Infinite products involving binary digit sums

Let $(u_n)_{n\ge 0}$ denote the Thue-Morse sequence with values $\pm 1$. The Woods-Robbins identity below and several of its generalisations are well-known in the literature \begin{equation*}\label{WR}\prod_{n=0}^\infty\left(\frac{2n+1}{2n+2}\right)^{u_n}=\frac{1}{\sqrt 2}.\end{equation*} No other such product involving a rational function in $n$ and the sequence $u_n$ seems to be known in closed form. To understand these products in detail we study the function \begin{equation*}f(b,c)=\prod_{n=1}^\infty\left(\frac{n+b}{n+c}\right)^{u_n}.\end{equation*} We prove some analytical properties of $f$. We also obtain some new identities similar to the Woods-Robbins product.Comment: Accepted in Proc. AMMCS 2017, updated according to the referees' comment

A model study of enhanced oil recovery by flooding with aqueous surfactant solution and comparison with theory

With the aim of elucidating the details of enhanced oil recovery by surfactant solution flooding, we have determined the detailed behavior of model systems consisting of a packed column of calcium carbonate particles as the porous rock, n-decane as the trapped oil, and aqueous solutions of the anionic surfactant sodium bis(2-ethylhexyl) sulfosuccinate (AOT). The AOT concentration was varied from zero to above the critical aggregation concentration (cac). The salt content of the aqueous solutions was varied to give systems of widely different, post-cac oil–water interfacial tensions. The systems were characterized in detail by measuring the permeability behavior of the packed columns, the adsorption isotherms of AOT from the water to the oil–water interface and to the water–calcium carbonate interface, and oil–water–calcium carbonate contact angles. Measurements of the percent oil recovery by pumping surfactant solutions into calcium carbonate-packed columns initially filled with oil were analyzed in terms of the characterization results. We show that the measured contact angles as a function of AOT concentration are in reasonable agreement with those calculated from values of the surface energy of the calcium carbonate–air surface plus the measured adsorption isotherms. Surfactant adsorption onto the calcium carbonate–water interface causes depletion of its aqueous-phase concentration, and we derive equations which enable the concentration of nonadsorbed surfactant within the packed column to be estimated from measured parameters. The percent oil recovery as a function of the surfactant concentration is determined solely by the oil–water–calcium carbonate contact angle for nonadsorbed surfactant concentrations less than the cac. For surfactant concentrations greater than the cac, additional oil removal occurs by a combination of solubilization and emulsification plus oil mobilization due to the low oil–water interfacial tension and a pumping pressure increase

Benzene formation in the inner regions of protostellar disks

Benzene (c-C6H6) formation in the inner 3 AU of a protostellar disk can be efficient, resulting in high abundances of benzene in the midplane region. The formation mechanism is different to that found in interstellar clouds and in protoplanetary nebulae, and proceeds mainly through the reaction between allene (C3H4) and its ion. This has implications for PAH formation, in that some fraction of PAHs seen in the solar system could be native rather than inherited from the interstellar medium.Comment: 9 pages, 2 colour figures, to be published in the Astrophysical Journal Letter

A high resolution study of complex organic molecules in hot cores

We present the results of a line identification analysis using data from the IRAM Plateau de Bure Inferferometer, focusing on six massive star-forming hot cores: G31.41+0.31, G29.96-0.02, G19.61-0.23, G10.62-0.38, G24.78+0.08A1 and G24.78+0.08A2. We identify several transitions of vibrationally excited methyl formate (HCOOCH$_3$) for the first time in these objects as well as transitions of other complex molecules, including ethyl cyanide (C$_2$H$_5$CN), and isocyanic acid (HNCO). We also postulate a detection of one transition of glycolaldehyde (CH$_2$(OH)CHO) in two new hot cores. We find G29.96-0.02, G19.61-0.23, G24.78+0.08A1 and 24.78+0.08A2 to be chemically very similar. G31.41+0.31, however, is chemically different: it manifests a larger chemical inventory and has significantly larger column densities. We suggest that it may represent a different evolutionary stage to the other hot cores in the sample, or it may surround a star with a higher mass. We derive column densities for methyl formate in G31.41+0.31, using the rotation diagram method, of $\times$10$^{17}$ cm$^{-2}$ and a T$_{rot}$ of $\sim$170 K. For G29.96-0.02, G24.78+0.08A1 and G24.78+0.08A2, glycolaldehyde, methyl formate and methyl cyanide all seem to trace the same material and peak at roughly the same position towards the dust emission peak. For G31.41+0.31, however, glycolaldehyde shows a different distribution to methyl formate and methyl cyanide and seems to trace the densest, most compact inner part of hot cores.Comment: Accepted to MNRA

