Abstract:
The micromixer, which has a rotor with a curved channel, is studied experimentally. The secondary flow in a curved channel of rectangular cross-section is investigated using PIV (Particle Image Velocimetry) and LIF (Laser Induced Fluorescence) methods. Two walls of the channel (the inner and top walls) rotate around the center of curvature and a pressure gradient is imposed in the direction of the exit of the channel. The non-dimensional channel curvature δ=a/R is taken to be about 0.1, where 2a is the width of the channel, R the curvature radius of the channel. Other non-dimensional parameters concerned are the Dean number De=Reδ^{1/2}, the Reynolds number Re=qd_{h}/v, where q is the mean flow velocity in the channel axis direction, ν the kinematic viscosity, dh the hydraulic diameter of the channel, and the Taylor number Tr=2(2δ)^{1/2}Ωa^{2}/(δv), where Ω is the angular velocity of the rotor. Photographs of the flow in a cross-section at 180° downstream from the curved channel entrance are taken by changing the flux (De) at a constant rotational speed (Tr) of the channel walls. It is found that good mixing performance is obtained in the case of De≤0.1|Tr| and for that case secondary flows show chaotic behaviors. And then we have confirmed the occurrence of reversal of the mean axial flow.

Abstract:
Chaotic mixing in a curved-square channel flow is studied experimentally and numerically. Two walls of the channel (inner and top walls) rotate around the center of curvature and a pressure gradient is imposed in the direction toward the exit of the channel. This flow is a kind of Taylor-Dean flows. There are two parameters dominating the flow, the Dean number De (∝ the pressure gradient or the Reynolds number) and the Taylor number Tr (∝ the angular velocity of the wall rotation). In the present paper, we analyze the physical mechanism of chaotic mixing in the Taylor-Dean flow by comparing experimental and numerical results. We produced a micromixer model of the curved channel several centimeters long with square cross section of a few millimeters side. The secondary flow was measured using laser induced fluorescence (LIF) method to examine secondary flow characteristics. We also performed three-dimensional numerical simulations for the exactly same configuration as the experimental system to study the mechanism of chaotic mixing. It is found that good mixing performance is achieved for the case of De ≤ 0.1Tr, and that mixing efficiency changes according to the difference in inflow conditions. The flow is studied both experimentally and numerically, and both results agree with each other very well.

Abstract:
Chaotic mixing in three different types of curved-rectangular channels flow has been studied experimentally and numerically. Two walls of the channel (inner and top walls) rotate around the center of curvature and a pressure gradient are imposed in the direction toward the exit of the channel. This flow is a kind of Taylor-Dean flow. There are two parameters dominating the flow, the Dean number De (∝ the pressure gradient or the Reynolds number) and the Taylor number Tr (∝ the angular velocity of the wall rotation). In this paper, we analyze the physical mechanism of chaotic mixing in the Taylor-Dean flow by comparing experimental results and numerical ones. We produced three micromixer models of the curved channel, several centimeters long, with rectangular cross-section of a few millimeters side. The secondary flow is measured using laser induced fluorescence (LIF) method to examine secondary flow characteristics. Also we performed three-dimensional numerical simulations with the open source CFD solver, OpenFOAM, for the same configuration as the experimental system to study the mechanism of chaotic mixing. It is found that good mixing performance is obtained in the case of De ≤ 0.1 Tr, and it becomes more remarkable when the aspect ratio tends to large. And it is found that the mixing efficiency changes according to the aspect ratio and inflow condition.

Abstract:
In all types of mice, including germfree (GF) animals, the genes most affected by two-week oral JTX treatment were the type 1 interferon (IFN)-related genes including Stat1, Isgf3g and Irf7, which play a critical role in the feedback loop of IFN-α production cascade. In IQI specific pathogen free (SPF) mice JTX increased the steady state level of the expression of IFN-related genes, but had the opposite effect in IQI GF and BALB/c SPF mice. Promoter analysis suggests that tandem repeated $IRFF (the promoter sequences for interferon regulatory factors) may be a primary target for JTX action. Pre-treatment of JTX accelerated the effects of an oral IFN "inducer" 2-amino-5-bromo-6-methyl-4-pyrimidinol (ABMP) (up-regulation of IFN-α production in IQI strain and down-regulation in BALB/c mice), which is in good accordance with the effect of JTX on gene expression of type 1 IFN-related genes.Microarray analysis revealed that the target of JTX might be the transcription machinery regulating the steady-state level of genes involved in the ISGF3-IRF7 cascade, whose effect is bi-directional in a strain- and microbiota-dependent manner.In Japan, certain traditional herbal medicines (Kampo medicines), which comprise hot water extracts from a mixture of medicinal plants, have been widely used as ethical drugs and become integrated into the modern medical system [1-4]. These traditional medicines are manufactured under strict scientific quality control and are covered by public health insurance. A large amount of clinical and basic research on Kampo medicines has been performed, including more than 10 multicenter, placebo-controlled, double-blind studies.We investigated the effects of Juzentaihoto (JTX) in this study. JTX is a well known Kampo medicine that comprises 10 different herbs; Ginseng radix, Astragali radix, Angelicae radix, Rehmanniae radix, Atractylodis lanceae rhizoma, Cinnamomi cortex, Poria, Paeoniae radix, Ligustici rhizoma and Glycyrrhizae radix. JTX has been used

Abstract:
Each orientation on a Dynkin graph $\Gamma$ defines a cone (in a certain real configuration space) which is further divided into chambers. We enumerate the number of chambers for two particular cones, which are called the pricipal $\Gamma$-cones and are attached to bipartite decompositions of $\Gamma$, by a use of hook length formulae. We prove that these pricipal cones are characterized by the maximality of the number of chambers in them.

Abstract:
The Dirichlet series associated to the eta-product $\eta(7\tau)^7/\eta(\tau)$ decomposes uniquely into the difference of two L-functions with Euler products. This expression gives a new proof of the positivity of the Fourier coefficients of the eta-product.

Abstract:
We introduce the {\it growth partition function} $Z_{\Gamma,G}(t)$ associate with any cancellative infinite monoid $\Gamma$ with a finite generator system $G$. It is a power series in $t$ whose coefficients lie in integral Lie-like space $\mathcal{L}_{\Z}(\Gamma,G)$ in the configuration algebra associated with the Cayley graph $(\Gamma,G)$. We determine them for homogeneous monoids admitting left greatest common divisor and right common multiple. Then, for braid monoids and Artin monoids of finite type, using that formula, we explicitly determine their limit partition functions $\omega_{\Gamma,G}$.

Abstract:
We develop an elementary theory of divisibility on the monoid $M(n,R)^\times$ consisting of all square matrices of size $n\ge 1$ of non-zero determinants with coefficients in a principal ideal domain $R$. In particular, we show that any finite subset of the monoid has the least left common multiple up to a right unit factor. When $R$ is residue finite, we consider a signed generating series, called the skew growth function, of least common multiples of finite right equivalence classes of irreducible elements. As an elementary application of the divisibility theory, we show that the skew-growth function decomposes into Euler products.

Abstract:
This is a report on the recent work "Mirror symmetry for exceptional unimodular singularities" joint with Changzheng Li, Si Li and Yefeng Shen.

Abstract:
We show the coherence of the direct images of the relative De Rham complex relative to a flat holomorphic map with suitable boundary conditions.