Integral equation formulation for buoyancy-driven convection problems

An integral equation formulation for buoyancy-driven convection problems is developed and illustrated. Buoyancy-driven convection in a bounded cylindrical geometry with a free surface is studied for a range of aspect ratios and Nusselt numbers. The critical Rayleigh number, the nature of the cellular motion, and the heat transfer enhancement are computed using linear theory. Green's functions are used to convert the linear problem into linear Fredholm integral equations. Theorems are proved which establish the properties of the eigenvalues and eigenfunctions of the linear integral operator which appears in these equations.     

New precision limit on the strange vector form factors of the proton

The parity-violating cross-section asymmetry in the elastic scattering of polarized electrons from unpolarized protons has been measured at a four-momentum transfer squared Q2 = 0.624 GeV2 and beam energy E(b) = 3.48 GeV to be A(PV) = -23.80 ± 0.78(stat) ± 0.36(syst) parts per million. This result is consistent with zero contribution of strange quarks to the combination of electric and magnetic form factors G(E)(s) + 0.517G(M)(s) = 0.003 ± 0.010(stat) ± 0.004(syst) ± 0.009(ff), where the third error is due to the limits of precision on the electromagnetic form factors and radiative corrections. With this measurement, the world data on strange contributions to nucleon form factors are seen to be consistent with zero and not more than a few percent of the proton form factors.     

Mother and Child Emotions during Mathematics Homework

Mathematics is often thought of as a purely intellectual and unemotional activity. Recently, researchers have begun to question the validity of this approach, arguing that emotions and cognition are intertwined. The emotions expressed during mathematics work may be linked to mathematics achievement. We used behavioral measures to identify the emotions expressed by U.S. mothers and their 11-year-old children while solving pre-algebra tasks in the home. The most notable positive emotions displayed by mothers and children included positive interest, affection, joy, and pride, whereas the most notable negative emotions expressed included tension, frustration, and distress. Reflecting the social aspects of doing homework together, mothers' and children's emotions were highly correlated. Independent of pre-existing differences in knowledge, children's emotions were associated with their performance on a mathematics post-test: tension was linked to poorer performance while positive interest, humor, and pride were linked to better performance. We found no evidence of gender differences in the emotions while working the tasks, although boys responded with more tension following an incorrect solution than did girls.     

Spin-label W-band EPR with Seven-Loop–Six-Gap Resonator: Application to Lens Membranes Derived from Eyes of a Single Donor

Spin-label W-band (94 GHz) electron paramagnetic resonance (EPR) with a five-loop–four-gap resonator (LGR) was successfully applied to study membrane properties (Mainali et al. J Magn Reson 226:35–44, 2013). In that study, samples were equilibrated with the selected gas mixture outside the resonator in a sample volume ~100 times larger than the sensitive volume of the LGR and transferred to the resonator in a quartz capillary. A seven-loop–six-gap W-band resonator has been developed. This resonator permits measurements on aqueous samples of 150 nL volume positioned in a polytetrafluoroethylene (PTFE) gas permeable sample tube. Samples can be promptly deoxygenated or equilibrated with an air/nitrogen mixture inside the resonator, which is significant in saturation-recovery measurements and in spin-label oximetry. This approach was tested for lens lipid membranes derived from lipids extracted from two porcine lenses (single donor). Profiles of membrane fluidity and the oxygen transport parameter were obtained from saturation-recovery EPR using phospholipid analog spin-labels. Cholesterol analog spin-labels allowed discrimination of the cholesterol bilayer domain and acquisition of oxygen transport parameter profiles across this domain. Results were compared with those obtained previously for membranes derived from a pool of 100 lenses. Results demonstrate that EPR at W-band can be successfully used to study aqueous biological samples of small volume under controlled oxygen concentration.     

Bicontinuous geometries and molecular self-assembly: comparison of local curvature and global packing variations in genus-three cubic, tetragonal and rhombohedral surfaces

Balanced infinite periodic minimal surface families that contain the cubic Gyroid (G), Diamond (D) and Primitive (P) surfaces are studied in terms of their global packing and local curvature properties. These properties are central to understanding the formation of mesophases in amphiphile and copolymer molecular systems. The surfaces investigated are the tetragonal, rhombohedral and hexagonal tD, tP, tG, rG, rPD and H surfaces. These non-cubic minimal surfaces furnish topology-preserving transformation pathways between the three cubic surfaces. We introduce `packing (or global) homogeneity', defined as the standard deviation Δd of the distribution of the channel diameter throughout the labyrinth, where the channel diameter d is determined from the medial surface skeleton centered within the labyrinthine domains. Curvature homogeneity is defined similarly as the standard deviation ΔK of the distribution of Gaussian curvature. All data are presented for distinct length normalisations: constant surface-to-volume ratio, constant average Gaussian curvature and constant average channel diameter. We provide first and second moments of the distribution of channel diameter for all members of these surfaces complementing curvature data from [A. Fogden, S. Hyde, Eur. Phys. J. B 7, 91 (1999)]. The cubic G and D surfaces are deep local minima of Δd along the surface families (with G more homogeneous than D), whereas the cubic P surface is an inflection point of Δd with adjacent, more homogeneous surface members. Both curvature and packing homogeneity favour the tetragonal route between G and D (via tG and tD surfaces) in preference to the rhombohedral route (via rG and rPD).     

Pseudo field modulation in EPR spectroscopy

This paper develops methodology for computer simulation of the effect on an experimental EPR spectrum that would occur if an additional field modulation were applied followed by eventual phase sensitive detection at the modulation frequency or at one its harmonics. The algorithm, which is called pseudomodulation, transforms the digitized spectrum and also filters the noise. If a second harmonic spectrum is desired in order to make subtle changes in curvature more apparent, it is shown that it is always preferable to obtain an experimental second harmonic spectrum. The signals are identical, but because of the filtering properties of the pseudomodulation algorithm, the noise is lower. Pseudomodulation should be applied to simulated spectra prior to fitting a model to data in order more precisely to simulate the experimental signal. It is argued that such fits ought to involve not only first harmonics but also higher harmonics, since the various harmonics are sensitive in different ways to input parameters in the spin Hamiltonian. Application of pseudomodulation to the EPR spectrum of the blue copper-protein azurin is described.     

AFM studies of metal deposition: instantaneous nucleation and the growth of cobalt nanoparticles on boron-doped diamond electrodes.

In situ atomic force microscopy (AFM) is used to study the growth of cobalt nuclei on a boron doped diamond electrode under potentiostatic control. The rate of growth of the nuclei at the electrode surface is monitored using AFM as a function of time at different deposition potentials. The nucleation of cobalt nuclei is found to be "instantaneous" and the growth of the nuclei is shown to be kinetically rather than diffusionally controlled over periods of tens and hundreds of seconds. At very short times (<10 seconds) the kinetics of nucleation are apparent.