Dynamics of a Cavitating Propeller in a Water Tunnel

This study investigates the unsteady dynamics and inherent instabilities of a cavitating propeller operating in a water tunnel. First, the steady characteristics of the cavitating propeller such as the thrust coefficient are obtained by applying continuity and momentum equations to a simple one-dimensional flow tube model. The effects of the tunnel walls as well as those of the propeller operating conditions (advance ratio and cavitation number) are explored. Then the transfer matrix of the cavitating propeller (considered to be the most appropriate way to describe the dynamics of propeller) is obtained by combining the simple stream tube model with the conventional cavity model using the quasi-static cavitation compliance and mass flow gain factor representation. Finally, the surge instability of a cavitating propeller observed by Duttweiler and Brennen (2001) is examined by coupling the present model of the cavitation with a dynamic model for the water tunnel. This analysis shows that the effect of tunnel walls is to promote the surge instability

Uniform families of minimal rational curves on Fano manifolds

It is a well-known fact that families of minimal rational curves on rational homogeneous manifolds of Picard number one are uniform, in the sense that the tangent bundle to the manifold has the same splitting type on each curve of the family. In this note we prove that certain --stronger-- uniformity conditions on a family of minimal rational curves on a Fano manifold of Picard number one allow to prove that the manifold is homogeneous

The total coordinate ring of a normal projective variety

The total coordinate ring TC(X) of a normal variety is a generalization of the ring introduced and studied by Cox in connection with a toric variety. Consider a normal projective variety X with divisor class group Cl(X), and let us assume that it is a finitely generated free abelian group. We define the total coordinate ring of X to be TC(X) = oplus_{D} H^0 (X, O_X (D)), where the sum as above is taken over all Weil divisors of X contained in a fixed complete system of representatives of Cl(X). We prove that for any normal projective variety X, TC(X) is a UFD, this is a corollary of a more general theorem that is proved in the paper. (Berchtold and Haussen proved the unique factorization for a smooth variety independently.) We also prove that for X, the blow up of P^2 along a finite number of collinear points, TC(X) is Noetherian. We also give an example that TC(X) is not Noetherian but oplus_n H^0 (X, O(nD)) is Noetherian for any Weil divisor D.Comment: This is the final version that will appear in the Journal of Algebra. 11 pages. LaTe

Efficient method for simulating quantum electron dynamics under the time dependent Kohn-Sham equation

A numerical scheme for solving the time-evolution of wave functions under the time dependent Kohn-Sham equation has been developed. Since the effective Hamiltonian depends on the wave functions, the wave functions and the effective Hamiltonian should evolve consistently with each other. For this purpose, a self-consistent loop is required at every time-step for solving the time-evolution numerically, which is computationally expensive. However, in this paper, we develop a different approach expressing a formal solution of the TD-KS equation, and prove that it is possible to solve the TD-KS equation efficiently and accurately by means of a simple numerical scheme without the use of any self-consistent loops.Comment: 5 pages, 3 figures. Physical Review E, 2002, in pres

Modulation of Superconducting Properties by Ferroelectric Polarization in Confined FE-S-FE Films

We show that the electric polarization at the interface with ultrathin superconducting (S) films sandwiched between ferroelectric (FE) layers allows achievement of substantially stronger modulation of inner carrier density and superconducting transition temperature as compared to FE-S bilayers typically used in superconducting FETs. We find that not only the larger penetration depths but also the pairing symmetry should be responsible for the fact that the electric field effect in high temperature superconductors is much stronger than in conventional systems. Discussing the advantages of multilayers, we propose a novel design concept for superconducting electric field-effect transistors based on ferroelectric films.Comment: 5 pages RevTex4, 6 figure

Spin-state transition and phase separation in multi-orbital Hubbard model

We study spin-state transition and phase separation involving this transition based on the milti-orbital Hubbard model. Multiple spin states are realized by changing the energy separation between the two orbitals and the on-site Hund coupling. By utilizing the variational Monte-Carlo simulation, we analyze the electronic and magnetic structures in hole doped and undoped states. Electronic phase separation occurs between the low-spin band insulating state and the high-spin ferromagnetic metallic one. Difference of the band widths in the two orbitals is of prime importance for the spin-state transition and the phase separation.Comment: 5 pages, 5 figure