Frame-dragging vortexes and tidal tendexes attached to colliding black holes: visualizing the curvature of spacetime

When one splits spacetime into space plus time, the spacetime curvature (Weyl tensor) gets split into an "electric" part E(jk) that describes tidal gravity and a "magnetic" part B(jk) that describes differential dragging of inertial frames. We introduce tools for visualizing B(jk) (frame-drag vortex lines, their vorticity, and vortexes) and E(jk) (tidal tendex lines, their tendicity, and tendexes) and also visualizations of a black-hole horizon's (scalar) vorticity and tendicity. We use these tools to elucidate the nonlinear dynamics of curved spacetime in merging black-hole binaries.     

The Riemann–Roch theorem and zero-energy solutions of the Dirac equation on the Riemann sphere

In this paper, we revisit the connection between the Riemann–Roch theorem and the zero-energy solutions of the two-dimensional Dirac equation in the presence of a delta-function-like magnetic field. Our main result is the resolution of a paradox—the fact that the Riemann–Roch theorem correctly predicts the number of zero-energy solutions of the Dirac equation despite counting what seem to be functions of the wrong type.     

Temperature dependence of metal-organic heteroepitaxy

The nucleation and growth of 2D layers of tetraphenyl porphyrin molecules on Ag(111) are studied with variable-temperature scanning tunneling microscopy. The organic/metal heteroepitaxy occurs by strict analogy to established principles for metal heteroepitaxy. A hierarchy of energy barriers for diffusion on terraces and along edges and around corners of adislands is established. The temperature is key to activating these barriers selectively, thus determining the shape of the organic aggregates, from a fractal shape at lower temperatures to a compact shape at higher temperatures. The energy barriers for the terrace diffusion of porpyrins and the molecule-molecule binding energy were determined to be 30 meV < E(terrace) < 60 and 130 meV < E(diss) < 160 meV, respectively, from measurements of island sizes as a function of temperature. This study provides an experimental verification of the validity of current models of epitaxy for the heteroepitaxy of organics and is thus expected to help establish design principles for complex metal-organic hybrid structures.     

A spinning thermometer to monitor microwave heating and glass transitions in dynamic nuclear polarization

As previously demonstrated by Thurber and Tycko, the peak position of ⁷⁹Br in potassium bromide (KBr) allows one to determine the temperature of a spinning sample. We propose to adapt the original design by using a compact KBr tablet placed at the bottom of the magic angle spinning rotor, separated from the sample under investigation by a thin disk made of polytetrafluoroethylene (or ‘Teflon’®). This design allows spinning the sample up to at least 16 kHz. The KBr tablet can remain in the rotor when changing the sample under investigation. Calibration in the range of 98 < T < 320 K has been carried out in a static rotor by inserting a platinum thermometer. The accuracy is better than ± 0.9 K, even in the presence of microwave irradiation. Irradiation with 5 W microwaves at 263 GHz leads to a small temperature increase of 3.6 ± 1.4 K in either static or spinning samples. The dynamic nuclear polarization enhancement decreases with increasing temperature, in particular when a frozen glassy sample undergoes a glass transition. Copyright © 2011 John Wiley & Sons, Ltd.     

Structure of the methyl radical

Carbon-13 hyperfine splittings equal to 41±3 gauss have been observed in the paramagnetic resonance of a mixture of C¹²H₃ and C¹³H₃ radicals produced by x-irradiation of CH₃I at 77°k. The observed splitting provides strong evidence that CH₃ is a planar molecule.     

Quantum dynamics of a nano-rod under compression

A nano-rod under compression, which is capacitively coupled to a Cooper-pair box, can be modelled in terms of a quartic oscillator linearly interacting with a tunnelling pseudo-spin. We have integrated numerically the quantum dynamics of this system in the partial Wigner representation and calculated the pseudo-spin population difference. Depending on the coupling, we have verified that the quantum tunnelling of the oscillator can lead to a more effective reduction of the Rabi oscillation amplitude of the pseudo-spin. Such findings suggest an experimental set-up that might be able to discriminate between the quantum and the classical motion of a nano-rod.     

Rank 3 Transitive Decompositions of Complete Multipartite Graphs

A transitive decomposition of a graph is a partition of the edge or arc set giving a set of subgraphs which are preserved and permuted transitively by a group of automorphisms of the graph. This paper deals with transitive decompositions of complete multipartite graphs preserved by an imprimitive rank 3 permutation group. We obtain a near-complete classification of these when the group in question has an almost simple component.     

Rheology modification of montmorillonite dispersions by colloidal silica

We have studied the effect of additions of both anionic and cationic spherical silica colloids of different sizes on the rheology of dispersions of a well-characterised montmorillonite clay, SWy-2. The systems have been studied above and below the critical hydrodynamic overlap concentration, c*, of the clay. For dispersions at c < c* on replacement of ～10 % w/w of the clay content by silica, it was found that whereas a cationic silica additive transformed a liquid-like, non-gelling montmorillonite dispersion into a substantial gel, anionic silica destroyed any nascent structure in the fluids, reducing the effective viscosity and virtually eliminating the rheological hysteresis characteristic of structured fluids. On the other hand, in the regime of c > c*, replacement of ～10 % w/w of the clay content by silica leads to enhancements of all the rheological parameters characteristic of a gelling system, for the addition of both anionic and cationic silica. A simple tentative microstructural model for this complex behaviour is presented. This work, alongside our previous studies, confirms significant rheological modification by the addition of small quantities of nanoparticles as a general phenomenon of clay-colloid systems. It further suggests that viscosity enhancement and control of the rates of sol-gel transitions for product applications can be achieved using relatively low-cost, commercially available materials, such as silica nanoparticles and natural clays of different mineralogy.     

Two-component Poisson mixture regression modelling of count data with bivariate random effects

Two-component Poisson mixture regression is typically used to model heterogeneous count outcomes that arise from two underlying sub-populations. Furthermore, a random component can be incorporated into the linear predictor to account for the clustering data structure. However, when including random effects in both components of the mixture model, the two random effects are often assumed to be independent for simplicity. A two-component Poisson mixture regression model with bivariate random effects is proposed to deal with the correlated situation. A restricted maximum quasi-likelihood estimation procedure is provided to obtain the parameter estimates of the model. A simulation study shows both fixed effects and variance component estimates perform well under different conditions. An application to childhood gastroenteritis data demonstrates the usefulness of the proposed methodology, and suggests that neglecting the inherent correlation between random effects may lead to incorrect inferences concerning the count outcomes.