Perceptions and Anticipation of Academic Literacy: ‘Finding Your Own Voice’

Based on data gathered via survey questionnaire and follow up in-class discussion, the paper explores the ways undergraduate students think of themselves as writers and readers. Data drawn from a pilot survey in 2007 and a second in 2009 provides the impetus for discussion of issues of literacy and identity in a digital world. Of interest is 1) what first-year students anticipate they need to do and know, and 2) how final-year students reflect on what they have learnt in terms of academic literacies and related skills. A key issue is the way students bring a particular identity as readers and writers to university, and how this is transformed and re-inscribed through their studies. The importance of teaching for the development of rhetorical dexterity in a digital environment is highlighted because students’ digital literacy is a core element in their literacy identity. The paper also asks ‘how far should educators go in working into the space of digital literacies?

A new study of an old sink of sulfur in hot molecular cores: the sulfur residue

Sulfur appears to be depleted by an order of magnitude or more from its elemental abundance in star-forming regions. In the last few years, numerous observations and experiments have been performed in order to to understand the reasons behind this depletion without providing a satisfactory explanation of the sulfur chemistry towards high-mass star-forming cores. Several sulfur-bearing molecules have been observed in these regions, and yet none are abundant enough to make up the gas-phase deficit. Where, then, does this hidden sulfur reside? This paper represents a step forward in our understanding of the interactions among the various S-bearing species. We have incorporated recent experimental and theoretical data into a chemical model of a hot molecular core in order to see whether they give any indication of the identity of the sulfur sink in these dense regions. Despite our model producing reasonable agreement with both solid-phase and gas-phase abundances of many sulfur-bearing species, we find that the sulfur residue detected in recent experiments takes up only ~6 per cent of the available sulfur in our simulations, rather than dominating the sulfur budget.Comment: 13 pages, 6 colourful figures, accepted by MNRA

Glycolaldehyde, methyl formate and acetic acid adsorption and thermal desorption from interstellar ices

We have undertaken a detailed investigation of the adsorption, desorption and thermal processing of the astrobiologically significant isomers glycolaldehyde, acetic acid and methyl formate. Here, we present the results of laboratory infrared and temperature programmed desorption (TPD) studies of the three isomers from model interstellar ices adsorbed on a carbonaceous dust grain analogue surface. Laboratory infrared data show that the isomers can be clearly distinguished on the basis of their infrared spectra, which has implications for observations of interstellar ice spectra. Laboratory TPD data also show that the three isomers can be distinguished on the basis of their thermal desorption behaviour. In particular, TPD data show that the isomers cannot be treated the same way in astrophysical models of desorption. The desorption of glycolaldehyde and acetic acid from water-dominated ices is very similar, with desorption being mainly dictated by water ice. However, methyl formate also desorbs from the surface of the ice, as a pure desorption feature, and therefore desorbs at a lower temperature than the other two isomers. This is more clearly indicated by models of the desorption on astrophysical time-scales corresponding to the heating rate of 25 and 5 M⊙ stars. For a 25 M⊙ star, our model shows that a proportion of the methyl formate can be found in the gas phase at earlier times compared to glycolaldehyde and acetic acid. This has implications for the observation and detection of these molecules, and potentially explains why methyl formate has been observed in a wider range of astrophysical environments than the other two isomers