Face algebras and unitarity of SU(N)_L-TQFT

Using face algebras (i.e. algebras of L-operators of IRF models), we construct modular tensor categories with positive definite inner product, whose fusion rules and S-matrices are the same as (or slightly different from) those obtained by $U_q (\frak{sl}_{N})$ at roots of unity. Also we obtain state-sums of ABF models on framed links which give quantum SU(2)-invariants of corresponding 3-manifolds.Comment: AMS-LaTeX, 36 pages, to appear in Commun. Math. Phy

Topological strings and 5d T_N partition functions

We evaluate the Nekrasov partition function of 5d gauge theories engineered by webs of 5-branes, using the refined topological vertex on the dual Calabi-Yau threefolds. The theories include certain non-Lagrangian theories such as the T_N theory. The refined topological vertex computation generically contains contributions from decoupled M2-branes which are not charged under the 5d gauge symmetry engineered. We argue that, after eliminating them, the refined topological string partition function agrees with the 5d Nekrasov partition function. We explicitly check this for the T_3 theory as well as Sp(1) gauge theories with N_f = 2, 3, 4 flavors. In particular, our method leads to a new expression of the Sp(1) Nekrasov partition functions without any contour integrals. We also develop prescriptions to calculate the partition functions of theories obtained by Higgsing the T_N theory. We compute the partition function of the E_7 theory via this prescription, and find the E_7 global symmetry enhancement. We finally discuss a potential application of the refined topological vertex to non-toric web diagrams.Comment: 79 pages, 27 figures; v2: minor improvements, references adde

Defect detection using quasi-scholte wave for plate loaded with water on single surface

Ultrasonic guided waves achieve non-destructive inspection of thin plates. However, issues such as large energy leakage and attenuation often plague guided wave inspection of storage tanks and pipes filled with fluid. This study experimentally investigated the non-destructive testing of a water-loaded flat aluminum alloy plate through the application of a quasi-Scholte (QS) wave that propagated along the fluid-plate interface without experiencing attenuation due to leakage. A QS wave was confirmed as having been generated and propagated in a plate loaded with water on the bottom surface using ultrasonic incidence and detection at the top water-free surface. Two-dimensional Fourier transform images of the waveforms revealed refiection of the QS wave from a defect as well as a forward incident QS wave. The visualization results experimentally confirmed-via measurements of waves in water using a laser Doppler vibrometer-that QS waves propagated along a plate surface, while scattered waves were generated by defects

Guided wave propagation in metallic and resin plates loaded with water on single surface

Our previous papers reported dispersion curves for leaky Lamb waves in a water-loaded plate and wave structures for several typical modes including quasi-Scholte waves [1,2]. The calculations were carried out with a semi-analytical finite element (SAFE) method developed for leaky Lamb waves. This study presents SAFE calculations for transient guided waves including time-domain waveforms and animations of wave propagation in metallic and resin water-loaded plates. The results show that non-dispersive and non-attenuated waves propagating along the interface between the fluid and the plate are expected for effective non-destructive evaluation of such fluid-loaded plates as storage tanks and transportation pipes. We calculated transient waves in both steel and polyvinyl chloride (PVC) plates loaded with water on a single side and input dynamic loading from a point source on the other water-free surface as typical examples of metallic and resin plates. For a steel plate, there exists a non-dispersive and non-attenuated mode, called the quasi-Scholte wave, having an almost identical phase velocity to that of water. The quasi-Scholte wave has superior generation efficiency in the low frequency range due to its broad energy distribution across the plate, whereas it is localized near the plate-water interface at higher frequencies. This means that it has superior detectability of inner defects. For a PVC plate, plural non-attenuated modes exist. One of the non-attenuated modes similar to the A0 mode of the Lamb wave in the form of a group velocity dispersion curve is promising for the non-destructive evaluation of the PVC plate because it provides prominent characteristics of generation efficiency and low dispersion.42ND ANNUAL REVIEW OF PROGRESS IN QUANTITATIVE NONDESTRUCTIVE EVALUATION: Incorporating the 6th European-American Workshop on Reliability of NDE, 26–31 July 2015, Minneapolis, MinnesotaTakahiro Hayashi and Daisuke Inoue, "Guided wave propagation in metallic and resin plates loaded with water on single surface", AIP Conference Proceedings 1706, 030003 (2016) https://doi.org/10.1063/1.494047

Defect imaging for plate-like structures using diffuse acoustic wave generated by modulated laser

Authors have studied defect imaging technique for plate-like structures, which creates an image beyond diffraction limit and can be applied to a plate-like structure with a complex shape because this technique just uses variations of flexural vibration energy due to the differences in nominal bending stiffness at laser spots. However, this technique generates spurious images caused by the resonance as well as defect images. The current study described how the spurious images can be reduced using diffuse acoustic wave, and then showed that images of defects and adhesive regions can be obtained appropriately even in such complex structures as a flat plate with a complex shape, a curved plate, and a branch pipe.45TH ANNUAL REVIEW OF PROGRESS IN QUANTITATIVE NONDESTRUCTIVE EVALUATION, VOLUME 38, 15–19 July 2018, Vermont, USATakahiro Hayashi and Shogo Nakao, "Defect imaging for plate-like structures using diffuse acoustic wave generated by modulated laser", AIP Conference Proceedings 2102, 050003 (2019) https://doi.org/10.1063/1.509976

パイプ周方向溝における超音波エネルギトラップ

パイプの周方向に管厚が薄くなるような溝部がある場合に，その溝部に沿って伝搬するガイド波が溝部のみにエネルギトラップされる現象について検討した．パイプの周方向を伝搬するガイド波の分散曲線より，そのエネルギトラップが予測され，半解析的有限要素法を用いた数値計算によって共振周波数および振動モードを算出することができた．さらに，レーザ超音波による非接触計測によって，それらのモードが数値計算により得られた共振周波数に非常に近い周波数において発生することが確認された．このパイプ周方向のガイド波のエネルギトラップは，管厚の薄い部分で起こるので，今後，高感度のセンサとしての利用が期待できる

Defect imaging for plate-like structures using diffuse field

Defect imaging utilizing a scanning laser source (SLS) technique produces images of defects in a plate-like structure, as well as spurious images occurring because of resonances and reverberations within the specimen. This study developed defect imaging by the SLS using diffuse field concepts to reduce the intensity of spurious images, by which the energy of flexural waves excited by laser can be estimated. The experimental results in the different frequency bandwidths of excitation waves and in specimens with different attenuation proved that clearer images of defects are obtained in broadband excitation using a chirp wave and in specimens with low attenuation, which produce diffuse fields easily