The decay of 91 min As

The energies and relative intensities of γ-rays following the β-decay of ⁷⁸As (and ⁷⁶As) to levels in ⁷⁸Se (and ⁷⁶Se) have been measured using an 8 cm³ Ge(Li) spectrometer. The β-decay of ⁷⁸As has been measured using a superconducting magnet beta-ray spectrometer with two 3 mm thick Si(Li) detectors. These data plus β-γ and γ-γ coincidence results have been used to construct a level scheme with 18 excited levels in ⁷⁸Se. The half-life of ⁷⁸As was measured to be 90.7±0.2 min.     

Influence of the group-velocity on the pulse propagation in 1D silicon photonic crystal waveguides

We present a detailed analysis of the influence of the group velocity (GV) on the dynamics of optical pulses upon their propagation in one-dimensional photonic crystal waveguides (PhCW). The theoretical model used in our analysis incorporates the linear optical properties of the PhCW (GV dispersion and optical losses), free-carrier (FC) effects (FC dispersion and FC-induced optical losses) and nonlinear optical effects (Kerr nonlinearity and two-photon absorption). Our analysis shows that, unlike the case of uniform waveguides, the GV of the pulse, dispersion coefficients, and the waveguide nonlinear coefficient are periodic functions with respect to the propagation distance. We also demonstrate that linear and nonlinear effects depend on the group velocity, v _g , as v_g^-1v_{g}^{-1} and v_g^-2v_{g}^{-2}, respectively.     

Concentrating membrane proteins using asymmetric traps and AC electric fields

Membrane proteins are key components of the plasma membrane and are responsible for control of chemical ionic gradients, metabolite and nutrient transfer, and signal transduction between the interior of cells and the external environment. Of the genes in the human genome, 30% code for membrane proteins (Krogh et al. J. Mol. Biol.2001, 305, 567). Furthermore, many FDA-approved drugs target such proteins (Overington et al. Nat. Rev. Drug Discovery 2006, 5, 993). However, the structure-function relationships of these are notably sparse because of difficulties in their purification and handling outside of their membranous environment. Methods that permit the manipulation of membrane components while they are still in the membrane would find widespread application in separation, purification, and eventual structure-function determination of these species (Poo et al. Nature 1977, 265, 602). Here we show that asymmetrically patterned supported lipid bilayers in combination with AC electric fields can lead to efficient manipulation of charged components. We demonstrate the concentration and trapping of such components through the use of a "nested trap" and show that this method is capable of yielding an approximately 30-fold increase in the average protein concentration. Upon removal of the field, the material remains trapped for several hours as a result of topographically restricted diffusion. Our results indicate that this method can be used for concentrating and trapping charged membrane components while they are still within their membranous environment. We anticipate that our approach could find widespread application in the manipulation and study of membrane proteins.     

Dimethylalkoxygallanes: monomeric versus dimeric gas-phase structures

The molecular structures of the vapors produced on heating dimethylalkoxygallanes of the type [Me(2)Ga(OR)](2) have been determined by gas electron diffraction and ab initio molecular orbital calculations. In the solid state [Me(2)Ga(OCH(2)CH(2)NMe(2))](2) (1) and [Me(2)Ga(OCH(2)CH(2)OMe)](2) (2) adopt dimeric structures, although only the monomeric forms [Me(2)Ga(OCH(2)CH(2)NMe(2))] (1a) and [Me(2)Ga(OCH(2)CH(2)OMe)] (2a) were observed in the gas phase. For comparison the structure of the vapor produced on heating [Me(2)Ga(O(t)Bu)](2) (3) was also studied by gas electron diffraction. In contrast to 1 and 2, compound 3 is dimeric in the gas phase, as well as in the solid state. The gas-phase structures of 1a and 2a exhibit five-membered rings formed by a dative bond between Ga and the donor atom (N or O) from the donor-functionalized alkoxide. In 3 there is no possibility of a monomeric structure being stabilized by the formation of such a dative bond since only a monofunctional alkoxide is present in the molecule.     

Sequential Power-Dependence Theory

Existing methods for predicting resource divisions in laboratory exchange networks do not take into account the sequential nature of the experimental setting. We extend network exchange theory by considering sequential exchange. We prove that Sequential Power-Dependence Theory—unlike Power-Dependence Theory and most other exchange theories—has a unique point prediction for resource divisions in every network, and we show that these point predictions fare well in comparison to those from established theories.     

