UV radiation: balancing risks and benefits

We use action spectra published by the International Commission on Illumination to examine diurnal, seasonal and latitudinal variations in erythemally weighted (sunburning) UV-a health risk, and vitamin D-weighted UV-a health benefit. Vitamin D-weighted UV is more strongly dependent on ozone and solar zenith angle. Consequently, its diurnal, seasonal and geographic variability is more pronounced than for erythemally weighted UV. We then investigate relationships between the two quantities. An algorithm is developed and used to relate vitamin D production to the widely used UV index, to help the public to optimize their exposure to UV radiation. In the summer at noon, there should at mid-latitudes be sufficient UV to photosynthesize optimal vitamin D in approximately 1 min for full body exposure, whereas skin damage occurs after approximately 15 min. Further, while it should be possible to photosynthesize vitamin D in the winter at mid-latitudes, the amount of skin that must be exposed is larger than from the hands and face alone. This raises the question of whether the action spectrum for vitamin D production is correct, since studies have reported that production of vitamin D is not possible in the winter at mid-latitudes.     

Avoidable structures, II: Finite distributive lattices and nicely structured ordered sets

Let be the ordered set of isomorphism types of finite distributive lattices, where the ordering is by embeddability. We characterize the order ideals in that are well-quasi-ordered by embeddability, and thus characterize the members of that belong to at least one infinite anti-chain in . While working on this paper, the second and third authors were supported by US NSF grant DMS-0604065. The second author was also supported by the Grant Agency of the Czech Republic, grant #201/05/0002 and by the institutional grant MSM0021620839 financed by MSMT.     

Revisiting Maxwell’s accommodation coefficient: A study of nitrogen flow in a silica microtube across all flow regimes

Gas flows have been studied quantitatively for more than a hundred years and have relevance in modern fields such as the control of gas inputs to processes, the measurement of leak rates and the separation of gaseous species. Cha and McCoy have derived a convenient formula for the flow of an ideal gas applicable across a wide range of Knudsen numbers (Kn) that approaches the Navier–Stokes equations at small Kn and the Smoluchowski extension of the Knudsen flow equation at large Kn  . Smoluchowski’s result relies on the Maxwell definition of the tangential momentum accommodation coefficient α$\alpha$, recently challenged by Arya et al. We measure the flow rate of nitrogen gas in a smooth walled silica tube across a wide range of Knudsen numbers from 0.0048 to 12.4583. We find that the nitrogen flow obeys the Cha and McCoy equation with a large value of α$\alpha$, unlike carbon nanotubes which show flows consistent with a small value of α$\alpha$. Silica capillaries are therefore not atomically smooth. The flow at small Kn   has α=0.91$\alpha =0.91$ and at large Kn   has α$\alpha$ close to one, consistent with the redefinition of accommodation coefficient by Arya et al., which also resolves a problem in the literature where there are many observations of α$\alpha$ of less than one at small Kn and many equal to one at large Kn. Silica capillaries are an excellent choice for an accurate flow control system.     

Nonequilibrium route to nanodiamond with astrophysical implications

Nanometer-sized diamond grains are commonly found in primitive chondritic meteorites, but their origin is puzzling. Using evidence from atomistic simulation, we establish a mechanism by which nanodiamonds form abundantly in space in a two-stage process involving condensation of vapor to form carbon onions followed by transformation to nanodiamond in an energetic impact. This nonequilibrium process is consistent with common environments in space and invokes the fewest assumptions of any proposed model. Accordingly, our model can explain nanodiamond formation in both presolar and solar environments. The model provides an attractive framework for understanding noble gas incorporation and explains all key features of meteoritic nanodiamond, including size, shape, and polytype. By understanding the creation of nanodiamonds, new opportunities arise for their exploitation as a powerful astrophysical probe.     

How do strain and steric interactions affect the reactions of aromatic compounds with free radicals? Characterization of the radicals formed by muonium addition to p-xylene and [2.2]paracyclophane by DFT calculations and muon spin spectroscopy

Muoniated radicals were produced by the addition of muonium (Mu) to the aromatic compound p-xylene (1) in the solid and liquid states and to the strained aromatic compound [2.2]paracyclophane (2) in the solid state. The radicals were characterized by avoided level crossing muon spin resonance spectroscopy and identified by comparing the experimentally determined muon hyperfine coupling constants with values obtained from DFT calculations. Mu was observed to add to both the secondary and tertiary carbons of 1, with the relative yield of the Mu adduct of the tertiary carbons estimated to be ～10% in the liquid phase. The relative yield of the tertiary adduct is much higher in the solid state although this cannot be calculated exactly due to the overlap of resonances and the apparent nonuniform distribution of the radical orientations. There are three possible addition sites in 2 due to the lower symmetry of the six-membered ring compared with 1. Mu can add to the secondary carbons either from the outside of 2, generating the "exo" adduct, or from the inside, generating the "endo" adduct. The relative yields of the exo, endo, and tertiary carbon adducts are 67.1(1), 21.8(1), and 11.1(1)%, respectively. The barriers to Mu addition at the different sites of isolated molecules were determined from DFT calculations. The barriers for Mu addition to 2 are lower than the barriers for Mu addition to 1, except for addition to the "endo" position, where the unfavorable steric interactions with the second ring of 2 raise the addition barrier considerably. The measured relative yields do not reflect the distribution of products calculated using the activation energies obtained from the DFT calculations due to strong steric interactions with neighboring molecules.     

Fractal analysis of fracture: A comparison of dimension estimates

In recent years considerable research effort has been expended in attempts to describe the tortuous nature of fracture edges. The authors have previously shown [3,4] that crack profiles generated in concrete beams subjected to bending can be classified with two parameters: the Hurst exponent (H), which controls the persistence of the crack and a diffusion type coefficient (K_f), which describes the spreading of the crack. As a result of these studies, it has been shown that fractures can be modeled using fractional Brownian motion functions. In addition, it has been found that the excursion of the crack normal to its mean direction of propagation may be defined by a time dependent, non-Fickian, probability density function which itself is the solution of an effective Fokker-Planck equation.It is now common for H to be used to describe the nature of a variety of random fractal signals. However, several methods have been utilised in classifying H, producing varying results. This paper compares some of the more popular methods (box counting, variable bandwidth, Fourier spectrum, wavelet spectrum) and in particular focuses on the problem of obtaining consistent results using only a limited (even single) number of realisations. We find that both the box counting and variable bandwidth methods produce the more consistent results. These results have implications for the methods in their application where often only a limited number of profiles are available.     

5‐(2‐Pyridyl)‐1,3‐di­thia­ne‐2‐thione

The title compound, C₉H₉NS₃, crystallizes with two mol­ecules in the asymmetric unit. In both mol­ecules, the di­thia­ne‐2‐thione rings adopt a symmetric half‐boat conformation with the C atom opposite the C—S_thione bond out of the plane. The pyridine ring is in an equatorial position and is twisted out of the plane of the half‐boat by 82.7 (2) and 84.5 (2)° in the two mol­ecules, so that the N atom is trans to the axial C—H bond in both cases.