive force is one order smaller than that required in chemical mechanical polishing

Implementation of advanced Riemann solvers in a neutrino-radiation magnetohydrodynamics code in numerical relativity and its application to a binary neutron star merger

We implement advanced Riemann solvers HLLC and HLLD \cite{Mignone:2005ft,MUB:2009} together with an advanced constrained transport scheme \cite{Gardiner:2007nc} in a numerical-relativity neutrino-radiation magnetohydrodynamics code. We validate our implementation by performing a series of one- and multi-dimensional test problems for relativistic hydrodynamics and magnetohydrodynamics in both Minkowski spacetime and a static black hole spacetime. We find that the numerical solutions with the advanced Riemann solvers are more accurate than those with the HLLE solver \cite{DelZanna:2002rv}, which was originally implemented in our code. As an application to numerical relativity, we simulate an asymmetric binary neutron star merger leading to a short-lived massive neutron star both with and without magnetic fields. We find that the lifetime of the rotating massive neutron star formed after the merger and also the amount of the tidally-driven dynamical ejecta are overestimated when we employ the diffusive HLLE solver. We also find that the magnetorotational instability is less resolved when we employ the HLLE solver because of the solver's large numerical diffusivity. This causes a spurious enhancement both of magnetic winding resulting from large scale poloidal magnetic fields, and also of the energy of the outflow induced by magnetic pressure

General-relativistic neutrino-radiation magnetohydrodynamics simulation of black hole-neutron star mergers for seconds

Seconds-long numerical-relativity simulations for black hole-neutron star mergers are performed for the first time to obtain a self-consistent picture of the merger and post-merger evolution processes. To investigate the case that tidal disruption takes place, we choose the initial mass of the black hole to be $5.4M_\odot$ or $8.1M_\odot$ with the dimensionless spin of 0.75. The neutron-star mass is fixed to be $1.35M_\odot$. We find that after the tidal disruption, dynamical mass ejection takes place spending $\lesssim 10\,{\rm ms}$ together with the formation of a massive accretion disk. Subsequently, the magnetic field in the disk is amplified by the magnetic winding and magnetorotational instability, establishing a turbulent state and inducing the angular momentum transport. The post-merger mass ejection by the magnetically-induced viscous effect sets in at $\sim 300$-$500\,{\rm ms}$ after the tidal disruption, at which the neutrino luminosity drops below $\sim 10^{51.5}\,{\rm erg/s}$, and continues for several hundreds ms. A magnetosphere near the rotational axis of the black hole is developed after the matter and magnetic flux fall into the black hole from the accretion disk, and high-intensity Poynting flux generation sets in at a few hundreds ms after the tidal disruption. The intensity of the Poynting flux becomes low after the significant post-merger mass ejection, because the opening angle of the magnetosphere increases. The lifetime for the stage with the strong Poynting flux is $1$-$2\,{\rm s}$, which agrees with the typical duration of short-hard gamma-ray bursts