Bulk and shear mechanical loss of titania-doped tantala

We report on the mechanical loss from bulk and shear stresses in thin film, ion beam deposited, titania-doped tantala. The numerical values of these mechanical losses are necessary to fully calculate the Brownian thermal noise in precision optical cavities, including interferometric gravitational wave detectors like LIGO. We found the values from measuring the normal mode mechanical quality factors, Q's, in the frequency range of about 2000-10,000 Hz, of silica disks coated with titania-doped tantala coupled with calculating the elastic energy in shear and bulk stresses in the coating using a finite element model. We fit the results to both a frequency independent and frequency dependent model and find ${?}_{\mathrm{shear}}=(8.3\pm 1.1)\times {10}^{?4}$, ${?}_{\mathrm{bulk}}=(6.6\pm 3.8)\times {10}^{?4}$ with a frequency independent model and ${?}_{\mathrm{shear}}\left(f\right)=(5.0\pm 0.7)\times {10}^{?4}+(5.4\pm 1.1)\times {10}^{?8}f$, ${?}_{\mathrm{bulk}}\left(f\right)=(11\pm 2.8)\times {10}^{?4}?(8.7\pm 4.7)\times {10}^{?8}f$ with a frequency dependent (linear) model. The ratio of these values suggest that modest improvement in the coating thermal noise may be possible in future gravitational wave detector optics made with titania-doped tantala as the high index coating material by optimizing the coating design to take advantage of the two different mechanical loss angles.     

The influence of cannabis smoke and cannabis vapour on simulated lung surfactant function under physiologically relevant conditions

The use of cannabis for medicinal/recreational purposes is widespread throughout the world. Smoke inhalation is known to cause airway irritation due to noxious substances (ie, benzene) within the mix. Thus, advanced vaporisation platforms (eg, Davinci IQ) have been developed to circumvent negative health implications. Here, we consider the impact that cannabis smoke and cannabis vapour have on simulated lung surfactant performance within a model pulmonary space (ie, 37°C, elevated humidity and related fluid hydrodynamics). In total, 50 mg of herbal material was ignited or placed within a Davinci IQ vaporiser with subsequent activation. The aliquots were collected and then analysed using gas chromatography-mass spectroscopy for composition and cannabinoid (eg, Δ9-tetrahydrocannabinol [Δ9-THC]) concentration. The average content within cannabis smoke was 2.84% (0.07%, SD) Δ9-THC, with the same for cannabis vapour being 0.88% (0.14%, SD). Aerosolised samples were transferred to the lung biosimulator. When compared with the pristine Curosurf system, challenge with cannabis smoke and cannabis vapour reduced the surface pressure term by 26% and 7% and increased film compressibility by 60% and 15% at 80% trough area, respectively. The net effect would be enhanced film elasticity and an increased work of breathing, being more pronounced on cannabis smoke inhalation. The trends noted were ascribed to two factors operating synergistically, namely the amount of Δ9-THC (plus others) within the aerosolised samples and the associated toxicity profile. Further research is required to establish mass-balance effects (ie, titrated outputs) along with detailed chemical profiling of material generated from the unrelated cannabis activation pathways.     

Stable,Reactive, and Orthogonal Tetrazines: Dispersion Forces Promote the Cycloaddition with Isonitriles

The isocyano group is a structurally compact bioorthogonal functional group that reacts with tetrazines under physiological conditions. Now it is shown that bulky tetrazine substituents accelerate this cycloaddition. Computational studies suggest that dispersion forces between the isocyano group and the tetrazine substituents in the transition state contribute to the atypical structure–activity relationship. Stable asymmetric tetrazines that react with isonitriles at rate constants as high as 57 L mol^?1 s^?1 were accessible by combining bulky and electron‐withdrawing substituents. Sterically encumbered tetrazines react selectively with isonitriles in the presence of strained alkenes/alkynes, which allows for the orthogonal labeling of three proteins. The established principles will open new opportunities for developing tetrazine reactants with improved characteristics for diverse labeling and release applications with isonitriles.     

Polyfunctionalised Nanoparticles Bearing Robust Gadolinium Surface Units for High Relaxivity Performance in MRI

The first example of an octadentate gadolinium unit based on DO3A (hydration number q=1) with a dithiocarbamate tether has been designed and attached to the surface of gold nanoparticles (around 4.4 nm in diameter). In addition to the superior robustness of this attachment, the restricted rotation of the Gd complex on the nanoparticle surface leads to a dramatic increase in relaxivity (r₁) from 4.0 mm ⁻¹ s⁻¹ in unbound form to 34.3 mm ⁻¹ s⁻¹ (at 10 MHz, 37 °C) and 22±2 mm ⁻¹ s⁻¹ (at 63.87 MHz, 25 °C) when immobilised on the surface. The one-pot synthetic route provides a straightforward and versatile way of preparing a range of multifunctional gold nanoparticles. The incorporation of additional surface units for biocompatibility (PEG and thioglucose units) and targeting (folic acid) leads to little detrimental effect on the high relaxivity observed for these non-toxic multifunctional materials. In addition to the passive targeting attributed to gold nanoparticles, the inclusion of a unit capable of targeting the folate receptors overexpressed by cancer cells, such as HeLa cells, illustrates the potential of these assemblies.     

Grünbaum colorings of toroidal triangulations

We prove that if G is a triangulation of the torus and χ(G)≠5, then there is a 3‐coloring of the edges of G so that the edges bounding every face are assigned three different colors. © 2009 Wiley Periodicals, Inc. J Graph Theory 63: 68–81, 2010     

On skew polynomial rings over locally nilpotent rings

We will show that skew polynomial rings in several variables over locally nilpotent rings cannot contain nonzero idempotent elements. We will also prove that such rings are Brown–McCoy radical.     

Tropical Hurwitz numbers

Hurwitz numbers count genus g, degree d covers of ℙ¹ with fixed branch locus. This equals the degree of a natural branch map defined on the Hurwitz space. In tropical geometry, algebraic curves are replaced by certain piece-wise linear objects called tropical curves. This paper develops a tropical counterpart of the branch map and shows that its degree recovers classical Hurwitz numbers. Further, the combinatorial techniques developed are applied to recover results of Goulden et al. (in Adv. Math. 198:43–92, 2005) and Shadrin et al. (in Adv. Math. 217(1):79–96, 2008) on the piecewise polynomial structure of double Hurwitz numbers in genus 0.