Confinement, average forces, and the Ehrenfest theorem for a one-dimensional particle

The topics of confinement, average forces, and the Ehrenfest theorem are examined for a particle in one spatial dimension. Two specific cases are considered: (i) A free particle moving on the entire real line, which is then permanently confined to a line segment or ‘a box’ (this situation is achieved by taking the limit V ₀?→?∞ in a finite well potential). This case is called ‘a particle-in-an-infinite-square-well-potential’. (ii) A free particle that has always been moving inside a box (in this case, an external potential is not necessary to confine the particle, only boundary conditions). This case is called ‘a particle-in-a-box’. After developing some basic results for the problem of a particle in a finite square well potential, the limiting procedure that allows us to obtain the average force of the infinite square well potential from the finite well potential problem is re-examined in detail. A general expression is derived for the mean value of the external classical force operator for a particle-in-an-infinite-square-well-potential, $\hat{F}$ . After calculating similar general expressions for the mean value of the position ( $\hat{X}$ ) and momentum ( $\hat{P}$ ) operators, the Ehrenfest theorem for a particle-in-an-infinite-square-well-potential (i.e., $\mathrm{d}\langle\hat{X}\rangle/\mathrm{d}t=\langle\hat{P}\rangle/M$ and $\mathrm{d}\langle\hat{P}\rangle/\mathrm{d}t=\langle\hat{F}\rangle$ ) is proven. The formal time derivatives of the mean value of the position ( $\hat{x}$ ) and momentum ( $\hat{p}$ ) operators for a particle-in-a-box are re-introduced. It is verified that these derivatives present terms that are evaluated at the ends of the box. Specifically, for the wave functions satisfying the Dirichlet boundary condition, the results, $\mathrm{d}\langle\hat{x}\rangle/\mathrm{d}t=\langle\hat{p}\rangle/M$ and $\mathrm{d}\langle\hat{p}\rangle/\mathrm{d}t=\mathrm{b.t.}+\langle\hat{f}\rangle$ , are obtained where b.t. denotes a boundary term and $\hat{f}$ is the external classical force operator for the particle-in-a-box. Thus, it appears that the expected Ehrenfest theorem is not entirely verified. However, by considering a normalized complex general state that is a combination of energy eigenstates to the Hamiltonian describing a particle-in-a-box with v(x)?=?0 ( $\Rightarrow\hat{f}=0$ ), the result that the b.t. is equal to the mean value of the external classical force operator for the particle-in-an-infinite-square-well-potential is obtained, i.e., $\mathrm{d}\langle\hat{p}\rangle/\mathrm{d}t$ is equal to $\langle\hat{F}\rangle$ . Moreover, the b.t. is written as the mean value of a quantity that is called boundary quantum force, f _B. Thus, the Ehrenfest theorem for a particle-in-a-box can be completed with the formula $\mathrm{d}\langle\hat{p}\rangle/\mathrm{d}t=\langle{{f_\mathrm{B}}}\rangle$ .     

Thermodynamic and transport properties of nitrogen and butane mixtures

A force field has been developed to describe the phase behaviour, interfacial, and transport properties of nitrogen and hydrocarbon mixtures under conditions relevant to those found in the high pressure extraction of oil from underground reservoirs. A Gibbs ensemble Monte Carlo method is used to parametrize intermolecular potentials for the pure components by matching experimental and simulated liquid and vapour coexisting densities. Also the surface tension, diffusion coefficient and shear viscosity of nitrogen and its mixtures with butane have been determined. The latter properties were obtained by canonical molecular dynamics simulations. The diffusion coefficient and shear viscosity were calculated by a Green-Kubo method. Results for pure nitrogen are given for temperatures ranging from 70 K to 110K. For mixtures of nitrogen with butane, results are presented at 339.4 K and 380.2 K. Good agreement is found between the results of simulations and available experimental data.     

A wavelet,fourier, and PCA data analysis pipeline: application to distinguishing mixtures of liquids

Using a new optical engineering technique for the "fingerprinting" of beverages and other liquids, we study and evaluate a range of features. The features are based on resolution scale, invariant frequency information, entropy, and energy. They allow mixtures of beverages to be very precisely placed in principal component plots used for the data analysis. To show this we make use of data sets resulting from optical/near-infrared and ultrasound sensors. Our liquid "fingerprinting" is a relatively open analysis framework in order to cater for different practical applications, in particular, on one hand, discrimination and best fit between fingerprints, and, on the other hand, more exploratory and open-ended data mining.     

Interference of homonuclear decoupling and exchange in the solid-state NMR of perfluorocyclohexane

We observe an interference between RF irradiation used for homonuclear decoupling of 19F and conformational exchange in the 13C spectrum of perfluorocyclohexane. We show that these effects can be readily reproduced in simulation, and characterise their dependence on the various NMR and experimental parameters. Their application to observing exchange rates on the kHz timescale is evaluated with respect to T(1rho) measurements and the connections between the two approaches established. The implications for experiments that use homonuclear decoupling of 1H to resolve 1J(CH)couplings in the solid-state are also evaluated in detail.     

The Numerical Solution of Laplace's Equation on a Wedge

Laplace's equation is considered on regions in the plane, withthe boundary having corners; and the double-layer potentialis used to derive a solution. The essential difficulties, boththeoretically and numerically, are reduced to the case in whichthe boundary is a simple open wedge. The theoretical behaviourof the double layer integral equation is studied explicitly,and then piecewise linear and piecewise quadratic collocationmethods are applied to the numerical solution of the equation.The major question of interest is the stability of the inversesof the approximating equations. The behaviour of the numericalmethods is somewhat surprising, and it is much better than pastanalyses would have led one to expect.