On the Whitham Equations for the Defocusing Nonlinear Schrodinger Equation with Step Initial Data

The behavior of solutions of the finite-genus Whitham equations for the weak dispersion limit of the defocusing nonlinear Schrodinger equation is investigated analytically and numerically for piecewise-constant initial data. In particular, the dynamics of constant-amplitude initial conditions with one or more frequency jumps (i.e., piecewise linear phase) are considered. It is shown analytically and numerically that, for finite times, regions of arbitrarily high genus can be produced; asymptotically with time, however, the solution can be divided into expanding regions which are either of genus-zero, genus-one, or genus-two type, their precise arrangement depending on the specifics of the initial datum given. This behavior should be compared to that of the Korteweg-de Vries equation, where the solution is divided into regions which are either genus-zero or genus-one asymptotically. Finally, the potential application of these results to the generation of short optical pulses is discussed: The method proposed takes advantage of nonlinear compression via appropriate frequency modulation, and allows control of both the pulse amplitude and its width, as well as the distance along the fiber at which the pulse is produced     

Numerical analysis of turbulent structure in compound meandering open channel by algebraic Reynolds stress model

The turbulent flow in a compound meandering channel with a rectangular cross section is one of the most complicated turbulent flows, because the flow behaviour is influenced by several kinds of forces, including centrifugal forces, pressure‐driven forces and shear stresses generated by momentum transfer between the main channel and the flood plain. Numerical analysis has been performed for the fully developed turbulent flow in a compound meandering open‐channel flow using an algebraic Reynolds stress model. The boundary‐fitted coordinate system is introduced as a method for coordinate transformation in order to set the boundary conditions along the complicated shape of the meandering open channel. The turbulence model consists of transport equations for turbulent energy and dissipation, in conjunction with an algebraic stress model based on the Reynolds stress transport equations. With reference to the pressure–strain term, we have made use of a modified pressure–strain term. The boundary condition of the fluctuating vertical velocity is set to zero not only for the free surface, but also for computational grid points next to the free surface, because experimental results have shown that the fluctuating vertical velocity approaches zero near the free surface. In order to examine the validity of the present numerical method and the turbulent model, the calculated results are compared with experimental data measured by laser Doppler anemometer. In addition, the compound meandering open channel is clarified somewhat based on the calculated results. As a result of the analysis, the present algebraic Reynolds stress model is shown to be able to reasonably predict the turbulent flow in a compound meandering open channel. Copyright © 2005 John Wiley & Sons, Ltd.     

Improved detectability with a polymer-based trapping device in rapid HPLC analysis for ultra-low levels of bisphenol A (BPA) in environmental samples.

A new high-performance liquid chromatography (HPLC) method has been developed to detect ultra-low concentrations of bisphenol-A (BPA) (below 1 ng/L (ppt)) using column switching electrochemical detection (ECD). The results were superior to those obtained from manual pretreatment procedure with membrane stationary phase. BPA is inherently ubiquitous in the environment, including tools and solvents used for its analysis; to obtain meaningful results, therefore, the concentration of the overall BPA contamination must be below the detection limit for BPA using the analytical system. Therefore, purified water for preparing the standard BPA solution must be filtered with a hydrophobic membrane to suppress BPA background levels of contamination. In addition, we investigated methods for effectively preserving environmental water containing BPA. The addition of a small amount of ethylenediaminetetraacetic acid (EDTA) provided good recovery even after overnight storage. By employing these precautionary measures and procedures to reduce BPA contamination from the analytical procedure, we could accurately determine l(-10) ppt of BPA in environmental water samples using a column switching HPLC system.     

Photo-Absorption and photochemical decomposition of copper and alkaline-earth ß-diketonates as source gases of high-Tc superconducting films

For low-temperature deposition of oxide films relating to Bi-Sr-Ca-Cu-O superconductors, photo-absorption and -decomposition properties were examined with respect to copper and alkaline-earth ß-diketonates. It was confirmed that all ß-diketonates examined were promising as source materials for photochemical vapour deposition (photo-CVD) using a low-pressure mercury lamp, in view of their large light absorption coefficients at wavelength 254 nm. The light irradiation was effective for the formation of highly crystalline oxide films at temperatures below 600 °C. By combining two sources, Ca₂CuO₃ and SrCuO₂ films were prepared. Photo-CVD of c-axis oriented Bi₂Sr₂CuO_x film was achieved by the irradiation of ternary sources of Bi(C₆H₅)₃ and strontium and copper ß-diketonates at 500 °C.     

Major-to-ultratrace elements in bone-marrow fluid as determined by ICP-AES and ICP-MS.

The major-to-ultratrace elements in human bone-marrow fluid were determined by ICP-AES (inductively coupled plasma atomic emission spectrometry), and ICP-MS (inductively coupled plasma mass spectrometry). The bone-marrow fluid sample was centrifuged prior to acid digestion to exclude the bone piece from bone marrow, and then digested with nitric acid. As a result, 20 elements could be determined over the concentration range from 1610 microg g(-1) for Na to 0.00043 microg g(-1) for W. It was found that Fe, Zn and Sb were enriched by ca. 264-, 7- and 15-fold, respectively, in bone-marrow fluid, compared to those in human blood serum. Alkali metals (K, Rb, Cs), except for Na, were also significantly enriched in bone-marrow fluid. Furthermore, the concentrations of various elements, such as Fe, P, Al, Zn, Cu, Se, Zr, Sn, Ag and W, were significantly higher than those in open seawater.     

Precise synthesis of porphyrin array scaffolding polyisocyanides

Aryl isocyanides bearing free‐base and metallo‐porphyrins were prepared and polymerized with a Pd–Pt μ‐ethynediyl complex as the initiator to give polymers with narrow polydispersity indices. The molecular weights of the resulting polymers were precisely controlled by the initial feed ratio of the porphyrin monomer to the initiator. The UV–VIS spectra suggested that the porphyrin pendants are regularly arranged to form stacked columns. Metallo‐porphyrin polymers were also prepared by reacting free‐base porphyrin polymers with metal salts. The successive reactions of free‐base and zinc‐porphyrin monomers resulted in the formation of diblock polymers. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 585–595, 2006     

Hasse-Witt matrices of Fermat curves

Let m be an integer with m3. Let K and K be perfect fields of characteristic p and p such that (p,m)=1 and (p,m)=1, respectively. Moreover let A and A be algebraic function fields over K and K defined by x^m+y^m=a(0, ak) and x^m+y^m=a(a0 ak), respectively. Put g=(m–1)(m–2)/2. Denote by M(K,p,a) and M(K,p,a) the Hasse-Witt matrices of A and A with respect to the canonical bases of holomorphic differentials. Then we show that if p+p0(mod.m) then rank M(K,p,a)+rank M(K,p,a)=g and if pp1 (mod.m) then rank M(K,p,a)=rank M(K,p,a).