Relationships between a roller and a dynamic pressure distribution in circular hydraulic jumps

We investigated numerically the relation between a roller and the pressure distribution to clarify the dynamics of the roller in circular hydraulic jumps. We found that a roller which characterizes a type II jump is associated with two high pressure regions after the jump, while a type I jump (without the roller) is associated with only one high pressure region. Our numerical results show that building up an appropriate pressure field is essential for a roller.     

Congruence of Siegel modular forms and special values of their standard zeta functions

In this paper, we consider the relationship between the congruence of cuspidal Hecke eigenforms with respect to Sp _n (Z) and the special values of their standard zeta functions. In particular, we propose a conjecture concerning the congruence between Saito-Kurokawa lifts and non-Saito-Kurokawa lifts, and prove it under certain condition. Partially supported by Grant-in-Aid for Scientific Research C-17540003, JSPS.     

A certain Dirichlet series of Rankin-Selberg type associated with the Ikeda lifting

We consider a certain Dirichlet series of Rankin-Selberg type associated with two Siegel cusp forms of the same integral weight with respect to Spn(Z). In particular, we give an explicit formula for the Dirichlet series associated with the Ikeda lifting of cuspidal Hecke eigenforms with respect to SL₂(Z). We also comment on a contribution to the Ikeda's conjecture on the period of the lifting.     

Enhancement in sensitivity of a blood perfusion parameter for frame-rate analysis of bio-speckle image

We have previously presented a blood perfusion parameter by means of the spatial contrast of speckle patterns observed for blood perfusion in skin tissue and a blood vessel. This parameter permits us to visualize a relative blood perfusion distribution from a single speckle pattern. Therefore, it can estimate the blood perfusion with a frame rate of an imaging device employed. This parameter is, however, dependent on the speckle size and the condition of image processing of speckle patterns. In the present study, we estimated this condition with relation to the speckle size for obtaining high sensitivity and good linearity of the parameter to the blood perfusion. Experiments were conducted for ground-glass model, flow model and human wrist to investigate perfusion sensing characteristics of the present parameter.

     

Elementary aspects of vortex motion

Several aspects of vortex motion are considered, with a special stress on the present status of idealization, such as point vortices or vortex filament. As an introduction, elements of vortices induced by the transient flow past an obstacle are considered and their role and development are stated.

Following this introduction, a general survey of the issues in this symposium is made sketchily. As an example, the motion of point vortices in the presence of an external flow or a boundary is discussed on the basis of the Hamiltonian formalism. The cases of linear flow and semicircular boundary are taken as examples of regular and chaotic motions. Secular behaviour of a pair of vortices in the flow is remarked.     

Origins of hole doping and relevant optoelectronic properties of wide gap p-type semiconductor, LaCuOSe

LaCuOSe is a wide band gap (～2.8 eV) semiconductor with unique optoelectronic properties, including room-temperature stable excitons, high hole mobility ～8 cm(2)/(Vs), and the capability of high-density hole doping (up to 1.7 × 10(21) cm(-3) using Mg). Moreover, its carrier transport and doping behaviors exhibit nonconventional results, e.g., the hole concentration increases with decreasing temperature and the high hole doping does not correlate with other properties such as optical absorption. Herein, secondary ion mass spectroscopy and photoemission spectroscopy reveal that aliovalent ion substitution of Mg at the La site is not the main source of hole doping and the Fermi level does not shift even in heavily doped LaCuOSe:Mg. As the hole concentration increases, the subgap optical absorption becomes more intense, but the increase in intensity does not correlate quantitatively. Transmission electron microscopy indicates that planar defects composed of Cu and Se deficiencies are easily created in LaCuOSe. These observations can be explained via the existence of a degenerate low-mobility layer and formation of complex Cu and Se vacancy defects with the assistance of generalized gradient approximation band calculations.     

Fabrication and electron transport properties of epitaxial films of electron-doped 12CaO·7Al2O3 and 12SrO·7Al2O3

Epitaxial growth and electron doping of 12CaO·7Al₂O₃ (C12A7) and 12SrO·7Al₂O₃ (S12A7) are reported. The C12A7 films were prepared on Y₃Al₅O₁₂ (YAG) single-crystal substrates by pulsed laser deposition at room temperature and subsequent thermal crystallization. X-ray diffraction patterns revealed the films were grown epitaxially with the orientation relationship of (001)[100] C12A7 || (001)[100] YAG. For S12A7, pseudo-homoepitaxial growth was attained on the C12A7 epitaxial layer. Upon electron doping, metallic conduction was achieved in the C12A7 film and the S12A7/C12A7 double-layered films. Analyses of optical absorption spectra for the S12A7/C12A7 films provided the densities of free electrons in each layer separately. Hall measurements exhibited larger electron mobility in the S12A7/C12A7 film than those in C12A7 and S12A7 films, suggesting free electrons may be accumulated at the S12A7/C12A7 interface due presumably to a discontinuity of the cage conduction bands.     

Explicit formulas for the twisted Koecher–Maaß series of the Duke–Imamoglu–Ikeda lift and their applications

We give an explicit formula for the twisted Koecher–Maaß series of the Duke–Imamoglu–Ikeda lift. As an application we prove a certain algebraicity result for the values of twisted Rankin–Selberg series at integers of half-integral weight modular forms, which was not treated by Shimura (J Math Soc Japan 33:649–672, 1981).