Finite element error analysis of a variational multiscale method for the Navier-Stokes equations

The paper presents finite element error estimates of a variational multiscale method (VMS) for the incompressible Navier–Stokes equations. The constants in these estimates do not depend on the Reynolds number but on a reduced Reynolds number or on the mesh size of a coarse mesh. This work is partially supported by NSF grants DMS9972622, DMS20207627 and INT9814115.     

Phase Transitions in Pure and Hybrid Hydrogels: A Fluorescence Study

Summary: Recent observations on phase transitions around the critical point showed that the critical exponents differed drastically from percolation results and classical results for pure hydrogel systems, depending on monomer concentration. In addition to pure hydrogels, the sol-gel phase transition during radical crosslinking copolymerization of acrylamide (AAm) and N-isopropylacrylamide (NIPA) hybrid was studied by using the steady state fluorescence (SSF) technique. N,N′-methylenebis(acrylamide) (BIS) and ammonium persulfate (APS) were used as crosslinker and initiator, respectively. Pyranine (trisodium 8-hydroxypyrene-1,3,6-trisulfonate acid, HPTS) was added as a fluoroprobe for monitoring the polymerization. It was observed that pyranine binds to AAm and NIPA chains on the initiation of the polymerization, thus the fluorescence spectra of the bonded pyranines shift to shorter wavelengths. Fluorescence spectra of the bonded pyranines allowed to monitor the sol-gel phase transition without disturbing the system mechanically and to test the universality of the sol-gel transition as a function of polymer concentration ratios. The observations around the gel point of PAAm-PNIPA hybrid show that the gel fraction exponent β obeyed the percolation result.     

Orientation in Nematic Liquid Crystals Doped with Orange Dyes and Effect of Carbon Nanoparticles

Some properties of nematic liquid crystal E7 doped with two disperse orange dyes used together and effect of addition of carbon nanoparticles (single walled carbon nanotube or fullerene C₆₀) on them were studied. Two dyes (disperse orange 11 and 13) having high solubility and order parameter were used as co-dopants. A notable increase in order pa-rameter was obtained comparing to that of liquid crystal doped with single dye. When carbon nanoparticles were used as dopant, a decrease in order parameter was observed at low temperatures while it increased at high temperatures. When applied voltage changed, the order parameter abruptly increased in its threshold value and saturated in higher voltages as expected. An appreciable change in textures was not observed with addition of dopants. This addition gave rise to an increase in nematic-isotropic phase transition temperatures compared with that of pure liquid crystal.     

Non-Darcian Forced Convection Flow of Viscous Dissipating Fluid over a Flat Plate Embedded in a Porous Medium

In this study, laminar boundary layer flow over a flat plate embedded in a fluid-saturated porous medium in the presence of viscous dissipation, inertia effect and suction/injection is analyzed using the Keller box finite difference method. The flat plate is assumed to be held at constant temperature. The non-Darcian effects of convection, boundary and inertia are considered. Results for the local heat transfer parameter and the local skin friction parameter as well as the velocity and temperature profiles are presented for various values of the governing parameters. The non-Darcian effects are shown to decrease the velocity and to increase the temperature. It is also shown that the local heat transfer parameter and the local skin friction parameter increase due to suction of fluid while injection reverses this trend. It is disclosed that the effect of the viscous dissipation for negative values of Ec (T _w < T _∞) is to enhance the heat transfer coefficient while the opposite is true for positive values of Ec (T _w > T _∞). The results are compared with those available in the existing literature and an excellent agreement is obtained.     

Radiation effect on MHD mixed convection flow about a permeable vertical plate

This study investigates mixed convection heat transfer about a permeable vertical plate in the presence of magneto and thermal radiation effects. The effects of the mixed convection parameter, the radiation–conduction parameter, the surface temperature parameter, the magnetic parameter and the suction/injection parameter on the local skin friction and local heat transfer parameters are presented and analyzed.     

