Realizing colloidal artificial ice on arrays of optical traps

We demonstrate how a colloidal version of artificial ice can be realized on optical trap lattices. Using numerical simulations, we show that this system obeys the ice rules and that for strong colloid-colloid interactions, an ordered ground state appears. We show that the ice-rule ordering can occur for systems with as few as 24 traps and that the ordering transition can be observed at constant temperature by varying the barrier strength of the traps.     

On the 1/3–2/3 Conjecture

Let (P, ≤) be a finite poset (partially ordered set), where P has cardinality n. Consider linear extensions of P as permutations x₁x₂?x_n in one-line notation. For distinct elements x, y ∈ P, we define ?(x ? y) to be the proportion of linear extensions of P in which x comes before y. For \(0\leq \alpha \leq \frac {1}{2}\), we say (x, y) is an α-balanced pair if α ≤ ?(x ? y) ≤?1 ? α. The 1/3–2/3 Conjecture states that every finite partially ordered set which is not a chain has a 1/3-balanced pair. We make progress on this conjecture by showing that it holds for certain families of posets. These include lattices such as the Boolean, set partition, and subspace lattices; partial orders that arise from a Young diagram; and some partial orders of dimension 2. We also consider various posets which satisfy the stronger condition of having a 1/2-balanced pair. For example, this happens when the poset has an automorphism with a cycle of length 2. Various questions for future research are posed.     

Defect chemistry, surface structures, and lithium insertion in anatase TiO2

Atomistic simulation techniques are used to investigate the defect properties of anatase TiO(2) and Li(x)TiO(2) both in the bulk and at the surfaces. Interatomic potential parameters are derived that reproduce the lattice constants of anatase, and the energies of bulk defects and surface structures are calculated. Reduction of anatase involving interstitial Ti is found to be the most favorable defect reaction in the bulk, with a lower energy than either Frenkel or Schottky reactions. The binding energies of selected defect clusters are also presented: for the Ti(3+)-Li(+) defect cluster, the binding energy is found to be approximately 0.5 eV, suggesting that intercalated Li ions stabilize conduction band electrons. The Li ion migration path is found to run between octahedral sites, with an activation energy of 0.45-0.65 eV for mole fractions of lithium in Li(x)TiO(2) of x < or = 0.1. The calculated surface energies are used to predict the crystal morphology, which is found to be a truncated bipyramid in which only the (101) and (001) surfaces are expressed, in accord with the available microscopy data. Calculations of defect energies at the (101) surface suggest that single Ti(3+) defects and neutral Ti(3+)-Li(+) pairs tend to segregate to the surface.     

Influence of cation on charge recombination in dye-sensitized TiO2 electrodes

The reaction of a dye cation recombining with an electron in TiO(2), in the presence of Li(+), Ca(2+), and TBA(+) cations, was studied with laser-induced transient absorption measurements. The active cations, Li(+) and Ca(2+), shorten the dye cation lifetime on sensitized TiO(2) but not ZnO electrodes. By combining the absorbance measurements of the dye cation with simultaneous measurements of the current transient, the contribution of the recombination reaction to the current is identified. Furthermore, classical porous electrode theory is used to quantify the behavior of the heterogeneous electrode, and in doing so, the processes contributing to photoinduced current are identified as Helmholtz layer charging, porous electrode charging, recombination reactions, and surface diffusion of the active cations. The rate of charge recombination is proportional to the concentration of initially deposited active cations. The effect of water on the recombination rate and the current is also observed.     

Synthesis, characterization, and tunable optical properties of hollow gold nanospheres

Nearly monodisperse hollow gold nanospheres (HGNs) with tunable interior and exterior diameters have been synthesized by sacrificial galvanic replacement of cobalt nanoparticles. It is possible to tune the peak of the surface plasmon band absorption between 550 and 820 nm by carefully controlling particle size and wall thickness. Cobalt particle size is tunable by simultaneously changing the concentration of sodium borohydride and sodium citrate, the reducing and capping agent, respectively. The thickness of the gold shell can be varied by carefully controlling the addition of gold salt. With successful demonstration of ensemble as well as single HGN surface-enhanced Raman scattering, these HGNs have shown great potential for chemical and biological sensing applications, especially those requiring nanostructures with near-IR absorption.     

The negative sign and exponential expressions: Unveiling students’ persistent errors and misconceptions

The purpose of this study was to determine whether or not certain errors made when simplifying exponential expressions persist as students progress through their mathematical studies. College students enrolled in college algebra, pre-calculus, and first- and second-semester calculus mathematics courses were asked to simplify exponential expressions on an assessment. Persistent errors are identified and characterized. Using quantitative and qualitative methods, we found that the concept of negativity played a prominent role in most of the students’ errors. We theorize that an underdeveloped conception of additive and multiplicative inverses is the root of these errors.     

