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      • Extended supersymmetry in Dirac action with extra dimensions

        Fujimoto, Yukihiro,Hasegawa, Kouhei,Nishiwaki, Kenji,Sakamoto, Makoto,Tatsumi, Kentaro,Ueba, Inori IOP 2018 JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL Vol.51 No.43

        <P>We investigate a new realization of extended quantum-mechanical supersymmetry. We first show that an <img ALIGN='MIDDLE' ALT='' SRC='http://ej.iop.org/images/1751-8121/51/43/435201/aaadea2ieqn001.gif'/> quantum-mechanical supersymmetry is hidden in the four-dimensional (4D) spectrum of the Kaluza–Klein decomposition for the higher dimensional Dirac field, that is, Kaluza–Klein mode functions of 4D right-handed spinors and 4D left-handed ones form <img ALIGN='MIDDLE' ALT='' SRC='http://ej.iop.org/images/1751-8121/51/43/435201/aaadea2ieqn002.gif'/> supermultiplets. In addition to <img ALIGN='MIDDLE' ALT='' SRC='http://ej.iop.org/images/1751-8121/51/43/435201/aaadea2ieqn003.gif'/> supersymmetry, we discover that an <img ALIGN='MIDDLE' ALT='' SRC='http://ej.iop.org/images/1751-8121/51/43/435201/aaadea2ieqn004.gif'/>-extended supersymmetry (<img ALIGN='MIDDLE' ALT='' SRC='http://ej.iop.org/images/1751-8121/51/43/435201/aaadea2ieqn005.gif'/> for <I>d</I>  =  even (odd) extra dimensions) is further hidden in the 4D spectrum. The extended symmetry can explain additional degeneracy of the spectrum. Furthermore, we show that a superpotential can be introduced into the <img ALIGN='MIDDLE' ALT='' SRC='http://ej.iop.org/images/1751-8121/51/43/435201/aaadea2ieqn006.gif'/>-extended supercharges and clarify the condition to preserve the supersymmetry. The partial breaking of the supersymmetry is also demonstrated.</P>

      • 6d Dirac fermion on a rectangle; scrutinizing boundary conditions, mode functions and spectrum

        Fujimoto, Y.,Hasegawa, K.,Nishiwaki, K.,Sakamoto, M.,Tatsumi, K. North Holland 2017 Nuclear physics, B Vol.922 No.-

        We classify possible boundary conditions of a 6d Dirac fermion Ψ on a rectangle under the requirement that the 4d Lorentz structure is maintained, and derive the profiles and spectrum of the zero modes and nonzero KK modes under the two specific boundary conditions, (i) 4d-chirality positive components being zero at the boundaries and (ii) internal chirality positive components being zero at the boundaries. In the case of (i), twofold degenerated chiral zero modes appear which are localized towards specific directions of the rectangle pointed by an angle parameter θ. This leads to an implication for a new direction of pursuing the origin of three generations in the matter fields of the standard model, even though triple-degenerated zero modes are not realized in the six dimensions. When such 6d fermions couple with a 6d scalar with a vacuum expectation value, θ contributes to a mass matrix of zero-mode fermions consisting of Yukawa interactions. The emergence of the angle parameter θ originates from a rotational symmetry in the degenerated chiral zero modes on the rectangle extra dimensions since they do not feel the boundaries. In the case of (ii), this rotational symmetry is promoted to the two-dimensional conformal symmetry though no chiral massless zero mode appears. We also discuss the correspondence between our model on a rectangle and orbifold models in some details.

      • Experimental Study of Wing-Wake Interactions of Insect Flapping Wing

        Hiroto Nagai,Koji Isogai,Tatsumi Fujimoto 한국항공우주학회 2008 한국항공우주학회 학술발표회 논문집 Vol.- No.-

        An experimental study is conducted to investigate wing-wake interactions of a flapping wing of an insect in hovering and forward flight. Unsteady aerodynamic forces acting on a flapping wing are measured using a dynamically scaled mechanical model in a water tunnel, which simulates hovering and forward flapping flight of insects. In addition, flow visualization is made around the scaled flapping wing model using digital particle image velocimetry (DPIV). A flapping wing experiences wing-wake interaction that the wing interacts with the wake induced in the previous stroke, called wake capture. We investigate effects of parameters of a flapping wing on the wake capture. The results indicate that the wake capture is principally dependent on the two parameters: reduced frequency and timing of feathering rotation. And the flow visualization shows that the vortex pair with counter-rotating, which induces a strong jet flow between the two vortices themselves, enhances wake capture effect. The wake capture effect in forward flight appears in a different manner from in hovering flight. While the wake capture is more effective in the stroke reversal from the down- to up-stroke, it is slight effective in the stroke reversal from the up- to down-stroke.

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