Nonlinear Boundary Layers of the Boltzmann Equation: I. Existence

 We study the half-space problem of the nonlinear Boltzmann equation, assigning the Dirichlet data for outgoing particles at the boundary and a Maxwellian as the far field. We will show that the solvability of the problem changes with the Mach number ℳ^∞ of the far Maxwellian. If ℳ^∞<−1, there exists a unique smooth solution connecting the Dirichlet data and the far Maxwellian for any Dirichlet data sufficiently close to the far Maxwellian. Otherwise, such a solution exists only for the Dirichlet data satisfying certain admissible conditions. The set of admissible Dirichlet data forms a smooth manifold of codimension 1 for the case −1<ℳ^∞<0, 4 for 0<ℳ^∞<1 and 5 for ℳ^∞>1, respectively. We also show that the same is true for the linearized problem at the far Maxwellian, and the manifold is, then, a hyperplane. The proof is essentially based on the macro-micro or hydrodynamics-kinetic decomposition of solutions combined with an artificial damping term and a spatially exponential decay weight. Received: 20 April 2002 / Accepted: 4 December 2002 Published online: 21 March 2003 Communicated by H.-T. Yau     

Applying a Mode Selector to Improve the Pulse-Compression Performance of Asymmetric-Coupled-Waveguide-Based Dispersion Compensators

An InGaAsP slab-type asymmetric-coupled-waveguide-based dispersion compensator with a mode selector has been designed and fabricated. The mode selector is necessary to select either a symmetric [with a positive group-velocity dispersion (GVD)] or antisymmetric (with a negative GVD) supermode. These supermodes exist simultaneously in the dispersion-compensation region of the device. Pulse-compression experiments were used to test the dispersion compensator, evaluating the function of the mode selector. A theoretical study of the experimental results shows that the mode selector obtains a very strong selectivity (nearly 100%) for the antisymmetric supermode.     

Linear optical switching in a FLC/waveguide composite device

A fast electrooptic modulation in a polymer waveguide using a ferroelectric liquid crystal has been proposed. In this device, the surface stabilized ferroelectric liquid crystal and the soft mode ferroelectric liquid crystal are used as an active material on the passive polymer waveguide, and electrooptic switching is realized by controlling the total reflection at the polymer waveguide-liquid crystal interface. The response time is of the order of several microseconds. The analogue electrooptic modulation in the waveguide is realized using the field induced linear molecular tilt of the electroclinic effect in the soft mode ferroelectric liquid crystal.     

A fast atom bombardment mass spectrometric analysis of crown ether complexes [1]

Analyses of crown ether complexes of alkali metal ions and characterization of the complexes formed inm-nitrobenzyl alcohol have been carried out by fast atom bombardment (FAB) mass spectrometry. By using m-nitrobenzyl alcohol as a matrix for measurements, the stoichiometry of the complexes was assessed on the basis of the observed FAB peaks. In addition, the formation of crown ether-alkali metal complexes at a 2 : 1 molar ratio was enhanced by increasing the ionic radius of the metal ion in agreement with previous observations. On these grounds, FAB mass spectrometry may provide a rapid means for investigation of the complexation behavior of crown ethers and the stoichiometry of the complexes.     

Simple and rapid determination of hydrogen peroxide using phosphine-based fluorescent reagents with sodium tungstate dihydrate.

A simple batch method for the fluorometric determination of hydrogen peroxide using phosphine-based fluorescent reagents has been developed. A rapid, mild and selective derivatization reaction was achieved by adding sodium tungstate dihydrate to the reaction mixture of hydrogen peroxide and a phosphine-based fluorescent reagent. When 4-diphenylphosphino-7-methylthio-2,1,3-benzoxadiazole was used as a reagent, the derivatization reaction was completed after 2 min at room temperature. The calibration curve was linear between 12.5 and 500 ng hydrogen peroxide in a 10 microL sample solution. This method is accurate and has potential for on-line applications.     

Enzyme-less amperometric biosensor for l-ascorbate using poly-l-histidine-copper complex as an alternative biocatalyst

A poly-l-histidine(PLH)-copper(II) complex can be used as an alternative biocatalyst in an O(2) detection-type amperometric enzyme-less l-ascorbate (AsA) sensor. The PLH-Cu(II) membrane was simply prepared by entrapping the PLH in polyacrylamide gel and subsequent treatment of the gel with CuCl(2) solution. This enzyme-less biosensor can be used over a relatively wide pH region from 4 to 11 and enables precise determination of AsA (RSD less than 3%, n=10) at pH 7.0. The fundamental performance characteristics (sensitivity, response time, and linear range) of this PLH-Cu(II)-based sensor is comparable to those of a native ascorbate oxidase-based sensor. Unfortunately, the selectivity is inherently rather low and, as a result, the response was degraded in the presence of higher concentrations (more than mM order) of quinones. However, reducing sugars caused no interference and the sensor could be used to detect AsA in some fruits and drinks. This enzyme-less sensor has excellent stability for at least 3 months of repeated analysis (more than 300 samples) without loss of ordinal activity.     

Thermodynamic Insight into the Origin of a Calix[n]arene-[60]fullerene Interaction and its Application to a Porphyrin-[60]fullerene Energy Transfer System

The calixarene-fullerene interaction,which causes only a slight change in the absorptionspectra, has been substantiated by calorimetricmeasurements: the H° values arecomparable with those obtained from the associationconstants estimated by a spectroscopic method. Furthermore, we determined the association constantbetween homooxacalix[3]arene and [60]fullerenederivatives with a porphyrin moiety by fluorescencespectra.     

First thermally responsive supramolecular polymer based on glycosylated amino acid

In materials science, a dynamic property sensitive to an environmental change (heat, light, electric current, pH, and other chemical or physical changes) is indispensable for intelligent materials. Such organic materials, however, are very limited even in conventional polymers. This paper clearly demonstrates that, regardless of the low molecular weight, a glycosylated amino acid derivative newly screened by a combinatorial method forms a macroscopic supramolecular hydrogel that reversibly swells or shrinks in response to the external temperature. Using the unique thermal response of the present hydrogel, we carried out the controlled release of DNA and the perfect removal of bisphenol A from the polluted water. Recently, advanced supramolecular polymers, in which monomers are noncovalently connected, are expected to be highly advantageous over traditional polymers because of their tunable and recyclable characteristics. The present result newly confers a dynamic feature on the supramolecular polymers, which is desirable for the sophisticated application in many fields.