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Associate Professor |
Assistant Professor |
- Matrix-theoretic high-performance algorithm construction, with application to the numerical computation of critically important quantities associated with difficult special functions occurring from 3-D wave equations, such as regular Coulomb wave functions, Mathieu functions, spheroidal wave functions, Lame functions, ellipsoidal wave functions. The Bessel function of the first kind, an easier function serves as a model case, where two types of computational problems were solved in the complex domain as well as real domain: given a complex order Bessel function, compute a given number of zeros closest to the origin to a specified accuracy; and given a complex number find a specified number of orders of Bessel functions closest to the origin, to a specified accuracy. There are no comparable algorithms known elsewhere which give as accurate an error estimate as ours.
- Construction of hyper English word study dictionary: it is available at http://hidic.u-aizu.ac.jp/. This represents a long-range project, aiming at compiling a database for the study of English words for Japanese students. The main feature is that the dictionary is organized to bring out the best fruits of comparative linguistics in the past century: the usefulness of IndoEuropean roots as presented in the wonderful book by Calvert Watkins, The American Heritage Dictionary of Indo-European Roots, Second Edition, HoughtonMifflin, 2000. Example: The organizing principle of the dictionary will tell you that the following words are best studied as a group: riddle, garble, crime, decree, discern, secret, hypocrisy (they are all derivatives from the same Indo-European root krei-, meaning "to sieve", indicating that a group of seemingly unrelated words come from the same notion "to sieve"). Another example: the usage of the so-called synonyms "anger, rage and wrath" can be clearly explained by tracing them back to their respective Indo-European root: anger to angh-, meaning painful, rage to rebh-, meaning violent, impetuous, and wrath to wreit-, meaning to turn, twist (anger is akin to angst, angina, rage is akin to rabid, rabies, and wrath is akin to wreath, writhe).
We conduct research works extensively related to the fundamental theories and advanced applications of mathematics, especially in numerical computation. |
| Prof. Kanda's research interests are mainly in numerical analysis of partial differential equations, and emphasis is placed on the development of program codes for Navier-Stokes Equation in complex-shaped flow fields. Differential geometry, tensor analysis, and grid generation are also studied as needed. |
| In 1883, Osborne Reynolds observed the transition between laminar and turbulent flows in circular pipes; the critical values of Rc were 12,830 for the color-dye method and 2030 for the pressure method. These values have yet to be theoretically obtained. Hence, Prof. Kanda succeeded in the calculation of the minimum critical Reynolds number, Rc(min), of 2040 in 1999 for the first time in history. Then, he wanted to confirm the Rc of 12,830 experimentally before starting calculations, but it is very difficult to reproduce Rc. Therefore, he has been carrying out experiments similar to Reynolds color-dye experiment everyday and every weekends since March 2003 to fix physical constants for Rc. Thus, he realized in 2004 that studies of science take three steps of analysis: verification of real phenomena, building of physical model, and calculation based on mathematical model. |
| Prof. Asai's major research fronts may be described as follows:
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Referred Proceeding Papers
| [kanda-01:2006] |
Hidesada Kanda. Laminar-Turbulent Transition: Calculation of Minimum Critical Reynolds Number in Channel Flow. In RIMS Kokyuroku Bessatsu, volume B1, pages 199.217. Research Institute for Mathematical Sciences, Kyoto University, 2007. |
| A conceptual model has been constructed for the problem of determining a critical Reynolds number (Rc) for laminar-turbulent transition in pipe and channel flows. For pipe flow, the minimum critical Reynolds number Rc(min) of approximately 2040 was obtained. In order to prove the validity of the model, another verification is required. Thus, for channel flow, results of previous investigations were studied, focusing on experimental data on Rc, the entrance length, and the transition length. Consequently, the model was confirmed and an experimental value of Rc(min) in the neighborhood of 1300 was found to exist, based on the channel height and average velocity. In this study, for channel flow, we obtained Rc(min) of approximately 1230 when using J0 = 101 grid points in the normal or y-direction, and 910 when J0 = 51. | |
| [nasai-01:2006] | Yoshinori MIYAZAKI, Nobuyoshi ASAI, DongSheng CAI, and Yasuhiko
IKEBE. Zeros of Whittaker Function with Accurate Error Estimation by Matrix Method. In IWASEP6iSixth International Workshop on Accurate Solution of Eigenvalue Problems, May 22-25, 2006, @ Pennsylvania State University, University Park, USAj, May 2006. |
| A method to compute the zeros of Whittaker function is proposed, as an application of a theorem on eigenvalues of a certain class of infinite matrices. Also, the simplicity of the algorithm enables the implementation with ease. As a result, precise and explicit asymptotic error estimates are obtained for the approximated eigenvalues. |
Unreferred Papers
| [nasai-02:2006] |
Yoshinori MIYAZAKI, Nobuyoshi ASAI, DongSheng CAI, and Yasuhiko IKEBE. Computation of Zeros of Whittaker Function by Matrix Method (in Japanese). In In the proceedings of 2006 Annual Meeting of the Japan Society for Industrial and Applied Mathematics, pages 78.79, Sep. 2006. |
| A method to compute the zeros of Whittaker function is proposed, as an application of a theorem on eigenvalues of a certain class of infinite matrices. Also, the simplicity of the algorithm enables the implementation with ease. As a result, precise and explicit asymptotic error estimates are obtained for the approximated eigenvalues. |
Ph.D, Master, and Graduation Theses
| [kanda-02:2006] |
Toshihiro Yamamoto. Phd thesis: Sinc-Galerkin Method for Poisson Problems in One Type of Curvilinear Coordinate Domain and Sinc Solution of Boundary Integral Equations, University of Aizu, 2007. Thesis Advisor: Hidesada Kanda |