Radial basis function (RBF)‐based parametric models for closed and open curves within the method of regularized stokeslets

The method of regularized Stokeslets (MRS) is a numerical approach using regularized fundamental solutions to compute the flow due to an object in a viscous fluid where inertial effects can be neglected. The elastic object is represented as a Lagrangian structure, exerting point forces on the fluid. The forces on the structure are often determined by a bending or tension model, previously calculated using finite difference approximations. In this paper, we study spherical basis function (SBF), radial basis function (RBF), and Lagrange–Chebyshev parametric models to represent and calculate forces on elastic structures that can be represented by an open curve, motivated by the study of cilia and flagella. The evaluation error for static open curves for the different interpolants, as well as errors for calculating normals and second derivatives using different types of clustered parametric nodes, is given for the case of an open planar curve. We determine that SBF and RBF interpolants built on clustered nodes are competitive with Lagrange–Chebyshev interpolants for modeling twice‐differentiable open planar curves. We propose using SBF and RBF parametric models within the MRS for evaluating and updating the elastic structure. Results for open and closed elastic structures immersed in a 2D fluid are presented, showing the efficacy of the RBF–Stokeslets method. Copyright © 2015 John Wiley & Sons, Ltd.     

Novel tricyclic diamines 2. Synthesis of 1,7-diazaisoadamantane, 1,5-diazaisoadamantane and 1,6-diazahomobrendane

Three novel tricyclic diamines (1,7-diazaisoadamantane, 1,5-diazaisoadamantane and 1,6-diazahomobrendane) were prepared. A flexible synthetic strategy was employed which used flat, aromatic azaindoles as the starting materials. The requisite azaindoles were prepared by a tandem Sonogashira coupling/intramolecular cyclization reaction. Ring saturation, appropriate functionalization and intramolecular alkylation provided the three novel tricyclic diamines cores.     

A miniaturized glucocorticoid receptor translocation assay using enzymatic fragment complementation evaluated with qHTS

Nuclear translocation is an important step in glucocorticoid receptor (GR) signaling and assays that measure this process allow the identification of nuclear receptor ligands independent of subsequent functional effects. To facilitate the identification of GR-translocation agonists, an enzyme fragment complementation (EFC) cell-based assay was scaled to a 1536-well plate format to evaluate 9,920 compounds using a quantitative high throughput screening (qHTS) strategy where compounds are assayed at multiple concentrations. In contrast to conventional assays of nuclear translocation the qHTS assay described here was enabled on a standard luminescence microplate reader precluding the requirement for imaging methods. The assay uses beta-galactosidase alpha complementation to indirectly detect GR-translocation in CHO-K1 cells. 1536-well assay miniaturization included the elimination of a media aspiration step, and the optimized assay displayed a Z' of 0.55. qHTS yielded EC(50) values for all 9,920 compounds and allowed us to retrospectively examine the dataset as a single concentration-based screen to estimate the number of false positives and negatives at typical activity thresholds. For example, at a 9 microM screening concentration, the assay showed an accuracy that is comparable to typical cell-based assays as judged by the occurrence of false positives that we determined to be 1.3% or 0.3%, for a 3sigma or 6sigma threshold, respectively. This corresponds to a confirmation rate of approximately 30% or approximately 50%, respectively. The assay was consistent with glucocorticoid pharmacology as scaffolds with close similarity to dexamethasone were identified as active, while, for example, steroids that act as ligands to other nuclear receptors such as the estrogen receptor were found to be inactive.     

Evaluating reproducibility and similarity of mass and intensity data in complex spectra—applications to tubulin

We present a data processing approach based on the spectral dot product for evaluating spectral similarity and reproducibility. The method introduces 95% confidence intervals on the spectral dot product to evaluate the strength of spectral correlation; it is the only calculation described to date that accounts for both the non-normal sampling distribution of the dot product and the number of peaks the spectra have in common. These measures of spectral similarity allow for the recursive generation of a consensus spectrum, which incorporates the most consistent features from statistically similar replicate spectra. Taking the spectral dot product and 95% confidence intervals between consensus spectra from different samples yields the similarity between these samples. Applying the data analysis scheme to replicates of brain tubulin CNBr peptides enables a robust comparison of tubulin isotype expression and post-translational modification patterns in rat and cow brains.