An upstream flux‐splitting finite‐volume scheme for 2D shallow water equations

An upstream flux‐splitting finite‐volume (UFF) scheme is proposed for the solutions of the 2D shallow water equations. In the framework of the finite‐volume method, the artificially upstream flux vector splitting method is employed to establish the numerical flux function for the local Riemann problem. Based on this algorithm, an UFF scheme without Jacobian matrix operation is developed. The proposed scheme satisfying entropy condition is extended to be second‐order‐accurate using the MUSCL approach. The proposed UFF scheme and its second‐order extension are verified through the simulations of four shallow water problems, including the 1D idealized dam breaking, the oblique hydraulic jump, the circular dam breaking, and the dam‐break experiment with 45° bend channel. Meanwhile, the numerical performance of the UFF scheme is compared with those of three well‐known upwind schemes, namely the Osher, Roe, and HLL schemes. It is demonstrated that the proposed scheme performs remarkably well for shallow water flows. The simulated results also show that the UFF scheme has superior overall numerical performances among the schemes tested. Copyright © 2005 John Wiley & Sons, Ltd.     

Finite‐volume multi‐stage schemes for shallow‐water flow simulations

A finite‐volume multi‐stage (FMUSTA) scheme is proposed for simulating the free‐surface shallow‐water flows with the hydraulic shocks. On the basis of the multi‐stage (MUSTA) method, the original Riemann problem is transformed to an independent MUSTA mesh. The local Lax–Friedrichs scheme is then adopted for solving the solution of the Riemann problem at the cell interface on the MUSTA mesh. The resulting first‐order monotonic FMUSTA scheme, which does not require the use of the eigenstructure and the special treatment of entropy fixes, has the generality as well as simplicity. In order to achieve the high‐resolution property, the monotonic upstream schemes for conservation laws (MUSCL) method are used. For modeling shallow‐water flows with source terms, the surface gradient method (SGM) is adopted. The proposed schemes are verified using the simulations of six shallow‐water problems, including the 1D idealized dam breaking, the steady transcritical flow over a hump, the 2D oblique hydraulic jump, the circular dam breaking and two dam‐break experiments. The simulated results by the proposed schemes are in satisfactory agreement with the exact solutions and experimental data. It is demonstrated that the proposed FMUSTA schemes have superior overall numerical accuracy among the schemes tested such as the commonly adopted Roe and HLL schemes. Copyright © 2007 John Wiley & Sons, Ltd.     

Silicon microlens structures fabricated by scanning-probe gray-scale oxidation

We report on the micromachining of silicon microlens structures by use of scanning-probe gray-scale anodic oxidation along with dry anisotropic etching. Convex, concave, and arbitrarily shaped silicon microlenses with diameters as small as 2 microm are demonstrated. We also confirm the high fidelity of pattern transfer between the probe-induced oxides and the etched silicon microlens structures. Besides the flexibility, the important features of scanning-probe gray-scale anodic oxidation are small pixel size and pitch (of the order of tens of nanometers), an unlimited number of gray-scale levels, and the possibility of creating arbitrarily designed microlens structures with exquisite precision and resolution. With this approach, refractive, diffractive, and hybrid microlens arrays can be developed to create innovative optical components.     

Covalent Interaction of Ru(terpy)(tmephen)Cl+ with DNA: A Potential Ruthenium‐Based Anticancer Drug

The use of ruthenium complexes in antitumor therapy was launched two decades ago. In view of their low toxicity and good selectivity for solid tumor metastasis, ruthenium complexes have great potential as alternative drugs to cisplatin in cancer chemotherapy. A series of monochloro ruthenium complexes, Ru(terpy) (NN)Cl⁺ (NN, bidentate nitrogen ligand), containing different electron‐donating groups were prepared. The reactivity towards the formation of Ru‐DNA adduct were revealed by gel mobility shift assay. Their DNA binding sites of Ru(terpy)(tmephen)Cl⁺ were located predominantly at the purine residues i.e., guanine and adenine, by terminating DNA elongation in vitro using PCR and primer extension techniques. Surprisingly, the ability of Ru(terpy)(tmephen)Cl⁺ to inhibit cell growth was found to be approximately two times better than that of a known cross‐linking agent, Ru(bpy)₂Cl₂. Therefore, the increase in liability of the chloro ligand was demonstrated to improve the reactivity of these ruthenium complexes towards the covalent bond formation in Ru‐DNA adducts and result also in a significant inhibition of cell growth. Based on our results, these ruthenium complexes modified with electron‐rich groups provide new consideration in the tune of ruthenium‐based drugs in cancer chemotherapy.     

Low loss second‐order non‐linear optical crosslinked polymers based on a phosphorus‐containing maleimide

A series of crossslinked organic and organic/inorganic polymers based on maleimide chemistry have been investigated for second‐order non‐linear optical (NLO) materials with excellent thermal stability and low optical loss. Two reactive chromophores (maleimide‐containing azobenzene dye and alkoxysilane‐containing azobenzene dye) were incorporated into a phosphorus‐containing maleimide polymer, respectively. The selection of the phosphorus‐containing maleimide polymer as the polymeric matrices provides enhanced solubility and thermal stability, and excellent optical quality. Moreover, a full interpenetrating network (IPN) was formed through simultaneous addition reaction of the phosphorus‐containing maleimide, and sol‐gel process of alkoxysilane dye (ASD). Atomic force microscopy (AFM) results indicate that the inorganic networks are distributed uniformly throughout the polymer matrices on a nano‐scale. The silica particle sizes are well under 100 nm. Using in situ contact poling, the r₃₃ coefficients of 2.2–17.0 pm/V have been obtained for the optically clear phosphorus‐containing NLO materials. Excellent temporal stability (100°C) and low optical loss (0.99–1.71 dB/cm; 830 nm) were also obtained for these phosphorus‐containing materials. Copyright © 2004 John Wiley & Sons, Ltd.