Density functional theory design D-D-A type small molecule with 1.03 eV narrow band gap: effect of electron donor unit for organic photovoltaic solar cell

Six new low-band-gap copolymers of donor–donor–acceptor (D-D-A) architecture have been designed using density functional theory and time-dependent density functional theory methods in order to use them in organic photovoltaic cell (OPVC). Phenanthro[3,4-d:9,10-d′]bis([1,2,3]thiadiazole)-10,12-dicarbonitrile moiety has been used as an acceptor for all compounds. We insert benzo[1,2-b:4,5-b′]dithiophene and N,N-diphenylbenzo[1,2-b:4,5-b′]dithiophen-2-amine units as donor to complete designing of copolymers. In order to tuning the optical and electronic properties, we have modified the donor unit by substituted with amine, methoxyamine, N-methylenethiophen-2-amine, methoxy, alkoxy moieties. The band gap (E_g), HOMO and LUMO values and plots, open circuit voltage (V_OC) as well as optical properties have been analysed for designed copolymers. The optimised copolymers exhibit low-band-gap lying in the range of 1.03–2.24 eV. DPTD-6 copolymer presents the optimal properties to be used as an active layer due to its low E_g (1.03 eV) and a moderate V_OC (0.56 eV). Thus, OPVC based on this copolymer in bulk-heterojunction composites with [6,6]-phenyl-C₆₁-butyric acid methyl ester (PCBM) as an acceptor has been modelled. E_g and V_OC values of composite material DPTD-6:PCBM are found as 1.32 and 0.65 eV, respectively. A model band diagram has been established for OPVC, simulating the energy transfer between active layers.     

Mehmet Nadir: An amateur mathematician in Ottoman Turkey

This note summarizes the results of a recent survey of all the mathematical work of Mehmet Nadir, a Turkish amateur mathematician and professional educator who lived from 1856 to 1927 during the last years of the Ottoman Empire and the first years of the Turkish Republic. It is shown that, although working in isolated and adverse conditions, Nadir was able to establish a continuous correspondence with mathematicians in western Europe and, through his studies in number theory, obtained some results of lasting value.     

Recognition of hepatotoxic homologues of Microcystin using a combination of selective adsorption media

Microcystin, a hepatotoxin produced by cyanobacteria, was chromatographically discriminated with newly prepared selective adsorption media. Since the name Microcystin refers to up to 70 different homologues, we have developed a novel technique to prepare selective recognition sites, based on the "Fragment Imprinting Effect". The homologues of Microcystin can be individually discriminated from each other by antigen-antibody assay as well as by C18-based HPLC. This is mainly due to differences in the three dimensional structure of Microcystin homologues; however, differences in toxicity are relatively small among the homologues. Therefore we have to measure the total amount of Microcystin homologues present to determine contamination by Microcystins. We have demonstrated the first group recognition for Microcystin homologues through combination of two different selective adsorption media prepared by a fragment imprinting technique.     

Observation of a narrow charm-strange meson D(+)(sJ)(2632)-->D(+)(s)eta and D(0)K(+)

We report the first observation of a charm-strange meson D(+)(sJ)(2632) at a mass of 2632.5+/-1.7 MeV/c(2) in data from SELEX, the charm hadro-production experiment E781 at Fermilab. This state is seen in two decay modes, D(+)(s)eta and D0K+. In the D(+)(s)eta decay mode we observe a peak with 101 events over a combinatoric background of 54.9 events at a mass of 2635.4+/-3.3 MeV/c(2). There is a corresponding peak of 21 events over a background of 6.9 at 2631.5+/-2.0 MeV/c(2) in the decay mode D0K+. The decay width of this state is <17 MeV/c(2) at 90% confidence level. The relative branching ratio Gamma(D0K+)/Gamma(D(+)(s)eta) is 0.14+/-0.06. The mechanism that keeps this state narrow is unclear. Its decay pattern is also unusual, being dominated by the D(+)(s)eta decay mode.     

Respiration activity of Escherichia coli entrapped in a cone-shaped microwell and cylindrical micropore monitored by scanning electrochemical microscopy (SECM)

The metabolic activity of E. coli cells embedded in collagen gel microstructures in a cone-shaped well and in a cylindrical micropore was investigated using scanning electrochemical microscopy (SECM), based on the oxygen consumption rate and the conversion rate from ferrocyanide to ferricyanide. The analysis of the concentration profiles for oxygen and ferrocyanide afforded the oxygen consumption rate and the ferrocyanide production rate. A comparison indicated that the ferrocyanide production rates were larger than the oxygen consumption rate, and also that the rates observed in the cylindrical micropore were larger than those observed in the cone-shaped well. The ferrocyanide production rate of a single E. coli cell was calculated to be (5.4 +/- 2.6) x 10(-19) mol s(-1), using a cylindrical micropore system.