The exponential power law: partial wetting kinetics and dynamic contact angles

An equation for the kinetics of partial drop spreading is proposed. This equation was empirically derived from experimental data for the spreading kinetics of partially wetting liquids in terms of the wet area versus time. The equation has the form of an exponential power law (EPL), and transforms into the well-known power law for complete wetting, when the equilibrium contact angle approaches zero. The EPL fits very well available experimental data. To lend additional support to the validity of this generalized equation, it will be demonstrated that when it is transformed to present the dynamic contact angle (DCA), it fits very well DCA experimental data for other wetting processes, such as capillary flow and tape coating.     

Crutch or Catalyst: Teachers' Beliefs and Practices Regarding Calculator use in Mathematics Instruction

This study investigated K‐12 teachers' beliefs and reported teaching practices regarding calculator use in their mathematics instruction. A survey was administered to more than 800 elementary, middle and high school teachers in a large metropolitan area to address the following questions: (a) what are the beliefs and practices of mathematics teachers regarding calculator use? and (b) how do these beliefs and practices differ among teachers in three grade bands? Factor analysis of 20 Likert scale items revealed four factors that accounted for 54% of the variance in the ratings. These factors were named Catalyst Beliefs, Teacher Knowledge, Crutch Beliefs, and Teacher Practices. Compared to elementary teachers, high school teachers were significantly higher in their perception of calculator use as a catalyst in mathematics instruction. However, the higher the grade level of the teacher, the higher the mean score on the perception that calculator use may be a way of getting answers without understanding mathematical processes. The mean scores for teachers in all three grade bands indicated agreement that students can learn mathematics through calculator use and using calculators in instruction will lead to better student understanding and make mathematics more interesting. The survey results shed light on teachers' self reported beliefs, knowledge, and practices in regard to consistency with elements of the National Council of Teachers of Mathematics Principles and Standards for School Mathematics (2000) technology principle and the NCTM use of technology position paper (2003). This study extended previous research on teachers' beliefs regarding calculator use in classrooms by examining and comparing the results of teacher surveys across three grade bands.     

Cell docking inside microwells within reversibly sealed microfluidic channels for fabricating multiphenotype cell arrays

We present a soft lithographic method to fabricate multiphenotype cell arrays by capturing cells within an array of reversibly sealed microfluidic channels. The technique uses reversible sealing of elastomeric polydimethylsiloxane (PDMS) molds on surfaces to sequentially deliver various fluids or cells onto specific locations on a substrate. Microwells on the substrate were used to capture and immobilize cells within low shear stress regions inside channels. By using an array of channels it was possible to deposit multiple cell types, such as hepatocytes, fibroblasts, and embryonic stem cells, on the substrates. Upon formation of the cell arrays on the substrate, the PDMS mold could be removed, generating a multiphenotype array of cells. In addition, the orthogonal alignment and subsequent attachment of a secondary array of channels on the patterned substrates could be used to deliver fluids to the patterned cells. The ability to position many cell types on particular regions within a two dimensional substrate could potentially lead to improved high-throughput methods applicable to drug screening and tissue engineering.     

Determination of Mg,Al, P,Cu and Mn in biological fluids by neutron activation analysis

Thermal and epithermal neutron activation analysis has been applied to determine the concentrations of magnesium, aluminium, phosphorus, copper and manganese in two biological fluids: blood serum and market milk. Both epithermal neutron irradiation and radiochemical separation (a chromatographic column of HAP) were used to get rid of the interferences from 24-Na. Strongly acidic solutions of the irradiated samples were passed through the columns of HAP, where sodium was completely adsorbed while, Al, Cu, Mg and Mn were eluted with an efficiency of 99±1%. Since both Al and P were determined through the formation of²⁸Al (2.24 min) thermal and epithermal neutron activation have been applied in order to determine the contribution of each radionuclide to²⁸Al activity. The determination of Mg, Al and P in milk samples was done instrumentally, whereas in the case of blood serum with higher concentration of Na, a radiochemical separation is essential in both cases. The concentrations of Al, Cu, Mg, Mn and P in blood serum and market milk were found to be 0.24±0.02 and 1.85±0.09 g Al/ml, 1.35±0.04 and 0.068±0.005 g Cu/ml, 22.9±1 and 98.9±8.6 g Mg/ml, 22±3 and 16±2 ng Mn/ml and 167±13 and 865±32 g P/ml, respectively.     

Determination of cobalt in solid matrices by neutron activation analysis

The concentration of cobalt in 2 solid matrices was determined by neutron activation analysis (NAA) using standard solutions which were prepared by dissolving pure cobalt in nitric acid. The matrices assayed were a cobalt-aluminium wire and an iron foil and the respective Co concentrations found were 0.488% and 0.138%. Both solid materials can equally be used as standard references of cobalt in NAA. Subcadmium and epicadmium neutron fluxes in the reactor core were determined using Co?Al and Au?Al alloy wires. Very good agreement was obtained for all irradiation configurations of the target monitors cobalt and gold.     

Preparation and reactions of [2,2-bis(carbethoxy)propyl]cyclopentadienyldicarbonyliron

Although

, (Fp  η-C₅H₅Fe(CO)₂) (I) is stable and characterizable, the lower homologue FpCH₂CH(CO₂CH₃)₂ (II) is not; this we attribute to a facile elimination reaction resulting from the relatively acidic β-hydrogen of II. Formation of I from Fp^? and XCH₂CE₂CH₃ (X  Br, Cl; E  CO₂CH₂CH₃) and cleavage of its FeC bonds (using H⁺, Br₂, Ce^IV and Hg^II) occur without major amounts of ester group migrations, even though ·CH₂CE₂CH₃ radicals are involved in some of these reactions.     

Determination of magnesium in botanical reference materials by instrumental neutron activation analysis

Instrumental neutron activation analysis (INAA) was applied to the rapid determination of magnesium in the botanical reference materials Beech Leaves-100 and Spruce Needles-101. The magnesium content was quantitatively determined by measuring the gamma-ray photopeak at 1014 keV of the short-lived radionuclide²⁷Mg (9.46 m). The magnesium concentrations in the two materials were found to be 834.6±50.2 g·g^–1 dry weight and 618.6±36.2 g·g^–1, respectively. When assaying a 0.1 g sample under the same experimental conditions the limit of detection is 30 g of Mg.Work carried out at Risø National Laboratory, Isotopes Division, DK-4000 Roskilde, Denmark.     

Quantum walk with jumps

We analyze a special class of 1-D quantum walks (QWs) realized using optical multi-ports. We assume non-perfect multi-ports showing errors in the connectivity, i.e. with a small probability the multi-ports can connect not to their nearest neighbor but to another multi-port at a fixed distance – we call this a jump. We study two cases of QW with jumps where multiple displacements can emerge at one timestep. The first case assumes time-correlated jumps (static disorder). In the second case, we choose the positions of jumps randomly in time (dynamic disorder). The probability distributions of position of the QW walker in both instances differ significantly: dynamic disorder leads to a Gaussian-like distribution, while for static disorder we find two distinct behaviors depending on the parity of jump size. In the case of even-sized jumps, the distribution exhibits a three-peak profile around the position of the initial excitation, whereas the probability distribution in the odd case follows a Laplace-like discrete distribution modulated by additional (exponential) peaks for long times. Finally, our numerical results indicate that by an appropriate mapping a universal functional behavior of the variance of the long-time probability distribution can be revealed with respect to the scaled average of jump size.